i

Biomechanical Models for the Analysis of

Partial Foot Amputee Gait

Submitted by

Michael Peter Dillon

Bachelor of Prosthetics and Orthotics (Honours), La Trobe University

A thesis submitted in total fulfilment

of the requirements for the degree of

Doctor of Philosophy

School of Mechanical, Manufacturing and Medical Engineering

Faculty of Built Environment and Engineering

and

Centre for Rehabilitation Science and Engineering

Queensland University of Technology

Brisbane, Queensland, Australia

April, 2001

ii

Key words

Gait, partial foot, amputee, anthropometry, inverse dynamics, model, biomechanics

iii

Abstract

Partial foot amputation is becoming a more viable and common surgical

intervention for the treatment of advanced diabetes, vascular insufficiency and trauma.

Statistics describing the incidence of partial foot amputation are scarce. In Australia, it

is not known how many people undergo partial foot amputation annually however in the

United States upwards of 10,000 partial foot amputations are performed each year.

Many of these procedures are likely to be in preference to below-knee amputation under

the pretext of improved function associated with preserving the ankle joint and foot

length despite common failings including ulceration and equinus contracture which can

lead to more proximal amputation.

There is a substantial body of literature, which lends support to the contention

that much of clinical practice has not been based on experimental evidence describing

the gait of partial foot amputees or the influence of prosthetic and orthotic intervention.

This limited scientific underpinning of practice may contribute to the common failures

and allow misconceptions, such that preserving foot length and the ankle joint improves

function, to perpetuate.

The aim of this investigation was to develop accurate mechanical models to

analyse the effects of amputation and prosthetic/orthotic intervention on the gait of

partial foot amputees.

Anthropometric and linked-segment inverse dynamic models were developed to

accurately depict the affected lower limb and account for prosthetic/orthotic

intervention and footwear. These novel techniques enhance the accuracy of kinetic

descriptions, affecting the results obtained for terminal swing phase. These models more

accurately portray the requirements of the hamstring and gluteus maximus muscles to

decelerate the swinging limb in response to the net increase in mass and inertia of the

limb segments due to prosthetic fitting.

With an appreciation of the influence these models have on the estimation of

kinetic parameters, the gait of partial foot amputees was investigated. Kinematic

abnormalities were primarily limited to the ankle and were characterised by poor control

iv

of tibial rotation during the mid-stance phase consistent with reduced eccentric work by

the triceps surae muscles. The centre of pressure excursion and anterior progression of

the trunk outside the reduced base of support was limited until contralateral initial

contact; which could reflect triceps surae weakness and an inability to substantially load

the prosthetic forefoot. Reductions in power generation across the affected ankle were

the result of reductions in the angular excursion of the ankle and reductions in the ankle

moment. Reductions in the ankle moment were consistent with the limited excursion of

the centre of pressure commensurate with peak ground reaction forces. During early

stance, concentric activity of the hip extensor musculature was observed, bilaterally, to

advance the body forward.

Results from these investigations focus on restoring power generation across the

ankle given that the primary reason for preserving the ankle joint and calf musculature

would seem to be the ability to use it functionally. Improvements in triceps surae

strength may allow individuals to capitalise on improvements in below ankle prosthetic

design and affect significant improvements in ankle power generation. In conjunction

with improvements in muscle strength, below ankle prosthetic design needs to

incorporate a socket and toe lever capable of comfortably distributing forces caused by

loading the prosthetic forefoot. In conjunction with improvements in muscle strength,

above ankle prosthetic design needs to incorporate an ankle joint. The development of a

suitable joint poses significant design challenges for the engineer and prosthetist.

This thesis provides new insights into the gait of partial foot amputees and the

influence of prosthetic/orthotic design, which challenge common misconceptions

underpinning clinical practice, prosthetic prescription and surgery. Aside from

advancing the understanding of partial foot amputee gait and the influence of

prosthetic/orthotic fitting, these investigations challenge and aim to improve current

prosthetic and rehabilitation practice. Thus reducing the incidence of complications,

such as ulceration which have been associated with the need for more proximal below

knee amputation and allow partial foot amputees to utilise the intact ankle joint

complex.

v

Table of contents

Biomechanical Models for the Analysis of Partial Foot Amputee Gait i

Certificate of acceptance ii

Keywords ii

Abstract iii

Table of contents v

List of figures x

List of tables xv

Nomenclature xviii

Levels of partial foot amputation xix

Types of prosthetic and orthotic fittings xx

Statement of authorship xxi

Acknowledgements xxii

Chapter 1. Introduction and thesis overview 1

Chapter 2. An Anthropometric Model of the Partial Foot Residuum 7

2.1 Introduction 7

2.2 Method 11

Subjects 11

Apparatus 13

Procedure 16

Determining BSP data using the anthropometric model 16

Determining BSP data using the plaster foot replicas 17

2.3 Results 22

2.4 Discussion 31

2.5 Conclusion 38

Chapter 3. Inverse Dynamic Models for the analysis of Partial Foot Amputee

Gait 39

3.1 Introduction 39

3.2 Method 44

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Subjects 44

Apparatus 45

Procedure 48

Laboratory set-up 48

Equipment accuracy 49

Equipment calibration 51

Subject preparation and examination 51

Data acquisition and processing 53

3.3 Results 56

3.4 Discussion 70

3.5 Conclusion 72

Chapter 4. A Biomechanical Analysis of Partial Foot Amputee Gait 75

4.1 Introduction 75

4.2 Method 82

Subjects 82

Apparatus 84

Subject preparation 85

Data acquisition and processing 85

4.3 Results 88

Joint range of motion and muscle strength 88

Temperospatial characteristics 89

Ground reaction force and centre of pressure excursion 94

Repeatability of kinematic, kinetic and electromyographic data 101

Kinematics 102

Kinetics 111

Ankle joint moments 111

Knee joint moments 115

Hip joint moments 117

Ankle joint powers 120

Knee Joint powers 123

Hip joint powers 127

Electromyography 130

4.4 Discussion 144

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Range of motion and muscle strength 144

Temperospatial parameters 145

Kinematics 148

Ankle kinematics 148

Knee kinematics 158

Hip kinematics 161

Kinetics 161

Signal processing issues affecting electromyographic data 171

4.5 Conclusion 175

Chapter 5. Clinical implications affecting prosthetic design and rehabilitation

practice 178

5.1 Introduction 178

5.2 Clamshell sockets 179

5.3 Below ankle sockets, orthoses and toe fillers 185

5.4 Prosthetic prescription 188

5.5 Conclusion 188

Chapter 6. Conclusion and indications for further investigation 191

6.1 Conclusion 191

6.2 Further research 196

Appendix A. Letter for patient recruitment 199

Appendix B. An anthropometric model of the partial foot residuum 202

B.1 Introduction 202

B.2 Determining foot mass 207

B.3 Determining foot centre of mass 218

B.4 Determining mass moment of inertia of the foot 222

B.5 Determining foot volume 230

B.6 Effect of errors in anthropometric input data 230

Appendix C. Validation of the incremental immersion technique for determining

volume and centre of volume 242

viii

C.1 Introduction 242

C.2 Method 243

Subject 243

Apparatus 243

Procedure 243

C.3 Results 244

C.4 Discussion 246

C.5 Conclusion 247

Appendix D. Subject consent form 248

Appendix E. Software to process and report kinematic and kinetic data 251

E.1 Introduction 251

E.2 Processing force plate data 251

E.3 Processing kinematic data 256

E.4 Processing kinetic data 258

E.5 Processing temperospatial data 260

E.6 Reporting kinematic and kinetic data 260

Appendix F. Linked-segment inverse dynamic models for the analysis of partial

foot amputee gait: implementation 263

F.1 Introduction 263

F.2 Obtaining the necessary anthropometric descriptions 264

F.3 Combining the individual segment anthropometric descriptions 265

F.4 Transformation of the mass centroid location between the local/joint

and global coordinate systems 267

F.5 Deriving the remaining input data necessary to calculate joint moments

and powers 269

F.6 Calculating joint moments and powers 270

Appendix G. Physical assessment forms 277

Anthropometric measurement form 278

ROM assessment form 283

Muscle strength assessment form 284

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Appendix H. Additional results and discussion 285

Chapter 2: Additional results and discussion 285

H2.1 Bland and Altman plots for assessing agreement between

two methods of measurement 285

Chapter 3: Additional results and discussion 289

H3.1 Peak moments and powers observed during stance and

swing phase 289

H3.2 Influence of anthropometry on joint moments and powers 289

Sample-A/partial foot model-A 295

Sample-B/partial foot model-B 300

Appendix I. Gait reports 304

References 321

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List of figures

2.1 Geometric model of a Metatarsophalangeal residuum 14

2.2 Pendulum trifilar system 16

2.3 Regression of modelled vs. experimentally derived foot mass 27

2.4 Regression of modelled vs. experimentally derived foot volume 27

2.5 Regression of modelled vs. experimentally derived CM along the x

axis

28

2.6 Regression of modelled vs. experimentally derived CM along the z

axis

28

2.7 Regression of modelled vs. experimentally derived k about the x axis 29

2.8 Regression of modelled vs. experimentally derived k about the y axis 29

2.9 Regression of modelled vs. experimentally derived k about the z axis 30

2.10 Illustration of basis vectors used to describe the position of the

centre of mass

33

3.1 Exploded view of force plate and kinematic calibration frame 49

3.2 Set up of gait laboratory 50

3.3 Points of interest examined on joint moment profiles 55

3.4 Points of interest examined on joint power profiles 56

3.5 Mean joint moments estimates using a standard linked-segment

model and the partial foot models

62

3.6 Mean joint powers estimates using a standard linked-segment model

and the partial foot models

63

3.7 Mean hip extension moment peaks during terminal swing for both

standard and partial foot linked-segment models

65

3.8 Mean knee extension moment peaks during terminal swing for both

standard and partial foot linked-segment models

66

3.9 Mean knee flexion moment peaks during terminal swing for both

standard and partial foot linked-segment models

67

3.10 Mean hip power generation/absorption during terminal swing for

both standard and partial foot linked-segment models

68

xi

3.11 Mean hip power absorption during terminal swing for both standard

and partial foot linked-segment models

69

4.1 Fore-aft ground reaction force for the affected and sound limbs of

the unilateral amputee subjects

95

4.2 Fore-aft ground reaction force for the bilateral amputee subjects 96

4.3 Vertical ground reaction force for the bilateral amputee subjects 97

4.4 Vertical ground reaction force for the affected and sound limbs of

the unilateral amputee subjects

98

4.5 Sagittal plane centre of pressure excursion for the affected and sound

limbs of the unilateral amputee subjects

100

4.6 Sagittal plane centre of pressure excursion for the bilateral amputee

subjects

101

4.7 Sagittal plane hip flexion/extension angles for the affected and sound

limbs of the unilateral amputee subjects

103

4.8 Sagittal plane hip flexion/extension angles for the bilateral amputee

subjects

104

4.9 Sagittal plane knee flexion/extension angles for the affected and

sound limbs of the unilateral amputee subjects

106

4.10 Sagittal plane knee flexion/extension angles for the bilateral amputee

subjects

107

4.11 Sagittal plane ankle dorsiflexion/plantarflexion angles for the

affected and sound limbs of the unilateral amputee subjects

109

4.12 Sagittal plane ankle dorsiflexion/plantarflexion angles for the

bilateral amputee subjects and those with Clamshell prostheses

110

4.13 Sagittal plane ankle moments for the affected and sound limbs of the

unilateral amputee subjects

112

4.14 Sagittal plane ankle moments for the bilateral amputee subjects 113

4.15 Sagittal plane ankle moments for the affected limbs of the Chopart

amputees

114

4.16 Sagittal plane knee moments for the affected and sound limbs of the

unilateral amputee subjects

116

4.17 Sagittal plane knee moments for the bilateral amputee subjects 117

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4.18 Sagittal plane hip moments for the affected and sound limbs of the

unilateral amputee subjects

118

4.19 Sagittal plane hip moments for the bilateral amputee subjects 119

4.20 Sagittal plane ankle power for the affected and sound limbs of the

unilateral amputee subjects

121

4.21 Sagittal plane ankle power for the bilateral amputee subjects 122

4.22 Sagittal plane ankle power for the affected limbs of Chopart

amputees

123

4.23 Sagittal plane knee power for the affected and sound limbs of the

unilateral amputee subjects

125

4.24 Sagittal plane knee power for the bilateral amputee subjects 126

4.25 Sagittal plane hip power for the affected and sound limbs of the

unilateral amputee subjects

128

4.26 Sagittal plane hip power for the bilateral amputee subjects 129

4.27 Mean EMG of tibialis anterior for the affected limb of subject 2103-

1906A

131

4.28 EMG of tibialis anterior for the affected limb of subject 2103-1906A 131

4.29 Mean EMG of tibialis anterior for both limbs of subject 2803-0410A 132

4.30 Bilateral EMG activity of tibialis anterior for subject 2803-0410A 133

4.31 EMG activity of tibialis anterior for affected limb for subject 2103-

2116A

134

4.32 Mean EMG activity of triceps surae for the affected limb of subject

2103-1906A

135

4.33 Mean EMG activity of triceps surae for the affected limb of subject

2703-1903A

136

4.34 EMG activity of soleus for the affected limb of subject 2103-1906A 136

4.35 EMG activity of biceps femoris long head for the affected limb of

subject 3004-1102A

137

4.36 Mean EMG activity of biceps femoris long head for both limbs of

subject 0904-1924A

138

4.37 EMG activity of biceps femoris long head for both limbs of subject

0904-1924A

139

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4.38 EMG activity of vastus lateralis for the affected limb of subject

2103-2116A

141

4.39 EMG activity of vastus lateralis for the sound limb of subject 3004-

1102A

141

4.40 EMG data for the affected limb of subject 2803-0410A 142

4.41 Mean EMG activity of tibialis anterior for affected limb of subject

2103-1903A

143

B.1 Geometric model of the partial foot 203

B.2 Geometric model of the partial foot – exploded view 204

B.3 Basic trapezoid plate 208

B.4 Basic parabolic plate 208

B.5 Schematic diagram showing modelled and anatomical shape of the

forefoot

210

E.1 Schematic of support phase calculation using a combination of force

platform and footswitch derived event times

255

E.2 Mean joint powers for the control sample 262

F.1 Schematic illustrating derivation of anthropometric characteristics

describing the lower limb of a Chopart amputee

266

F.2 Depiction of a frame of the gait cycle shortly after heel contact for a

Chopart amputee

270

F.3 Free body diagram of a transmetatarsal amputee at mid-stance

modelled using partial foot model-A

273

F.4 Free body diagram of the “lumped” foot, leg, prosthesis and shoe of

a Chopart amputee modelled using partial foot model-B

276

H2.1 Differences between modelled and experimentally derived foot mass 286

H2.2 Differences between modelled and experimentally derived foot

volume

286

H2.3 Differences between modelled and experimentally derived foot CM

in the x-direction

287

H2.4 Differences between modelled and experimentally derived foot CM

in the z-direction

287

H2.5 Differences between modelled and experimentally derived value of k

about the x-axis

288

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H2.6 Differences between modelled and experimentally derived value of k

about the y-axis

288

H2.7 Differences between modelled and experimentally derived value of k

about the z-axis

289

H3.1 Contributions to the knee joint moment equation using a standard

linked-segment model and partial foot model-A

297

H3.2 Contributions to the hip joint moment equation using a standard

linked-segment model and partial foot model-A

298

H3.3 Contributions to the knee joint moment equation using a standard

linked-segment model and partial foot model-B

301

H3.4 Contributions to the hip joint moment equation using a standard

linked-segment model and partial foot model-B

302

xv

List of tables

2.1 Anthropometric characteristics of the normal and amputee samples 12

2.2 Mean modelled and experimentally derived BSP data for the normal

sample

23

2.3 Mean modelled and experimentally derived BSP data for the

amputee sample

24

2.4 Results from regression analysis for the normal sample 25

2.5 Results from the regression analysis for the amputee sample 26

2.6 Mean difference between modelled and experimentally derived body

segment parameter data

31

2.7 Differences in the value of k between normal and amputee sample

derived using the model and experimental techniques

35

3.1 Amputee subject characteristics 44

3.2 Mean anthropometric data of the isolated foot segment for standard

linked-segment models and the partial foot models

57

3.3 Mean anthropometric data of the isolated leg segment for standard

linked-segment models and the partial foot models

58

3.4 Mean anthropometric data of the isolated thigh segment for standard

linked-segment models and the partial foot models

59

3.5 Characteristics of the combined prosthesis/orthosis and shoe for

samples A and B

59

3.6 Mean anthropometric data of the lumped segments for standard

linked-segment models and the partial foot models

60

3.7 Mean hip extension moment peaks during terminal swing for

standard linked-segment models and the partial foot models

65

3.8 Mean knee extension moment peaks during initial swing for standard

linked-segment models and the partial foot models

66

3.9 Mean knee flexion moment peaks during terminal swing for standard

linked-segment models and the partial foot models

67

3.10 Mean hip power generation/absorption during terminal swing for

standard and partial foot linked-segment models

68

xvi

3.11 Mean knee power absorption during terminal swing for standard and

partial foot linked-segment models

69

4.1 Characteristics of the amputee subjects 83

4.2 Spatial characteristics of the amputee subjects 91

4.3 Temporal characteristics of the amputee subjects 92

4.4 Single and double support phase characteristics of the amputee

subjects

93

4.5 Inter-subject variability of kinematic and kinetic patterns of the

normal population

102

4.6 Inter-subject variability of EMG patterns of the normal population 102

4.7 Periods of vastus lateralis activity observed during stance phase

including mean intensity

140

B.1 Notations 205

B.2 Anthropometric notation and measurement descriptions 206

B.3 Constants 207

B.4 Maximum errors in anthropometric input data 231

B.5 Errors in BSP data caused by errors in parameter 'b' 232

B.6 Errors in BSP data caused by errors in parameter 'c' 233

B.7 Errors in BSP data caused by errors in parameter 'l' and 'la' 234

B.8 Errors in BSP data caused by errors in parameter 'h2' 235

B.9 Errors in BSP data caused by errors in parameter 'h1' 236

B.10 Errors in BSP data caused by errors in parameter 'aml' 237

B.11 Errors in BSP data caused by errors in parameter 'aap' 238

B.12 Errors in BSP data caused by errors in parameter 'lhf' 239

B.13 Errors in BSP data caused by errors in parameter 'aaphf' 240

B.14 Errors in BSP data caused by errors in parameter 'rr' 241

C.1 Comparison of theoretical and experimentally derived V and CV of

the steel calibration block for the water only condition

244

C.2 Comparison of the theoretical and experimentally derived V and CV

of the steel calibration block for the water plus soap condition

245

C.3 Weight of liquid in the immersion container pre and post experiment

for the water only condition

245

C.4 Weight of liquid in the immersion container pre and pot experiment 246

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for the water plus soap condition

F.1 Anthropometric data of the remnant foot, leg, thigh, and

prosthesis/shoe stored in cell matrix format

264

F.2 A complete set of anthropometric characteristics of the “lumped” leg,

foot, prosthesis and shoe for the affected limb of a single Chopart

amputee

267

H3.1 Mean hip joint moment peaks for both standard and partial foot

linked-segment models

290

H3.2 Mean knee joint moment peaks for both standard and partial foot

linked-segment

291

H3.3 Mean ankle joint moment peaks for both standard and partial foot

linked-segment models

292

H3.4 Mean hip joint power peaks for both standard and partial foot linked-

segment models

292

H3.5 Mean knee joint power peaks for both standard and partial foot

linked-segment models

293

H3.6 Mean ankle joint power peaks for both standard and partial foot

linked-segment models

294

xviii

Nomenclature

MTP Metatarsophalangeal BF Biceps femoris long head

TMT Transmetatarsal VL Vastus lateralis

BSP Body segment parameter SOL Soleus

M Mass RoM Range of Motion

V Volume EMG Electromyography

CM Centre of mass A/D Analogue to Digital

CV Centre of volume MMT Manual Muscle Test

k Radius of gyration Bi Bilateral

I Mass moment of inertia Uni Unilateral

CV Coefficient of variability GC Gait cycle

IFL Intact foot length AL Affected limb

RFL Residual foot length SL Sound limb

CI Confidence interval CHC Contralateral heel contact

PTB Patella Tendon bearing Fx Horizontal ground reaction force

CoP Centre of pressure Fz Vertical ground reaction force

GCS Global coordinate system SL Shoe length

LCS Local coordinate system Deg. Degrees

HM Hip moment Flex. Flexion

KM Knee moment Ext. Extension

AM Ankle moment SD Standard deviation

HP Hip power GRF Ground Reaction Force

KP Knee power R Right

AP Ankle power L Left

HA Hip angle ABS Absolute (as in error)

KA Knee angle LFP Leg/foot/prosthesis/shoe

AA Ankle angle FP Foot/prosthesis/shoe

TA Tibialis anterior CMC Coefficient of multiple

determination

GM Gastrocnemius medial head

GL Gastrocnemius lateral head

xix

Levels of partial foot amputation

Figure I Schematic of a various levels of partial foot amputation which will be referred

to throughout the thesis

A. Metatarsophalangeal (MTP)

MTP amputation is a complete

disarticulation of the MTP joint

B. Transmatatarsal (TMT)

TMT amputation is a complete

transverse amputation through part of the

metatarsal bones

C. Lisfranc

Lisfranc amputation leaves the talus,

calcaneus and some or all of the

cuniforms and navicular as remnant

bones

D. Chopart

Chopart amputation leaves the calcaneus

and talus as remnant bones

xx

Types of prosthetic and orthotic fittings

Figure II Types of prosthetic and orthotic fittings referred to throughout the thesis

Clamshell prosthesis

The clamshell prosthesis, often referred to as the clamshell

patella tendon bearing (PTB) prosthesis when the socket

extends proximally to (and loads) the patella tendon, is

typically fitted to Chopart amputees. This device encompass

the remnant foot and leg segment (or a portion there of) and

as such eliminates ankle motion. The clamshell prosthesis

often contains a carbon fibre forefoot (depicted here) or part

of a prosthetic foot bonded onto the anterior and/or inferior

portion of the socket such as used by subjects in this

investigation

Foot orthoses, shoe inserts and toe fillers

Subjects in the present investigation had polypropylene foot

orthoses, Pelite or EVA shoe inserts with or without toe

fillers made from Plastizote.

Below ankle slipper sockets

This picture depicts below ankle slipper sockets with

supramalleolar suspension. Subjects in the present

investigation used similar devices without supramalleolar

suspension. In this picture, the forefoot section was replaced

with a carbon fibre footplate. Subjects in the presented

investigation had their forefoot replaced with a portion of a

prosthetic forefoot or replaced with foams such as

EVA/pelite

xxi

Statement of authorship

The work contained in this thesis has not been previously submitted for a degree

or diploma at any other higher education institution. To the best of my knowledge and

belief, the thesis contains no material previously published or written by any other

person except where due reference is made.

Michael Dillon

April 24th, 2001

xxii

Acknowledgments

I would like to acknowledge with love and sincere gratitude the many ways my wife

and best friend, Andrea, has enriched my life with grace, patience, thoughtfulness and

most of all love. Andrea’s contributions to this thesis go back many years. I wish to

thank Andrea for the support she has demonstrated to my research which was no more

evident than by her move to Australia so that I could pursue answers to the questions I

had about partial foot amputee gait. I recognise, but cannot begin to appreciate, how

difficult a move this was for her to leave behind her family, friends and those bitterly

cold Edmonton winters. Since that time, Andrea has contributed in many ways, only a

few of which I’m sure I’ve noticed. Andrea once gave me a poem by Patrick Overton,

which has continued to be my inspiration when I felt that the challenge was beyond me.

When you come to the edge of all the light you

have, and must take a step into the darkness of

the unknown, believe that one of two things will

happen to you: either there will be something

solid for you to stand on or you will be taught

how to fly. – Patrick Overton

To my supervisor, Dr. Tim Barker, who demonstrated tremendous patience given my

lack of skills in engineering or measuring pretty much anything, but always respected

my background in prosthetics. I think Tim recognised the formidable challenge ahead of

him when as a student in one of his mathematical modelling classes to fourth year

engineering students I asked, ‘What’s a matrix?’ I would like to acknowledge the

tremendous contribution Tim has made in giving me many of the skills necessary to

begin a career in biomechanics and an appreciation of the many skills I don’t yet have.

I wish to acknowledge a debt to Professor John Evans, whose door is always open. As a

friend, John listened to my woes and gave me the advice, support and encouragement to

continue in the face of many adversities. As a mentor, John taught me by example, a

love of research and the excitement and possibilities that come with learning something

new. I thank John for the opportunity to work alongside some tremendous people and

xxiii

contribute to many of the exciting projects being undertaken by the Centre for

Rehabilitation Science and Engineering.

I wish to thank Dr Graeme Pettet, for his extensive contribution to the development of

the anthropometric model. Graeme was the first person I’ve met with a real passion for

mathematics, which was matched only be his ability to apply it. I would like to thank

Graeme for the patience he demonstrated in teaching me the skills I needed to tackle the

challenge of developing a mathematical model and for a newfound interest in

mathematics.

I would like to acknowledge my gratitude to Dr James Smeathers for the insightful

contribution he made to the initial examination of my thesis.

My initial interest in partial foot amputee gait and the prosthetic/orthotic attempts to

replace the lost foot were sparked by Les Barnes, my third year prosthetics lecturer. Les

had an obvious interest in the problems of fitting partial foot amputees, which must

have been infectious.

Dr. Tim Bach, influenced my career forever when during a second year biomechanics

lecture on how gait aids reduce joint compressive forces I recognised the tremendous

insight that could be gained into how things work using biomechanics.

To Rod Goodrick and the staff at Goodwill Orthopaedics for giving me the freedom and

space to practice in prosthetics while undertaking my PhD.

I have been fortunate enough to have the support and friendship of so many people who

have also contributed to my thesis in so many ways. I wish offer my sincere thanks and

debt to Stef, Kurt, Michelle, Ros, Laurent, Jarrod and Joan.

I wish to thank the many people who gave so generously of their time to participate in

the research. Hopefully soon your contributions will be rewarded.

xxiv

to Tim Barker.

________________________________________________________ Chapter 1. 1

Introduction and thesis overview

Partial foot amputation has long been thought of as an alternative to below knee

amputation (McKittrick et al., 1949) and is becoming a more viable and common

surgical intervention (Imler, 1985; Sobel, 1995 – cited Sobel, 2000) for the treatment of

advanced diabetes, vascular insufficiency and trauma where previously a below knee

amputation may have been the only reasonable choice. These surgical choices have

been enabled by a better understanding of diabetes and vascular disease, improvements

in surgical techniques for revascularising the arteriole structure of the foot (Habershaw

et al., 1993; Pomposelli et al., 1993) and antibiotic therapy for controlling ascending

infection (Habershaw et al., 1993; Pomoselli et al., 1993; Mueller and Sinacore, 1994)

and septicemia (Mueller and Sinacore, 1994).

Statistics describing the incidence of partial foot amputation are scarce. In

Australia it is not known how many people undergo partial foot amputation annually or

how many individuals are living in the community with partial foot amputation. The

National Centre for Disease Statistics in the United States reports that approximately

10,000 transmetatarsal amputations were performed in the USA in 1991 (Mueller and

Sinacore, 1994) and presumably, many alternate forms of partial foot amputation were

also performed. Many of these procedures are likely to have been in preference to below

knee amputation (Chrzan et al., 1993; Quigley et al., 1995; Stuck et al., 1995; Sanders,

1997).

Chapter 1

________________________________________________________ Chapter 1. 2

The preferential decision for partial foot amputation could be influenced by a

broad array of factors including the likelihood of losing the contralateral lower limb

(Sobel, 2000), the ability to weight bear on the residuum (Mc Kittrick et al., 1949;

Miller et al., 1991; Mueller and Sinacore, 1994; Boyd et al., 1999), improved cosmesis

at distal levels, psychological impact of higher amputation, lower mortality rate (Lee et

al., 1993 cited - Mueller et al., 1995), improved function associated with the

preservation of foot length (Lieberman et al., 1993; Mueller and Sinacore, 1994;

Garabolsa et al., 1996; Sanders, 1997; Mueller et al., 1998), the desire to maintain ankle

motion (Condie, 1970; Schwindt et al., 1973; Imler, 1985; Lange, 1987; Heim, 1994) or

at the patient's request for less invasive surgery.

There is little doubt that preserving a portion of the weight-bearing limb has

certain advantages. The ability to ambulate short distances without a prosthesis is easier

and safer for the partial foot amputee compared to the below knee amputee who may

hop to the toilet during the night or from a pool change room to the waters edge. In less

active individuals, the preservation of a portion of the foot may increase mobility.

Moreover, for many people unfortunate enough to loose the contralateral lower limb,

bilateral or unilateral partial foot amputation may aid transfers in and out of a

wheelchair or bed and offer enhanced mobility compared to a bilateral below knee

amputee. While there is little experimental evidence to support these views, they would

seem to be logical and clinically well accepted.

Although partial foot amputation may be preferable to more proximal

amputation for any number of these reasons, there is considerable evidence highlighting

that the procedure has a significant failure rate (Sage et al., 1989; Hodge et al., 1989;

Miller, 1991; Sanders and Dunlap, 1992; Mueller and Sinacore, 1994) and numerous

complications including ulceration (Sage et al., 1989), skin breakdown (Brand, 1983;

Sage et al., 1989; Birkie and Sims, 1988; Mueller and Sinacore, 1994) and equinus

contracture (Parzaile and Hahn, 1988; Chrzan et al., 1993; Garabolsa et al., 1996;

Sanders, 1997) which can lead to more proximal amputation. Many of these

complications have, rightly, tainted the perception of patients, surgeons, physicians and

allied health clinicians who have witnessed, first hand, these problems limit the mobility

and quality of life of many people with partial foot amputation. Complications such as

________________________________________________________ Chapter 1. 3

ulceration and delayed would healing are likely to increase length of hospital stay,

which in hindsight often serves little purpose other than to delay below knee

amputation.

Many of the complications which can result in more proximal, below knee,

amputation are likely to be influenced by the limited knowledge of partial foot amputee

gait and the effect of prosthetic/orthotic intervention. Much of the knowledge basis that

underpins clinical practice is often illogical, speculative and anecdotal, despite general

clinical acceptance.

There is a substantial body of literature, which lends weight to the contention

that current clinical practice is based largely without experimental evidence or logical

argument based on the biomechanics of partial foot amputee gait. Instead, validation for

clinical practice is drawn from an understanding of normal gait or that of other amputee

groups. The strength of this contention is evidenced in virtually any aspect of literature

concerning prescription, prosthetic/orthotic design, surgery and, to a lesser extent,

biomechanics.

For example, the literature illustrates a common belief that preserving foot

length should be a primary surgical objective, necessary to maintain function or normal

gait (Barry et al., 1993; Giurini et al., 1993; Pinzur et al., 1997; Sobel, 2000) despite

virtually no experimental evidence to support the existence of any such relationship.

Implications that foot length should be preserved because energy expenditure is

increased with more proximal amputation (Barry et al., 1993; Santi et al., 1993; Stuck

et al., 1995; Garabolsa et al., 1996; Sobel, 2000) were founded on investigations of

metabolic expenditure in transfemoral, transtibial and Symes amputees (Walters et al.,

1976) or implied from investigations of the ground reaction force in mid-foot amputees

(Pinzur et al., 1997). Moreover, authors speculate that prosthetic/orthotic devices or

footwear are able to restore the lost foot length/lever arm (Condie, 1970; Rubin, 1984;

Rubin, 1985; Pullen, 1987; Stills, 1987; Condie and Stills, 1988, Weber, 1991; Mueller

and Sinacore, 1994; Sanders, 1997; Sobel, 2000) or that full-length shoes increase the

lever arm and magnitude of the ground reaction force (Sanders, 1997). These

contentions are founded largely without experimental evidence and seem illogical given

the clinical inability of most partial foot amputees to perform a simple activity such as

________________________________________________________ Chapter 1. 4

'standing up on their toes.' Similarly, alarming contentions suggest that these devices

also aid propulsion or push-off (Rubin and Denisi, 1971; Rubin, 1984; Rubin, 1985;

Stills, 1987; Sobel, 2000) or that hallux or toe amputation results in a loss of push-off or

propulsion (Sanders, 1997; Sobel, 2000). Some authors suggest that individuals should

advance the lower limb forward using the hip flexor musculature to reduce plantar

pressures or push-off (Mueller and Sinacore, 1994; Mueller et al., 1995) as has been

advocated in diabetics with intact feet (Brand, 1983; Mueller and Sinacore, 1994). More

recent work suggests that partial foot amputees adopt a hip flexor gait to compensate for

a lack of power generation across the ankle (Mueller et al., 1998) but the experimental

evidence supporting this view is unconvincing.

Recently, many of these more common contentions have received attention as a

result of a growing awareness of the inadequacies of our understanding of partial foot

amputee gait, prescription and clinical practice. There is an increasing body of literature

examining the kinematic, ground reaction force, kinetic, temperospatial, plantar

pressure and muscle strength parameters of, primarily, the affected limb. These data

have been contributed by a small number of authors who have each, examined limited

aspects of gait, primarily at or distal to the transmetatarsal level (Dillon, 1995;

Garabolsa et al., 1996; Hirsch et al., 1996; Dorostkar et al., 1997; Burnfield et al., 1998;

Muller et al., 1998; Boyd et al., 1999). Much of this work remains ongoing with limited

details appearing in conference abstracts or research progress reports. Collectively,

these investigations raise questions about the causes and compensatory effects of

abnormal movement.

Of particular interest is the lack of power generated across the ankle (Dillon,

1995; Mueller et al., 1998) given that one important function of preserving the ankle

and calf musculature would seem to be the ability to use it. The cause of power

reduction is poorly understood and explained (Dillon, 1995; Mueller et al., 1998), as is

the influence of prosthetic/orthotic design on the ability to generate power across the

ankle. It is not yet known how partial foot amputees generate sufficient power to

advance the lower limb into swing phase and the body forward given that there appears

to be no obvious or convincing evidence (Dillon, 1995; Mueller et al., 1998) describing

compensations for reductions in ankle power generation on the affected limb. Perhaps,

as in transfemoral amputees, power is generated across the sound hip during the

________________________________________________________ Chapter 1. 5

preswing phase to advance the lower limb into swing phase and the body forward. A

thorough investigation documenting the biomechanics of partial foot amputee gait

would seem timely.

The objective of this thesis was to describe the effects of amputation and

prosthetic/orthotic fitting on gait with particular attention to why power generation

across the ankle is negligible, how sufficient power is generated to advance the lower

limb into swing phase and the influence of prosthetic/orthotic fitting.

This thesis is presented in a series of five subsequent chapters describing the

development and application of biomechanics models for the analysis of partial foot

amputee gait and prosthetic/orthotic fitting.

In Chapter 2, a geometric model is presented to provide a means for readily

estimating accurate anthropometric data of the partial foot residuum. This model may be

advantageous to investigators of partial foot amputee gait because it acknowledges the

unique anthropometry of the partial foot residuum, thus addressing one of the

limitations of previous kinetic investigations. The accuracy of the model was compared

with experimentally derived anthropometric estimates obtained using incremental

immersion and torsional table experiments.

The linked-segment inverse dynamic models presented in Chapter 3, incorporate

these improved anthropometric characteristics of the remnant foot and any

prosthetic/orthotic fitting and footwear to enhance the accuracy of biomechanical

descriptions of partial foot amputee gait. The linked-segment models describe novel and

more accurate representations of the lower limb of partial foot amputees. The effect of

these improved mechanical descriptions was contrasted against kinetic estimates

obtained from a standard linked-segment model.

Given that the primary objective of the thesis was to evaluate causes and

compensatory effects of abnormal power generation, linked-segment models were

developed for a sagittal plane analysis only, given that the major proportion of work is

performed in the plane of progression (Eng and Winter, 1995).

________________________________________________________ Chapter 1. 6

With an appreciation of the influence these models have on joint moments and

powers, they were used to document the walking patterns of a cohort of partial foot

amputees and describe the affect of amputation and prosthetic/orthotic fitting on gait in

Chapter 4. This investigation documents bilateral kinematic, kinetic, temperospatial,

ground reaction force, electromyography and joint range of motion and muscle strength

parameters of a cohort of normal and partial foot amputees.

In Chapter 5, results from the preceding investigation of partial foot amputee

gait were used to explore some of the clinical implications of these findings in relation

to the design of prosthetic/orthotic devices and rehabilitation practices for individuals

with partial foot amputation.

The major findings of these investigations are brought together in Chapter 6 and

indications for further investigation are discussed.

________________________________________________________ Chapter 2. 7

An anthropometric model of the partial foot

residuum

2.1 Introduction

Knowledge of the dimensional and inertial characteristics of the human body

are of significance to research in fields as diverse as space technology, automotive

vehicle design, physical education, gait analysis and prosthetics. As a result, a number

of researchers have devoted substantial effort toward providing these fundamental data

(Dempster, 1955; Hanavan, 1964; Clauser et al., 1969; McConville et al., 1980;

Plagenhoef, 1983; Zatsiorsky et al., 1990).

There are numerous methods of determining these data, the most accurate of

which would be to determine these measurements in vivo (Zatsiorsky and Seluyanov,

1985; Zatsiorsky et al., 1990). These methods are complex, time consuming and still

rely on assumption (McConville et al., 1980) and are, therefore, not routinely utilised.

The methods currently utilised to estimate body segment parameters (BSP) data can be

divided into two methodological groups: proportional data sets and geometric models

(Kingma et al., 1996).

Chapter 2

________________________________________________________ Chapter 2. 8

Proportional anthropometric data sets estimate body segment parameters using

regression equations, requiring minimal anthropometric measurements such as body

mass, stature and/or limb length and mid-segment circumference. Segment

characteristics are determined as a proportion of body mass or stature. Much of the data

utilised by these models were derived using small samples of cadaver specimens in an

aged population (Dempster, 1955; Clauser et al., 1969). Other studies have focused on

a specific population, such as athletes (Plagenhoef, 1983), soldiers (McConville et al.,

1980) or physical education students (Zatsiorsky et al., 1990) to determine these

measurements in vivo. While these anthropometric data sets may provide useful data

when applied within the populations the studies are based on, the uncertainty about the

data will grow as the models are applied to subjects with anthropometric characteristics

differing from the mean of that population (Kingma et al., 1996).

Geometric anthropometric models determine body segment parameters from

simple geometric shapes. Geometric representations of the human body have previously

utilised ellipses and elliptical cylinders (Hanavan, 1964) or segments divided into small

elliptical zones (Jensen, 1986). Other models utilise a variety of geometric forms to

represent the human body (Hatze, 1979; Vaughan et al., 1992). The drawbacks of these

geometric models are that they require more input measurements to derive the model

and many do not utilise the geometric form to estimate segment mass (M) (Hanavan,

1964; Vaughan et al., 1992) or centre of mass (CM) (Vaughan et al., 1992). Most of

these geometric models also assume uniform density of the limb segment. Geometric

models of human segments have the advantage that they can, in principle, be applied to

any population although the resulting accuracy is often not adequately reported (Hatze,

1979; Vaughan et al., 1992).

BSP have been used extensively for gait analysis as input data into

mathematical representations of the human body so that determinants of human

walking, such as joint moments and powers, can be estimated.

The majority of these models have limited applicability for analysis of amputee

gait because they are based on normal, non-amputee, populations and do not reflect the

unique anthropometric changes which occur due to amputation or prosthetic/orthotic

fitting.

________________________________________________________ Chapter 2. 9

When normal BSP are used to represent the partial foot residuum (Dillon, 1995;

Boyd et al., 1999) the increased M, change in the position of the CM and increased

inertial parameters relative to that of the amputee may yield inaccurate joint moment

and power estimates, especially during swing phase. In the same way, certain types of

partial foot prosthesis, such as the clamshell patella tendon bearing prosthesis, may

significantly modify the total segment M, CM and mass moment of inertia (I) and yield

inaccurate joint moment and power estimates.

Previous studies, on transfemoral and transtibial amputees, have attempted to

address these shortcomings by estimating anthropometric parameters for the residual

limb (Contini, 1970; Krouskop, 1988; Bach, 1994) and prosthesis (Capozzo et al.,

1976; Miller, 1987; Czerniecki et al., 1991; Bach, 1994). Investigations into partial foot

amputee gait have not reported addressing either of these issues (Dillon, 1995; Muller

et al., 1998; Boyd et al., 1999).

While the physical characteristics of the prosthesis/orthosis are readily

determined using standard dynamics techniques, the same characteristics of the partial

foot residuum are not so readily obtained. A number of techniques may be suitable to

determine these parameters for use with living subjects (Reid and Jensen, 1990).

Among these, incremental immersion is the most convenient and inexpensive method

of determining volume (V) and centre of volume (CV). If assumptions are made about

segment density this technique can yield estimates of M and CM. The value of I of

isolated body segments can be determined easily using the 'torsional table' or

'pendulum' method. However, this technique is not suitable for in vivo measurement.

Typically, these inertial data are obtained on cadaver specimens or plaster models of

limb segments (Contini, 1972). Mathematical modelling has the advantage that these

BSP data can be determined in a fraction of the time, once the model is developed.

Incremental immersion involves submerging a limb segment to a series of

specified depths and measuring the volume of water displaced by each successive

increment. If a constant density is assumed, M and CM (assumed equivalent to the CV

for a limb with constant density) can be estimated by summation across incremental

volumes. This method has been used with good results on normal subjects (Drillis and

________________________________________________________ Chapter 2. 10

Contini, 1966; Pagenhoef, 1971), transtibial (Fernie and Holliday, 1982) and

transfemoral amputees (Contini, 1970). Some authors have measured the volume of a

plaster cast of the residuum (Contini, 1970) or of the prosthetic socket (Bach, 1994) as

an alternate method for determining the residuum V and CV.

It is not possible to use the incremental immersion techniques to derive values

of I of the limb segment. The 'torsional table ' and 'pendulum' methods have been

widely used to determine I of isolated body segments (Nubar, 1962 -cited Drillis et al.,

1964; Drillis et al., 1964; Contini, 1972; McConville et al., 1980) and prosthetic

components (Drillis et al., 1964; Drillis and Contini, 1966; Bach, 1994; Burkett, 1998).

These techniques are most easily executed using a plaster model of the limb segment

(Contini, 1972) and are recommended over other methods of determining I such as the

'quick release method' (Drillis and Contini, 1966).

Mathematical modelling of segments through geometric representation may be

advantageous because a generic model of the partial foot residuum characterised by a

few anthropometric measurements would simplify the process of deriving the required

anthropometric data. The difficulty with selecting a suitable mathematical technique is

that many do not predict segment M (Hanavan, 1964; Vaughan et al., 1992) or CM

(Vaughan et al., 1992) using the geometric representation of the limb segment. Some,

more complex, models do predict M, CM and I using the geometric form (Hatze, 1979)

but still have limited application for certain populations due to the models' assumptions

of segment density (Schneider et al., 1990; Schneider and Zernicke, 1992). The utility

of the Hatze (1979) model is further limited by the lack of documentation describing

the input parameters necessary to execute the model and in some cases, inconsistencies

exist between the published mathematical notation and the geometric form1.

1 There appears to be some inconsistencies in the height measurements of the foot (h2,h1) between themathematical notation, the schematic figures and sample measurements in Appendix 4 (Hatze, 1979).These were confirmed by derivation of Hatze's equations from first principles. Based on the derivationfrom first principles, the sample measurements and schematic figures, h2 seems to describe the height ofthe foot from the floor to the apex of the lateral malleolus and h1 describes the height from the floor to thetop of the 1st Metatarsal head. If these deductions are true, then the height of top segment of the foot (S14)should be given by h2-h1 and not by h2, as indicated by Hatze, (1979). The schematic of the foot modeland associated measurements (Hatze, 1979) imply that the S14 segment height is equal to h2, however, thesample input data in Appendix 4 (Hatze, 1979) and the derivation of Hatze's equations from firstprinciples contradict this. Without clear descriptions of the actual measurements used to execute themodel and their relationship to the mathematical equations described by Hatze, (1979) there is no way tovalidate these equations.

________________________________________________________ Chapter 2. 11

Proportional anthropometric data sets, which predict segment M or CM as a

function of weight and height are not sensitive to the changes in BSP which occur due

to partial foot amputation. Partial foot amputation does not alter stature or significantly

alter body mass despite making large differences to the foot segment characteristics.

The differences observed in foot length, M, CM and I are not reflected by these

proportional anthropometric data sets and as such may not be suitable for this

population of amputees.

The aim of this work is to:

1. develop an anthropometric model to predict the V, M, CM and I of the partial foot

residuum and the normal foot;

2. compare the modelled predictions of M, V, CM and I to those BSP predicted from

incremental immersion and torsional table experiments using cast replicas of both

the intact and partial foot

2.2 Method

Subjects

A number of individuals were recruited, both with and without forefoot

amputation, for a number of concurrent gait investigations. Amputee subjects were

recruited through the definitive prosthetic budget holder; Queensland Amputee Limb

Service (QALS). Letters were sent to QALS for distribution to individuals currently

listed on their books with partial foot amputation (Appendix A). Subjects then

responded by telephone to acknowledge their wish to participate. Amputee subjects

were also recruited from definitive prosthetic/orthotic service providers.

QALS issued 56 letters to individuals listed as partial foot amputees. Many of

the respondents were Symes amputees or others who had been incorrectly categorised.

Fourteen individuals with partial foot amputation were identified through QALS and of

those recruited through the definitive prosthetic/orthotic service providers, all had

already received invitations from QALS. Three of the respondent's were children, all of

whom were excluded after pilot testing, due to the lengthy data collection period (4-5

hours) which made data collection difficult and unpleasant for the children. One subject

________________________________________________________ Chapter 2. 12

was excluded because of polio after presenting to the university, which was not

identified at the time the subject initially responded to acknowledge their wish to

participate. Another subject failed to attend three appointments and another became ill

and required further surgery prior to testing.

The primary cause of amputation amongst the remaining sample was trauma.

Some individuals had partial foot amputation from gangrene secondary to frostbite or

full thickness burns. No subjects in the sample had an amputation as a result of vascular

disease. Amputation level was assessed by a qualified prosthetist/orthotist (the author)

using palpation of the residual limb. Measurements of residual foot length were taken

and expressed as a percentage of intact foot length to verify amputation level (Dillon,

1995). Where possible, amputation level was also assessed using x-rays of the residual

foot.

Subjects were excluded from participation if they ambulated with the use of gait

aids, had previous limb operations or concomitant health problems such as ulcers,

which might affect gait or prevent them from undertaking all aspects of the evaluation.

Both bilateral and unilateral partial forefoot amputees were accepted as participants.

Amputation level, aetiology, age, sex and years since amputation were not included as

selection criteria because it was felt that this would place undue restriction on the

number of partial foot amputees who could be recruited. Control subjects satisfied the

same inclusion criteria as the amputee subjects. Individual control subjects were

matched for sex, age, stature and mass to one of the amputee subjects. Anthropometric

characteristics have been reported in Table 2.1 for both the normal and amputee

samples.

Modelled and experimentally derived BSP data were computed for 19 feet

including nine intact feet, two Metatarsophalangeal (MTP), one Transmetatarsal (TMT),

five Lisfranc and two Chopart residuums. Dental plaster replicas of the subjects feet

were preferable to true in vivo measurements because the I calculations were simplified,

CM estimates could be obtained for all directional axes and subjects would not have to

endure the tedious incremental immersion process to obtain V and CV data.

________________________________________________________ Chapter 2. 13

Table 2.1 Anthropometric characteristics of the normal and amputee samples.

Mean values for stature, body mass, residual foot length (RFL) and intact foot length (IFL) are presented

and the standard deviation (SD) reported in brackets. SD for mass and stature was not reported for the

MTP and TMT amputees, as there was only one amputee in each group. The MTP amputee was bilateral,

hence the SD values reported for RFL. IFL were estimated for the MTP subject as a proportion of stature

(Dempster, 1955).

Sub samples of the Amputee sampleNormal

sample

(n=9)

Amputee

Sample

(n=10)

MTP

(n=2)

TMT

(n=1)

Lisfranc

(n=5)

Chopart

(n=2)

Stature (m) 1.81

(0.07)

1.75

(0.08)

1.74

(.)

1.82

(.)

1.74

(0.11)

1.77

(0.02)

Body mass (kg) 85.49

(9.20)

73.10

(14.95)

64.85

(.)

84.50

(.)

67.74

(16.30)

89.05

(5.59)

Foot length

-IFL (m) 0.27

(0.01)

0.26

(0.01)

0.26

(0.00)

0.27

(.)

0.26

(0.01)

0.27

(0.01)

-RFL (m) 0.27

(0.01)

0.15

(0.03)

0.20

(0.00)

0.17

(.)

0.14

(0.02)

0.11

(0.00)

-RFL (% IFL) 100.00

(0.00)

52.67

(12.64)

76.72

(0.54)

62.26 55.36

(5.42)

41.15

(1.63)

Apparatus

Dimensional and inertial characteristics of the partial and normal feet were

derived using a geometric model based on work by Hatze, (1979). From first principles,

the model was derived as an assemblage of 103 plates of varying dimensions and

densities (Appendix B). Three trapezoidal plates represent the most inferior portion of

the ball of the foot (S11), the heel (S12), and the sole above these regions (S13) (Figure

2.1). The remaining 100 plates account for the middle and upper part of the foot (S14)

which were described using parabolic (S14P) and trapezoidal (S14

T) plates (Figure 2.1).

The model is symmetrical about the x-axis (Figure 2.1).

________________________________________________________ Chapter 2. 14

Figure 2.1. Geometric model of a Metatarsophalangeal residuum

Further information about the component pieces of the model including an exploded view have been

documented in Appendix B.

Anthropometric measurements of the subject's feet were taken using a set of

anthropometric callipers, with a maximum measuring range of 15cm, and a 30cm ruler.

The resolution of the measuring equipment was one millimetre. As an example of the

effect of errors in anthropometric input data, each anthropometric input parameter for a

single normal subject was independently manipulated by subtracting/adding the

maximum error associated with each input measurement and recording the BSP

calculated (Appendix B). Comparisons of the resulting BSP data to baseline values

highlighted that errors in the measurement of the lateral malleolus height (h2) and the

height of the first metatarsal (h1) had the largest affect on the prediction of BSP data

and as such should be measured with the greatest care (Appendix B). A ±3mm error

associated with the measurement of either h2 or h1 resulted in a 30ml change in foot V

(3.4%), 40g change in foot M (3.8%) and 2mm change in location of the mass centroid

along the z-axis (4.3%) (Tables B.8 and B.9). Errors in the measurement of length of

the hindfoot (lhf) of ±4mm resulted in ±3mm changes (6.3%) in the location of the

mass centroid along the z-axis (Table B.12). Errors in the measurement of other

anthropometric input data did not make significant differences to the prediction of BSP

data (Appendix B).

Z

X

YS11

S14P

S14T

S13

S12

________________________________________________________ Chapter 2. 15

The subject's feet were cast using plaster of Paris bandage and the negative

moulds were filled with dental plaster to produce the replicas. Obvious anomalies, such

as those caused by joins in the plaster negative were removed with a surform or filled

with dental plaster. The casts were then cleaned with sand screen prior to being sealed

with shellac.

Two containers were used during all immersion study experiments. The first

container was a Décor 5ltr (model 396) with an internal height of 16cm. The sides of

the container were not square. The internal dimensions of the top of the container were

30x12cm and the bottom 28.5x11cm. This container was used for immersion of the foot

model along the z-axis and will now be referred to as the z-axis immersion container.

The model axes are depicted in Figure 2.1. The second container was a ClickClack

2.1ltr canister (model 302502), with an internal height of 19.8cm and the radius at the

top of the container was 14cm. From the bottom of the container to 3cm from the top

the radius was 12.5cm. This container was used for immersion of the foot model along

the x-axis and will now be referred to as the x-axis immersion container (Figure 2.1).

An Ohanus electronic scale (model GT4100), with a resolution of 0.1g, was used to

weigh the displaced water and plaster model. A surgical steel tray with external

dimensions of 0.52×0.32×0.06m was used to catch the displaced water before decanting

into a one litre Biomex measuring beaker. A cake cooling rack was placed in the

catchment tray to keep the immersion container out of the displaced water.

Liquid soap (Bactercidal liquid soap no.563-214, RS components Pty Ltd.

Brisbane) was used to decrease the water surface tension during the incremental

immersion experiments (Appendix C). The soap was proportioned at 5g to every 2000g

of water.

A trifilar pendulum system (Figure 2.2) and an electronic, handheld, stopwatch

were used to determine the period of oscillation; a component in the calculation of the

value of I (Maltbaek, 1988). The bottom plate of the trifilar had a mass of 0.977 kg and

the value of I was theoretically determined to be 0.0168 kg.m2.

________________________________________________________ Chapter 2. 16

Figure 2.2 Pendulum Trifilar system for calculating of the inertia of isolated body

segments.

Procedure

Partial foot amputees and normal subjects presented to the university gait

laboratory for the collection of data for this investigation, as part of a comprehensive

gait analysis. Prior to the collection of data, the experimental procedures and equipment

were explained to each participant and any questions they had regarding the session

were answered prior to them consenting to participate in the experiment as required by

the University Human Research ethics committee (Appendix D). A physical

examination and medical history were documented (Appendix I) and any details about

the condition of the residuum were noted. Attempts were made to access the subject's

medical records so that details about the surgical intervention such as heel cord

lengthening, muscle reattachment or special bony modifications could be noted. These

medical records were extremely difficult to obtain, even with subject's written consent,

and the information about the surgical procedure was often sketchy and inadequate.

Determining BSP data using the anthropometric model

Physical dimensions of the partial and normal foot were recorded as described

in Table B.2 (Appendix B).

Anthropometric measurements of intact foot length (l) and the height of the 1st

metatarsal head (h1) were unable to be obtained for the bilateral MTP subject. These

measurements were estimated using regression equations. Intact foot length was

________________________________________________________ Chapter 2. 17

estimated as a proportion of stature according to Dempster (1955). The regression

equation used to estimate h1 was derived from height measurements, of the 1st

metatarsal head of a sample of intact feet and normalised for stature. The regression

coefficient was obtained by averaging these normalised data and is presented in Table

B.2 (Appendix B).

The recorded anthropometric measurements, describing the physical

characteristics of the foot, were then entered into a Matlab 5.3 (Mathworks Inc.

Englewood Cliffs, NJ) script and stored to file. Estimates of M, V, CM and I were then

derived using the geometric model described in Appendix B and stored to file for use in

the inverse dynamic model (Chapter 3).

If the density of the mathematical model was made uniform or constant, and

equivalent to that of the plaster foot being analysed, the modelled M, V, CM and I

could be compared to the experimentally derived BSP data. Density of the plaster foot

in kg/m3 was given by

(1)

where, Mpf described the mass of the plaster foot and Vpf the volume of the

plaster foot being studied.

Modelled values of I were expressed as radii of gyration, k, to account for the

reduction in M of the plaster foot replicas between the incremental immersion and

trifilar experiments; presumably as a result of the plaster feet dehydrating. These

changes in M were assumed not to affect the assumption of uniform density.

Determining BSP data using the plaster foot replicas

To obtain the negative mould, necessary to produce the plaster foot replica,

subjects were positioned prone on a treatment plinth. Prior to casting the foot in a non-

weight bearing position with the ankle at 90 degrees and the subtalar joint in neutral,

lines horizontally and vertically bisecting the lateral malleolus were marked with

indelible pencil. The foot and ankle were cast in 2 stages so that the plaster mould did

not have to be cut off the subject. The negative impression was removed once the

pf

pfpf

V

M=γ

________________________________________________________ Chapter 2. 18

plaster had cured and immediately reassembled. Subjects then participated in the gait

analysis testing session.

To create the replica plaster foot, the negative plaster mould of the subject's feet

was positioned such that the horizontal line bisecting the lateral malleolus was level.

Dental plaster was then poured into the negative cast to the horizontal line bisecting the

lateral malleolus. Once cured, the plaster bandage was removed and any obvious

anomalies, such as those caused by joins in the plaster negative were removed with a

surform or filled with dental plaster. The casts were then cleaned with sand screen prior

to being sealed with several coats of shellac.

Increments of immersion were marked on the foot along the z and x-axes. One-

centimetre increments were marked along the negative z-axis and numbered

consecutively from the top of the foot to approximately 1.5cm from the sole. The x-axis

origin was located at the line vertically bisecting the lateral malleolus. Immersion

increments were consecutively marked every 2cm along the negative and positive x-

axis from the origin to approximately 1.5cm from the heel and from the origin to

approximately 3.5cm in the intact foot - appropriately shorter for the partial feet. It was

not possible to establish more distal increments of immersion along the positive x-axis

as the volume of displaced water was too small to measure accurately. In some

instances, the origin of the foot was moved distally as only two thirds of an intact foot

was able to be immersed at any time due to the size of the immersion container

available. When calculating the CM, the origin of the plaster replica was adjusted

accordingly such that the origin of the model and plaster foot replica matched.

During the pilot investigations, it was noted that the plaster foot was able to

absorb water despite being sealed; a finding also reported by Contini (1970). If the foot

was left to soak in water for a period of 30 minutes prior to the study, the water

absorption noted was negligible as evidenced by the pre and post experiment weight of

the plaster foot replica.

Pilot investigations also demonstrated that the volume of liquid held in the tank

pre-test was an important predictor of the volume displacement during the immersion

study. Once the tank appeared full, it was possible to still add more liquid creating a

________________________________________________________ Chapter 2. 19

meniscus on the surface of the tank. During initial experiments each tank was filled

until the liquid begun to flow over the tank. The volume of liquid in the tank was

recorded and duplicated, prior to the commencement of each experiment. The weight of

liquid in the tank was noted prior to each experiment so that the error due to this

variable could be adequately assessed.

Prior to the commencement of each experimental session, the plaster foot was

left to soak in a bucket of water for 30 minutes. During this time, the stainless steel

catchment tray was placed on a level laboratory bench and the desired immersion

container placed on the cake cooling rack in the tray. The z-axis immersion container

was filled with 5.8kg of liquid and the x-axis immersion container was filled with 2.7

kg of liquid (Appendix C). The liquid decanted into each immersion container was

weighed using a Biomex 1ltr measuring beaker and this value recorded on the data

collection sheet. The plaster foot was also weighed at this time and the value recorded.

The plaster foot was immersed to each immersion increment marked on the plaster foot

and the liquid displaced in the catchment tray was decanted into the measuring beaker

and the water weight was recorded. This decanted liquid was returned to the immersion

container prior to data collection for the next immersion increment. Immediately after

the volume of the last increment was recorded the plaster foot was weighed and the

volume of liquid left in the immersion container was recorded. This experimental

procedure was repeated three times for each directional axis.

The volume of each immersion increment was determined by the change in

displaced liquid volume between immersion increments. Foot V was determined by

summation of the volume of each immersion increment. The total foot V was calculated

as the average foot V of each directional axis.

Foot CM was given by the sum of the products of the segment volumes and the

segment lever-arms, from the origin of the foot, divided by the total foot volume. Foot

CM data were derived and averaged across the trials for each directional axis.

With knowledge of the dimensional characteristics of the trifilar, the M and CM

of the plaster foot, the value of I of the plaster foot replica could be calculated. The

________________________________________________________ Chapter 2. 20

plaster foot was weighed using electronic scales and the position of the CM of the foot

had already been determined from the incremental immersion studies.

To determine the value of I, the CM of the plaster foot was located over the

centre of the bottom disc of the Trifilar. The bottom disc of the trifilar was displaced

slightly to produce a small amplitude oscillation and the time taken to produce 10

oscillations was recorded. This process was repeated five times and the period of

oscillation averaged across the trials. This process was repeated for each directional

axis.

The value of I of the plaster foot and the bottom plate combined, Ic, was

determined in a similar manner to that by Maltbaek (1988), and is given by

(2)

where Mc is the mass of the plaster foot and the bottom plate of the trifilar

combined, Rp, the distance from the centre of the bottom plate to the wire attachment

and l, the wire length. A value of 9.81m/s2 was used for the acceleration due to gravity,

g, in the calculations. The frequency of oscillation, f, was given by

(3)

where, t is the time period for 10 oscillations of the combined foot replica and

bottom plate of the trifilar.

The value of I of the plaster foot, Ipf was given by

(4)

where, Ic describes the combined I of the plaster foot and the bottom plate of the

trifilar and It describes the I of the bottom plate of the trifilar which can be theoretically

determined using the geometric equation for I of a circular plate

tf

10=

tcpf III −=

( ) lf

RpgMcIc 2

2

.2

..

π=

________________________________________________________ Chapter 2. 21

(5)

where, Mt is the mass of the bottom plate of the trifilar and R is the radius of the

plate.

The value of I was calculated for each directional axis using this process and

converted into radius of gyration to account for differences in foot mass between the

modelled and experimentally derived values of I.

Density of each subject's plaster foot replica was calculated (Eq. 1) and applied

to the model. BSP data were calculated using the mathematical model and the V, M,

CM and k data were recorded for comparison to the experimentally determined BSP

obtained from the incremental immersion and torsional table experiments using the

subject's replica plaster feet.

Paired two tailed t-tests and linear regression analyses comparing the slope of

the regression line were used to provide information about the differences between

paired observations and whether changes in BSP predicted using the geometric model

and experimental techniques were linear. The linear regression analysis compared the

95%CI of the slope of the regression line, when the y-intercept was forced through

zero, to the slope of the theoretical line of identity (Zar, 1984). The coefficient of

determination (r2) has been reported for the sake of completeness and not as a definitive

measure of the linearity of the relationship between BSP predicted using two different

techniques. While these statistical measures provide information about differences

between paired observations and describe the linearity of changes in BSP predicted

using these two techniques, the magnitude of the differences observed is not obvious.

To augment the interpretation of the paired t-test and regression analyses, the

differences between BSP data predicted using the model and experimental techniques

have been presented in Appendix H according the method described by Bland and

Altman (1986). Additional information about the mean differences between paired

observations was determined by using the basic formula (Eq 6). As an example, the

relative volume difference, v, between each experimental and modelled BSP was given,

as a percentage, by

2

.2

RMI

tt =

________________________________________________________ Chapter 2. 22

(6)

Hatze, (1979) where Vm denotes the modelled volume and Ve the experimentally

derived segment volume. By interchanging the variable, V, for other BSP data, the

relative difference for all characteristics was determined.

2.3 Results

Modelled and experimentally derived BSP data were computed for 19 feet

including nine normal (intact), two MTP, one TMT, five Lisfranc and two Chopart

residuums. These feet were categorised into a normal and amputee sample. A two tailed

t-test for sample means revealed significant differences in RFL expressed as both an

absolute difference (p<0.001) and as a percentage of IFL (p<0.001) between the normal

and amputee samples. Differences in body mass between the normal and amputee

samples approached significance (p=0.05) due to the inclusion of one male subject. If

this subject was removed from the sample there were no significant differences

observed (p=0.10). Given that each parameter tested was a paired sample (modelled vs.

experimental) the difference observed was not of concern. No significant differences in

IFL (p=0.32) or stature (p=0.15) were observed between groups.

Paired two tailed t-tests were used to determine any statistically significant

differences between the modelled and experimentally derived BSP data. The absolute

differences and percentage difference in M, V, CM and k values for the normal and

amputee samples have been presented in Tables 2.2-2.3, respectively. No significant

differences were observed between paired modelled and experimentally derived

estimates of foot M, V, CM in either the sample of intact (Table 2.2) or amputated feet

(Table 2.3). No significant differences were noted for values of k about the y and z-axes

in the sample of intact feet (Table 2.2) however, significant differences in the value of k

about the x-axes were observed (p=0.04). Estimates of k obtained for the sample of

partial feet were also significant different for all directional axes (Table 2.3).

−=

e

m

V

Vv 1.100

________________________________________________________ Chapter 2. 23

Table 2.2 Mean modelled and experimentally derived BSP data for the normal sample

γ constant denotes constant density. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Standard

deviation is reported in brackets. * denotes statistically significant differences (p<0.05).

Modelled

BSP data

Experimental

BSP data

Difference

γ constant γ constant Absolute % Significance

Mass (kg) 1.416

(0.150)

1.469

(0.155)

-0.053 3.6

p = 0.09

Volume (litres) 1.011

(0.100)

1.047

(0.069)

-0.036 3.4

p = 0.08

CMx (m) 0.063

(0.004)

0.062

(0.004)

0.001 -1.6

p = 0.33

CMy (m) - - - - -

CMz (m) -0.044

(0.004)

-0.044

(0.004)

0.000 0.0

p = 0.75

kxx (m) 0.031

(0.001)

0.045

(0.016)

-0.014 31.1 *

p = 0.04

kyy (m) 0.073

(0.003)

0.073

(0.007)

0.000 0.0

p = 0.98

kzz (m) 0.075

(0.003)

0.071

(0.008)

0.004 -5.6

p = 0.22

________________________________________________________ Chapter 2. 24

Table 2.3 Mean modelled and experimentally derived BSP data for the amputee

sample

γ constant denotes constant density. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Standard

deviation is reported in brackets. * denotes statistically significant differences (p<0.05)

Modelled

BSP data

Experimental

BSP data

Differences

γ constant γ constant Absolute % Significance

Mass (kg) 0.879

(0.223)

0.877

(0.201)

0.002 -0.2

p = 0.81

Volume (litres) 0.597

(0.170)

0.594

(0.154)

0.003 -0.5

p = 0.71

CMx (m) 0.014

(0.021)

0.014

(0.021)

0.00 0.0

p = 0.73

CMy (m) - - - - -

CMz (m) -0.037

(0.004)

-0.038

(0.004)

0.001 2.6

p = 0.43

kxx (m) 0.028

(0.003)

0.047

(0.04)

-0.019 40.4 *

p = 0.00

kyy (m) 0.045

(0.008)

0.064

(0.006)

-0.019 29.7 *

p = 0.00

kzz (m) 0.048

(0.008)

0.063

(0.006)

-0.015 23.8 *

p = 0.00

Results from the linear regression analysis have been reported for the sample of

intact and partial feet in Tables 2.4-2.5 and Figures 2.3-2.9. The regression coefficients

for M, V and CM were not significantly different from one across both the samples of

intact and partial feet. (Figures 2.3-2.6). The large confidence intervals of the

regression coefficients highlight the variability in predicting values of k compared to

other BSP data (Tables 2.4-2.5). All regression coefficients of k for the amputee sample

were different from one (Table 2.5). For the normal sample, the regression coefficients

________________________________________________________ Chapter 2. 25

of kyy and kzz were not significantly difference from one (Table 2.4). In comparison to

the experimentally derived values of kxx the model predictions were substantially biased

(Figure 2.7) across both the normal and amputee samples (Tables 2.4-2.5) and the

distribution of residuals was not bivariate (Figure 2.7). In the amputee sample,

predictions of kyy and kzz were quite variable (Figures 2.8-2.9) and the biases observed

were not as strong as for kxx (Table 2.5).

Table 2.4 Results from regression analysis for the normal sample.

Coefficient of determination (R2). Regression coefficient (ß) and 95%CI of the slope of the regression

line when the y-intercept was forced through zero. Standard error of estimate of modelled on

experimental BSP (SEme). Standard errors of the regression coefficient (ß) are reported in brackets.

Regression Coefficient

ß 95% Confidence Interval

R2 SEme

Mass (kg) 1.04

(0.02)

0.99 1.08 0.74 0.08

Volume (l) 1.03

(0.02)

0.99 1.08 0.73 0.06

CMx (m) 0.99

(0.01)

0.96 1.01 0.78 0.00

CMy (m) - - - - -

CMz (m) 0.98

(0.04)

0.88 1.08 0.04 0.01

kxx (m) 1.42

(0.17)

1.03 1.82 0.05 0.02

kyy (m) 1.0

(0.04)

0.91 1.09 0.09 0.01

kzz (m) 0.95

(0.04)

0.86 1.04 0.01 0.01

________________________________________________________ Chapter 2. 26

Table 2.5 Results from regression analysis for the amputee sample.

Coefficient of determination (R2). Regression coefficient (ß) and 95%CI of the slope of the regression

line when the y-intercept was forced through zero. Standard error of estimate of modelled on

experimental BSP (SEme). Standard errors of the regression coefficient (ß) are reported in brackets.

Regression Coefficient

ß 95% Confidence Interval

R2 SEme

Mass (kg) 0.99

(0.01)

0.97 1.02 0.99 0.03

Volume (l) 0.99

(0.01)

0.96 1.01 0.99 0.02

CMx (m) 0.98

(0.02)

0.94 1.01 1.00 0.00

CMy (m) - - - - -

CMz (m) 1.01

(0.02)

0.98 1.05 0.81 0.00

kxx (m) 1.62

(0.10)

1.40 1.84 0.21 0.01

kyy (m) 1.37

(0.09)

1.16 1.57 0.01 0.01

kzz (m) 1.27

(0.08)

1.09 1.46 0.00 0.01

Values of r2 could be said to reveal a strong linear relationship between

modelled and experimentally derived M, V and CM in the amputee sample (Tables 2.5)

however, the results are likely to be affected by the range of foot lengths and masses

observed (Figures 2.3-2.6). These relationships were not as strong in the normal sample

indicating a marginal increase in the variability and that the range of each variable was

more limited than that of the amputee sample because all the intact feet were of a

similar size (Figures 2.3-2.5). Coefficients of determination for kxx, kyy, kzz, across the

normal and amputee samples indicate the poor strength in the linear relationship

between modelled and experimentally derived parameters (Tables 2.4-2.5).

________________________________________________________ Chapter 2. 27

Figure 2.3 Modelled versus experimentally derived foot mass of both the normal and

amputee samples.

Figure 2.4 Modelled versus experimentally derived foot volume of both the normal and

amputee sample.

y = 1.0361x

R2 = 0.7362

y = 0.9912x

R2 = 0.98690

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Modelled foot mass (kg)

Exp

erim

enta

lly d

eriv

ed foot

ma

ss (

kg)

Normal sample Amputee sample

Trend line -normal sample Trend line - amputee sample

y = 1.0316x

R2 = 0.7295

y = 0.9894x

R2 = 0.98110

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Modelled foot volume (l)

Exp

erim

enta

lly d

erive

d fo

ot

volu

me

(l)

Normal sample Amputee sample

Trend line - normal sample Trend line - amputee sample

________________________________________________________ Chapter 2. 28

Figure 2.5 Modelled versus experimentally derived CM in the x direction for both the

normal and amputee samples.

Figure 2.6 Modelled versus experimentally derived CM in the z direction for both the

normal and amputee samples.

y = 0.9783x

R2 = 0.0430

y = 1.0124x

R2 = 0.8078

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

-0.06 -0.04 -0.02 0

Modelled CMz (m)

Exp

erim

enta

lly d

eriv

ed C

Mz

(m

)

Normal sample Amputee sample

Trend line - normal sample Trend line - amputee sample

y = 0.9882x

R2 = 0.7798y = 0.9767x

R2 = 0.9961

-0.02

0

0.02

0.04

0.06

0.08

-0.02 0 0.02 0.04 0.06 0.08

Modelled CMx (m)

Exp

erim

enta

lly d

eriv

ed C

Mx

(m)

Normal sample Amputee sample

Trend line - normal sample Trend line - amputee sample

________________________________________________________ Chapter 2. 29

Figure 2.7 Modelled versus experimentally derived k about the x axis through the CM

for both the normal and amputee samples.

Figure 2.8 Modelled versus experimentally derived k about the y axis through the CM

for both the normal and amputee samples.

y = 0.9983x

R2 = 0.0873

y = 1.3653x

R2 = 0.00500.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.03 0.05 0.07 0.09

Modelled kyy (m)

Exp

eri

me

nta

lly d

eri

ved

kyy

(m

)

Normal sample Amputee sample

Trend line - normal sample Trend line - amputee sample

y = 1.4236x

R2 = 0.0454y = 1.6221x

R2 = 0.2137

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.02 0.025 0.03 0.035

Modelled kxx (m)

Exp

erim

enta

lly d

eriv

ed k

xx (

m)

Normal sample Amputee sample

Trend line - normal sample Trend line - amputee sample

________________________________________________________ Chapter 2. 30

Figure 2.9 Modelled versed experimentally derived k about the z axis through the CM

for both the normal and amputee samples.

The mean absolute and percentage differences between paired observations of

BSP predicted using the geometric model and the experimental techniques have been

presented in Table 2.6 for both the normal and amputee sample.

y = 0.9469x

R2 = 0.0121

y = 1.2706x

R2 = 0.00020.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.03 0.05 0.07 0.09

Modelled kzz (m)

Exp

eri

me

nta

lly d

eri

ved

kzz

(m

)

Normal sample Amputee sample

Trend line - normal sample Trend line - amputee sample

________________________________________________________ Chapter 2. 31

Table 2.6 Mean absolute and percentage differences between modelled and

experimenterially derived body segment parameter data

Standard deviations have been reported in brackets.

Normal sample

Differences

Amputee sample

Differences

Absolute % Absolute %

Mass (kg) -0.053

(0.082)

3.5

(5.2)

0.003

(0.033)

0.4

(4.7)

Volume (litres) -0.036

(0.055)

3.5

(5.2)

0.003

(0.022)

0.4

(4.6)

CMx (m) 0.001

(0.002)

-1.2

(3.4)

0.000

(0.001)

-4.3

(11.0)

CMy (m) - - - -

CMz (m) -0.001

(0.006)

-2.4

(13.5)

0.001

(0.002)

1.2

(5.3)

kxx (m) -0.011

(0.017)

18.3

(21.1)

-0.016

(0.007)

32.7

(12.7)

kyy (m) 0.000

(0.009)

-1.4

(10.4)

-0.017

(0.008)

27.1

(10.4)

kzz (m) 0.004

(0.009)

-6.2

(11.0)

-0.014

(0.008)

21.8

(10.9)

2.4 Discussion

The geometric model provides reasonable estimates of M and V across the

sample of intact feet and excellent estimates for the sample of partial feet compared to

experimentally derived data obtained using incremental immersion. The average

absolute difference in foot M was 53g (3.5%) for the sample of intact feet (Table 2.6)

and about 3g (<1%) for the sample of partial feet. (Table 2.6). Absolute errors in the

estimation of foot M were overstated compared to previous investigations because in

the present investigation estimates of foot M were computed using the density of each

plaster foot replica which was substantially larger than that of a normal foot. If the

________________________________________________________ Chapter 2. 32

density values used in the present investigation were assumed equivalent to estimates of

normal foot density provided by Dempster (1955), the average absolute difference in

foot M for the normal sample would be 38g. Estimates of foot V are not complicated by

assumptions of density and as such provide a better basis for comparison with other

investigations. Previous investigation using comparable models and experimental

techniques have reported errors in the estimation of intact foot volume of

approximately 1.2% with maximum errors of 3.85% (Hatze, 1980). Similar differences

were observed between estimates of modelled and experimentally derived foot V in the

amputee sample (Table 2.6) however, these differences were larger for the sample of

intact feet (Table 2.6). The geometric model tended to underestimate the foot M and V

of the intact foot compared to the data derived experimentally (Table 2.4) however, the

differences observed were not statistically significant (Table 2.4)

The geometric model also provides excellent estimates of CM across both the

normal and amputee samples. The average absolute difference in foot CM for both the

normal sample and amputee sample was about 1mm (Table 2.6). The modelled

estimates of the mass centroid location along the z-axis were quite variable (Figure 2.6)

for the sample of intact feet as quantified by the large 95%CI about the regression

coefficient (Table 2.4).

It was difficult to draw direct comparison of these results with previous

mathematical modelling literature (Hatze, 1979) because the location of the mass

centroid was described relative to a rotated set of basis vectors. Vectors are represented

using the following notation; a = a1i + a2j. The main axis of the basis system (X), once

rotated by θθθθ, passes through the CM. In this way, the position of the CM can be

described by a single vector, r, assuming θθθθ is known (Figure 2.10).

________________________________________________________ Chapter 2. 33

Figure 2.10 Illustration of basis axes and rotated axes used to describe the position of

the centre of mass (CoM)

The vector r, in terms of the basis axes (X,Y), was given by

(7)

and the length of vector r was

(8)

r in terms of the rotated axes (XR,YR) was given by

(9)

Hatze, (1979) did not report values for θθθθ or the length of the vector r but instead

reported the relative CM error in percent; the basic form of which is described by

Equation 6. Hatze, (1979) expressed the computed centroid values as a ratio between

the centroid coordinate value in the direction of the main axis of the segment, and the

RXrr =

( )22bar +=

( )bar +=

________________________________________________________ Chapter 2. 34

length of the segment (R); these values were also not reported for the foot segment. The

relative CM error (in %) was, therefore, given by

(10)

where R* was obtained from comparable cadaver data of Dempster (1955) and

z bar is the mass centroid location obtained using the geometric model.

It was not possible to ascertain the exact location of the origin of Hatze's foot

model and as such it was not possible to utilise Equation 10 to provide comparison data

for the present study because values R* of would be incorrect. However, the basic form

(Eq. 6) can be utilised to provide relative CM error estimates between the modelled and

experimental CM data for the present study. In which case the length of vector r is

given by Equation 8 and the relative error between the modelled and experimental CM

data is given by Equation 6. Hatze, (1979) found the average CM error to be

approximately 1.6%. For the present study, CM error for both the normal and amputee

sample was approximately 1% which compares favourably to those errors reported by

Hatze, (1980).

Differences in the value of k, about the long axis (kxx) of the intact foot were

significant (-0.011m, 18%) compared to those observed about the kyy and kzz axes

which, were -1.4% and -6.2%, respectively. Discrepancies between the modelled and

experimentally derived estimates of k for the partial foot sample were significant with

differences in kxx -0.016m (33%), kyy -0.017m (27%) and kzz -0.014m (22%)

highlighting a systematic error quantified by the 95%CI of the regression coefficient

(Table 2.5).

It would seem logical that following forefoot amputation, differences in the

distribution of M would result in substantial decreased in the values of k about the y-

and z-axis yet have minimal influence in values of k about the x-axis (Figure 2.1).

Comparison of modelled values of k between the normal and amputee samples (Tables

2.2 and 2.3), revealed such decreases; 10% about the x-axis and ≈37% about the z- and

y-axes (Table 2.7). However, if the experimentally derived values of k are compared

−=

lR

zr

*1100

________________________________________________________ Chapter 2. 35

for the normal and amputee samples (Tables 2.2 and 2.3), the differences observed

were significantly smaller for the y- and z-axes (≈12%) and larger for the x-axis (4%)

(Table 2.7).

Table 2.7 Differences in the value of k between normal and amputee derived using the

model and the experimental technique

kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Values extracted from Tables

2.2-2.3.

Normal Sample Amputee Sample Differences

Modelled BSP data %

kxx (m) 0.031 0.028 9.7

kyy (m) 0.073 0.045 38.4

kzz (m) 0.075 0.048 36.0

Experimental BSP data

kxx (m) 0.045 0.047 -4.4

kyy (m) 0.073 0.064 12.3

kzz (m) 0.071 0.063 11.3

Discrepancies between the computed and experimentally derived values of k are

likely to reflect the inherent inaccuracy associated with orienting the plaster foot replica

on the trifilar. The accuracy of experimentally derived values of k are reliant on the CM

of the plaster replica being positioned directly over the centre of the trifilar pendulum

and the desired axis being perpendicular to the plane of oscillation. Correctly

establishing the principle x-axis would logically seem to be the most difficult and the

range of the 95% CI of the regression coefficients reflects the experimental variability

thought to be associated with orienting the replica foot on the trifilar pendulum (Tables

2.4-2.5).

Some authors have previously recognised that it is difficult to experimentally

verify computed values of I (Hanavan, 1964; Hatze, 1980) and have utilised published

________________________________________________________ Chapter 2. 36

cadaver or in vivo data to validate modelled estimates (Hanavan, 1964; Hatze, 1979)

rather than provide direct experimental verification.

Hatze (1979) drew comparisons between modelled values of I for the foot

segments of a single individual, against comparable cadaver data from Dempster,

(1955). Corresponding values of I in kg.m2 for Hatze's subject (C.P.) and Dempster's

cadaver no. 15097 (in brackets) have been presented for the foot segment: left foot

0.0051 (0.0037), right foot 0.0051 (0.0040) kg.m2 (Hatze, 1979). Direct comparison to

previous literature is difficult given the differences in methodology. However, the

errors reported by Hatze (1979) were comparable to those observed in the partial foot

sample in the present investigation.

Detailed experimental validation and statistical analyses allows the limitations

of the geometric model and experimental technique to be recognised and adequately

described so that at least potential users of such anthropometric models can be better

informed about the data they choose to utilise.

Studies such as these are affected by the assumption of constant or varying

segment density. The present model describes varying segment density which increases

linearly from proximal to distal similar to that described by Drillis and Contini, 1972 -

cited Bach, 1994) as the proportion of muscle and bone changes (Roebuck, 1975 - cited

Bach, 1994; Ackland et al., 1988). It is difficult to assess the accuracy of Hatze's

segment density values without knowledge of the derivation of these values and it

seems impossible to verify these segment density values in vivo. It appears that these

segment density values were based on tissue density values reported by Clauser et al.,

(1969). It is possible to make a limited assessment of the accuracy of the segment

density values by comparing the average foot density against previously published

literature. The average segment density can be given by

(11)

where Vi describes the volume and γγγγi describes the density of each slice of the model.

∑

∑

=

==103

1

103

1

.

i

i

i

ii

V

Vγγ

________________________________________________________ Chapter 2. 37

Using equation 11, the average density of feet in the normal sample was

approximately 1.22 kg/m2 when Hatze's (1979) segment density values were used.

Comparable values reported elsewhere (Dempster, 1955; Drillis and Contini, 1966;

Contini, 1972), found the density of the foot segment to be about 9% smaller.

This could be due to the difference in the shape of the foot between the present

model and the Hatze (1979) model. This results in an increase in foot volume

proximally, where the larger segment density values occur, thus increasing the average

modelled density value.

Previous modifications to the model of Hatze (1979) have focused on reducing

segment density coefficients such that total body mass, measured experimentally,

matched that predicted by the model in paediatric populations (Schneider et al., 1990

and Schneider and Zernicke, 1995). Both of these adaptations did not experimentally

assess the predicted segment V and CM thereby not accounting for a scenario where the

model's predicted volume may be overestimated thus causing the segment mass to be

overestimated. Reducing the segment density values may result in values which do not

match the segment tissue densities reported by Clauser et al., (1969). The sole of the

foot model, for instance, has a segment density value of 990kg/m3 (Hatze, 1979) which

seems reasonable given that the sole is comprised mostly of fat, which has an average

density of 960kg/m3 (Clauser et al., 1969). A 17.7 % reduction in the density of this

segment (Schneider and Zernicke, 1995) would result in an average density value of

815 kg/m3, which does not reflect the density of any tissue found in the foot.

The segment density values reported by Hatze (1979) might be correct for

application to his model, however the differing shape of the present model

overestimates the average foot density when Hatze's segment density coefficients are

used. Where the average tissue values reported by Clauser et al. (1969) were not

violated, the present model reduced Hatze's (1979) segment density values by

approximately 9 % (Appendix B). Globally reducing the segment density values would

seem reasonable given that the predicted V and CM, of feet in both the normal and

amputee samples, were reasonable. In this way, the average density of the foot segment

________________________________________________________ Chapter 2. 38

was reduced in line with previous work and the experimentally validated V and CM

estimates were not altered.

This model may be advantageous to investigators of partial foot amputee gait

because it addresses one of the shortcomings of previous kinetic descriptions by

acknowledging the unique anthropometry of the partial foot residuum. Linked segment

inverse dynamic models could incorporate these improved anthropometric descriptions

of the partial foot residuum to improve the accuracy of joint moments and powers over

kinetic estimates which assume that the remnant foot can be adequately described using

BSP of the intact foot.

2.5 Conclusion

The model provides an acceptable means of quickly and easily obtaining

anthropometric data of both the normal and partial foot, with an equivalent accuracy to

previously published experimental techniques, without recourse to laborious and

arguably inaccurate experimental data.

The model provides good estimates of foot mass, volume and centre of mass

across a variety of intact and amputated feet compared to experimentally derived

estimates. The average differences did not exceed 5% and were not significantly biased.

Computed values of the radius of gyration for, primarily, the partial foot sample were

significantly different compared to experimentally derived estimates. These differences

seem to reflect the difficulty associated with accurately orienting the principal axes of

the foot replica on the trifilar pendulum and were comparable to differences observed

by previous investigators, who have reported similar difficulties in experimentally

verifying computed value of inertia.

The model provides an alternative method for estimating anthropometric

characteristics of both the partial and intact foot, which is easier and less time

consuming than experimental techniques without compromising accuracy.

________________________________________________________ Chapter 3. 39

Inverse dynamic models for the analysis of partial foot

amputee gait

3.1 Introduction

In an attempt to determine the mechanical behaviour of the human body,

engineers have developed a process of modelling the human body as a simple system

whereby the body is represented as a chain of rigid segments connected by hinge or pin

joints. This model simplifies the anatomical structure, such that the body can be

mathematically represented. This mathematical model is called a linked-segment model.

Linked-segment models of the human body have proven useful in estimating those

determinates of human walking which can not be directly measured, such as joint

reaction forces or muscle moments. The process used to derive these parameters is

known as inverse dynamics, so called because it is possible to work back from these

kinematic, anthropometric and externally measured force data to derive the kinetics

thought to be responsible for the motion.

The following assumptions are made with regard to the inverse dynamic, link-

segment model (Winter, 1990).

• Each segment has a fixed mass located as a point mass at its centre of mass

Chapter 3

________________________________________________________ Chapter 3. 40

• The location of each segment's centre of mass remains fixed during the

movement

• The joints are considered to be a simple hinge

• The mass moments of inertia of each segment remains constant during the

movement

• The length of each segment remains constant during the movement

While these assumptions are certainly not always valid, such simplified

representations of the human limb provide useful approximations for parameters that

can only be mathematically estimated.

The accuracy of data derived from the mathematical model depends on how well

the system being studied has been represented and the assumptions of the system. Other

sources of error may be derived from the kinematic, anthropometric or ground reaction

force data utilised by the model. These include the estimation of joint rotation centres

(De Looze et al., 1992b; Kingma et al., 1996), movement of markers on the skin

(Capozzo et al., 1993), varying segment lengths (De Looze et al., 1992a), estimation of

body segment parameters (Capozzo and Berme, 1990; Davis, 1992), varying cadence

and stride length (White and Lage, 1993) and errors in measurement of the magnitude

and position of the ground reaction force (Davis, 1992).

Analysis of pathological gait may violate some of the basic assumptions of the

linked-segment model and/or require additional assumptions. Anthropometric data may

be derived from models of segment geometry or experimentally measured. Inadequacies

of these techniques to describe the anthropometry of pathological body segments may

affect the accuracy of net joint moment and powers.

Previous studies on Transfemoral and Transtibial amputees have attempted to

address these issues by estimating anthropometric characteristics of the prosthesis

(Capozzo et al., 1976; Miller, 1987; Czerniecki et al., 1991; Bach, 1994) and residual

limb (Contini, 1970; Krouskop, 1988; Bach, 1994) to provide more accurate input data.

However, previous studies on partial foot amputees have not acknowledged addressing

either of these issues. Instead investigators have ignored the anthropometric

________________________________________________________ Chapter 3. 41

characteristics of any prosthetic/orthotic replacement (Dillon, 1995; Muller et al., 1998)

and/or assuming that the remnant foot can be adequately described using normal body

segment parameter (BSP) data (Dillon, 1995; Burnfield et al., 1998; Muller et al., 1998;

Boyd et al., 1999).

For many researchers, providing more accurate anthropometric input data may

seem unnecessary due to the relatively small change in mass (M), centre of mass (CM)

and mass moment of inertia (I) that occurs due to partial foot amputation and most

prosthetic/orthotic fittings. Small changes in BSP data, have been shown to impact little

on the accuracy of muscle moment data (Davis, 1992) and given the considerable effort

required to provide these anthropometric input data, have probably been assumed

insignificant by most researchers.

This assumption may be reasonable for the majority of research, which has

focussed on the gait of individuals with minor amputation of the forefoot, where

conditions of barefoot walking (Burnfield et al., 1998; Boyd et al., 1999) and orthotic

intervention (Dillon, 1995; Muller et al., 1998) have been investigated. However, when

significant portions of the forefoot are compromised the efficacy of this assumption

may become questionable. Not so much because of the significant change in

anthropometry of the remnant foot, due to Chopart or Lisfranc amputation, but because

of the substantial M and I of the Clamshell patella tendon bearing (PTB) prosthesis

typically fitted to individuals with proximal forefoot amputation.

The efficacy of this assumption could be investigated using a linked-segment

inverse dynamic model, which accounted for the change in M, CM and I of the remnant

foot and included anthropometric descriptions of any prosthetic/orthotic intervention as

well as footwear

Modelling the anthropometry of orthotic/prosthetic intervention and footwear

within the constraints of a linked-segment inverse dynamic modelling approach would

be relatively simple when these devices do not compromise motion of the ankle joint.

The M, CM and I of devices, such as insoles, toe fillers or slipper sockets, could be

combined with BSP data of the remnant foot segment and not affect the assumptions of

the linked-segment model. Orthotic replacements such as ankle foot orthoses encompass

________________________________________________________ Chapter 3. 42

multiple limb segments and as such, the anthropometric characteristics of these devices

should be partitioned appropriately to those segments encompassed by the device.

Accounting for the significant change in foot anthropometry due to partial amputation

of the forefoot, and the comparatively insignificant addition of an orthotic replacement

to the inverse dynamic model are not expected to alter ankle, knee or hip moment and

power data.

Modelling prosthetic intervention in the form of a clamshell PTB prosthesis,

within the constraints of the inverse dynamic modelling approach, is rather more

challenging because the prosthesis eliminates ankle motion. The ankle kinematic pattern

has been thought to be the result of the force-deflection characteristics of the prosthetic

foot (Dillon, 1995) or movement of the leg segment within the prosthesis rather than

true joint motion.

The elimination of ankle motion, or the assumption that the ankle motion is

negligible, is quite convenient because the leg, remnant foot, prosthesis and footwear

can be modelled as a single free body segment, which acts about the knee joint. As such

the M, CM and I of the prosthesis need not be partitioned to the foot and leg segments

separately to accurately depict the anthropometry of the amputees lower limb.

Modelling the remnant limb and prosthesis/footwear as a single segment may alter the

amputee’s joint moment and power patterns because the M of the modelled lower limb

would be increased as would the value of I due to the more distal location of the mass

centroid. The altered anthropometry of the linked-segment model may increase the knee

flexion and hip extension moments during swing phase, reflecting the increased

requirement of the hamstrings muscle group and gluteus maximus to decelerate the knee

into full extension and the hip into the initial contact hip flexion angle, respectively.

Increased power absorption across the knee and power generation across the hip joint

would be expected in line with these hypothesised moment pattern changes. The

changes in muscle moment and power data would manifest during swing phase when

the contributions of inertia and angular acceleration are largest and affect the knee and

hip where the leg and thigh segment masses are large. The ankle joint moment

calculation is dominated by the magnitude of the ground reaction force and its lever arm

about the ankle and as such is not greatly subject to angular and inertial influences.

________________________________________________________ Chapter 3. 43

Net joint moment and power data obtained from the inverse dynamic approach

are routinely interpreted as being indicative of muscular response (Powers et al., 1998).

However, the accuracy of these data may be questionable when accurate mechanical

descriptions of partial foot amputee gait are dependant on the anthropometric

characteristics or the residual foot and prosthesis/orthosis being appropriately modelled.

The requirement for an inverse dynamic model for the analysis of partial foot

amputee gait is clearly evident, given the unique anthropometric and prosthetic

constraints which have been poorly modelled by pervious investigators. The accuracy of

kinetic data seems arguable when inverse dynamic models, based on normal

individuals, are used to describe the gait of partial foot amputees wearing prosthetic

devices such as Clamshell PTB prostheses. At the very least, quantifiable data is

required to support the efficacy of disregarding the anthropometry of orthotic devices

and below ankle prosthetic sockets within the inverse dynamic model. The addition of a

clamshell PTB prosthesis to the linked-segment model is expected to alter knee and hip

moments and powers during swing phase reflecting a more accurately portrayal of the

demand on the hamstring and gluteus maximums muscles to moderate the increased

inertia and angular acceleration of the limb segment.

The aim of this work is to:

1. develop inverse dynamic models for the analysis of normal and partial foot

amputee gait, which address the inadequacies of current kinetic analysis by

adequately depicting M, CM and I of the remnant foot, proximal limb segments

and prosthesis/orthosis/shoe;

2. compare ankle, knee and hip muscle moment and power data derived using the

partial foot inverse dynamic models and a standard inverse dynamic model, such

as that used by previous investigators of partial foot amputee gait;

3. determine the accuracy of previous kinetic descriptions of partial foot amputee

gait and highlight how more accurate anthropometric descriptions affect the net

muscle moment and power estimates.

________________________________________________________ Chapter 3. 44

3.2 Method

Subjects

Subject recruitment and the provision of informed consent has previously been

described in Chapter 2.

Subjects with unilateral partial foot amputation were categorised into one of two

samples according to whether prosthetic/orthotic fitting eliminated ankle motion. Based

on this criterion, one of two linked-segment inverse dynamic models was used to

estimate net joint moments and powers for ‘Sample A - with ankle motion’ and

‘Sample B - without ankle motion’. Bilateral subjects were not included in this

investigation because body segment parameter data from the sound limb was needed to

describe comparatively 'normal' segment dimensional and inertia characteristics.

Characteristics of individuals comprising the two samples including age, stature,

mass, cause of amputation and descriptions of the prosthetic/orthotic devices fitted are

given in Table 3.1.

Table 3.1 Amputee subject characteristics

TMT is an abbreviation for Transmetatarsal. Standard deviations (SD) are reported in brackets.

Subject ID Amputation

Level

Aetiology Age

(years)

Stature

(m)

Mass

(kg)

Type of fitting

Sample A - with ankle motion

2103-2116A TMT Trauma 54 1.82 84.5 Toe filler

2103-1906A Lisfranc Trauma 55 1.80 80.7 Toe filler

2703-1903A Lisfranc Trauma 53 1.82 76.6 Slipper socket

0704-0403A Lisfranc Trauma 22 1.84 81.5 Slipper socket

Mean

SD

46

(16)

1.82

(0.02)

80.8

(2.8)

Sample B - without ankle motion

3004-1102A Chopart Trauma 19 1.79 93.0 Clamshell socket

________________________________________________________ Chapter 3. 45

Apparatus

Anthropometric characteristics of the partial and intact foot were determined

using the anthropometric model described in Chapter 2. Anthropometric characteristics

of the thigh and leg segments were determined using the anthropometric models

described by Hatze (1979). A water-soluble marker was used to identify the necessary

anatomical landmarks and a set of anthropometric callipers, 30cm ruler and tape

measure were used to record the necessary input data. A stadiometer and a set of

electronic scales were used to determine stature and body mass. The callipers, tape

measure and ruler had a resolution of 1mm and the scales had a resolution of 1g.

The M of the prosthesis/orthosis and shoe was determined using a 2kg electronic

scale with a resolution of 1g. The CM was determined using a plumb-bob and the value

of I was determined using a Trifilar pendulum system and an electronic, handheld,

stopwatch with a resolution of 1ms as described in Chapter 2.

Kinematic data were collected using a Peak 3D-motion analysis system and

Motus version 4.3.0 software (Peak Performance Technologies. Englewood CO, USA).

Six Burle TC354AX cameras (Burle Security. Ireland), with a resolution of 720x526-

PAL, were fitted with Cosmicar, 6mm, 1:1.2 TV lenses and Tiffen 40.5mm infra red

filters (Peak Performance Technologies. Englewood CO, USA). This camera set-up

sampled the location of 20mm Scotchlite reflective markers at a rate of 50Hz.

An A.M.T.I. OR6-5, six channel, strain gauge force platform and amplifier

(Advanced Mechanical Technology Inc. Waterton Mass., USA) was used to sample

ground reaction force and moment data at a rate of 1000Hz. The force platform

amplifier had a bridge excitation of 5V and a gain of 2000. The amplifier output range

was ±10V. The force platform amplifier automatically low-pass filtered data using one

of two default settings. Data were low-pass filtered at a cut-off frequency of 1050Hz

rather than at 10Hz so that the data would not be attenuated at this point. Data were

recorded using a multiplexing, 16 channel, 12 bit, analogue-to-digital (A/D) conversion

card with a ±10V range and a resolution of 4.8mV/bit (Data Translation. Marlboro

Mass., USA. Model DT 2821 ).

________________________________________________________ Chapter 3. 46

The Peak-Motus software controlled kinematic and kinetic data synchronisation.

A transistor-to-transistor logic (TTL) pulse of approximately 5V was recorded in the

analogue data in response to an increase in the voltage signal recorded on the vertical

force channel of the force platform. An event marker was also recorded in the kinematic

data at this time. Data were then synchronised by matching the event marker in the

kinematic data with the analogue pulse recorded.

Kinematic and kinetic data were derived using software coded in Matlab 5.3

(Mathworks Inc. Englewood Cliffs, NJ USA) and detailed information on data

reduction, processing and reporting has been presented in Appendix E.

Using one of two linked-segment inverse dynamic models, based on the type of

prosthetic/orthotic intervention, net joint moments and powers were estimated for the

three lower limb segments of each leg (Appendix F).

The first linked-segment model (Partial foot model-A) was based on a standard

set of inverse dynamic assumptions (Winter, 1990) and was used to describe the kinetic

patterns of partial foot amputees wearing insoles, toe fillers and slipper sockets

(Appendix F). These types of prosthetic/orthotic devices do not compromise the ankle

joint and as such the M, CM, and I of these devices could be combined with the BSP of

the remnant foot without affecting the basic assumptions of the linked-segment model.

However, in order to describe the prosthesis/orthosis and shoe within the constraints of

a standard linked-segment model it was necessary to assume that:

• the prosthesis/orthosis did not eliminate ankle motion

• the prosthesis/orthosis encompassed only the foot segment

• the residual foot, prosthesis/orthosis and shoe could be considered as a

'lumped' free body segment which rotated about the ankle joint

• the 'lumped' segment could be described by a single set of BSP data such

that the M, CM and I of the residual foot, prosthesis/orthosis and shoe were

combined

A standard linked-segment inverse dynamic model (Winter, 1990) such as that

utilised by Dillon (1995) and presumably by other investigators of partial foot amputee

________________________________________________________ Chapter 3. 47

gait (Muller et al., 1998; Burnfield et al., 1998; Boyd et al., 1999) could be easily

replicated using partial foot model-A. Utilising anthropometric descriptions of the

sound foot, leg and thigh (assumed equivalent to normal) and ignoring any

prosthesis/orthosis and footwear, partial foot model-A could be used to estimate net

joint moments and powers comparable to those determined by previous investigators of

partial foot amputee gait.

The second, linked-segment inverse dynamic model (partial foot model-B) was

used to describe kinetic parameters of amputees wearing Clamshell PTB prostheses

(Appendix F). These types of prosthetic intervention eliminate ankle motion, which for

modelling purposes was quite convenient because the leg, remnant foot, prosthesis and

shoe could be considered as a single 'lumped' free body segment about the knee joint.

As such, the M, CM and I of the prosthesis and shoe need not be partitioned to the foot

and leg segment separately to accurately depict the amputee's lower limb, assuming

that:

• the Clamshell PTB prosthesis eliminated ankle motion

• the Clamshell PTB prosthesis encompassed the remnant foot and the leg

segment or a portion there of

• the residual foot, leg, prosthesis and shoe could be considered as a 'lumped'

free body segment which rotated about the knee joint

• the 'lumped' segment could be described by a single set of BSP data such

that the M, CM and I of the residual foot, leg, prosthesis and shoe were

combined

These assumptions allow the anthropometry of the residual foot, leg and

prosthesis/shoe to be represented as a single free body segment about the knee joint.

The location of the mass centroid was described relative to the knee joint and the value

of I of the 'lumped' segment was taken through the CM of the 'lumped' segment

(Appendix F).

________________________________________________________ Chapter 3. 48

Procedure

Laboratory set-up

The force platform was embedded midway along an elevated 10m walkway. The

true origin of the force plate coordinate system was located at offsets of XO,YO, ZO from

the geometric centre, of the top surface, of the force plate (AMTI, 1999). The geometric

centre of the force plate was used to define the force plate coordinate system in X and Y

given that the true origin differed from the geometric origin by less than one millimetre

(AMTI, 1999). The offset ZO was appreciable (38mm) and was accounted for when

calculating centre of pressure (CP).

An 'L' shaped calibration frame, consisting of four markers was used to

determine the origin of the kinematic coordinate system (Figure 3.1). One arm of the

calibration frame comprised three co-linear markers and was aligned, with one edge of

the force platform, such that this arm was parallel to the direction of walking (Figure

3.1). The second arm of the calibration frame comprised two markers and was aligned

with the perpendicular edge of the force platform (Figure 3.1). Vectors connecting the

centroids of markers C and A and markers C and D defined the X and Y-axes,

respectively (Figure 3.1). The Z-axis was orthogonal to the XY plane. The kinematic

coordinate system was located at floor level.

A Scotchlite reflective marker was located on the edge of the walkway at a

known position from the force plate coordinate system (Figure 3.1). The position of this

marker was recorded in the kinematic data and allowed force data collected relative to

the force plate coordinate system to be transformed relative to the kinematic coordinate

system.

Cameras were positioned in a semicircular arrangement with three cameras

located each side of the walkway (Figure 3.2). Camera locations were based on work

examining the optimal camera locations such that the largest percentage of marker

displacement data could be tracked and the number of potential marker identifications

was minimised (Frossard and Dillon, 1999A).

________________________________________________________ Chapter 3. 49

Figure 3.1 An exploded view of the force plate and kinematic calibration frame.

The force plate coordinate system was assumed equivalent to the geometric centre of the force plate and

was identified by the orthogonal axes set (Fx, Fy, Fz). The kinematic coordinate system was identified by

the orthogonal axes set (X, Y, Z) and also identified the laboratory or global coordinate system.

Equipment accuracy

It was necessary to thoroughly examine the accuracy of the Peak-Motus system

and AMTI force platform given that the facility had previously not been commissioned.

The kinematic system was able to determine the location of a single marker in

3D space to within 0.5cm across the entire data collection area (Frossard and Dillon,

1999B). The data collection area was 5.3m (X), 1.6m (Y) and 2.2m (Z) (Figure 3.2) and

commensurate with the calibrated volume. The expected accuracy was calculated

according the system manufacturer, where the root mean square (RMS) error was

expressed relative to the distance from the base of each camera to the object observed.

The expected RMS errors were 1.78%, 1.13% and 0.89% along the X, Y and Z-axes.

________________________________________________________ Chapter 3. 50

The actual RMS errors along the X, Y and Z-axes were 0.19%, 0.34% and 0.20%,

respectively (Frossard and Dillon, 1999B). Small errors in the systems ability to

accurately predict the location of a single marker were not compounded when

reconstructing a limb segment defined by a marker at either end. Using a 92cm

calibration wand to represent an individual limb segment, the RMS error associated

with reconstructing the length of a static wand was 0.012cm (Frossard and Dillon,

1999B). During dynamic situations, the length of the wand could be reconstructed with

less accuracy as evidenced by the increased RMS error (0.105cm) (Frossard and Dillon,

1999B).

Figure 3.2 Set up of the gait laboratory.

Cameras are numbered from 1-6 with numerals at floor level next to each camera. The global coordinate

system, calibration frame and force platform are depicted in the middle of the walkway.

________________________________________________________ Chapter 3. 51

The magnitude of forces recorded in shear (Fx, Fy) and compression (Fz) were

quite accurate with differences between the applied and measured forces, expressed as a

percentage of the force applied, were 3.24±0.68%, 3.15±0.19% and 1.21±0.56%,

respectively (Frossard and Dillon, 1999B). As the magnitude of vertical force increased

to approximately body weight, the error observed along Fz reduced to 0.5% of the

applied force (Frossard and Dillon, 1999B). The mean error associated with the location

of the centre of pressure was 1.5±0.7mm and 2.2±1.7mm along the x and y-axes,

respectively (Frossard and Dillon, 1999B). These results were far superior to those

previously reported by Bobbert and Schamhardt, (1990) and simular to those reported

more recently by Middleton et al., (1999).

Equipment calibration

Prior to each testing session the laboratory was set-up as illustrated in Figures

3.1-3.2. The Peak-Motus software controlled calibration of the kinematic system.

During the calibration procedure a wand, of known dimensions, was swept through the

data collection area. The data collection area was compliant with the calibrated area. If

the calibration was unsuccessful the equipment was checked and the process repeated.

Subject preparation and examination

Subjects presented to the university biomechanics laboratory. Participants were

interviewed to obtain a medical history and standard anthropometric measurements of

stature and weight were recorded. Anthropometric characteristics of the normal and

partial foot were determined using the anthropometric model, and measurement

techniques described in Chapter 2. Anthropometric characteristics of the leg and thigh

segments were determined using the anthropometric models described by Hatze (1979).

The coordinate systems of the leg and thigh segments were altered to reflect the global

coordinate system (GCS) of the laboratory used in the present investigation. No

principal axes transformations were undertaken as described by Hatze (1979). Instead

the position of the segments CM was described relative to the joint local coordinate

system (LCS) and transformations were undertaken between the local and global

coordinate systems (Appendix F). The anthropometric input data required to execute

these models were not reported by Hatze (1979) or in other literature utilising these

models (Schneider et al., 1990; Schneider and Zernicke, 1992). These anthropometric

________________________________________________________ Chapter 3. 52

input measurements were, therefore, determined by deriving Hatze's (1979)

mathematical notation from first principles.

The leg model has been described as an assemblage of ten horizontal elliptical

cylinders and two paraboloids of revolution, which represent the medial and lateral

malleoli (Hatze, 1979). The length of the leg segment was defined as the distance

between the tibial plateau and the apex of the lateral malleolus. By dividing the leg

length into ten equal segments and taking both circumference and medio-lateral

measurements at the centre of each elliptical segment, the measurements required to

describe the M, CM and I of each elliptical cylinder were obtained (Appendix G). The

width of the lateral malleolus defined the radius and height of the two paraboloids of

revolution (Appendix G).

The thigh model has been described as an assemblage of ten elliptical cylinders

and an ellipto-parabolic hoof (Hatze, 1979). The height of each elliptical cylinder of the

thigh model was described as a tenth of the length measurement from the ramus to the

tibial plateau. Circumference and mediolateral measurements taken at the centre of each

elliptical cylinder completed the complement of input data required to describe this

portion of the thigh model. A second thigh length measurement, from the tibial plateau

to the apex of the greater trochanter of the femur, less the distance from the tibial

plateau to the ramus, describes the height of the ellipto-parabolic hoof. The diameter

across the greater trochanters, firstly including any soft tissue without compression, and

secondly a bone-to-bone diameter was used to describe the soft tissue mass around the

pelvis (Hatze, 1979). The anthropometric measurement form used to record the

necessary input data forms part of Appendix G.

The anthropometric characteristics of the prosthesis/orthosis and shoe were

determined using standard techniques describing the dynamics of a rigid body. The M

of the prosthesis/orthosis and shoe was determined using an electronic scale. The

location of the mass centroid of the prosthesis/orthosis and shoe was given by the

intersection of three plumb lines marked on the prostheses when suspended from three

different points. With the prosthesis/orthosis and shoe on the patient, the vertical and

horizontal distances from the CM to the proximal joint centre were recorded. The value

________________________________________________________ Chapter 3. 53

of I about each orthogonal axis was determined using a Trifilar pendulum system using

the techniques described in Chapter 2.

20mm Scotchlite retroflective markers were located on the following anatomical

landmarks: Spinous process of the fifth lumber vertebra, anterior superior iliac spine,

greater trochanter of the femur, knee joint space inferior to the lateral epicondyle of the

femur, lateral malleolus, posterior calcaneus at the level of the fifth metatarsal head,

fifth metatarsal head or its estimated location. Markers were also located mid-thigh and

mid-leg just anterior to a line connecting the proximal and distal segment markers.

The location of the absent 5th metatarsal head was duplicated from the sound

foot by placing a ruler posterior to the shoed foot and measuring the distance from the

ruler to the centre of the marker.

Data acquisition and processing

Subjects were allowed to practise traversing the walkway with the reflective

markers in place. The subjects were instructed to practise contacting the force platform

so that their walking velocity remained the same and they did not change their step

length or coordination to contact the platform. The subjects were allowed to practise and

adjust their starting position on the walkway until they felt confident that they could

perform the task.

Kinematic data describing the neutral segment angles were collected with the

subject standing with their arms crossed over their chest. Dynamic data were then

collected, at the subject's self-selected walking speed, until seven successful trials were

obtained for each limb.

Kinematic data were initially processed using the Peak-Motus software. Three

dimensional marker coordinates, for approximately four gait cycles, were obtained and

tracked so that any change in walking velocity or coordination to target the force

platform could be evidenced and those trials rejected. The 3D marker coordinates were

then reconstructed and any missing data interpolated using spline routines standard to

the Motus software. The unfiltered marker coordinate data were then exported for

further processing.

________________________________________________________ Chapter 3. 54

Raw marker displacement data were filtered using a fourth order low pass

Butterworth filter with a cut-off frequency of 6Hz (Appendix E). Segment angles

describing the orientation of the pelvis, thigh, leg and foot relative to the horizontal axis

of the GCS were determined using an arc tangent function. Joint angles were then

determined as the difference between adjacent segment angles (Winter, 1990).

Force platform voltage data were then filtered using a fourth order Butterworth

digital filter with a cut-off frequency of 125Hz to remove the unwanted electrical noise

affecting the signal (Appendix E). Force platform data were converted to Newtons

(Appendix E). Differences in force and moment data, from absolute zero, were

accounted for by offsetting the force and moment data by the mean of a one-second

sample of data collected before heel contact for each force plate measurement

(Appendix E). Force platform data were then sub-sampled from 1000Hz to match the

kinematic sampling rate of 50Hz (Appendix E). Centre of pressure excursion was

calculated and accounted for the offset between the true and geometric origin of the

force plate in the vertical direction (Appendix E).

To reflect kinetic estimates provided by previous investigators, net joint

moments were estimated for both samples A and B using a standard inverse dynamic

model. Anthropometric characteristics of the sound foot, leg and thigh were used and

characteristics of any prosthesis/orthosis and shoe were disregarded. Net joint moments

were also estimated for sample A using 'partial foot model-A' and for sample B using

'partial foot model-B'. Anthropometric descriptions of the affected limb including the

residual foot were used and any prosthetic/orthotic replacement and footwear were also

accounted for (Appendix F).

Joint powers were calculated as the scalar product of moment and angular

velocity and accounted for power transfer across joints (Winter, 1990). The resultant

components of the joint moments and powers were normalised by body mass (Winter,

1990; Allard et al., 1997; Craik and Oatis, 1995) in preference to alternate techniques

which as an example, normalise joint moments by body mass and limb length (Perry,

1992). Normalisation of kinetic parameters by body mass alone seems to be the

standard convention and little evidence could be found to support the use of, non-

________________________________________________________ Chapter 3. 55

dimensional, techniques which also results in kinetic parameters that are less readily

interpreted by clinicians and biomechanists.

The magnitude and timing of peak joint moments and powers were extracted

from each subject's ensembled average using a set of mouse driven crosshairs

(Appendix E). Figures 3.3 and 3.4 illustrate the points analysed. The crosshairs

displayed the x-y coordinates of each point (Appendix E) and those data points selected

were averaged within each sample. Absolute and percentage differences were calculated

using the technique described by Hatze (1979) which was presented in Chapter 2.

Figure 3.3 Points of interest examined on joint moment profiles.

H, K and A denote hip, knee and ankle, respectively. M denotes moment. Positive values along the y-axis

indicate extension moments. Encircled values describe the data points examined and are numbered

consecutively. The solid line delineates swing and stance phase.

0 20 40 60 80 100-1

0

1

2

Hip Moment (-)

(Nm

/kg)

Ext

. >

0 20 40 60 80 100

-1

0

1

Knee Moment (-)

(Nm

/kg)

Ext

. >

0 20 40 60 80 100

0

1

2

Ankle Moment ()

Gait Cycle [%]

(Nm

/kg)

Ext

. >

HM1

HM2

HM3

KM1

KM2

KM3

KM4

KM5

AM1

AM2

________________________________________________________ Chapter 3. 56

Figure 3.4 Points of interest examined on joint power profiles.

H, K and A denote hip, knee and ankle respectively. P denotes power. Positive values along the y-axis

indicate power generation. Encircled values describe the data points examined. These data points were

numbered consecutively. The solid line delineates swing and stance phase.

3.3 Results

Anthropometric characteristics were computed for each subject in samples A

and B. Mean M, CM and I of the isolated foot, leg and thigh segments are presented in

Tables 3.2-3.4, respectively. Anthropometric characteristics of the prosthesis/orthosis

and shoe for each sample are presented in Table 3.5 and the characteristics of the

'lumped' segments are reported in Table 3.6.

0 20 40 60 80 100-1

0

1

2

Hip Power (-)(W

/kg)

Gen

. >

0 20 40 60 80 100

-2

-1

0

1

2Knee Power (-)

(W/k

g) G

en.

>

0 20 40 60 80 100-2

0

2

4

6Ankle Power ()

(W/k

g) G

en.

>

Gait Cycle [%]

AP1

AP2

KP1

KP2

KP3KP4

HP1

HP2

HP3

HP4

________________________________________________________ Chapter 3. 57

Although no formal statistical analyses were undertaken, data presented in Table

3.2 highlights a reduction in the M and I of the isolated foot segment and the more

proximal location of the CM when the partial foot models were used compared to the

standard inverse dynamic model. There were no differences of note in the

anthropometry of the leg and thigh segments, between modelling approaches, for

subjects in sample-A (Tables 3.3 and 3.4). However, for the subject in sample-B, the M

and I of the leg segment was substantially less than that observed using a standard

model (Table 3.3). There were no differences in the anthropometry of the thigh segment

for this subject between the affected and sound/normal limb (Table 3.4).

Table 3.2 Mean anthropometric data of the isolated foot segment for a standard linked-

segment model and the partial foot models

Standard deviation reported in brackets.

Inverse Dynamic Model Differences

Standard Partial Foot absolute %

Sample A - with ankle motion

Mass (kg) 1.065

(0.030)

0.793

(0.036)

-0.272 25.5

CMx (m) 0.060

(0.001)

0.019

(0.005)

-0.041 68.3

CMz (m) -0.042

(0.002)

-0.038

(0.001)

0.004 9.5

Iyy (kg.m2) 0.006

(0.002)

0.002

(0.000)

-0.004 66.7

Sample B - without ankle motion

Mass (kg) 1.064 0.443 -0.621 58.4

CMx (m) 0.054 -0.013 -0.067 106.7

CMz (m) -0.041 -0.036 0.005 12.2

Iyy (kg.m2) 0.005 0.001 -0.004 80.0

________________________________________________________ Chapter 3. 58

Table 3.3 Mean anthropometric data of the lower leg segment generated for a standard

linked-segment model and the partial foot models

Standard deviation reported in brackets.

Inverse Dynamic Model Differences

Standard Partial Foot absolute %

Sample A - with ankle motion

Mass (kg) 3.365

(0.059)

3.178

(0.084)

-0.187 5.6

CMx (m) 0.000 0.000 0.000 0.0

CMz (m) -0.173

(0.002)

-0.173

(0.001)

0.000 0.0

Iyy (kg.m2) 0.046

(0.001)

0.045

(0.002)

-0.001 2.2

Sample B - without ankle motion

Mass (kg) 3.992 2.673 -1.319 33.0

CMx (m) 0.000 0.000 0.000 0.0

CMz (m) -0.171 -0.158 0.013 7.6

Iyy (kg.m2) 0.053 0.040 -0.013 24.5

The anthropometric characteristics of the prosthesis/orthosis and shoe rivalled

that of the isolated foot segment in sample-A (Table 3.5). The addition of a

prosthesis/orthosis and shoe to the linked-linked segment model (partial foot model-A)

resulted in a net increase in the M and I of the 'lumped' segment of about 30% compared

to the standard model (Table 3.6). The position of the CM of the 'lumped' segment was

significantly closer to the ankle joint along the long axis (x-axis) and more distally

along the z-axis, compared to a standard linked-segment model (Table 3.6).

________________________________________________________ Chapter 3. 59

Table 3.4 Mean anthropometric data of the thigh segment for a standard linked-

segment model and the partial foot models.

Standard deviation reported in brackets.

Inverse Dynamic Model Differences

Standard Partial Foot absolute %

Sample A - with ankle motion

Mass (kg) 8.205

(0.629)

8.417

(0.719)

0.212 -2.6

CMx (m) 0.000 0.000 0.000 0.0

CMz (m) -0.193

(0.003)

-0.192

(0.003)

0.001 0.5

Iyy (kg.m2) 0.131

(0.010)

0.134

(0.011)

0.003 -2.3

Sample B - without ankle motion

Mass (kg) 11.000 10.654 -0.346 3.1

CMx (m) 0.000 0.000 0.000 0.0

CMz (m) -0.181 -0.180 0.001 0.6

Iyy (kg.m2) 0.164 0.158 -0.006 3.7

Table 3.5 Characteristics of the combined prosthesis/orthosis/shoe for samples A and B

For sample - B the position of the CM was described relative to the knee joint and the value of I, through

the CM of the lumped segment. Standard deviation reported in brackets.

Sample A -

with ankle motion

Sample B -

without ankle motion

Mass (kg) 0.731

(0.261)

1.589

CMx (m) 0.052

(0.013)

0.028

CMz (m) -0.058

(0.020)

-0.375

Iyy (kg.m2) 0.006

(0.001)

0.034

________________________________________________________ Chapter 3. 60

Table 3.6 Mean anthropometric data of the lumped segments for a standard linked-

segment model and the partial foot models

For sample - B the position of the CM was described relative to the knee joint and the value of I, through

the CM of the lumped segment. Due to the differences in the way the segments have been modelled it was

not possible to draw comparisons between anthropometric data of the lumped segment for partial foot

model-B and a standard linked-segment model. Standard deviation reported in brackets.

Inverse Dynamic Model Differences

Standard Partial Foot absolute %

Sample A - with ankle motion

Mass (kg) 1.066

(0.060)

1.524

(0.203)

0.458 -43.0

CMx (m) 0.060

(0.002)

0.034

(0.01)

-0.026 43.3

CMz (m) -0.042

(0.004)

-0.048

(0.004)

-0.006 -14.3

Iyy (kg.m2) 0.006

(0.000)

0.008

(0.001)

0.002 -33.3

Sample B - without ankle motion

Mass (kg) - 4.705 - -

CMx (m) - 0.008 - -

CMz (m) - -0.259 - -

Iyy (kg.m2) - 0.161 - -

Due to the differences in the way the segments were modelled it was not

possible to draw direct numeric comparisons between anthropometric data of the

'lumped' segment for partial foot model-B and a standard linked-segment model. As

such, the characteristics of the lumped segment have been presented in isolation (Table

3.6). For partial foot model-B the position of the CM of the lumped segment was given

relative to the knee axis and the value of I was taken through the CM of the lumped

segment.

________________________________________________________ Chapter 3. 61

The M of the clamshell prosthesis in sample-B was about half of the combined

M of the remnant foot and leg (Tables 3.2, 3.3 and 3.5). The position of the CM of the

'lumped' segment in sample-B was anteriorly displaced relative to the sagittal mid-line

of the leg and significantly closer to the ankle (Table 3.6) primarily due to the anterior

and distal location of the CM of the prosthesis (Table 3.5). The value of I of the

'lumped' segment (Table 3.5) was comparable to that observed for the thigh (Table 3.4),

again due to the distal location of the CM of the 'lumped' segment relative to the knee

joint (Table 3.6).

Data comparing the timing of these peak moments and powers (as a percentage

of the gait cycle) have not been presented because, on the whole, only the magnitudes of

the peaks were affected by differences in the linked-segment models. The small

differences in timing of these moment or power peaks did not exceed 2% of the gait

cycle and were limited to periods when the data points were identical to several decimal

places. Figures 3.5 and 3.6 illustrates that the timing of peak joint moments and powers

were unaffected by differences in the linked-segment models.

________________________________________________________ Chapter 3. 62

Figure 3.5 Mean joint moments estimated using a standard linked-segment model and

partial foot model - A for subject 2103-2116A (n=3).

Positive figures on the y-axis indicate an extension moment. Negative figures on the y-axis indicate a

flexion moment. Toe-off occurred at 61%of the gait cycle.

0 20 40 60 80 100-0.5

0

0.5

1Hip Moment

(Nm

/kg)

Ext

. >

0 20 40 60 80 100-0.4

-0.2

0

0.2

0.4Knee Moment

(Nm

/kg)

Ext

. >

0 20 40 60 80 100-0.5

0

0.5

1Ankle Moment

Gait Cycle [%]

(Nm

/kg)

Ext

. >

Standard model Partial foot model A

________________________________________________________ Chapter 3. 63

Figure 3.6 Mean joint powers estimated using a standard linked-segment model and

partial foot model - A for subject 2103-2116A (n=3).

Positive figures on the y-axis indicate power generation. Negative figures on the y-axis indicate power

absorption. Toe-off occurred at 61%of the gait cycle.

0 20 40 60 80 100-0.5

0

0.5

1Hip Power

(W/k

g) G

en.

>

0 20 40 60 80 100-1

-0.5

0

0.5Knee Power

(W/k

g) G

en.

>

0 20 40 60 80 100-1

-0.5

0

0.5

1Ankle Power

(W/k

g) G

en.

>

Gait Cycle [%] Standard Partial foot model AStandard model

________________________________________________________ Chapter 3. 64

Differences in peak joint moments and powers, between the standard and partial

foot linked-segment models, were limited to the hip and knee and almost exclusively

affected terminal swing. There were no differences of note between modelling

approaches during stance phase and as such only differences during swing phase have

been presented. A complete set of results including peak moments and powers observed

during stance phase has been presented in Appendix H. Peak joint moments and powers

selected from the each subject's ensembled average have presented in Tables 3.7-3.11

and Figures 3.7-3.11.

Compared to a standard linked-segment model, partial foot models increased the

mean hip extension moment (HM3) and knee flexion moment (KM5) peaks during

terminal swing (Tables/Figures 3.7 and 3.9). An increase in the knee extension moment

during initial swing (KM4) was observed in sample-B only (Table/Figure 3.8). No

differences in the peak ankle joint moments were observed between models for sample-

A (Appendix H). For sample-B the ankle joint was irrelevant due to the 'lumped'

segment created with partial foot model-B and therefore, the ankle moment was not

calculated.

Compared to a standard linked-segment model, partial foot model-A increased

the power generated across the hip joint during terminal swing (HP4) (Table/Figure

3.10). A negligible increase in power absorption was observed across the hip joint with

the use of partial foot model-B (Table/Figure 3.10). Increased power absorption was

observed at the knee during terminal swing (KP4) with the use of the partial foot models

compared to a standard linked-segment model (Table/Figure 3.11). No difference in

ankle power absorption or generation peaks (AP1 and AP2) were observed as a result of

the application of the different inverse dynamic models (Appendix H).

________________________________________________________ Chapter 3. 65

Table/Figure 3.7 Mean hip joint extension moment peaks during terminal swing

(HM3) for both the standard and partial foot linked-segment models.

HM denotes hip moment. Positive values indicate a hip extension moment. Standard deviation reported in

brackets.

Inverse Dynamic Model Differences

Standard Partial foot absolute %

Sample A - with ankle motion

HM3 (Nm/kg) 0.208

(0.041)

0.301

(0.032)

0.093 -44.7

Sample B - without ankle motion

HM3 (Nm/kg) 0.188 0.242 0.054 -28.7

Sam

ple

-B

Sam

ple

-A

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

HM

3 E

xt.>

(N

m/k

g)

Sta

ndard

m

od

el

Part

ial f

oot

mo

de

l

Ab

solu

tediff

ere

nce

________________________________________________________ Chapter 3. 66

Table/Figure 3.8 Mean knee joint extension moment peaks during initial swing (KM4)

for both the standard and partial foot linked-segment models.

KM denotes knee moment. Positive values indicate a knee extension moment. Standard deviation

reported in brackets.

Inverse Dynamic Model Differences

Standard Partial foot absolute %

Sample A - with ankle motion

KM4 (Nm/kg) 0.116

(0.034)

0.120

(0.034)

0.004 -3.5

Sample B - without ankle motion

KM4 (Nm/kg) 0.040 0.066 0.026 -65.0

Sam

ple

-B

Sam

ple

-A

0.00

0.02

0.04

0.06

0.08

0.10

0.12

KM

4 E

xt.>

(N

m/k

g)

Sta

nd

ard

mo

de

l

Part

ial f

oo

tm

od

el

Ab

solu

ted

iffe

ren

ce

________________________________________________________ Chapter 3. 67

Table/Figure 3.9 Mean knee joint flexion moment peaks during terminal swing (KM5)

for both the standard and partial foot linked-segment models.

KM denotes knee moment. Negative values indicate a knee flexion moment. Standard deviation reported

in brackets.

Inverse Dynamic Model Differences

Standard Partial foot absolute %

Sample A - with ankle motion

KM5 (Nm/kg) -0.195

(0.024)

-0.256

(0.026)

-0.061 -31.3

Sample B - without ankle motion

KM5 (Nm/kg) -0.181 -0.222 -0.041 -22.7

Sam

ple

-B

Sam

ple

-A

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

KM

5 F

lex.

< (N

m/k

g)

Sta

nd

ard

mo

de

l

Pa

rtia

l fo

ot

mo

de

l

Ab

solu

ted

iffe

ren

ce

________________________________________________________ Chapter 3. 68

Table/Figure 3.10 Mean hip joint power generation/absorption during terminal swing

(HP4) for both the standard and partial foot linked-segment models.

HP denotes hip power. Positive values indicate power generation. Negative values indicate power

absorption. Standard deviation reported in brackets.

Inverse Dynamic Model Differences

Standard Partial foot absolute %

Sample A - with ankle motion

HP4 (W/kg) 0.079

(0.080)

0.132

(0.160)

0.053 -67.1

Sample B - without ankle motion

HP4 (W/kg) -0.013 -0.016 -0.003 -23.1

Sa

mp

le-B

Sa

mp

le-A

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

HP

4 G

en.>

(W

atts/

kg)

Sta

nd

ard

mo

de

l

Pa

rtia

l fo

ot

mo

de

l

Abso

lute

diff

ere

nce

________________________________________________________ Chapter 3. 69

Table/Figure 3.11 Mean knee joint power absorption during terminal swing (KP4) for

both the standard and partial foot linked-segment models.

KP denoted knee power. Negative values indicate power absorption. Standard deviation reported in

brackets.

Inverse Dynamic Model Differences

Standard Partial foot absolute %

Sample A - with ankle motion

KP4 (W/kg) -0.831

(0.176)

-1.070

(0.280)

-0.239 -28.8

Sample B - without ankle motion

KP4 (W/kg) -0.665 -0.797 -0.132 -19.8

Sa

mp

le-B

Sa

mp

le-A

-1.20

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

KP

4 A

bs.

< (

Wa

tts/

kg)

Sta

ndard

model

Part

ial f

oot

model

Ab

solu

tediff

ere

nce

________________________________________________________ Chapter 3. 70

3.4 Discussion

Researchers of partial foot amputee gait have investigated conditions of barefoot

walking and prosthetic/orthotic intervention. However the unique anthropometry of the

partial foot residuum and any prosthetic/orthotic intervention (including footwear) have

not previously been acknowledged.

For conditions of barefoot walking where the partial foot would be considered in

isolation, the M and I of the isolated/modelled foot segment would be substantially

reduced and the location of the mass centroid closer to the ankle joint when the partial

foot model was used (Table 3.2).

There were significant anthropometric differences between the modelled limb

segments with the use of a standard linked-segment model and the partial foot models.

These anthropometric differences were due, in part, to amputation of the foot and the

addition of a prosthesis/orthosis and shoe (Table 3.2). In the case of individuals with

clamshell prostheses, these anthropometric differences were also due to how the limb

segments were modelled within the constraints of the inverse dynamic modelling

approach and the reduction in the M of the leg segment (Table 3.3), reflecting atrophy

of the triceps surae musculature. It is difficult to separate whether the differences in

joint moments and powers were due to anthropometry or the assumptions of partial foot

model-B because the two were linked. Without the basic assumptions used to describe

the clamshell prosthesis within the constraints of the linked-segment model, the

prosthesis would have to be dissected and the anthropometric characteristics of each

piece uniquely assigned to the foot and leg segment separately.

The net joint moment profiles for the knee and hip, obtained using the partial

foot models, illustrate a systematic percentage increase in the knee flexion and hip

extension moments during swing phase compared to a standard model (Tables 3.7-

3.11). Estimates of work at the knee and hip joints reflect differences in the moment

profiles observed. These differences are indicative of a more accurate portrayal of the

activity of the hamstring and hip extensor muscle groups to decelerate the knee into full

extension and the hip joint into its initial contact hip flexion angle and prevent further

hip flexion prior to initial contact.

________________________________________________________ Chapter 3. 71

While such clinical interpretations of the joint moment profiles provide useful

information about the causes of movement, their usefulness for observing how

anthropometric changes affect the net joint moments are limited because only changes

caused by differences in anthropometric data as a whole can be observed.

By dissecting the joint moment equations into their components it was possible

to gather more information about how the moment equations were affected by changes

in segment anthropometry (Appendix H). To better illustrate the mass-acceleration

terms of the moment equation, joint moments were subsequently taken about the

proximal end of the free body segments rather than about the mass centroid. The value

of I was transposed using the parallel axis theorem.

The joint moment profiles calculated using partial foot model-A, were

dominated by the additional M of the modelled foot segment (Appendix H). In terms of

the ankle joint moment equation, the additional M was reflected in the mass-

acceleration products (Appendix H). In turn, these ankle joint reaction forces affected

the knee and hip joint moment calculations. The small differences in the location of the

mass centroid and value of I between modelling approaches seemed to be of little

consequence. Hence, only the M of the modelled segment would be of major concern

with this modelling approach (partial foot model-A).

The knee joint moment patterns, observed with partial foot model-B compared

to the standard linked-segment model, reflected not only changes in the M of the

modelled segments but the influence of I proved dominant during both initial and

terminal swing (Appendix H). Differences in the location of the segment's mass centroid

were also evident (Appendix H). Differences in the hip extension moments observed

during terminal swing were exclusively due to the carry over knee joint moments

(Appendix H). With this modelling approach it seems imperative that not only the M,

but also the location of the mass centroid and the value of I be adequately depicted.

Future investigations considering incorporating anthropometric characteristics of

the Clamshell prosthesis without accurate anthropometric modelling of the

anthropometry of the residuum and lower leg segments would be likely to overestimate

________________________________________________________ Chapter 3. 72

the swing phase moments and powers. For the Chopart amputee subjects, substantial

differences in the joint moments and powers were not observed because the additional

mass and inertia of the prosthesis and shoe were offset by reductions in the mass and

inertia of the affected leg and remnant foot segments due to muscle atrophy and

amputation. During the pilot investigation, when the mass and inertia of the clamshell

prosthesis was combined with these characteristics of the normal leg and intact foot,

derived using regression equations based on stature and body mass, significantly

differences in the swing phase moments were observed. As such, future investigations

should accurately depict the anthropometry of the remnant foot and lower leg segment if

the anthropometry of the clamshell prosthesis is being incorporated into the model.

Alternatively, investigators could ignore the anthropometry of the clamshell prosthesis

and assume that the anthropometry of the free body segments can be adequately

approximated using anthropometric descriptions of the intact foot and sound leg

segment. The efficacy of this alternative approach can be verified by comparing the

anthropometric characteristics of the combined leg, foot and prosthesis/shoe of the

Chopart amputee with the same characteristics of the sound leg and intact foot segment.

For example, the mass of the combined prosthesis/shoe, lower leg and remnant foot

segment of the Chopart amputee was equal to 4.7kg (Table 3.6) compared to 5.0kg for

the combined intact foot (Table 3.2) and leg segment (Table 3.3) of the same individual.

3.5 Conclusion

Linked-segment inverse dynamic models have been developed to incorporate

improved anthropometric descriptions of the partial foot residuum as well as account for

any prosthetic/orthotic intervention and footwear with a view to providing more

accurate kinetic estimates. This addresses the shortcoming of previous kinetic

descriptions of partial foot amputee gait, which have not acknowledged the

anthropometric contributions of the prosthesis/orthosis/shoe and have assumed that the

residuum can be adequately described using body segment parameter data of the intact

foot.

The partial foot models significantly modified the anthropometry of the free

body segments compared to the standard model. These differences were due to

amputation of the foot and the addition of a prosthesis/orthosis and shoe. However, in

________________________________________________________ Chapter 3. 73

the case of individuals with clamshell prostheses, these anthropometric differences were

linked to how the limb segments were modelled within the constraints of the inverse

dynamic modelling approach. These anthropometric differences manifested in the joint

moments during swing phase and depending on the partial foot model used, the

influence of mass, centre of mass location and mass moment of inertia differ. For partial

foot model-A, the mass of the modelled segment dominated the moment patterns

observed however, for partial foot model-B not only was the mass of the modelled

segment important, but the value of the mass moment of inertia was the primary

influence on the swing phase joint moments.

The joint moment profiles obtained with these partial foot models increased the

knee flexion and hip extension moments during terminal swing phase compared to a

standard model. These findings are indicative of a more accurate portrayal of the

requirement of the hamstrings muscle group and gluteus maximum to decelerate the

knee into full extension and the hip joint into its initial contact hip flexion angle and

prevent further hip flexion prior to heel contact, respectively. Increased power

absorption was observed across the knee and hip joints in line with the changes

observed in the moment profiles.

Previous investigators of partial foot amputee gait are likely to have

underestimated the magnitude of these peak joint moments and powers by not

accurately describing the anthropometry of the free body segments. In relative terms the

differences observed were significant. However, in absolute terms these differences

were negligible. For comparison, these differences were within the range of values

typically reflected by the 95% confidence interval of a normal population. Such small

difference would not affect clinical interpretation or treatment planning.

Many investigators of partial foot amputee gait may feel that the additional work

required to generate these improved anthropometric input data and additional

complexity of the linked-segment models were not warranted by the small, absolute,

differences observed in the swing phase moments and powers. While the partial foot

models are not likely to be used routinely given the small absolute differences in joint

moments and powers, these models do demonstrate the influence of accurate

anthropometric modelling which is advantageous to all investigators of partial foot

________________________________________________________ Chapter 3. 74

amputee gait. Results from this study indicate that a conventional linked-segment model

would yield kinetic data of sufficient accuracy for the study of partial foot amputee gait,

particularly given that stance phase seems to be of particular concern for this

population. Studies specifically interested in swing phase kinetics of high inertial

activities, such as kicking, may benefit from the modelling techniques developed.

________________________________________________________ Chapter 4. 75

A Biomechanical Analysis of Partial Foot Amputee Gait

4.1 Introduction

Partial foot amputation has become a more viable surgical intervention for the

treatment of advanced diabetes, vascular insufficiency and trauma where previously a

below knee amputation may have been required (Boyd et al., 1999; Burnfield et al.,

1998; Dorostkar et al., 1997). This is due largely to improvements in surgical

techniques for revascularising the micro arteriole structure of the foot and antibiotic

therapy for controlling ascending infection and septicemia (Muller and Sinacore, 1994).

Despite these medical advances, the perception of patients, surgeons, physicians

and allied health clinicians, toward partial amputation of the foot, has been tainted by a

long and chequered history of ongoing complications often resulting in surgical

revision. Questions about the efficacy of partial foot amputation as a viable long-term

alternative to more proximal amputation have been raised (Hirsch et al., 1996). The

occurrence of many ongoing complications such as ulceration (Sage et al., 1989), skin

breakdown (Brand, 1983; Sage et al., 1989; Birke and Sims, 1988; Muller and Sinacore,

1994) and equinus deformity (Chrzan et al., 1993; Parzaile and Hahn, 1988) could be

reduced given a better understanding of the gait of partial foot amputees and how

prosthetic/orthotic intervention influences the mechanics of locomotion.

Chapter 4

________________________________________________________ Chapter 4. 76

Until recently, our understanding of the biomechanics of partial foot amputee

gait was based largely on that of normal individuals with authors speculating about the

effect of amputation and socket design on gait (Condie, 1970; Condie and Stills, 1988;

Chrzan et al., 1993). Condie (1970) provided some biomechanical merit to the

speculation by analysing the forces acting on the residuum and socket in conventional

below and above ankle socket designs.

The crux of this work (Condie, 1970) demonstrated that the forces experienced

by the Tarso-Metatarsal or Chopart residuum, to resist the external moments generated

during initial contact and toe-off, were alarmingly large when below ankle fitting

concepts were employed. Extending the socket proximally could reduce the magnitude

of forces experienced by the residual foot and the majority of force could be transmitted

away from the sensitive distal residuum to the naturally adapted fatty pad of tissue

covering the heel (Condie, 1970).

While these findings were exciting, their validity seemed questionable. For to

undertake such a static force analysis, whereby a series of forces are resolved for

equilibrium, the magnitude, point of application and line of action of each force must be

known. While some of this information can be measured, such as the magnitude, point

of application and line of application of the ground reaction force (GRF), much of the

required information cannot be obtained easily. Without these data, assumptions about

these forces must be made. It may be reasonable to make assumptions about the line of

action of forces (for example, the forces acting on the stump are normal to the stump

surface). However, unless the point of application of each force is known an infinite

number of solutions for force and moment equilibrium exist.

Condie's (1970) static force analyses depicting toe-off in Transmetatarsal and

Tarso-Metatarsal amputees, using below ankle fitting concepts, demonstrates how by

varying the point of application of the superincumbent weight force it is possible to

reach an alternate solution for force and moment equilibrium. While this was probably

not Condie's original intention, inconsistencies such as this cast doubt on the efficacy of

comments about transmitting the majority of force away form the distal residuum to the

heel pad. Such conclusions could be explained by the limitations of determining the

point of application of the forces analysed.

________________________________________________________ Chapter 4. 77

Despite the over simplicity of Condie's (1970) work, this original contribution

formed the foundation underpinning our biomechanical understanding of partial foot

amputee gait for more than two decades. Comparable static force analyses have been

presented by a number of authors (Condie and Stills, 1988; Weber, 1991; Muller and

Sinacore, 1994) without addressing the potential limitations of such analyses. Despite

the limitations of these works, the collective contribution raises questions and

misconceptions about prosthetic prescription, ankle range of motion (ROM), socket

design and the excursion of the centre of pressure and its affect on joint moments.

Many of the questions and misconceptions have recently received attention as a

result of a growing awareness of the inadequacies of laying a foundation of knowledge

about partial foot amputee gait and prosthetic design based on speculative and anecdotal

evidence. There is an increasing body of literature examining the kinematics (Dillon,

1995; Garabolsa et al., 1996; Hirsch et al., 1996; Dorostkar et al., 1997; Muller et al.,

1998), ground reaction forces (Dillon, 1995; Boyd et al., 1999; Burnfield et al., 1998;

Muller et al., 1998), kinetics (Dillon, 1995; Boyd et al., 1999; Muller et al., 1998),

temperospatial (Dillon, 1995; Dorostkar et al., 1997; Burnfield et al., 1998; Muller et

al., 1998), plantar pressure (Garabolsa et al., 1996) and muscle strength (Burnfield et

al., 1998; Dorostkar et al., 1997) parameters of, primarily, the affected limb. However,

much of this work remains unpublished, appearing as conference abstracts or research

progress reports where detailed discussion is usually not permitted.

Empirical studies have focused primarily on the gait of individuals with

amputation distal to and including the Transmetatarsal (TMT) level (Garabolsa et al.,

1996; Burnfield et al., 1998; Boyd et al., 1999; Dorostkar et al., 1997; Dillon, 1995;

Muller et al., 1998) with a limited number of studies examining more proximal

amputation levels (Dillon, 1995). Studies have examined conditions of bare-foot

walking (Garabolsa et al., 1996; Burnfield et al., 1998; Boyd et al., 1999; Dorostkar et

al., 1997) or prosthetic/orthotic intervention (Dillon, 1995; Hirsch et al., 1996; Muller et

al., 1998).

As a result of these empirical studies, it has been demonstrated that unilateral

partial foot amputees walk at about two-thirds the velocity of normal individuals with

________________________________________________________ Chapter 4. 78

little difference evident between groups based on amputation level (Boyd et al., 1999;

Burnfield et al., 1998; Dorostkar et al., 1997; Dillon, 1995; Muller et al., 1998).

Significant reductions in stride length, cadence (Burnfield et al., 1998; Boyd et al.,

1999; Dorostkar et al., 1997; Dillon, 1995) and step length (Muller et al., 1998) were

observed, with reductions in stride length being implicated as the primary reason for

reduced walking velocity (Dorostkar et al., 1997). There were no differences evident in

stride length (Dillon, 1995; Dorostkar et al., 1997) or cadence (Dorostkar et al., 1997)

between amputee groups. The duration of the gait cycle and proportions of swing and

stance phase were comparable to normal on the affected limb irrespective of residual

foot length (Dillon, 1995).

Joint angular kinematic patterns have focused, primarily, on the ankle joint

(Boyd et al., 1999; Dorostkar et al., 1997; Garabolsa et al., 1996) with limited work

examining more proximal joints (Dillon, 1995; Muller et al., 1998) or reporting swing

phase kinematics (Dillon, 1995). At the ankle, static range of motion was not

statistically different from normal (Garabolsa et al., 1996; Dillon, 1995). During gait, it

appears that TMT amputees utilise a much smaller proportion of the available range

than do their normal counter parts (Garabolsa et al., 1996). Dillon (1995) also identified

this trend across both Metatarsophalangeal (MTP) and TMT groups however, a

statistically significant difference was not observed. Some authors have observed a

number of kinematic abnormalities at the ankle joint once amputation compromises the

Metatarsal heads. Boyd et al., (1999), Dorostkar et al., (1997) and Garabolsa et al.,

(1996) all reported a reduction in ankle dorsiflexion peak in TMT amputees. Dillon

(1995) observed an increase in the peak ankle dorsiflexion in the same group and Muller

et al. (1998) observed no difference. Irrespective of the peak dorsiflexion angle, most

authors agree that there is a significant delay in the timing of this angle peak compared

to normal or MTP groups (Boyd et al., 1999; Dorostkar et al., 1997; Dillon, 1995). Peak

ankle plantarflexion was significantly reduced in TMT amputees relative to normal

(Dillon, 1995; Muller et al., 1998) and the MTP group (Dillon, 1995). Kinematic

profiles of a single Chopart amputee identified that the ankle motion observed was the

result of the force/deflection characteristics of the prosthetic foot because the Clamshell

patella tendon bearing (PTB) prosthesis eliminated true ankle motion (Dillon, 1995).

The kinematic patterns observed at the knee and hip joint appear to be relatively normal

across the MTP and TMT groups. However, small variations in maximum knee flexion

________________________________________________________ Chapter 4. 79

and initial contact hip flexion angles were observed (Dillon, 1995; Muller et al., 1998)

and found to be significantly different from normal by Muller et al., (1998). The

initiation of knee flexion into swing phase was delayed by about 10% of the gait cycle

in TMT amputees (Dillon, 1995).

A number of differences in the GRF data have been reported. Some authors have

found that there was no difference in the vertical GRF irrespective of amputation level

compared to the normal population (Dillon, 1995; Boyd et al., 1999; Burnfield et al.,

1998). However, when adjusted for velocity, the normalised peak magnitudes were

significantly reduced in the toe and TMT groups relative to normal and each other

(Burnfield et al., 1988). Boyd et al., (1999) found that the rise toward the second

vertical GRF peak was significantly delayed in TMT amputees and those with

Metatarsal ray resections. Hirsch et al., (1996) also observed a similar trend however no

statistical analyses were performed. During loading response, the magnitude of the

vertical GRF was increased on the sound limb compared to the residual limb (Burnfield

et al., 1998). A reduction in the magnitude of the horizontal GRF peaks was observed

by Hirsch et al., (1996) and Dillon (1995), which approached statistical significance in

the MTP and TMT groups, compared to normal (Dillon, 1995). Centre of pressure

(CoP) excursion was significantly reduced in TMT amputees relative to normal and the

MTP amputee group (Dillon, 1995). A strong correlation was observed between

residual foot length and CoP excursion irrespective of orthotic fitting (Dillon, 1995).

The ankle foot orthoses and insoles fitted to these amputees were unable to restore the

normal excursion of the CoP past the distal residuum (Dillon, 1995). It appears that

prosthetic fitting was able to restore normal CoP excursion in a single Chopart amputee

(Dillon, 1995). Replacing the lost lever arm with a suitably rigid material in conjunction

with a socket capable of distributing forces caused by loading the toe lever may be

responsible for restoring normal CoP excursion in this Chopart amputee (Dillon, 1995).

This theory may also explain why similar findings were not evident in the MTP and

TMT amputee groups fitted with orthotic devices as neither a socket nor a rigid forefoot

lever was incorporated into the prosthetic replacement (Dillon, 1995).

Kinetic anomalies were prevalent particularly once amputation compromised the

metatarsal heads. Small decreases in the maximum ankle plantarflexion moment were

observed with small reductions in residual foot length (Dillon, 1995). A significant

________________________________________________________ Chapter 4. 80

reduction in the ankle plantarflexion moment peak was observed in the MTP and TMT

amputees compared to normal (Dillon, 1995; Boyd et al., 1999; Muller et al., 1998).

Similar results have also been reported for toe amputees and those with metatarsal ray

resection (Boyd et al., 1999). The peak ankle plantarflexion moment was delayed in

TMT amputees (Boyd et al., 1999) as it was in a single Chopart amputee (Dillon, 1995).

Amputation proximal to the TMT level did not appear to greatly reduce the peak

dorsiflexion moment from that observed in the TMT group (Dillon, 1995). Ankle power

generation in the MTP group was significantly reduced compared to normal as a result

of reductions in the excursion of the CoP given that no differences in the dynamic ankle

range were observed (Dillon, 1995). Once the metatarsal heads had been compromised,

ankle power generation was reduced to the point of being negligible (Dillon, 1995;

Muller et al., 1998). Questions about the ability of TMT amputees to utilise the

available ankle motion, as measured by plantarflexor power generation, have been

raised (Dillon, 1995).

An extension moment was observed about the knee joint from foot-flat to toe-off

in both the MTP (Dillon, 1995) and TMT amputee groups (Dillon, 1995; Muller et al.,

1998). In the MTP group, the normal knee moment pattern was maintained (Dillon,

1995), however it was completely absent in the TMT amputees (Dillon, 1995; Muller et

al., 1998). Dillon (1995) observed little power absorption immediately before toe-off in

the TMT amputee group. In contrast, Muller et al., (1998) observed a period of

relatively normal power absorption across the knee at this time. In both studies, the

absence of the normal power exchange, between 25-50%GC was notable.

The hip moment and power patterns observed in the MTP cohort, closely

resemble that of the normal population (Dillon, 1995). Muller et al., (1998) reported the

early onset of a flexion moment about the hip joint. In contrast, Dillon (1995) reported a

delay in the hip extension moment peak and the maintenance of an extension moment

about the hip in the TMT amputee group until about 45%GC. The hip flexion moment

peak was considerably delayed and substantially smaller than normal in the TMT

amputees (Dillon, 1995). In the TMT amputee group, hip power generation during

initial stance was comparable to that observed in the normal population however, the

power peak was delayed (Dillon, 1995). Mueller et al., (1998), however, observed very

little concentric muscle activity at this time. Power generation at the hip during the

________________________________________________________ Chapter 4. 81

propulsive phase was comparable to that observed in the normal population (Dillon,

1995; Mueller et al., 1998). However, Mueller et al., (1998) reported that the small

differences were indicative of a hip flexor gait strategy.

Substantial reductions in both sound and residual limb strength have been

observed in toe (Dorostkar et al., 1997) and TMT (Dorostkar et al., 1997; Burnfield et

al., 1998) amputees compared to normal with the most pronounced deficits occurring in

the residual limb ankle plantarflexors (Dorostkar et al., 1997). Burnfield et al., (1998)

identified that there were no differences in plantarflexor strength between the sound and

residual limbs in TMT amputees.

There is little doubt that a substantial number of empirical contributions have

been made over the last five years, particularly given the relatively small population of

partial foot amputees whom may benefit from such work. These empirical studies have

advanced our understanding of partial foot amputee gait from the theoretical static force

analyses presented some 30 years ago. For the most part, authors have tended to

document the mechanical abnormalities without substantial explanation or insightful

comment illustrating the underlying causes for the mechanical behaviours observed.

Perhaps this is merely a reflection of reviewing very recent and ongoing works, which

have been presented largely as conference abstracts or research progress reports where

sufficient detail is usually not permitted.

To date, research has tended to focus on limited aspects of partial foot amputee

gait such as ankle kinematics, stance phase or the affected limb. The existing body of

knowledge raises questions about the causes and compensatory effects of abnormal

movement.

For example, there appears to be some fundamental issue surrounding the

inability of partial foot amputees to load the distal residuum. This poorly understood

problem seems to manifest itself in a number of gait parameters including: reductions in

the excursion of the CoP; reductions in the ankle plantarflexion range utilised during

gait; and reductions in the horizontal GRF associated with push-off. The inability to

load the distal residuum, at least in part, limits the ability of the amputee to generate

power across the ankle.

________________________________________________________ Chapter 4. 82

Given that TMT amputees generate negligible power across the affected ankle,

and that power generation across the affected hip appears to be comparable to normal,

how is power generated to advance the body forward? Perhaps, as in transtibial and

transfemoral amputees, the sound hip extensor musculature work concentrically during

the propulsive phase of the affected limb to push the body forward from the rear.

It would be prudent not to speculate too much about the potential causes of

abnormal movement and what compensatory adaptations may occur but instead to

provide a thorough biomechanical description of partial foot amputee gait.

The purpose of this investigation was to document bilateral ankle, knee and hip

kinematic, kinetic, electromyographic and temperospatial parameters on a cohort of

normal and partial foot amputees to more fully describe the effects of amputation and

prosthetic/orthotic fitting on gait.

4.2 Method

Subjects

The method by which amputee subjects were recruited (including exclusion

criteria and assessment of amputation level) has previously been described in Chapter 2.

Of the amputee subjects recruited for these studies, bilateral gait data were obtained

from a cohort of eight partial foot amputees. Of the eight amputee subjects, five

unilateral partial foot amputees including one Transmetatarsal (TMT), three Lisfranc

and one Chopart amputee were studied. The three remaining subjects had bilateral

amputation including one Metatarsophalangeal amputation (MTP), one Lisfranc

amputation and one subject had bilateral Chopart amputation with partial resection of

the posterioinferior portion of the calcaneus. This individual was not a true forefoot

amputee however the gait patterns observed were dominated by the Clamshell patella

tendon bearing (PTB) prosthesis and were comparable to those observed in the other

Chopart amputee with similar prosthetic fitting. Given the limited number of individuals

with Clamshell PTB prostheses, data from this subject were also considered. Amputee

subjects had a variety of orthotic/prosthetic replacements including toe fillers, custom

________________________________________________________ Chapter 4. 83

orthoses, slipper sockets or Clamshell PTB prostheses. Due to the limited sample and

the variability of individuals in terms of amputation level, number of limbs affected and

prosthetic/orthotic fitting, each subject was considered in isolation relative to a normal,

non-amputee control sample. Characteristics of the amputee subjects have been

presented in Table 4.1.

Table 4.1 Characteristics of the amputee subjects

Bi denotes bilateral; uni denotes unilateral; *Gangrene secondary to frostbite; ‡ Gangrene secondary to

water burns. Standard deviation (SD).

Subject Level Aetiology Age

(years)

Stature

(m)

Mass

(kg)

Device

Amputee subjects

1004-1307A Bi MTP Gangrene* 40 1.74 64.92 Custom orthosis

2103-2116A Uni TMT Trauma 54 1.84 84.50 Toe filler

2703-1903A Uni Lisfranc Trauma 53 1.82 76.60 Slipper socket

0704-0403A Uni Lisfranc Trauma 22 1.84 81.45 Slipper socket

2103-1906A Uni Lisfranc Trauma 55 1.82 80.65 Stuffed shoe

2803-0410A Bi Lisfranc Gangrene 63 1.61 50.00 Toe filler

0904-1924A Bi Chopart Gangrene‡ 31 1.73 82.24 Clamshell PTB

3004-1102A Uni Chopart Trauma 19 1.79 93.00 Clamshell PTB

Mean 42.13 1.77 76.67

SD 16.60 0.08 13.35

Eight non-amputee control subjects were also recruited. Control subjects

satisfied the same inclusion criteria as the amputee subjects. Each control subject was

age, weight, height and sex matched to an amputee subject. Control subjects were

grouped to provide a description of a 'normal' population. In this way, the gait of any

amputee subject could be compared to the mean and 95% confidence interval (CI) of a

normal population rather than to the idiosyncratic pattern of locomotion of a single

control subject with similar anthropometric characteristics. Any given able body subject

may exhibit large variations from the mean control group data, making comparison

either difficult or misleading (Allard et al., 1997). The mean age, stature and mass of

________________________________________________________ Chapter 4. 84

the control sample, including standard deviations in parentheses, were 41.13 years

(±14.81), 1.74m (±0.08) and 77.11kg (±6.83), respectively.

Apparatus

Joint ROM measurements were undertaken using a plastic goniometer with

angles marked in 2-degree increments and muscle strength was rated using the Oxford

Manual muscle test scale. A treatment plinth was used during all measurements, which

were conducted according to the techniques described by Clarkson and Gilewich

(1989). The subject assessment forms used to record the results of the joint ROM and

muscle strength tests are part of Appendix G.

Anthropometric models for the description of the thigh and leg segments as well

as the intact and partial foot have previously been described in Chapters 2 and 3.

Anthropometric descriptions of any prosthetic/orthotic replacement and footwear were

obtained using standard dynamics techniques described in Chapter 3. One of two

linked-segment inverse dynamic models, based on the type of prosthetic/orthotic

intervention (if any), was used to calculate net joint moments and powers as described

in Chapter 3.

In addition to the equipment used to collect the kinematic and kinetic data

described in Chapter 3, EMG signals were detected using 22mm wide bipolar,

silver/silver chloride, pregelled electrodes (Biotabs - MIE Medical Research Ltd. Leeds

UK). The electrodes were attached to the preamplifier at the skin surface. EMG

preamplifiers had a gain of 1000. Footswitch signals were obtained using compression

closing, individual heel and toe switches and voltage dividers (MIE Medical Research

Ltd. Leeds UK). EMG and footswitch signals were obtained at a rate of 1000Hz, using a

waist belt transmitter and FM receiver as part of the MT8 Biological Telemetry System

(MIE Medical Research Ltd. Leeds UK). Analogue footswitch and EMG signals were then

passed to the A/D conversion card. Characteristics of the A/D card have been described

in Chapter 3.

________________________________________________________ Chapter 4. 85

Subject preparation

The preparation of subjects including the provision of informed consent,

documentation of a medical history and anthropometric measurements as well as

kinematic marker placement have previously been described in Chapter 3.

For the collection of joint ROM data and muscle strength testing, subjects were

positioned on a treatment plinth (Clarkson and Gilewich, 1989). Each test manoeuvre

was explained to the subject and instruction provided until the subject could perform the

required task. Measurements were compared bilaterally and against normative data

(Kendall and McCreary, 1993) so that mismeasurements could be identified.

Subsequent measurements were taken where necessary to verify measurements that

were questionable.

Preparation of the skin before the application of the EMG electrodes was

accomplished by shaving and lightly abrading the skin surface with fine grit sand paper

and cleaning with alcohol wipes. Electrodes were then placed on vastus lateralis, biceps

femoris long head, gastrocnemius medial and lateral heads, soleus and tibialis anterior

(Perotto, 1994) with a centre to centre interelectrode distance of 25mm. Foot switches

were placed bilaterally on both the heel and toe. With the electrodes and footswitches in

place, the subject was asked to perform a number of test manoeuvres (Kendall and

McCreary 1993) to assess the placement of the electrode and the efficacy of the EMG

signal.

Data acquisition and processing

The acquisition and processing of force platform and kinematic data have

previously been described in Chapter 3. Kinetic data were calculated using the linked-

segment inverse dynamic models described in Chapter 3 and included anthropometric

descriptions of the remnant foot, leg and thigh segment as well as any

prosthesis/orthosis and footwear. EMG data were collected simultaneously with the

force and kinematic data and synchronisation was controlled by the Peak-Motus

software as described in Chapter 3.

________________________________________________________ Chapter 4. 86

For the normal and amputee subjects, kinetic and kinematic data obtained from

multiple trials were averaged for each limb (Appendix E). A time dependent 95%CI was

created from the ensembled averages to reflect the range of values observed in the

normal population. For each amputee subject, data from both limbs were depicted

relative to the 95% CI of the normal population to facilitate comparison.

The timing and magnitude of certain peak angles, moments, powers and ground

reaction forces were obtained and analysed in more detail (Appendix E). For the normal

population, the timing and magnitude of these points of interest were obtained from the

ensembled averages of each individual. The timing and magnitude of these points of

interest for the normal population were represented by a 95%CI for each parameter.

Similarly, the range of temperospatial, joint ROM values observed in the normal

population were also represented by a 95%CI to facilitate comparison of data from each

limb of the amputee subjects. Views on the presentation of particularly stride length

vary considerably because of attempts to account differences in stature or limb length

between individuals. Stature (or limb length) has been demonstrated to influence stride

length (Dean, 1965; Greive and Gear 1966 -both cited; Inman et al., 1981; Perry, 1992;

Craik and Dutterer, 1995) hence the recommendation that stride length routinely be

defined as a ratio of stature (Winter et al., 1974; Greive and Gear, 1966 - all cited Perry,

1992). The normalisation of stride parameters by stature has become common place as

illustrated by Craik and Dutterer (1995) despite reports that only a weak relationship

exists between these parameters at normal walking speeds (Perry, 1992). In adults only

4-28% of the variability in stride length can be explained by differences in stature

(Perry, 1992). Some authors oppose such normalisation on the basis that the relative

values do not present a clear picture of the distances covered (Das and Ganguli, 1979 -

cited Perry, 1992). In the present investigation stride length has been presented in basic

units of meters as well as normalised by stature given the lack of clear consensus

regarding how this parameter should be reported.

Raw EMG data were initially inspected across multiple strides to ensure a

synchronous pattern of EMG activity that was free from artefact and unsuitable data

were rejected at this stage. EMG data were then filtered using a 4th order high pass

Butterworth filter with 6Hz cut-off (Solomonow, 1990; Nilsson et al., 1993; Acierno et

________________________________________________________ Chapter 4. 87

al., 1998) to eliminate movement artefact and stabilise the baseline signal. Data were

then low pass filtered using a 4th order Butterworth filter with 500Hz cut-off (Yang and

Winter, 1984; Nilsson et al., 1993; Acierno et al., 1998). The effective bandwidth was

therefore 6-500Hz. Data were full wave rectified and integrated over 10ms intervals

(Powers et al., 1998; Perry, 1992). EMG data were amplitude normalised using the

manual muscle test (MMT) method (Perry, 1992; Powers et al., 1998) and MMT data

were collected using the standard test positions described by Kendall and McCreary

(1993). Subjects were given encouragement during the MMT data collection.

Much of the EMG signal characteristic of the noise observed in the present

investigation was well in excess of the 5%MMT threshold utilised by Powers et al.,

(1998) to distinguish meaningful muscle activity from the background noise. The 5%

MMT threshold reflects the equivalent to the clinically effective grade 2 level of muscle

activity (Beasley, 1961 - cited Perry, 1992) and is a means by which meaningful muscle

activity can be identified from the occasional spike, small burst or extremely small

signal which are functionally insignificant (Perry, 1992).

The maximum MMT voltage, representing 100% activity, was determined to be

the mean voltage of a stable sample of MMT data (Powers et al., 1998; Perry, 1992).

Perry (1992) describes utilising the peak one-second sample of the isometric manual

muscle test. In the present study, the maximum MMT values were given by determining

the peak voltage of each 10ms interval of the integrated MMT signal over a stable one-

second sample of MMT data. The 100% MMT value was given by the average of all of

the peak MMT values from the one-second sample of integrated MMT data. This signal

processing technique increased the maximum MMT voltage to a value approximately

midway between the mean and peak MMT voltage. This technique also overcame the

inadequacies associated with normalisation to a single peak (Yang and Winter, 1984).

Determining the maximum MMT voltage in this manner reduced the overall magnitude

of the gait EMG (as a percentage of MMT) and the noise observed was typically below

the 5%MMT threshold.

An ensembled average was created from the multiple trials of EMG data

recorded for each subject. From the ensembled average of each individual limb, the

periods of muscle activity were determined as EMG data exceeding the 5% threshold

________________________________________________________ Chapter 4. 88

level (Powers et al., 1998; Perry, 1992). Packets of EMG activity separated by less than

5% of the gait cycle were combined and any packets of EMG smaller than 5% of the

gait cycle were removed (Powers et al., 1998; Perry, 1992). The mean intensity of EMG

packets together with the time of muscle onset and offset, as a percentage of the gait

cycle, were determined (Powers et al., 1998).

Good approximations of the onset and cessation of packets of EMG activity,

relative to those expected from visual observation of the filtered and rectified signal,

were obtained when this technique was applied to a group of individuals, such as the

ensembled average of the normal cohort. However, when applied to an individual,

rather than to a group ensembled average, the onset and cessation times of packets of

EMG activity were sensitive to small changes in the 5%MMT threshold. As such, the

packets of EMG activity obtained were checked to ensure that the packets of EMG

activity reflected the onset and cessation times expected from visual inspection of the

filtered and rectified signal. Where necessary, the threshold level was adjusted from

5%MMT until the packets of EMG activity of each muscle reflected those expected

from observation of the filtered and rectified signal. When the threshold level was not

5%MMT, the figures were marked with the threshold level used.

4.3 Results

Joint range of motion and muscle strength

A number of differences in hip and knee joint ranges of motion (ROM) were

observed between the normal population and individual amputee subjects. Differences

in many amputee subjects were very close the 95%CI of the normal population.

Differences in joint ROM that did not exceed the 95%CI of the normal population by

more the 5° were not considered clinically significant given that the resolution of the

technique which was about 5°, depending on the joint assessed.

Ankle plantarflexion ROM was significantly reduced in the bilateral Lisfranc

(21°±1°), unilateral Chopart (20°) and bilateral Chopart amputee (30° ± 3°) compared to

the 95%CI of the normal population (32° to 60°). Reductions in plantarflexion range

________________________________________________________ Chapter 4. 89

approached significance on the affected limbs of the unilateral TMT (36°) and Lisfranc

cohort (35°±10°) however were not considered to be functional gait limitations.

Reductions in the available dorsiflexion range approached functional

significance in the affected limbs of the unilateral TMT (10°), Lisfranc cohort (12±5°)

and Chopart amputees (8°) compared to the normal population (95%CI, 6° to 18°).

Dorsiflexion range on the sound limb was also reduced in the TMT (5°), Lisfranc

(12±8°) and Chopart amputees (8°).

Ankle inversion range was significantly compromised in the bilateral Lisfranc

(6±2°) and Chopart (2±0°) amputee compared to normal (95%CI, 12° to 31°). Ankle

inversion was also significantly reduced on the affected limb of the unilateral Chopart

amputee (8°) compared to normal. Compared to the ankle eversion ROM observed in

the normal population (95%CI, 7° to 15°), the eversion ROM observed in the bilateral

Lisfranc (2±0°) and Chopart amputees (2±0°) was significantly compromised. Similar

reductions in ankle eversion ROM were also observed on the affected limb of the TMT

(5°), Lisfranc (2°±2°) and Chopart amputees (2°).

Using the Oxford Manual Muscle Test scale, strength of hip, knee and ankle

musculature on both the sound and affected limb was typically grade 5, as for the

normal population. Reductions in muscle strength were observed in the hip adductors

(grade 4) of subject 2103-1906A. Reductions in muscle strength were also observed

across the hip extensors, adductors and abductors in subject 2803-0410A. Grade 2 ankle

inversion and eversion strength was also observed in this subject.

Temperospatial characteristics

A number of temporal and spatial anomalies were observed among the amputee

cohort. Spatial parameters of stride length, walking velocity and cadence are presented

in Table 4.2. Temporal components including gait cycle duration and proportions of

swing and stance time are presented in Table 4.3. Single and double support phase data

as well as timing of contralateral initial contact are presented in Table 4.4.

________________________________________________________ Chapter 4. 90

Walking velocity was significantly reduced in the unilateral TMT

(1.18±0.04m/s) and Chopart (1.18±0.03m/s) amputees as well as in the bilateral

Lisfranc amputee (0.92±0.02m/s) compared to the 95%CI of the normal population

(1.41-1.71m/s) (Table 4.2). Reductions in walking velocity were commensurate with

reductions in stride length in the unilateral TMT (1.40±0.05m) and the bilateral Lisfranc

amputees (0.99±0.02m) compared to the normal population (95%CI, 1.41 to 1.71m)

(Table 4.2). In the unilateral Chopart amputee, reductions in stride length approached

significance (1.45±0.05m) as did reductions in cadence (97.3±0.6 steps/minute) (Table

4.2). For the cohort of unilateral Lisfranc amputees reductions in stride length

(1.49±0.04m) approached significance however, walking velocity was comparable to

that observed in the normal population (1.32±0.05m/s) as was cadence (106

steps/minute) (Table 4.2). No significant differences in cadence were observed in the

amputee subjects compared to the normal population (95%CI, 91.9 steps/min to 119.7

steps/min).

No significant differences in the duration of the gait cycle were observed in the

amputee subjects compared normal population (95%CI, 0.99s to 1.29s) (Table 4.3). In

the normal population, stance and swing occupied an average of 60±1%GC and 40±1

%GC, respectively (Table 4.3). The proportion of the gait cycle occupied by sound limb

stance phase was significantly larger than that spent in affected limb stance for the

unilateral TMT, Chopart and several of the Lisfranc amputees (Table 4.3). The duration

of sound limb stance, as a percentage of the gait cycle, was significantly larger than that

the normal population (95%CI, 59%GC to 62%GC) for several of these individuals

(Table 4.3). For subject 2803-0410A, the duration of stance phase, as a percentage of

the gait cycle, was increased bilaterally (Table 4.3). Proportionate reductions in the

duration of swing phase, as a percentage of the gait cycle, were observed.

The proportion of the gait cycle spent in affected limb single support was

decreased for the unilateral TMT (38%GC) and Chopart (37%GC) amputees compared

to the normal population (95%CI, 38%GC to 41%GC) (Table 4.4). A similar decrease

was seen for the bilateral Lisfranc amputee (37±0%GC) and the unilateral Lisfranc

amputee subject 0704-0403A (Table 4.4). The duration of affected limb single support,

as a percentage of the gait cycle, was shorter than that of the sound limb in all the TMT

________________________________________________________ Chapter 4. 91

and Lisfranc amputees except subject 2103-1906A (Table 4.4). The statistical

significance of these results (ie: values outside the 95%CI of the normal population)

were varied when compared to the normal population (Table 4.4). For subject 2103-

1906A, affected limb single support was comparable to normal however, the proportion

of the gait cycle spent in sound limb single support was significantly reduced (Table

4.4).

Table 4.2 Spatial characteristics of the amputee subjects.

Standard deviations reported in brackets.* denotes parameter outside the 95% confidence interval of

normal population. 'norm' indicates parameters normalised by stature in meters.

Stride length Walking velocitySubject Cadence

(step/min) (m) norm (m/s) norm (s-1)

Control 105.8

(6.93)

1.56

(0.08)

0.90

(0.05)

1.37

(0.07)

0.80

(0.06)

1004-1304A Bi MTP 103.9

(0.42)

1.57

(0.02)

0.90

(0.01)

1.36

(0.01)

0.78

(0.01)

2103-2116A Uni TMT 100.9

(0.70)

1.40*

(0.05)

0.77*

(0.03)

1.18*

(0.04)

0.64*

(0.02)

2703-1903A Uni Lisfranc 103.9

(3.25)

1.56

(0.08)

0.85

(0.04)

1.35

(0.11)

0.74

(0.06)

0704-0403A Uni Lisfranc 106.2

(2.14)

1.44

(0.02)

0.78*

(0.01)

1.28

(0.01)

0.69

(0.01)

2103-1906A Uni Lisfranc 109.7

(1.21)

1.48

(0.01)

0.82

(0.00)

1.35

(0.02)

0.75

(0.01)

2803-0410A Bi Lisfranc 111.2

(0.84)

0.99*

(0.02)

0.61*

(0.01)

0.92*

(0.02)

0.57*

(0.01)

0904-1924A Bi Chopart 103.8

(2.89)

1.44

(0.05)

0.83

(0.03)

1.25

(0.08)

0.72

(0.05)

3004-1102A Uni Chopart 97.34

(0.61)

1.45

(0.05)

0.81

(0.03)

1.18*

(0.03)

0.66*

(0.02)

________________________________________________________ Chapter 4. 92

For the unilateral Chopart amputee, the duration of double support following

affected limb initial contact was increased (13%GC) compared to the normal population

(95%CI, 9%GC to 12%GC). For the unilateral TMT amputee and subject 0704-0403A

the proportion of the gait cycle spent in double support following sound limb initial

contact was significantly increased. The duration of double support, as a percentage of

the gait cycle, was 14±1%GC for the bilateral Lisfranc amputee.

Table 4.3 Temporal characteristics of the amputee subjects.

Standard deviations reported in brackets.* denotes parameter outside the 95% confidence interval of

normal population. AL denotes affected limb. SL denotes sound limb.

Stance time Swing timeSubject Gait

cycle

(sec) (sec) (%GC) (sec) (%GC)

Control 1.176

(0.074)

0.688

(0.048)

60.4

(0.8)

0.451

(0.029)

39.6

(0.8)

1004-1304A Bi MTP 1.156

(0.005)

0.688

(0.007)

59.6

(0.9)

0.467

(0.012)

40.4

(0.9)

2103-2116A Uni TMT AL

SL

1.183

1.195

0.720

0.750

60.9

62.8*

0.463

0.445

39.1

37.2*

2703-1903A Uni Lisfranc AL

SL

1.130

1.181

0.663

0.731

58.7

61.9

0.467

0.450

41.3

38.1

0704-0403A Uni Lisfranc AL

SL

1.147

1.114

0.703

0.697

61.3

62.6*

0.443

0.417

38.7

37.4*

2103-1906A Uni Lisfranc AL

SL

1.105

1.086

0.680

0.644

61.7

59.3

0.423

0.442

38.3

40.7

2803-0410A Bi Lisfranc 1.080

(0.007)

0.690

(0.015)

63.9*

(1.1)

0.3900

(0.014)

36.1*

(0.1)

0904-1924A Bi Chopart 1.158

(0.032)

0.694

(0.015)

59.9

(0.4)

0.464

(0.017)

40.1

(0.4)

3004-1102A Uni Chopart AL

SL

1.228

1.238

0.750

0.777

61.1

62.7*

0.478

0.462

38.9

37.3*

________________________________________________________ Chapter 4. 93

Table 4.4 Single and double support phase characteristics of the amputee subjects.

Standard deviations reported in brackets.* denotes parameter outside the 95% confidence interval of

normal population. AL denotes affected limb. SL denotes sound limb. CHC denotes time of contralateral

heel contact as a percentage of the gait cycle. Double support phase AL, indicates the double support

phase after affected limb heel contact. Similarly, double support SL, indicates the double support phase

after sound limb heel contact.

Single support Double SupportSubject CHC

(%GC) (sec) (%GC) (sec) (%GC)

Control 49.8

(0.2)

0.452

(0.029)

39.7

(0.8)

0.120

(0.014)

10.5

(0.9)

1004-1304A Bi MTP 49.7

(0.3)

0.467

(0.013)

40.2

(1.1)

0.114

(0.006)

9.9

(0.6)

2103-2116A Uni TMT AL

SL

47.8*

52.8*

0.444

0.460

38.0*

39.4

0.119

0.156

10.2

13.4*

2703-1903A Uni Lisfranc AL

SL

49.2*

50.6*

0.452

0.466

38.5

40.8

0.133

0.108

11.3

9.5

0704-0403A Uni Lisfranc AL

SL

48.9*

50.7*

0.416

0.443

36.5*

38.4

0.133

0.144

11.7

12.4*

2103-1906A Uni Lisfranc AL

SL

51.6*

48.5*

0.443

0.419

40.5

37.8*

0.116

0.113

10.6

10.2

2803-0410A Bi Lisfranc 50.4*

(0.1)

0.388

(0.014)

36.8*

(0.4)

0.147

(0.011)

14.0*

(1.4)

0904-1924A Bi Chopart 49.3*

(0.9)

0.464

(0.015)

39.9

(0.1)

0.123

(0.010)

10.6

(1.2)

3004-1102A Uni Chopart AL

SL

50.6*

49.5

0.461

0.478

37.0*

38.32

0.165

0.129

13.2*

10.3

________________________________________________________ Chapter 4. 94

Contralateral heel contact occurred at 49.8±0.2%GC for the normal population

and the 95%CI was very tight (49.4%GC to 50.2%GC). For the majority of unilateral

amputee subjects, affected limb contralateral initial contact occurred prematurely and

sound limb initial contact was delayed compared to normal population (Table 4.4).

However, for subject 2103-1906A the opposite affect was observed (Table 4.4). For the

bilateral Lisfranc amputee, contralateral heel contact was also delayed (50.4±0.1%GC).

Contralateral initial contact was more variable for the bilateral Chopart amputee with

significant differences observed on only one limb but on average, was premature

(49.3±0.9%GC).

Ground reaction force and centre of pressure excursion

The ground reaction force (GRF) and centre of pressure (CoP) excursion

patterns observed for the partial foot amputees were similar to those observed in the

normal population.

Figures 4.1 to 4.4 describe the body-mass-normalised, fore-aft and horizontal

GRF patterns for the bilateral amputees and both limbs of the unilateral amputees

compared to the 95% CI of the normal population. The timing of the first horizontal

shear force (Fx1) was delayed in the bilateral Lisfranc amputee (14±1%GC) as well as

on the affected limb of the unilateral Chopart (16%GC) amputee (Figure 4.1) compared

to the normal population (95%CI, 9%GC to 12%GC).

The magnitude of Fx1 was significantly smaller in the bilateral Lisfranc amputee

(-1.36±0.12N/kg) (Figure 4.2) compared to the normal population (95%CI, -1.56N/kg to

-2.63N/kg). In the bilateral Chopart amputee, the magnitude of the breaking force was

substantially smaller than normal for the left limb (-0.80N/kg) however, no clear peak

was observed for the right limb. Of particular interest is the small impulse in the

horizontal GRF observed between initial contact and mid-stance compared to that

observed from mid-stance until toe-off in the bilateral Chopart amputee (Figure 4.2). In

the normal population and the remaining amputee subjects, the impulses of these two

periods were relatively similar (Figure 4.1-4.2).

________________________________________________________ Chapter 4. 95

Figure 4.1 Fore-aft ground reaction force for the affected and sound limbs of the

unilateral amputee subjects relative to the normal population

10 20 30 40 50 60 70 80 90 100-3

-2

-1

0

1

2

3Fore-aft ground reaction force for affected limbs(-)

Fx

(N/k

g)

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

10 20 30 40 50 60 70 80 90 100-3

-2

-1

0

1

2

3Fore-aft ground reaction force for sound limbs (-)

Fx

(N/k

g)

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 96

Figure 4.2 Fore-aft ground reaction force for the bilateral amputee subjects relative to

the 95% confidence interval of the normal population.

The letters R and L before the subject codes denote right and left limbs.

The timing of the second horizontal GRF peak (Fx2) was premature on the

affected limbs of the unilateral TMT (48%GC) and Lisfranc cohort (48±3%GC)

compared to the normal population (95%CI, 50%GC to 54%GC) (Figure 4.1). The

magnitude of Fx2 was substantially smaller in the bilateral Lisfranc amputee

(1.21±0.03N/kg) compared to the normal population (95%CI, 1.65N/kg to 2.66N/kg)

(Figure 4.2).

The magnitude of the first vertical GRF peak (Fz1) was larger on the sound limb

of the Lisfranc cohort (12.92±0.60N/kg) compared to the normal population (95%CI,

10.20N/kg to 12.02N/kg) (Figure 4.3). The timing of Fz2 was delayed on both limbs of

the unilateral Chopart amputee (35±1%GC) (Figure 4.3) as well as in the bilateral

Chopart amputee (33±1%GC) compared to the normal population (95%CI, 23%GC to

31%GC) (Figure 4.4). Delays in the timing of Fz2 approached significance in the

bilateral Lisfranc amputee (31±2%GC) as did differences on the sound limb of the

unilateral TMT amputee (31%GC). Differences in the magnitude of Fz3 were

10 20 30 40 50 60 70 80 90 100-3

-2

-1

0

1

2

3Fore-aft ground reaction force for Bilateral amputees(-)

Fx

(N/k

g)

Gait Cycle [%]

R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 97

significant on the affected limbs of the unilateral TMT subjects 2703-1903A (9.95N/kg)

and 2103-1906A (9.51N/kg) (Figure 4.3) compared to the normal population (95%CI,

10.04N/kg to 11.96N/kg). Reductions in the magnitude of Fz3 approached significance

on the affected limb of the unilateral TMT amputee (10.20N/kg). On the right limb of

the bilateral Lisfranc amputee, reductions in the magnitude of Fz3 were significant only

on the right limb (9.44N/kg) and approached significance on the left limb (10.30N/kg)

(Figure 4.4).

Figure 4.3 Vertical ground reaction force for the bilateral amputee subjects relative to

the normal population.

The letters R and L prefixing the subject codes denotes right and left limb for each of the bilateral

amputees.

10 20 30 40 50 60 70 80 90 100

0

5

10

15Vertical ground reaction force for Bilateral amputees(-)

Fz

(N/k

g)

Gait Cycle [%]

R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 98

Figure 4.4 Vertical ground reaction force for the affected and sound limbs of the

unilateral amputee subjects relative to the normal population

10 20 30 40 50 60 70 80 90 100

0

5

10

15Vertical ground reaction force for affected limbs(-)

Fz

(N/k

g)

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

10 20 30 40 50 60 70 80 90 100

0

5

10

15Vertical ground reaction force for sound limbs (-)

Fz

(N/k

g)

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 99

No significant reductions in the total excursion of the centre of pressure,

normalised by shoe length (SL), were observed compared to the normal population

(95%CI, 95.02%SL to 103.24%SL). On the sound limbs of the unilateral amputees, a

relatively normal, linear excursion of the CoP was observed, except in the unilateral

Chopart amputee (Figure 4.5). On the sound limb of the unilateral Chopart amputee the

GRF progressed very rapidly until about mid-stance where it remained at a relatively

constant lever-arm until approximately 50%GC (Figure 4.5).

On the affected limbs of the unilateral TMT and Lisfranc amputees, the CoP

progressed relatively normally until foot-flat when the excursion of the CoP was at

about 30-40%SL (Figure 4.5-4.6). The GRF then remained at a relatively fixed lever-

arm until about 45%GC (Figures 4.5 and 4.6). The CoP progressed rapidly during the

propulsive phase as evidenced clearly on the affected limb of the unilateral TMT

amputee (Figure 4.5) and the bilateral Lisfranc amputee (Figure 4.6). The profiles

observed in the bilateral MTP amputee, were similar to those of the normal population

(Figure 4.6). The CoP excursion profiles observed on the affected limbs of the Chopart

amputees were distinctly different from those observed in the TMT and Lisfranc

amputees (Figures 4.5-4.6). On the affected limb of the unilateral Chopart amputee, the

progression of the CoP was relatively linear, as in the normal population. However in

the bilateral Chopart amputee, an extraordinary progression of the CoP was observed.

Irrespective of the profiles observed in these individuals, the excursion of the CoP

commensurate with the peak GRF, were similar to normal.

________________________________________________________ Chapter 4. 100

Figure 4.5 Sagittal plane centre of pressure excursion (as a percentage of shoe length,

SL) for the affected and sound limbs of the unilateral amputee subjects relative to the

normal population.

10 20 30 40 50 60 70 80 90 100-20

0

20

40

60

80

100

120

Centre of pressure excursion for affected limbs(-)

CoP

(%S

L)

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

10 20 30 40 50 60 70 80 90 100-20

0

20

40

60

80

100

120

Centre of pressure excursion for sound limbs (-)

CoP

(%

SL)

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 101

Figure 4.6 Sagittal plane centre of pressure excursion profile (as a percentage of shoe

length, SL) for the bilateral amputee subjects relative to the normal population.

The letters R and L prefixing the subject codes denote the right and left limb, respectively.

Repeatability of kinematic, kinetic and electromyographic data

The repeatability of kinematic, kinetic and electromyographic data was assessed

using the coefficient of variation (CV) (Winter, 1991; Winter, 1984) and the coefficient

of multiple determination (CMC) (Kadaba et al., 1989). The CV is expressed as a

percentage of the mean value of the signal. In effect, it is a measure of the variability-to-

signal ratio (Winter, 1991). The CV was found to be inadequate when the mean of the

signal was close to zero and gave abnormally large values. The fore-aft GRF or hip joint

moment profiles are typical examples of data that is symmetrical about zero. The CMC

is an alternate technique for describing the variability of waveforms that is not affected,

like the CV, by waveforms with a mean close to zero. The CMC is expressed as a ratio

where one indicates a perfect match between waveforms. For the normal population, the

CV and CMC measured of variability have been presented in Tables 4.5 and 4.6. Due to

the extensive measures of intra-subject variability for the amputee subjects, these data

have been presented as part of the individual gait reports (Appendix I).

10 20 30 40 50 60 70 80 90 100-20

0

20

40

60

80

100

120

Centre of pressure excusrion for Bilateral amputees(-)

CoP

(%

SL)

Gait Cycle [%]

R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 102

Table 4.5 Inter-subject variability of the kinematic and kinetic patterns of the normal

population.

Angle Moment Power

CV(%) CMC CV(%) CMC CV(%) CMC

Ankle 81 0.85 24 0.96 166 0.88

Knee 20 0.95 168 0.83 161 0.74

Hip 34 0.91 1037 0.82 134 0.71

Table 4.6 Inter-subject variability of the EMG patterns of the normal population.

CV(%) CMC

Soleus 76 0.47

Gastrocnemius Lateral Head 97 0.43

Gastrocnemius Medial Head 87 0.47

Tibialis Anterior 53 0.69

Biceps Femoris Long Head 115 0.25

Vastus Lateralis 87 0.43

Kinematic

While the majority of kinematic abnormalities observed occurred at the ankle,

many individuals displayed idiosyncrasies affecting the hip and knee joints.

The kinematic pattern of hip motion for both the sound and affected limbs of the

unilateral, and both limbs of the bilateral, amputees closely resembled that observed for

the normal population (Figures 4.7 and 4.8). For the affected limbs in all but the

bilateral MTP amputee (Figure 4.8) and the unilateral Chopart amputee (Figure 4.7), the

hip extended immediately after heel contact.

________________________________________________________ Chapter 4. 103

Figure 4.7 Sagittal plane hip flexion and extension angles for the affected and sound

limbs of the amputee subjects relative to the normal population

Positive values along the y-axis indicate hip flexion. Negative values on the y-axis indicate hip extension.

10 20 30 40 50 60 70 80 90 100-40

-20

0

20

40

Hip Angle Affected limbs (-)

(Deg

.) F

lex.

>

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

10 20 30 40 50 60 70 80 90 100-40

-20

0

20

40

Hip Angle Sound Limb (-)

(Deg

.) F

lex.

>

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 104

Figure 4.8 Sagittal plane hip flexion and extension angles for the bilateral amputee

subjects relative to the normal population

Positive values along the y-axis indicate hip flexion. Negative values on the y-axis indicate hip extension.

Premature maximum hip extension was observed on the affected limbs of the

combined unilateral Lisfranc cohort (49±0%GC) (Figure 4.7) and the bilateral Chopart

amputee (49±1%GC) (Figure 4.8) with respect to the normal population (95%CI,

50%GC to 52%GC). In contrast, maximum hip extension was delayed on the sound

limb of the TMT amputee (54%GC), the Lisfranc cohort (53±1%GC), the bilateral

Lisfranc amputee (54±1%GC) and the affected limb of the unilateral Chopart amputee

(53±0%GC) with respect to the normal population (Figure 4.7). The magnitude of

maximum hip extension was significantly larger on the affected limb of the unilateral

Chopart amputee (-21.27± 0.71°) compared to the normal population (95%CI, -4.03° to

–18.16°). In the bilateral Lisfranc amputee, reductions in maximum hip extension (-

2.72± 2.02°) approached significance.

The hip flexion/extension angle at toe-off was substantially less than the 95% CI

of the normal population (-10.63° to 4.39°) on the affected limb of the unilateral

10 20 30 40 50 60 70 80 90 100-40

-20

0

20

40

Hip Angle Bilateral limbs (-)

(Deg

.) F

lex.

>

Gait Cycle [%]

R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 105

Chopart amputee (-14.42±0°) (Figure 4.7) and substantially larger in the bilateral

Lisfranc amputee (7.07±1.85°) (Figure 4.8).

The patterns of knee motion observed on the sound and affected limbs were very

similar to that of the normal population. For the bilateral MTP subject, substantial knee

flexion at initial contact (9.27±2.29°) was observed compared to the normal population

(95%CI, -4.56° to 5.57°) (Figure 4.10). Excessive stance phase knee flexion was also

observed in the bilateral MTP amputee (26.37±1.85°) compared to the normal

population (95%CI, 10.82° to 22.71°).

Substantial reductions in stance phase knee flexion were observed on the

affected limb of the TMT amputee (6.55°) (Figure 4.9) and the bilateral Chopart

amputee (8.00±2.42°) (Figure 4.10). In contrast, excessive stance phase knee flexion

was observed on the sound and affected limbs of a single unilateral Lisfranc amputee

(2703-1903A) (29.19° and 24.62°, respectively) (Figure 4.9). The timing of stance

phase knee flexion was substantially delayed in the bilateral Chopart amputee

(19±1%GC) (Figure 4.10) compared to the normal population (95%CI, 13%GC to

17%GC).

Knee hyperextension was observed on the affected limb of the unilateral

Chopart (Figure 4.9) and the bilateral Chopart amputees (Figure 4.10), which seemed to

delay the initiation of knee flexion into swing phase to varying degrees (Figure 4.9).

The knee flexion angle at toe-off on the affected limb of the unilateral Chopart amputee

(23.11°) and in the bilateral Chopart amputee (25.75 ±1.92°) were marginally less than

the normal population (95%CI, 26.20° to 46.97°).

Maximum knee flexion was delayed in the bilateral Lisfranc amputee

(75±0%GC) and difference on the sound limb of the unilateral TMT amputee (74%GC)

approached significance in comparison to the normal population (95%CI, 70%GC to

74%GC).

________________________________________________________ Chapter 4. 106

Figure 4.9 Sagittal plane knee flexion/extension angles for the affected and sound

limbs of the unilateral amputee subjects relative to the normal population

Positive values along the y-axis indicate knee flexion. Negative values on the y-axis indicate knee

extension.

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0

20

40

60

80Knee Angle Affected Limb (-)

(Deg

.) F

lex.

>

Gait Cycle [%]

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0

20

40

60

80Knee Angle Sound Limb (-)

(Deg

.) F

lex.

>

Gait Cycle [%]

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________________________________________________________ Chapter 4. 107

Figure 4.10 Sagittal plane knee flexion angles for the bilateral amputee subjects

relative to the normal population

Positive values along the y-axis indicate knee flexion. Negative values on the y-axis indicate knee

extension.

At initial contact, substantial dorsiflexion was observed in the bilateral MTP

amputee (5.38±1.00°) (Figure 4.12) and on the affected limbs of a number of Lisfranc

amputees (Figure 4.11) compared to the normal population (95%CI, -13.15° to 3.67°).

The mean dorsiflexion angle at initial contact for the cohort of Lisfranc amputees

(5.85±3.39°) was substantially larger than normal due to the excessive dorsiflexion

observed in subjects 2103-1906A (9.53°) and 2703-1903A (5.18°).

The timing of initial plantarflexion was substantially delayed on the affected

limb of the unilateral Chopart amputee (12%GC) and on both limbs of the bilateral

Chopart amputee (12±1%GC) compared to the normal population (95%CI, 5%GC to

9%GC) (Figure 4.12). For the bilateral Chopart amputee, the mean plantarflexion angle

obtained (-5.06±1.45°) was marginally less than that observed in the normal population

(95%CI, -16.74° to -5.53°). For the bilateral MTP amputee similar reductions in the

mean initial plantarflexion peak were observed (-3.28± 3.14°).

10 20 30 40 50 60 70 80 90 100-20

0

20

40

60

80

Knee Angle Bilateral Amputees(-)

(Deg

.) F

lex.

>

Gait Cycle [%]

R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 108

Peak dorsiflexion was substantially delayed on the affected limbs of all subjects

except the bilateral MTP amputee. In comparison to the normal population (95%CI,

40%GC to 49%GC) peak dorsiflexion was delayed on the affected limb of the unilateral

TMT (51±0%GC) and Lisfranc (51±2%GC) amputees. Differences in the unilateral

Chopart amputee also bordered significance (50±0%GC). Peak dorsiflexion was also

delayed in the bilateral Lisfranc (55±5%GC) and Chopart (54±0%GC) amputees

compared to the normal population (Figure 4.12). The magnitude of peak dorsiflexion

was substantially larger than the normal (95%CI, 4.17° to 12.17°) in the bilateral MTP

amputee (17.27±2.43°) and the affected limbs of the unilateral TMT (13.91°) and

Lisfranc group (14.00±2.93°). Peak dorsiflexion was substantially reduced in the

unilateral Chopart amputee on both the sound (2.41°) and affected limbs (0.26°)

compared to the normal population (Figure 4.11-4.12).

Significant reductions in the plantarflexion angle at toe-off were observed on the

affected limbs of the unilateral TMT (-4.20°), Lisfranc (-0.93±3.60°) and Chopart (-

4.89°) amputees as well as the bilateral MTP (-2.27±2.14°), Lisfranc (1.28±8.42°) and

Chopart (1.76±1.17°) amputees (Figures 4.11-4.12).

Substantial reductions in maximum plantarflexion were also observed on the

affected limb of the unilateral Chopart amputee (-9.25°) and the Lisfranc cohort (-

9.22±4.59°) compared to the normal population (95%CI, -15.95° to -32.35°). Maximum

plantarflexion was also substantially reduced in the bilateral MTP (-9.65±1.88°),

Lisfranc (-11.53±1.28°) and Chopart amputees (-4.00±1.67°).

________________________________________________________ Chapter 4. 109

Figure 4.11 Sagittal plane ankle dorsiflexion/plantarflexion angles for the sound and

affected limbs of the unilateral amputee sample

Positive values along the y-axis indicate ankle dorsiflexion or flexion. Negative values on the y-axis

indicate ankle plantarflexion or extension.

10 20 30 40 50 60 70 80 90 100-40

-30

-20

-10

0

10

20Ankle Angle Affected Limbs (-)

(Deg

.) F

lex.

>

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

10 20 30 40 50 60 70 80 90 100-40

-30

-20

-10

0

10

20Ankle Angle Sound Limbs (-)

(Deg

.) F

lex.

>

Gait Cycle [%]

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________________________________________________________ Chapter 4. 110

Figure 4.12 Sagittal plane ankle dorsiflexion/plantarflexion angles for the bilateral

amputees and those with Clamshell PTB prostheses

Positive values along the y-axis indicate ankle dorsiflexion or flexion. Negative values on the y-axis

indicate ankle plantarflexion or extension.

10 20 30 40 50 60 70 80 90 100-40

-30

-20

-10

0

10

20

30Ankle Angle Bilateral amputees (-)

(Deg

.) F

lex.

>

Gait Cycle [%]

R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancControl ±2SD

10 20 30 40 50 60 70 80 90 100-40

-30

-20

-10

0

10

20

30Ankle Angle Chopart amputees with Clamshell PTB prostheses (-)

(Deg

.) F

lex.

>

Gait Cycle [%]

R0904-1924A - ChopartL0904-1924A - Chopart3004-1102A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 111

Maximum plantarflexion was substantially delayed in the bilateral Lisfranc

(72±1%GC) and Chopart (69±1%GC) amputees compared to normal population

(95%CI, 62%GC to 66%GC). Similar delays were also observed on both limbs of the

TMT amputee (67±0%GC) and the affected limb of the unilateral Chopart amputee

(69.0%GC). Delays in the timing of maximum plantarflexion were commensurate with

delays in the timing of toe-off on the sound limb of the unilateral TMT and bilateral

Lisfranc amputees.

Two distinct kinematic profiles were observed during swing phase on the

affected limb of the unilateral amputees (Figure 4.11) which, appear to be related to the

maximum plantarflexion angle and initial contact angle.

Kinetic

Ankle joint moments

Ankle moment data has been presented in Figures 4.13 and 4.14. Following

initial contact, a dorsiflexion moment was observed in the partial foot amputees as in

the normal population. The peak dorsiflexion moment was delayed in the bilateral

Lisfranc amputee (7±1%GC) and was premature on the sound limb of the TMT

amputee (4%GC). Compared to the normal population (95%CI, 4%GC to 7%GC)

delays in the peak dorsiflexion moment approached significance in the bilateral Lisfranc

amputee (7±1%GC) and on the affected limb of the Lisfranc cohort (7±2%GC) due to

differences in subjects 0704-0403A (8%GC) and 2103-1906A (7%GC). The magnitude

of the dorsiflexion moment was significantly increased on the affected limb of subject

2103-1906A (-0.45Nm/kg) compared to the normal population (95%CI, -0.22Nm/kg to

–0.05Nm/kg).

The ankle moment patterns on the sound limbs of subjects 3004-1102A and

2103-2116A were distinctly different, during the loading and mid-stance phases, from

those observed in the normal population (Figure 4.13).

________________________________________________________ Chapter 4. 112

Figure 4.13 Sagittal plane ankle moments for the affected and sound limbs of the

unilateral amputee sample.

Positive values along the y-axis indicate an ankle extension moment. Negative values on the y-axis

indicate an ankle flexion moment.

10 20 30 40 50 60 70 80 90 100-0.5

0

0.5

1

1.5

2

2.5Ankle Moment Affected Limbs (-)

(Nm

/kg)

Ext

. >

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - LisfrancControl ±2SD

10 20 30 40 50 60 70 80 90 100-0.5

0

0.5

1

1.5

2

2.5Ankle Moment Sound Limbs (-)

(Nm

/kg)

Ext

. >

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 113

Figure 4.14 Sagittal plane ankle moments for the bilateral amputee sample.

Positive values along the y-axis indicate an ankle extension or plantarflexion moment. Negative values on

the y-axis indicate an ankle flexion or dorsiflexion moment.

One of the most startling differences about the gait of partial foot amputees was

the reduction in the magnitude of the plantarflexion moment peak (Figures 4.13 and

4.14). In comparison to the normal population (95%CI, 1.49Nm/kg to 1.95Nm/kg),

significant reductions in the peak plantarflexion moments were observed on the affected

limbs of the Lisfranc cohort (0.85±0.30Nm/kg), the TMT amputee (0.85Nm/kg) and

both limbs of the bilateral Lisfranc amputee (0.59±0.22Nm/kg).

The ankle moment data for the affected limbs of the Chopart amputees were

calculated using a standard linked-segment model because these data could not be

calculated given the basic assumptions governing partial foot model-B. Given that the

ankle joint moment equation is dominated by the magnitude and lever-arm of the

vertical GRF and, therefore, robust to errors in the anthropometric, angular and linear

input data the joint moment data were considered to be accurate. For the unilateral

10 20 30 40 50 60 70 80 90 100-0.5

0

0.5

1

1.5

2

2.5Ankle Moment Bilateral Amputees(-)

(Nm

/kg)

Ext

. >

Gait Cycle [%]

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________________________________________________________ Chapter 4. 114

Chopart amputee, anthropometric characteristics of the sound limb were used. For the

bilateral Chopart amputee, the anthropometric characteristics for each affected limb

were maintained, however the prosthesis and footwear were not considered.

The dorsiflexion moment peak observed on the left limb of the bilateral Chopart

amputee was absent and on the right, the dorsiflexion moment was relatively prolonged

(Figure 4.15). The relatively linear moment pattern observed in the normal population

was not observed in the unilateral Chopart amputee or on the right limb of the bilateral

Chopart amputee (Figure 4.15).

Figure 4.15 Sagittal plane ankle moments for the affected limbs of the Chopart

amputees

Positive values along the y-axis indicate an ankle extension or plantarflexion moment. Negative values on

the y-axis indicate an ankle flexion or dorsiflexion moment.

10 20 30 40 50 60 70 80 90 100-0.5

0

0.5

1

1.5

2

2.5Ankle Moment Chopart Amputees (-)

(Nm

/kg)

Ext

. >

Gait Cycle [%]

3004-1102A - Chopart R0904-1924A - ChopartL0904-1924A - ChopartControl ±2SD

________________________________________________________ Chapter 4. 115

The ankle plantarflexion moment peak observed on the affected limb of the

unilateral Chopart amputee (1.72N/kg) was comparable to that observed in the normal

population (Figure 4.15). For the bilateral Chopart amputee, the peak plantarflexion

moments were reduced on the right limb (1.39Nm/kg) and bordered the 95%CI on the

left (1.52Nm/kg) (Figure 4.15). The timing of the plantarflexion moment peak observed

on the affected limb of the unilateral Chopart amputee (50%GC) bordered the 95%CI of

the normal population (45.12%GC to 49.63%GC) (Figure 4.15).

Knee joint moments

A normal knee moment pattern was observed on the sound limb of all unilateral

partial foot amputees and the timing and magnitude of the moment peaks were

comparable to the range of values observed in the normal population (Figure 4.16).

The maximum extension moment (KM2), associated with stance phase knee

flexion, was delayed in the bilateral Lisfranc (16±1%GC) and Chopart amputees

(18±0%GC) compared to the normal population (95%CI, 12%GC to 15%GC) (Figure

4.17). The magnitude of the KM2 peak was increased in the bilateral MTP amputee

(0.95±0.10Nm/kg) and decreased the bilateral Chopart amputee (0.16±0.15Nm/kg)

compared to the normal cohort (95%CI, 0.31Nm/kg to 0.86Nm/kg) (Figure 4.17).

Reductions in the magnitude of the KM2 peak approached significance on the affected

limb of the unilateral TMT (0.32Nm/kg) and Chopart amputees (0.33Nm/kg) (Figure

4.16).

The timing of the knee flexion moment associated with knee flexion into swing

phase (KM3) was significantly delayed on the affected limb of the unilateral Chopart

amputee (47%GC) compared to the 95%CI of the normal cohort (40%GC to 46%GC).

The KM3 moment peak was absent on the affected limb of the unilateral TMT (Figure

4.16) and bilateral Lisfranc amputees (Figure 4.17) and therefore, the timing and the

magnitude of this moment peak were unable to be identified.

________________________________________________________ Chapter 4. 116

Figure 4.16. Sagittal plane knee moment for the affected and sound limbs of the

unilateral amputee sample

Positive values along the y-axis indicate a knee extension moment. Negative values on the y-axis indicate

a knee flexion moment.

10 20 30 40 50 60 70 80 90 100-1.5

-1

-0.5

0

0.5

1

1.5

2Knee Moment Affected limbs (-)

(Nm

/kg)

Ext

. >

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

10 20 30 40 50 60 70 80 90 100-1.5

-1

-0.5

0

0.5

1

1.5

2Knee Moment Sound Limbs (-)

(Nm

/kg)

Ext

. >

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 117

Figure 4.17 Sagittal plane knee moment for the bilateral amputees

Positive values along the y-axis indicate a knee extension moment. Negative values on the y-axis indicate

a knee flexion moment.

The knee flexion moment peak was significantly decreased on the affected limb

of the unilateral TMT amputee and Lisfranc amputees 2103-1906A (-0.05Nm/kg) and

0704-0403A (-0.04Nm/kg) as well as in the bilateral Lisfranc amputee compared to

normal population (95%CI, -0.76Nm/kg to -0.27Nm/kg). The magnitude of the KM3

peak observed in subject 2703-1903A (-0.39Nm/kg) was comparable to normal (Figure

4.16). The knee flexion moment peaks observed on the affected limbs of the unilateral

Chopart (-0.75Nm/kg) and bilateral Chopart amputees (-0.63Nm/kg ±0.24Nm/kg) were

quite substantial and bordered the 95%CI of the normal population (Figures 4.16-4.17).

The swing phase knee moments observed in the amputee subjects were

comparable to those of the normal population.

Hip joint moments

The hip joint moments have been presented in Figures 4.18 and 4.19.

10 20 30 40 50 60 70 80 90 100-1.5

-1

-0.5

0

0.5

1

1.5

2

Knee Moment Bilateral Amputees(-)

(Nm

/kg)

Ext

. >

Gait Cycle [%]

R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 118

Figure 4.18 Sagittal plane hip moment for the affected and sound limbs of the unilateral

amputee sample

Positive values along the y-axis indicate a hip extension moment. Negative values on the y-axis indicate a

hip flexion moment.

10 20 30 40 50 60 70 80 90 100-1

-0.5

0

0.5

1

1.5

2Hip Moment Affected limbs (-)

(Nm

/kg)

Ext

. >

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

10 20 30 40 50 60 70 80 90 100-1

-0.5

0

0.5

1

1.5

2Hip Moment Sound Limbs (-)

(Nm

/kg)

Ext

. >

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 119

Figure 4.19 Sagittal plane hip moment for the bilateral amputees

Positive values along the y-axis indicate a hip extension moment. Negative values on the y-axis indicate a

hip flexion moment.

The basic pattern of the hip moment profile was relatively normal for the

amputee subjects although the patterns observed were variable reflecting the

heterogeneous nature of the sample. Many individuals maintained an extension moment

about the hip joint well into stance phase and in some cases until the propulsive phase of

gait (Figures 4.18-4.19). The stance phase hip extension moment peaks (HM1) were

relatively poorly defined in both the normal and amputee populations. The HM1 peaks

occurred bilaterally at about 10-15% of the gait cycle commensurate with contralateral

initial contact. Substantial HM1 peaks were observed on the affected limb in subject

2703-1903A and on the sound limbs of subjects 2103-2116A and 2103-1906A

compared to those observed in the normal population (Figure 4.18). In the bilateral

Lisfranc and Chopart amputees, the hip extension moments observed on the left limb

were substantially larger than that observed on the right limb (Figure 4.19).

The hip flexion moment peak (HM2) was well defined in both the normal

population and the amputee subjects. Compared to the 95%CI of the normal population

(47%GC to 56%GC) the HM2 peak was substantially delayed on both the sound

10 20 30 40 50 60 70 80 90 100-1

-0.5

0

0.5

1

1.5

2Hip Moment Bilateral Amputees(-)

(Nm

/kg)

Ext

. >

Gait Cycle [%]

R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 120

(63%GC) and affected limbs (60%GC) of the unilateral TMT amputee (Figure 4.18).

Similar delays were observed unilaterally in the bilateral Lisfranc (63.0%GC) and

Chopart (61.0%GC) amputees (Figure 4.19) and on the affected limbs of subjects 2703-

1903A and 2103-1906 (Figure 4.18).

During swing phase, no differences in the hip moment patterns or extension

moment peaks were observed between the amputee subjects and the normal population

(Figure 4.18 and 4.19).

Ankle joint powers

Ankle power data have been presented in Figures 4.20-4.22. A relatively normal

pattern of power absorption then generation was observed on the sound limb of the

unilateral amputees as well as all affected limbs.

Substantial power absorption was observed following initial contact on the

affected limb of subject 2103-1906A (Figure 4.20). Peak power absorption (AP1) was

not well defined in either the normal or amputee subjects however, the AP1 peak

seemed to be delayed on the affected limbs of the TMT and Lisfranc amputees

compared to the normal population (Figures 4.20-4.21). The magnitude of peak power

absorption seemed to be largely unaffected except for the affected limb of subject 2703-

1903A (Figure 4.20).

The ankle power generation peak associated with push-off (AP2), was delayed

on the sound limb of the TMT amputee (57%GC) and both limbs of the bilateral

Lisfranc amputee (59±4%GC) compared to the normal population (95%CI, 52%GC to

55%GC) (Figure 4.20-4.21). Delays in the timing of the AP2 peak approached

significance on the sound limb of the Lisfranc cohort (55±0%GC) and the unilateral

Chopart amputee (55%GC) (Figure 4.20-4.21).

________________________________________________________ Chapter 4. 121

Figure 4.20 Sagittal plane ankle power for the affected and sound limbs of the

unilateral amputee sample

Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power

absorption.

10 20 30 40 50 60 70 80 90 100-2

0

2

4

6Ankle Power Affected Limbs(-)

(Wat

ts/k

g) G

en.

>

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - LisfrancControl ±2SD

10 20 30 40 50 60 70 80 90 100-2

0

2

4

6Ankle Power Sound Limbs (-)

(Wat

ts/k

g) G

en.

>

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 122

Figure 4.21 Sagittal plane ankle power for the bilateral amputees

Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power

absorption.

Once the metatarsal heads were compromised, the magnitude of the AP2 peak

was significantly reduced on the affected limbs of the unilateral TMT amputee

(0.72W/kg) and the Lisfranc cohort (0.91±0.39W/kg) as well as in the bilateral Lisfranc

amputee (0.41±0.41W/kg) compared to normal cohort (95%CI, 2.56W/kg to 5.06W/kg)

(Figures 4.21-4.22). Power generation observed in the bilateral MTP amputee flanked

the lower boundary of the 95%CI but was not significantly different from the normal

population (Figure 4.22). Power generation on the sound limb of the unilateral amputee

subjects was comparable to that observed in the normal population (Figure 4.21).

Figure 4.22 illustrates the power generation observed in the Chopart amputees

using a conventional linked-segment model. The data was derived using the

assumptions previously described for the ankle moment calculation for these amputees.

10 20 30 40 50 60 70 80 90 100-2

0

2

4

6Ankle Power Bilateral Amputees(-)

(Wat

ts/k

g) G

en.

>

Gait Cycle [%]

1004-1307A - MTP 2803-0410A - Lisfranc Control ±2SD

________________________________________________________ Chapter 4. 123

Figure 4.22 Sagittal plane ankle power for the affected limbs of the Chopart amputees

Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power

absorption.

The timing of the AP1 peaks appeared to be delayed in the bilateral Chopart

amputee. Similarly, the timing of the AP2 peak was significantly delayed in both the

bilateral Chopart (57±0%GC) and unilateral Chopart amputees (56%GC) compared to

the normal population (Figure 4.22). Reductions in work across the ankle joint during

push-off were similar to those observed in the Lisfranc and TMT amputees. The

unilateral Chopart and bilateral Chopart amputees generated 0.78W/kg and

0.32±0.17W/kg, respectively (Figure 4.22).

Knee joint powers

Figures 4.23 and 4.24 illustrate the work observed across the knee joint.

Following initial contact, a period of power absorption describes eccentric activity of

the knee extensor musculature to control stance phase knee flexion (KP1). Normal

power absorption (KP1) was observed on the sound limb of the amputee subjects except

in subject 2703-1903A where excessive eccentric activity was observed (-1.84W/kg)

compared to the normal population (95%CI, -1.48W/kg to -0.24W/kg). Normal power

10 20 30 40 50 60 70 80 90 100-2

0

2

4

6Ankle Power Chopart Amputees (-)

(Wat

ts/k

g) E

xt.

>

Gait Cycle [%]

3004-1102A - Chopart R0904-1924A - ChopartL0904-1924A - ChopartControl ±2SD

________________________________________________________ Chapter 4. 124

absorption was observed on the affected limbs of the unilateral Lisfranc cohort (-

1.03±0.26W/kg) and bilateral MTP amputee (1.46±0.21W/kg). In contrast, significantly

less power absorption was observed on the affected limbs of the unilateral TMT (-

0.18W/kg) and Chopart amputees (-0.21W/kg) compared to the normal population.

Reductions in the KP1 peak approached significance in the bilateral Lisfranc (-

0.38±0.08W.kg) and Chopart amputees (-0.27W/kg). The KP1 peak was normally timed

(95%CI, 9%GC to 11%GC) except in the bilateral Chopart amputee where delays

appeared to be significant bilaterally, but only a true peak existed for the right limb

(14%GC).

The knee extensor musculature contract concentrically to extend the knee into

mid-stance following the relatively flexed position attained during stance phase knee

flexion (KP2). Typically, changes in KP2 are commensurate with changes in KP1. For

example, the bilateral MTP amputee (0.86±0.11W/kg) and Lisfranc subject 2703-1903A

(0.69W/kg) displayed greater power generation (KP2) than that observed in the normal

population (95%CI, 0.02W/kg to 0.67W/kg). This exaggerated power generation would

be required to extend the knee from the relatively large flexion angle attained during

stance phase compared to the normal population (Figure 4.9 and 4.10).

Power generation across the knee during the propulsive phase of gait was

comparable to normal on the sound limbs of the unilateral amputee subjects and the

bilateral MTP amputee (Figures 4.23-4.24). Normal power generation was also

observed across the knee joint on the affected limb of subject 2703-1903A, which was

in stark contrast to the negligible work observed in the other Lisfranc and TMT

amputees. In comparison to the normal population, significantly more power was

generated across the knee during the propulsive phase on the affected limb of the

unilateral Chopart amputee. Substantial power generation was also observed in the

bilateral Chopart amputee at this time however, these differences were not significantly

different from the normal population (Figure 4.24).

________________________________________________________ Chapter 4. 125

Figure 4.23. Sagittal plane knee power for the affected and sound limbs of the unilateral

amputee sample

Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power

absorption.

10 20 30 40 50 60 70 80 90 100-2

-1

0

1

2

3Knee Power Affected limbs (-)

(Wat

ts/k

g) G

en.

>

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

10 20 30 40 50 60 70 80 90 100-2

-1

0

1

2

3Knee Power Sound Limbs (-)

(Wat

ts/k

g) G

en.

>

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 126

As the knee continues to flex, power was absorbed by the knee extensors during

push off (KP3). Peak power absorption at this time was delayed on the sound limb of

the unilateral TMT (66%GC) and Lisfranc subject 2103-1906A (65%GC) compared to

normal (Figure 4.24). KP3 appeared to be comparably delayed on the affected limb of

the unilateral Chopart amputee (66%GC) however, this peak was not well defined

(Figure 4.24). The magnitude of KP3 was comparable to normal except on the affected

limb of subject 2103-1906A (Figure 4.23).

No significant differences in the swing phase powers or the timing and

magnitude of KP4 were observed indicating relatively normal power absorption by the

hamstrings to decelerate the leg segment into full extension.

Figure 4.24 Sagittal plane knee power for the bilateral amputees

Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power

absorption.

10 20 30 40 50 60 70 80 90 100-2

-1

0

1

2

3

Knee Power Bilateral Amputees(-)

(Wat

ts/k

g) G

en.

>

Gait Cycle [%]

R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 127

Hip joint powers

Substantial differences in work across the hip joint were observed on both the

sound and affected limbs of the amputee subjects compared to normal (Figures 4.25 and

4.26). The mechanical power patterns observed at the hip were extremely variable,

especially during the beginning of stance phase where a brief period of power

generation describes work done by the hip extensors as the hip joint extends as the knee

flexes (HP1). The HP1 peak was not well defined in the normal population or among

the amputee subjects. In the normal population, 95% of the HP1 peaks occurred within

the ranged of 0.38W/kg to 0.70W/kg. The power generated on the sound limb during

HP1 was substantially larger than normal for the unilateral TMT (1.21W/kg) and

Chopart amputees (0.86W/kg) as well as Lisfranc subject 2103-1906A (1.14W/kg)

(Figure 4.25). Substantial power generation was also observed on the sound limb of

subject 2703-1903A (0.65W/kg) but was not significantly greater than normal.

Similarly, substantial power was also generated on the affected limbs of the unilateral

Chopart amputee (0.86W/kg), Lisfranc subject 2703-1903A (1.66W/kg) and 2103-

1906A (0.76W/kg) (Figure 4.25). For the bilateral amputee subjects, HP1 was

significantly larger than normal on the left limb of subject 2803-0410A (1.26W/kg)

however, these differences were not observed bilaterally (Figure 4.26). Relatively

substantial power generation was also observed during this time on both limbs of the

bilateral Chopart amputee (Figure 4.26). HP1 occurred at about 15%GC in the entire

amputee population except on the affected limb of the unilateral Chopart amputee

(20%GC). The normal timing of HP1 was difficult to establish given the poorly defined

power generation peak, but the timing of this peak does not seem to be abnormal in the

amputee population.

Relatively normal power absorption was observed by the hip flexors to

decelerate the backward rotating thigh during the middle of the gait cycle (HP2).

However, HP2 was delayed on the sound limb of the TMT subject (55%GC) and on the

affected limb of the unilateral Chopart amputee (49%GC) compared to normal (95%CI,

43%GC to 48%GC) (Figure 4.25). Similar delays were also observed in isolation on the

left limbs of the bilateral Lisfranc and Chopart amputees, which approached

significance (Figure 4.26).

________________________________________________________ Chapter 4. 128

Figure 4.25 Sagittal plane hip power for the affected and sound limbs of the unilateral

amputee sample

Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power

absorption.

10 20 30 40 50 60 70 80 90 100-1

-0.5

0

0.5

1

1.5

2

2.5Hip Power Affected limbs (-)

(Wat

ts/k

g) G

en.

>

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

10 20 30 40 50 60 70 80 90 100-1

-0.5

0

0.5

1

1.5

2

2.5Hip Power Sound Limbs (-)

(Wat

ts/k

g) G

en.

>

Gait Cycle [%]

2103-2116A - TMT 0704-0403A - Lisfranc2703-1903A - Lisfranc2103-1906A - Lisfranc3004-1102A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 129

Figure 4.26 Sagittal plane hip power for the bilateral amputees

Positive values along the y-axis indicate power generation. Negative values on the y-axis indicate power

absorption.

Good power generation was observed on both the sound and affected limbs by

the hip flexor muscles to advance the lower limb forward during the terminal stages of

the propulsive phase (HP3). Delays in the timing of HP3 approached significance on the

sound limbs of the unilateral TMT (65%GC) and Lisfranc amputees (65±2%GC) and

both limbs of the bilateral Lisfranc amputee (66±2%GC) compared to normal (95%CI,

58%GC to 64%GC). HP3 was normally timed on the affected limb of the unilateral

amputee subjects (Figure 4.25).

The magnitude of HP3 was marginally larger than that of the normal population

(95%CI, 0.46W/kg to 1.27W/kg) on the affected limb of subject 2103-1906A

(1.34W/kg). The magnitude of HP3 was comparable to normal on both the sound and

affected limbs of the other amputee subjects (Figures 4.25-4.26).

No significant differences in power generation across the hip joint were

observed during terminal swing (HP4) except in subject 0704-0403A. In this subject,

10 20 30 40 50 60 70 80 90 100-1

-0.5

0

0.5

1

1.5

2

2.5

Hip Power Bilateral Amputees(-)

(Wat

ts/k

g) G

en.

>

Gait Cycle [%]

R1004-1307A - MTP L1004-1307A - MTP R2803-0410A - LisfrancL2803-0410A - LisfrancR0904-1924A - Chopart L0904-1924A - Chopart Control ±2SD

________________________________________________________ Chapter 4. 130

power generation across the hip joint was 0.38W/kg and 0.56W/kg for the affected and

sound limbs, respectively (Figure 4.25).

Electromyography

Electromyography is a useful means of identifying abnormal muscle activity and

provides useful information, which aids the interpretation of joint moments and powers.

As a means of identifying abnormal muscle activity, 'normal' muscle function has been

described as the intensity and timing of EMG activity, which is within one standard

deviation from the mean EMG activity of the normal cohort. While this standard

excludes 33% of the data observed in the 'normal' population, correlations with gait

motion indicate EMG activity outside this range represents inefficient muscle action and

should not be a standard for normal function (Perry, 1992). In the present investigation,

the 'significance' of any given period of muscle activity was assessed using the mean

intensity of the EMG activity (as a percentage MMT) and periods of activation (as a

percentage of the gait cycle). However, without considering the profile of muscle

activation in relation to the functional phases of the gait cycle this is a relatively

arbitrary and inaccurate process. EMG data presented in Figure 4.27 provides an

excellent illustration in that it is difficult to compare the mean amplitude of tibialis

anterior (TA) during loading response given that the mean intensity of EMG activity of

the amputee was spread over 30% of the gait cycle. In considering loading response

alone, it would be reasonable to conclude that there was an increase in EMG activity

observed in the amputee subjects compared to normal. It is possible to make

interpretations about the significance of these differences when the mean and standard

deviation values are considered. For the normal population, the mean intensity of EMG

activity during loading response was 16%MMT and varied between 13%MMT and

21%MMT (mean ±1SD). For the amputee subject, the intensity of EMG during loading

response peaked at about 25-30%MMT. The mean intensity of TA in the amputee

during loading response is likely to be only marginally above the confidence interval of

the normal population and not outside a 95%CI.

In the normal population, TA was active during loading response from initial

contact through until between 5-9%GC. Mean intensity of normal TA varied between

13%MMT and 21%MMT. For the majority of amputee subjects, the timing, duration

________________________________________________________ Chapter 4. 131

and intensity of TA activity during loading response was comparable to that observed in

the normal population. However, for the affected limbs of subjects 2103-1906A, 2103-

2116A and 2803-0410A EMG activity was prolonged well into stance phase and was

characterised by significant variability. EMG activity was unable to be recorded for the

affected limbs of the Chopart amputees because the preamplifier and electrode units

could not fit inside the socket.

Figure 4.27 Mean EMG activity of tibialis anterior for the affected limb of subject

2103-1906A compared to the mean of the normal population

Figure 4.28 EMG activity of tibialis anterior for the affected limb of subject 2103-

1906A (n=5).

0 20 40 60 80 1000

10

20

30

40

50Tibialis Anterior (-)

EM

G -

Nor

mal

ised

to

100%

MM

T

Gait Cycle [%]

________________________________________________________ Chapter 4. 132

For the affected limb of subject 2103-1906A, TA activity seemed to be

marginally increased during loading response compared to that observed in the normal

population (Figure 4.27). Following loading response, the activity of TA was more

variable and as such the mean EMG signal between 10-30%GC does not reflect the

actual EMG activity observed in a number of trials (Figure 4.28). The variability of the

EMG pattern was characterised by CV and CMC measures, which were 69% and 0.34,

respectively. EMG activity was observed until mid-stance (Figure 4.27-4.28).

The activity of tibialis anterior was also prolonged in the bilateral Lisfranc

amputee (2803-0410A) on the right (1-71%GC) and the left (1-35%GC) limbs

compared to the normal population (Figure 4.29). However, the reliability of these

periods of muscle activity could certainly be questioned given that the patterns of

activity were very erratic, except during terminal swing phase (Figure 4.30). The

usefulness of this EMG data is certainly questionable due to the large variability. The

CV and CMC measures of variability for the right limb were 59% and 0.31,

respectively. For the left limb, the CV was 72% and the CMC was 0.35.

Figure 4.29 Mean EMG activity of tibialis anterior for the right and left limbs of subject

2803-0410A compared to the mean of the normal population

________________________________________________________ Chapter 4. 133

Figure 4.30 EMG activity of tibialis anterior for the right (n=5) and left (n=4) limbs of

subject 2803-0410A.

For the affected limb of subject 2130-2116A, excessive EMG activity of tibialis

anterior was observed during stance phase (Figure 4.31). Determining the periods of

muscle activity was difficult and probably unreliable given the variability observed

during stance phase. The stance phase periods of muscle activity were determined to be

1-14%GC and 28-43%MMT. The mean intensity of these periods of activity were both

6%MMT (Figure 4.31).

In the normal population, gastrocnemius medial head (GM) activity commenced

between 8-17%GC and terminated between 45-50%GC (95%CI). The CI of GM

intensity was 9-25%MMT. The initiation of gastrocnemius lateral head activity (GL)

was more varied with muscle activation commencing between 14-29%GC and

concluding between 44-51%GC. The mean intensity of GL activity varied between 7-

0 20 40 60 80 1000

10

20

30Tibialis Anterior (-)

EM

G -

Nor

mal

ised

to

100%

MM

T

0 20 40 60 80 1000

10

20

30

40

50Tibialis Anterior (-)

EM

G -

Nor

mal

ised

to

100%

MM

T

Gait Cycle [%]

Gait Cycle [%]

Right

Left

________________________________________________________ Chapter 4. 134

17%MMT. Soleus activity commenced between initial contact and 18%GC and

concluded between 46-54%GC. The CI of soleus intensity was 9-19%MMT.

Figure 4.31 EMG of tibialis anterior for the affected limb of subject 2103-2116A (n=7).

In many amputee subjects, the activity of one or more calf muscles on the

affected limb was substantially delayed relative to the normal population. These delays

were most evident on the affected limb GM and GL in both subjects 2103-1906A and

2703-1903A and soleus only in subject 2703-1903A (Figures 4.32-4.33). In these cases,

EMG activity was not observed until about mid-stance (Figures 4.32 and 4.33). Similar

delays in the initiation of GL activity were observed in subject 2103-2116A (40%GC)

and soleus activity in subject 0704-0403A (32%GC).

Figure 4.32 depicts a period of soleus inactivity between ≈20-30%GC, which

may not be an accurate reflection given the EMG data from each trial (Figure 4.34). No

EMG data were recorded for the triceps surae muscles on the affected limbs of the

Chopart amputees because the electrodes were unable to be placed inside the socket. No

meaningful EMG data could be obtained for the triceps surae group in subject 2803-

0410A. Sound limb triceps surae activity was comparable to that of the normal

population. Mean intensity of soleus, GM and GL observed in the amputee subjects

were comparable to that of the normal population.

0 20 40 60 80 1000

10

20

30

40Tibialis Anterior (-)

EM

G -

Nor

mal

ised

to

100%

MM

T

Gait Cycle [%]

________________________________________________________ Chapter 4. 135

Figure 4.32 Mean EMG activity of triceps surae for the affected limb of subject 2103-

1906A compared to the mean of the normal population

________________________________________________________ Chapter 4. 136

Figure 4.33 Mean EMG activity of triceps surae for the affected limb of subject 2703-

1903A compared to the mean of the normal population

Figure 4.34 EMG activity of soleus for the affected limb of subject 2103-1906A (n=5).

0 20 40 60 80 1000

10

20

30Soleus (-)

Gait Cycle [%]EM

G -

Nor

mal

ised

to

100%

MM

T

________________________________________________________ Chapter 4. 137

The normal pattern of biceps femoris (BF) activity was maintained following

partial foot amputation except for the affected limbs of the Chopart amputees.

Abnormal EMG activity was not limited to just the affected limb. On the sound limb of

the unilateral amputee subjects, BF activity was prolonged in subjects 3004-1102A (1-

18%GC), 2103-2116A (1-22%GC), 2703-1903A (1-24%GC) and 2103-1906A (1-

21%GC) compared to the CI of the normal population (1-12%GC). The mean intensity

of BF activity was comparable to the CI of the normal population (2-14%MMT).

For the affected limbs of the Chopart amputees, BF activity was observed from

initial contact until mid-stance for the right limb of subject 0904-1924A and until about

45%GC for the left limb (Figure 4.36-4.37) as well as for subject 3004-1102A (Figure

4.35). For subject 3004-1102A and the left limb of subject 0904-1924A, substantial

aphasic activity was observed during the later portions of the mid-stance period.

Figure 4.35 EMG activity of biceps femoris long head for the affected limb of subject

3004-1102A (n=3)

0 20 40 60 80 1000

10

20

30

40Biceps Femoris (-)

EM

G -

Nor

mal

ised

to

100%

MM

T

Gait Cycle [%]

________________________________________________________ Chapter 4. 138

Figure 4.36 Mean EMG activity of biceps femoris long head for the right and left limbs

of subject 0904-1924A compared to the mean of the normal population.

________________________________________________________ Chapter 4. 139

Figure 4.37 EMG activity of biceps femoris long head for the right (n=6) and left (n=6)

limbs of subject 0904-1924A.

Mean intensity of vastus lateralis activity in the normal population was 6-

13%MMT. For many amputee subjects, the mean intensity of packets of VL activity

were reduced (Table 4.7). The reduction in mean intensity did not seem to be the cause

for prolonged activity following initial contact.

( )

0 20 40 60 80 1000

10

20

30

40

50Biceps Femoris (-)

EM

G -

Nor

mal

ised

to

100%

MM

T

Gait Cycle [%]

Right

0 20 40 60 80 1000

10

20

30

40Biceps Femoris (-)

EM

G -

Nor

mal

ised

to

100%

MM

T

Gait Cycle [%]

Left

________________________________________________________ Chapter 4. 140

Table 4.7 Periods of vastus lateralis activity observed during stance phase including

mean intensity.

R = right. L = left. AL denotes affected limb. SL denotes sound limb. * denotes significant differences

greater then mean ±2SD. ‡ denotes differences greater then mean ±1SD but less then mean ±2SD.

Active period Mean intensitySubject Comments

%GC %GC %MMT

Control 1 11-16 6.3:12.6

1004-1304A Bi MTP R

L

1

1

19*

14

4.7‡

10.2

2103-2116A Uni TMT AL

SL

1

1

40*

17‡

11.3

8.3

2703-1903A Uni Lisfranc AL

SL

1

1

26*

15

10.15

12.1

0704-0403A Uni Lisfranc AL

SL

1

1

16

13

3.6‡

5.8‡

2103-1906A Uni Lisfranc AL

SL

1

1

27*

20*

10.2

11.9

2803-0410A Bi Lisfranc R

L

Erratic

Erratic

1

1

28*

48*

15.3

3.7‡

0904-1924A Bi Chopart R

L

1

1

15

17‡

4.1‡

5.7‡

3004-1102A Uni Chopart AL

SL

1

39*

1

23*

49*

13

5.2‡

5.9‡

5.9‡

________________________________________________________ Chapter 4. 141

Figure 4.38 EMG activity of vastus lateralis for the affected limb of subject 2103-

2116A (n=7).

Figure 4.39 EMG activity of vastus lateralis for the sound limb of subject 3004-1102A

G i l l h d ( )

0 20 40 60 80 1000

10

20

30Vastus Lateralis (-)

EMGE

MG

- N

orm

alis

ed t

o 10

0% M

MT

Gait Cycle [%]

0 20 40 60 80 1000

5

10

15Vastus Lateralis (-)

EMG

EM

G -

Nor

mal

ised

to

100%

MM

T

Gait Cycle [%]

________________________________

Figure 4.40 EMG data for the affected limbs of subject 2803-0410A

During swing phase, the activit

and tibialis anterior were very similar

population.

The initiation of vastus lateralis

85%GC and 89%GC for the normal p

normal population, the intensity of V

duration of VL activity during swing

amputee subjects. The mean intensity o

minus one standard deviation and not

number of amputee subjects.

t

0 20 40

5

10

15Vastus Lateralis (-)

EMG

0 20 40 60 80 1000

10

20

30

40Vastus Lateralis (-)

EMG

EM

G -

Nor

mal

ised

to

100%

MM

T

G

Right

eft

LefL

________________________ Chapter 4. 142

ies of vastus lateralis, biceps femoris long head

between the amputee subjects and the normal

activity during swing phase occurred between

opulation and continued until 100%GC. In the

L activity occurred between 4-12%MMT. The

phase was comparable to normal in all the

f vastus lateralis was marginally below the mean

below, the two standard deviation mark for a

0 60 80 100

ait Cycle [%]

________________________________________________________ Chapter 4. 143

The initiation of biceps femoris activity during swing phase commenced

between 75-86%GC and terminated between 97-100%GC. A large range of muscle

intensities were observed with the CI being 3-17%MMT. The 95%CI of muscle

intensity was 0-24%MMT. The duration and intensity of BF activity was comparable to

normal in the partial foot amputees.

The initiation of tibialis anterior activity observed in the normal population

during swing phase (54-57%GC) was comparable to that observed in most of the

amputee subjects. However, the initiation of tibialis anterior activity occurred

prematurely on the affected limb of subject 2103-1906A (49%GC) (Figure 4.27-4.28)

and was delayed on the affected limb of subject 2703-1903A (86%GC) (Figure 4.41).

The initiation of tibialis anterior activity during swing phase was also delayed on the left

limb of subject 2803-0410A (Figure 4.29-4.30). On the right limb of this subject, tibialis

anterior was active from initial contact through until mid-swing (Figure 4.29) and was

active again between 83%GC and 100%GC (Figure 4.29). No differences were

observed between the intensity of TA in the normal population during swing phase (7-

13%MMT) and the amputee subjects.

Figure 4.41 Mean EMG activity of tibialis anterior for the affected limb of subject

2103-1903A compared to the mean of the normal population

________________________________________________________ Chapter 4. 144

4.4 Discussion

The aim of this investigation was to provide a thorough bilateral description of

the gait of a cohort of partial foot amputees to better describe the effects of amputation

and prosthetic/orthotic fitting on gait. The temperospatial, kinematic, kinetic and

electromyographic characteristics showed changes in many partial foot amputees

compared with those of the normal, able-bodied population studied.

The joint ranges of motion and muscle strength, temperospatial, kinematic and

kinetic parameters have been presented as individual discussions. A brief discussion of

the EMG signal processing technique follows the discussion of the results. EMG and

force platform data have not been presented in isolation, but rather as part of the

kinematic and kinetic analysis to augment interpretation of the gait data. Where

possible, the discussion of each topic follows the following basic phases of the gait

cycle: initial contact, loading response, the mid-stance phase, pre-swing, initial swing,

mid-swing and terminal swing phases (Perry, 1992).

Range of motion and muscle strength

The available static range of motion observed at the hips, knees and ankles of

the normal population were comparable to previous reports (Kendall and McCreary,

1993; Clarkson and Gilewich, 1989). Static ankle range was substantially compromised

on the affected residua of primarily the Lisfranc and Chopart amputees. Reductions in

plantarflexion/dorsiflexion and inversion/eversion range were characteristic of the

equinus deformity observed in many amputees. Equinus deformity is often a long-term

consequence of, primarily, Lisfranc and Chopart amputation because tibialis anterior is

often reattached more proximally, where the effective lever-arm is reduced and the

tendons of extensor digitorum longus and extensor hallucis longus are often not

reattached at all. Reductions in the available ankle range are likely to make functional

differences particularly during stance phase dorsiflexion where the available range was

roughly equivalent to the range utilised by these amputees during gait (Figures 4.11-

4.12). Reductions in ankle range of the Chopart residuums may also be a long-term

consequence of the elimination of ankle range within the clamshell prosthesis. Previous

investigations have studied TMT, MTP amputees or individuals with metatarsal ray

resection have found static ankle ROM to be comparable to normal (Garabolsa et al.,

________________________________________________________ Chapter 4. 145

1996; Dillon, 1995). However, these same data have not previously been reported for

individuals with Lisfranc and Chopart amputation.

The Oxford Manual Muscle test provided a basis for documenting 'significant'

areas of muscle weakness, particularly with reference to the sound limb. Significant

weakness, as evidenced through the muscle test, was generally not observed in the

amputee population despite the fact that the ankle kinematic patterns were indicative of

triceps surae weakness. Such discrepancies were not surprising, given that the amputee

subjects were able to ambulate independently with, arguably, minor variations on the

basic pattern of normal locomotion. Clinically, individuals can often perform well on

the test despite obvious limitations in performing functional activities such as walking

or descending stairs for a number of reasons.

The Oxford test measures an individual's isometric muscle strength through the

available joint range, which is not indicative of an individuals ability to perform an

eccentric activity. The ability to control the angular joint range, such as is necessary to

moderate tibial rotation over the stance foot or control the knee when descending stairs,

is not necessarily a measure related to isometric muscle strength. Moreover, individuals

can often perform well on the Oxford test because the influence of fatigue is minimal

unlike repetitious activities such as walking. Results from the muscle strength test can

be relatively subjective when differentiating between grades 4 and 5 where the test

activity is performed against gravity with varying degrees of resistance. When both

limbs demonstrate similar isometric strength is difficult to distinguish between grades 4

and 5 because the strength of an individual is a relatively subjective measure. For

example, a 60-year-old will likely produce more muscle force to achieve a grade 4 than

a 90-year-old. When the affected limb can be compared to the sound limb, a more

accurate grade 4 can be established if the affected limb is weaker than the sound limb.

In essence, the utility of the technique is limited for distinguishing relatively minor

areas of muscle weakness, such as those evident in this population.

Temperospatial

In the present investigation, temperospatial parameters for the normal population

were comparable to previously published investigations of normal gait (Allard et al.,

1997; Craik, 1995; Sadeghi et al., 1997; Murry et al., 1964; Winter, 1991; Perry, 1992).

________________________________________________________ Chapter 4. 146

In comparison to previous investigations (Boyd et al., 1999; Burnfield et al.,

1998; Dorostkar et al., 1997; Dillon, 1995; Muller et al., 1998), very few amputee

subjects displayed abnormal stride length and walking velocity. However, substantial

reductions in walking velocity were observed in the unilateral TMT and Chopart

amputees as well as in the bilateral Lisfranc amputee (Table 4.2). Significant reductions

in stride length appeared to be the reason for reduced walking velocity in the unilateral

TMT and Lisfranc amputees, as no differences in cadence were evident. For the

unilateral Chopart amputee, significant reductions in walking velocity seemed to be the

result of reductions in both stride length and cadence.

The chronological age of the bilateral Lisfranc amputee (63) is unlikely to have

resulted in the substantial reductions in walking velocity observed given that the

influence of age to 60 has little effect (Grabiner et al., 1997) and that mean decreases in

walking velocity between 60-65 are just 3% (Murry et al., 1969 - cited Perry, 1992).

However, the biological age seemed to be a primary influence in this subject who

almost appeared 'frail.' The influence of arthritis or other health pathologies not detected

during the subject evaluation may have confounded the results.

Reductions in walking velocity and contralateral step length are common

mechanisms to control tibial rotation (Sutherland et al., 1980; Lehmann et al., 1985;

Simon et al., 1978) but do not explain the differences observed across the wider

population. Reductions in power generation across the ankle (Winter, 1990) also do not

seem to explain the differences in stride length and walking velocity in these individuals

given reductions in ankle power generation observed across the entire group. It is

questionable whether reductions in stride length are a result of reductions ankle power

generation or whether the reduced plantarflexor work simply reflects the mechanical

requirement of the reduced stride length (Grabiner et al., 1997). Stability may be a

primary concern in these individuals or the altered stride length and velocity may

optimise energy expenditure. Neither of these characteristics were assessed.

In comparison to previous investigations (Boyd et al., 1999; Burnfield et al.,

1998; Dorostkar et al., 1997; Dillon, 1995; Muller et al., 1998) amputees in the present

study tended to walked faster (≈85% of normal vs. ≈65% of normal). Individuals in the

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present investigation had forefoot amputation due to trauma or gangrene secondary to

non-systemic vascular diseases such as frostbite rather than vascular disease secondary

to diabetes. Previous investigations have found consistent differences in both stride

length and cadence (Burnfield et al., 1998; Boyd et al., 1999; Dorostkar et al., 1997;

Dillon, 1995) which were not observed in the present study. Reductions in stride length

have previously been implicated as the primary reason for reductions in walking

velocity over differences in cadence (Dorostkar et al. 1997). As in the present

investigation no clear differences were evident between levels of amputation (Dillon,

1995; Dorostkar et al., 1997).

The duration and phasing of swing and stance has received little attention in

published literature presumably because, as in the present study, there were no

differences from normal on the affected limb. Studies have not previously examined the

sound limb where the proportion of stance phase was increased and swing phase

decreased, relative to the normal population in the unilateral TMT, Chopart and bilateral

Lisfranc amputees (Table 4.3).

Reductions in the proportion of the gait cycle spent in single support on the

affected limb were commensurate with reductions in swing time on the sound limb of

the unilateral TMT, Chopart and bilateral Lisfranc amputees. The proportion of the gait

cycle spent in double limb support following sound limb initial contact was increased

for the unilateral TMT as it was for the unilateral Chopart amputee following affected

limb initial contact. For the bilateral Lisfranc amputee, increases in double support

proportions were relatively symmetrical. Identifying the cause of prolonged double

support is difficult to ascertain given the variability observed in the small number of

individuals who exhibited abnormal double support time (as a percentage of the gait

cycle). Previous investigations have not reported support phase data for either the sound

or affected limbs.

In the present study, no differences in the total excursion of the CoP were

observed between the amputee subjects and the normal population. In comparison,

previous investigation has reported a significant correlation between reductions in total

CoP excursion and residual foot length (Dillon, 1995). Differences in the total excursion

of the CoP are likely to reflect differences in the force threshold criteria between these

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investigations. In the present study, CoP data were calculated once the magnitude of the

vertical GRF exceeded 10N which was substantially less than the 200N threshold

utilised by Dillon (1995).

Kinematics

Mean kinematic patterns of motion observed at the hip, knee and ankle of the

normal population were comparable to published analyses of normal gait, in terms of

both timing and peak magnitudes (Perry, 1992; Winter, 1983). The variability of these

kinematic patterns was also comparable to previous reports of normal gait (Winter,

1983; Winter, 1991). Intra-subject kinematic variability of individuals in the normal

cohort were similar to those reported by Kadaba et al., (1989).

Previous investigations reporting joint angular kinematics of partial foot

amputee gait have focused primarily on the affected ankle joint (Boyd et al., 1999;

Dorostkar et al., 1997; Garabolsa et al., 1996) with limited work examining proximal

joints (Dillon, 1995; Mueller et al., 1998) or reporting swing phase kinematics (Dillon,

1995). Kinematic patterns of the sound limb have not previously been reported. Very

few kinematic anomalies were observed at the hip and knee joints however, substantial

differences from the normal population were observed, primarily, at the affected ankle.

Ankle kinematics

Affected limb ankle kinematic data have been discussed, firstly, for the bilateral

MTP amputee where no functionally significant differences were observed from the

normal population. Secondly, ankle kinematic data for the TMT and Lisfranc amputees

have been presented and could be characterised by excessive ankle dorsiflexion during

terminal stance and reduced peak plantarflexion. There were no clear differences

between TMT and Lisfranc amputees based on the type of prosthetic fitting which

included insoles, toe fillers or slipper sockets. Finally, ankle kinematic data for the

Chopart amputees have been presented. For the Chopart amputees, the kinematic

patterns observed at the ankle were dominated by the clamshell prosthesis.

For a bilateral MTP amputee, the ankle kinematic patterns were very similar to

those of the normal population (Figure 4.12). The timing of peak joint angles and the

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dynamic range were also comparable to the normal population. However, the ankle

motion pattern was biased toward dorsiflexion. There was no evidence to suggest errors

in marker placement based on the neutral segment angles. Functionally, there were no

significant differences in the kinetic patterns describing the causes of movement and as

such, the unexplained dorsiflexion bias was not of particular concern.

During initial contact, substantial dorsiflexion was observed on the affected limb

of the Lisfranc cohort. Increased dorsiflexion at initial contact is likely to cause an

exaggerated heel rocker given the large angle between the foot segment and the floor.

The foot will be driven to the floor more rapidly. The exact purpose of this dynamic

response is difficult to explain. However, it is likely to draw the tibia more rapidly

forward as the foot plantarflexes and increase the heel only time given the exaggerated

height of the toe from the floor an additional time to it would take to reach foot-flat.

Both of these actions contribute to forward limb progression and roll the body weight

forward on the heel (Perry, 1992) and may be required to keep the tibial advancement in

line with that of the thigh and trunk segments. The rapid change in ankle angle would

necessitate some compensatory mechanism, such as additional eccentric work by the

pre-tibial muscles or increased stance phase knee flexion and eccentric quadriceps

activity. In subject 2103-1906A substantial power absorption was observed across the

ankle (Figure 4.20) to resist the large external torque (Figure 4.13). Prolonged and

marginally increased eccentric activity of tibialis anterior controlled the kinematic

pattern (Figure 4.27). An alternate mechanism may be to increase knee flexion during

stance phase such as was observed in subject 2703-1903A. This kinematic pattern

would reduce the activity level of tibialis anterior to a more normal level (Figure 4.41).

However, it would tend to increase the demand on the quadriceps musculature, as was

observed in this subject (Table 4.5). For the affected limb of many amputee subjects, the

activity of vastus lateralis was prolonged, presumably in an attempt to control the

trajectory of the knee (Table 4.5). The relatively normal plantarflexion angle during

loading response actually reduces the heel rocker effect so the tibia will not advance too

rapidly (Perry, 1992).

Following loading response, the progressive increase into ankle dorsiflexion on

the affected limbs of the TMT and Lisfranc amputees (Figures 4.11-4.12) reflects

increasing anterior tilt of the tibia as the contralateral limb swings through and the upper

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body moves anteriorly over the fixed foot (Perry, 1992). Eccentric activity of, primarily,

soleus (augmented by the gastrocnemius muscles when the trunk is anterior to the knee

axis) typically moderates tibial progression and helps control forward movement of the

trunk over the stance foot (Meinders et al., 1998; Perry, 1992; Sutherland et al., 1980;

Simon et al., 1978). However, the ankle moment profiles of the affected limbs show

substantial reductions in the resistance to ankle dorsiflexion from loading response

through to heel-off (Figures 4.13-4.14). Reductions in the external moment, and

therefore, the internal muscle requirements, are the result of the relatively fixed lever-

arm of the GRF about the ankle (Figures 4.5-4.6). The CoP remained relatively fixed at

about 40% of shoe length, just proximal to the distal residuum.

It would not be possible for the CoP to move substantially beyond the remnant

foot as the position of the trunk is unlikely to be modulated by the weak soleus and

gastrocnemii muscles unless alternate gait strategies, such as increased knee flexion and

eccentric quadriceps activity, were engaged. It is difficult to ascertain whether the

primary purpose of modulating the position of the CoP was to reduce the requirement of

the soleus muscle and maintain trunk stability or to avoid substantial force on the

sensitive distal residuum, which will be examined later in the discussion. Perhaps both

of these gait strategies are of equal importance and the adoption of the observed gait

pattern enhances stability and protects the distal residuum.

Control of tibial rotation during the initial portion of the mid-stance period

seems to be largely a reflection of the moderated trunk position to minimise the

muscular requirement. Anterior progression of the tibia does not seem to have been

controlled by soleus activity in subjects 2703-1903A (Figure 4.33) and 0704-0403A

where muscle activity was absent until mid-stance on the affected limbs. For the

remaining subjects, the timing of soleus activity was comparable to that observed in the

normal population. Despite the mean electrical activity of soleus being similar to that of

the normal population, the accompanying force generation is likely to be substantially

less given the atrophy of triceps surae muscles observed. Atrophied muscle has the same

number of motor units as normal muscle; hence, the electrical activity recorded is

similar. However, each muscle fibre is substantially smaller and can only produce a

fraction of the force of normal muscle. The normal function of soleus may have been

augmented by concentric activity of vastus lateralis following the KP2 power generation

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associated with knee extension following stance phase knee flexion. EMG activity of

Vastus lateralis was prolonged on the affected limbs of the TMT and most Lisfranc

amputees until about mid-stance, which may help moderate progression of the tibia over

the stance foot.

Terminal stance could be characterised as the most demanding period of the gait

cycle for the TMT and Lisfranc amputees and a period when the amputee 'fell over' the

end of the remnant foot. The CoP progressed anterior to the distal residuum presumably

as the CM of the trunk progressed substantially forward of the reduced base of support

(the remnant foot). The ankle dorsiflexed rapidly during terminal stance compared to

the mid-stance phase (Figures 4.11-4.12). The resulting dorsiflexion angle was

excessive (Figure 4.11) and the peak delayed (Figures 4.11-4.12) compared to the

normal population, which is likely to reflect substantial anterior tibial tilt resulting from

the relatively unrestrained forward fall of the trunk.

It is difficult to substantiate the anterior position of the trunk in relationship to

the reduced base of support without kinematic data however, a number of parameters

would indicate the relatively anterior position of the trunk. Firstly, the anterior

orientation of the tibia over the fixed foot with the knee (Figure 4.9) and hip extended

(Figure 4.7) would imply that the trunk must be positioned anteriorly over the base of

support by virtue of the alignment of the rest of the limb. With the limb in this

orientation, the only mechanism by which the trunk could be brought back over the foot

would be to extend the lumbar spine substantially. Secondly, the absence of a knee

flexion moment during the mid-stance phase on the affected limbs of the TMT and

Lisfranc amputees (Figures 4.16-4.17) would suggest that the tibial angle, and therefore

knee position, moved in unison with the line of action of the GRF presumably in an

attempt to reduce the requirement of the weak gastrocnemius musculature. The effect of

muscle activity on the knee moment is likely to be negligible given the atrophied soleus

and gastrocnemius and the absence of other muscle activity and that no co-contraction

with tibialis anterior was evidenced. Thirdly, the fore-aft GRF peaks typically

associated with the forward thrust of push-off (Figure 4.1-4.2) occurred prematurely

before the ankle had reached peak dorsiflexion and the commencement of push-off

(Figure 4.11-4.12). These horizontal GRF peaks are therefore likely to be a reflection of

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the leverage produced by body alignment (Murry et al., 1978; Sutherland et al., 1980;

Perry, 1974; Simon et al., 1978).

Peak eccentric activity of soleus and the gastrocnemii muscle was observed

during terminal stance phase in an attempt to decelerate and arrest the rapid rotation of

the tibia and reverse the dorsiflexion angle (Sutherland et al., 1980) as illustrated in

Figures 4.32 and 4.33. However, the muscle activity observed seemed to be ineffective

given that the ever-increasing dorsiflexion angle was eventually checked by the

premature contralateral heel contact (Sutherland et al., 1980) marking the end of

terminal stance phase (Table 4.4). This mechanism was observed on all the TMT and

Lisfranc residuums except the right leg of subject 2803-0410A (Figure 4.12) where

contralateral heel contact preceded peak dorsiflexion by nearly 10% of the gait cycle.

During pre-swing, the CoP progressed rapidly from approximately 40% of shoe

length to the end of the foot on the affected limbs of the Lisfranc and TMT amputees

(Figure 4.5). Immediately after contralateral initial contact, a substantial proportion of

body weight was redistributed from the sensitive distal residuum to the sound limb as

evidenced by the increased magnitude of the vertical GRF peak (FZ1) above that

normally associated with loading response (Figure 4.4). The GRF did not progress

substantially beyond the remnant foot until the magnitude of the vertical GRF was

rapidly diminishing (Figure 4.4) which would seem to be a useful method of protecting

the distal end of the remnant foot from undesirable forces and moments. As mentioned

earlier, it is difficult to establish whether the primary aim of limiting substantial

excursion of the CoP until double support was an attempt to protect the distal residuum

or control the position of the trunk.

During double support, as the sound limb accepted weight and the CoP moved

anterior to the distal residuum, the affected ankle began to plantarflex rapidly (Figure

4.11). Plantarflexion of the partial foot during the pre-swing phase seemed to be a

relatively passive activity as the trunk, being well forward of the remnant foot, drew the

tibia forward once the ankle's passive range had been reached. Similar gait patterns have

been observed in individuals with plantarflexor weakness (Perry, 1992; Perry, 1974)

and temporary tibial nerve paralysis (Simon et al., 1978; Sutherland et al., 1980).

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In the present investigation there seems to be little evidence suggesting that

ankle plantarflexion was not a passive activity given the negligible work observed

across the affected ankle of the TMT and Lisfranc amputees (Figure 4.20-4.21). The

premature timing of the fore-aft GRF did not seem to support the concept of active

plantarflexion nor did the premature timing and reduced magnitude of the vertical GRF

peak (FZ3) (Figures 4.3). EMG activity of the triceps surae muscle group was absent

during this time but is likely to be a reflection of the lag between electrical activity and

force production (Winter, 1990; Meinders et al., 1998).

Reductions in the magnitude of peak plantarflexion from normal are difficult to

explain but are likely to be related to triceps surae weakness. Weakness of the triceps

surae muscle group may result in an inability to lock the ankle so that the tibia and foot

act together (Perry, 1974). Loss of metatarsal length and reduced inversion/eversion

range would likely result in such instability. Metatarsal length is typically required to

create eversion moments about the oblique axis of the midtarsal joint. The coordinated

actions between the midtarsal joint and the subtalar joint are likely to be lost. An

inability to lock the midtarsal joint onto the subtalar joint may result in additional

synchronous movements of adduction, abduction, dorsiflexion and plantarflexion about

the oblique axis and eversion and inversion movements about the longitudinal axis of

the midtarsal joint (Norkin and Levangie, 1992). Flexor stabilisation provided by

intrinsic foot muscles, such as flexor digitorum brevis, is also likely to be compromised

due to fore foot amputation. It is unlikely that difficulties associated with weight bearing

on the sensitive distal residuum are an issue during pre-swing given that the CoP has

progressed substantially past the distal residuum and that the majority of body weight

has been transferred to the contralateral limb.

During the terminal stages of pre-swing and the early stages of initial swing, two

distinct peak plantarflexion angles were observed on the affected limbs of the unilateral

TMT and Lisfranc amputees (Figure 4.11). In subjects 2703-1903A and 2103-1906A,

the peak plantarflexion angle was normally timed but substantially reduced in

magnitude (Pattern-A) compared to that observed in subjects 2103-2116A and 0704-

0403A (Pattern-B). Differences in these kinematic profiles may be a reflection of the

necessity to achieve adequate stability during double support phase before progressing

to single support. Subjects who exhibited pattern B, seemed to take longer to transfer

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weight off the affected limb to the sound limb than subjects who exhibited pattern A

(Figure 4.3). It is difficult to ascertain whether these weight transfer delays were simply

a reflection of reduced walking velocity (Table 4.2) and increased time spent in double

support (Table 4.4) and sound limb stance (Table 4.3) compared to subjects who

exhibited Pattern-A or the primary cause. The increased plantarflexion angles

characterised by Pattern-B are likely to reflect how the foot continued to freely rotate

until sufficient sound limb stability had been achieved to lift the foot off the ground and

conclude double support phase. The kinematic patterns observed in the bilateral

Lisfranc amputee (Figure 4.12) were characteristic of Pattern-B and reflect the increased

proportion of the gait cycle spent in stance and double support and reductions in

walking velocity (Tables 4.2-4.4).

Differences in maximum plantarflexion and swing phase kinematics were not

likely to be of clinical significance, given the trailing position of the limb during initial

swing and that the foot seemed to have adequately cleared the ground during mid-swing

(Figure 4.11). However, these functional abnormalities do have implications for the

ankle position at initial contact.

During terminal pre-swing and initial swing, the initiation and intensity of

tibialis anterior activity exhibited by the majority of the unilateral Lisfranc and TMT

amputees was comparable to that observed in the normal population. However, the

initiation of tibialis anterior activity was delayed until 85% of the gait cycle in subject

2703-1903A (Figure 4.41). Despite these delays in the onset of tibialis anterior activity,

there appeared to be substantial toe clearance during mid-swing evidenced by the

excessive dorsiflexion angle observed (Figure 4.11). There did not appear to be any

compensatory increases in knee or hip flexion or sound limb plantarflexion, which may

indicate some coronal plane compensation.

For the Chopart amputees, the kinematic patterns at the ankle were dominated

by the Clamshell prosthesis (Figure 4.12). The dynamic ankle range was limited to

approximately 10° which was about half that observed in below knee amputees with

various fixed ankle feet (Torburn et al., 1990). The ankle kinematic patterns have

previously been thought to reflect the force/deflection characteristics of the prosthetic

foot (Dillon, 1995). During swing phase, the kinematic patterns of the Chopart

amputees are likely to be the result of movement of the leg segment within the

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prosthetic socket given that the prosthetic foot was not loaded. This measurement error

will also affect the kinematic data observed during stance phase.

Measurement of this unwanted motion between the socket and leg reflects

limitations in the kinematic marker set. The accuracy of measuring displacement of the

leg and prosthetic socket could be improved with individual marker triads located on the

socket and leg segments. Future investigation could look at utilising the small space

between the proximal portion of the socket and the knee joint axis to locate a suitable

marker triad however, this is likely to be difficult.

During loading response, the Chopart amputees exhibited a loss of normal

plantarflexion (Figure 4.12) because the prosthetic socket eliminated ankle motion. It

was expected that the fixed 90° angle between the tibia and foot would progress the

tibia forward at the same rate that the foot moves toward the ground (Perry, 1992).

However, the heel of the prosthetic foot seemed to effectively modulate the transition

from initial contact to foot flat (Figure 4.12). This transition seemed somewhat slower

than normal given the relatively delayed initial plantarflexion peak (Figure 4.12). The

kinematic pattern and timing of peak plantarflexion was comparable to that observed in

below knee amputees using various fixed ankle prosthetic feet (Torburn et al., 1990).

The kinematic pattern observed during loading response seems to be due to the type of

prosthetic heel incorporated into the prosthesis.

During the mid-stance phase, tibial progression appears to have been moderated

more normally than in the TMT and Lisfranc amputees (Figure 4.15). Tibial progression

is likely to be resisted by a counterforce generated across the anterior wall of the socket

in response to the increasing external torque, as the GRF continues to move toward the

toe. Soleus and gastrocnemius are not likely to contribute effectively given the restricted

range and clinically observed atrophy of the calf musculature. The ankle moment

profiles of the affected limbs of the Chopart amputees show substantial reductions in the

resistance to ankle dorsiflexion from 25-40%GC (Figures 4.15). In subjects 3004-

1102A and on the right limb of subject 0904-1924A, the ankle moment plateaus were

commensurate with periods when the CoP remained at a relatively fixed lever-arm from

the ankle (Figure 4.5-4.6). The CoP and joint moment patterns seem to describe a lack

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of resistance to the external torque which could be the result of how the leg segment

moves within the socket, just prior to, and following mid-stance.

As the limb approaches mid-stance, a reaction force has been generated on the

posterior surface of the calf to resist the plantarflexion movement into foot-flat. From

this period through to just after mid-stance, the prosthesis is flat on the floor and the leg

segment may rotate anteriorly within the socket. Resistance to the external torque, and

progression of the CoP, could not occur until a sufficient counterforce was generated

between the anterior socket wall and the leg segment to overcome the external

plantarflexion moment caused by the anterior position of the GRF relative to the ankle.

During terminal stance, tibial progression appears to have been restrained in the

Chopart amputees by knee recurvatum causing posterior alignment of the tibia relative

to the femur (Figure 4.9-4.10). In subject 3004-1102A and on the left limb of subject

0904-1924A where knee hyperextension was significantly larger than normal, EMG

activity of biceps femoris long head was observed (Figures 4.35-4.37). Activity of

biceps femoris is likely to play a role in protecting the knee joint from uncontrolled

hyperextension. Increased power absorption was observed across the knee joint in these

amputees (Figure 4.23-4.24) commensurate with a protective function.

During pre and initial swing phases, there was a substantial lag between toe-off

and the peak plantarflexion angle (Figure 4.12). This pattern of ankle motion has not

been observed in transtibial amputees with fixed ankle feet (Torburn et al., 1990) where

following toe-off, foot deformation recovers promptly with negligible angular changes

during swing phase. The delayed peak plantarflexion and swing phase kinematic

patterns observed in the Chopart amputees are likely to reflect movement of the leg

segment within the prosthetic socket. During initial swing, the posterior wall of the

prosthetic socket is likely to rotate until supported against the compressed tissue of the

posterior calf. The angulation between the markers located on the knee and prosthetic

socket over the lateral malleolus, when reconstructed, would have created a leg segment

at an angle larger then 90° to the foot segment. Thus, the orientation of the leg segment

relative to the foot segment would create a plantarflexion angle.

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The majority of previous investigations report a reduction in peak ankle

dorsiflexion in TMT amputees (Boyd et al., 1999; Garabolsa et al., 1996; Dorostkar et

al., 1997). These studies have investigated conditions of barefoot ambulation (Boyd et

al., 1999; Garabolsa et al., 1996) or have reported utilising footwear in addition to

barefoot examination but have not reported which condition resulted in the data reported

(Dorostkar et al., 1997). Other investigations have studied orthotic intervention with

footwear and have reported an increase in peak dorsiflexion in the same group (Dillon,

1995) or that there was no real difference (Muller et al., 1998). Studies investigating the

effects of prosthetic/orthotic intervention may be complicated by errors associated with

motion of the residuum within the footwear or movement of the remnant limb inside the

prosthesis/orthosis. Some of the kinematic patterns observations in the present

investigation and by other investigators (Dillon ,1995; Mueller et al., 1998), may be

complicated by limitations imposed by using reflective marker triads utilising one or

more markers located on the shoe. Other marker sets have utilised a marker triad located

exclusively on the rear foot for barefoot ambulation studies (Garabolsa et al., 1996) and

are likely have been used by other investigators (Boyd et al., 1999; Dorostkar et al.,

1997). Substantial reductions in maximum plantarflexion (Dillon, 1995) and the

plantarflexion angle at toe off (Mueller et al., 1998) have previously been reported at

the TMT level.

Kinematic patterns of the sound ankle were similar to the basic motion pattern

observed in the normal population (Figure 4.11). At initial contact, a variety of

responses were observed from substantial dorsiflexion in the Lisfranc cohort to

plantarflexion in the TMT amputee (Figure 4.11). Irrespective of the differences

observed, these responses were not significantly different from the normal population.

During loading response, the initial plantarflexion peak was comparable to that

observed in the normal population however, significant variability was observed (Figure

4.11).

During the initial stages of the mid-stance phase, excessive dorsiflexion was

observed on the sound ankle of subject 2703-1903A which is likely to reflect rapid tibial

rotation following loading response (Figure 4.11). It is difficult to explain the

requirement for this gait pattern. Excessive knee flexion (Figure 4.9) was commensurate

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with increased power absorption across the knee joint (Figure 4.23) which would seem

to be a typical mechanism to control the position of the trunk given the rapid tibial

rotation.

On the sound ankle of the unilateral Chopart amputee the ankle remained at

virtually neutral from 20% of the gait cycle to maximum dorsiflexion (Figure 4.11).

Restricting and maintaining the dorsiflexion range may be a mechanism to control the

substantial progression of the CoP that occurred from initial contact to mid-stance

(Figure 4.5). By mid-stance the CoP had progressed to about 70% of shoe length and

remained at this position until maximum dorsiflexion (Figure 4.5).

During pre and initial swing phases, peak ankle plantarflexion was comparable

to normal on the sound limb of all unilateral amputee subjects except subject 2703-

1906A (Figure 4.11). Reductions in peak plantarflexion in this subject are difficult to

explain but appear to be a functional choice rather than due to limitations in the

available joint range.

During swing phase, the ankle kinematic patterns were quite variable (Figure

4.11). Excessive ankle dorsiflexion dominated the swing phase kinematic profile

observed in subject 2703-1903A and excessive plantarflexion was observed during mid

and terminal swing phases in subject 2103-2116A (Figure 4.11). The swing phase

kinematic pattern observed in subject 2703-1903A is not likely to be of clinical

significance given the adequate foot clearance evidenced by the ankle dorsiflexion angle

(Figure 4.11). However for subject 2103-2116A, foot clearance may be more of an issue

but deviant plantarflexion did not commence until just after mid-swing (Figure 4.11).

The functional significance of these swing phase kinematic profiles is difficult to

explain.

Knee kinematics

At the knee joint, the kinematic patterns observed in the amputee subjects were

very similar to those of the normal population (Figures 4.9-4.10).

For the affected limbs of the bilateral MTP amputee and subject 2703-1906A

increased stance phase knee flexion was observed (Figures 4.9-4.10). Increases in stance

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phase knee flexion were commensurate with increases in the knee extension moments

(Figure 4.17) and power absorption across the knee in the bilateral MTP amputee

(Figure 4.24) but not subject 2703-1906A (Figure 4.23). For the bilateral MTP amputee

the increased knee flexion is likely to be a mechanism to control the trunk position in

lieu of the dorsiflexion range through which the ankle operates (Figure 4.12). In subject

2703-1903A this pattern of knee motion may be a mechanism to control rapid tibial

progression. However, there was no substantial increases in the knee extension moment

(Figure 4.16) and power absorption across the knee (Figure 4.23) which would typically

be commensurate with this type of gait pattern.

Reductions in stance phase knee flexion were observed in the bilateral Chopart

amputee and on the affected limb of the unilateral TMT amputee (Figures 4.9-4.10).

Reductions in the knee extension moment (Figures 4.16-4.17), power absorption (KP1)

and power generation (KP2) across the knee joint were commensurate with reductions

in the angular excursion of the knee. Reductions in stance phase knee flexion may be

the result of reductions in walking velocity in the TMT amputee however, such

reductions in walking speed were not observed in the bilateral Chopart amputee.

Reductions in stance phase knee flexion may be employed to reduce the demand of the

quadriceps musculature and preserve walking velocity (Perry, 1992).

On the affected limb of the unilateral Chopart amputee, the magnitude of stance

phase knee flexion was comparable to that observed in the normal population (Figure

4.9). It is difficult to explain how this gait pattern was controlled given that the kinetic

descriptions more closely resemble that observed in individuals with compromised

stance phase knee flexion. Reductions in the knee extension moment (KM2) approached

significance (Figure 4.16) as did reductions in power absorption (KP1) and power

generation (KP2) across the knee joint (Figure 4.23).

In the bilateral Chopart amputee, the stance phase knee flexion peak was

significantly delayed compared to normal (Figure 4.10) and commensurate delays in the

knee extension moment peak (KM1) (Figure 4.17), power absorption (KP1) and power

generation (KP2) were observed. These anomalies seem to reflect delays in the

progression of weight onto the limb, particularly given the delayed vertical GRF peak

(FZ1) (Figure 4.4).

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During terminal stance, knee recurvatum was observed on the affected limbs of

the Chopart amputees, presumably to control tibial rotation by posteriorly aligning the

tibia relative to the femur (Figure 4.9-4.10). A consequence of this movement pattern is

the relatively delayed initiation of knee flexion into swing phase such as that observed

in subject 3004-1102A (Figure 4.9) which has also previously been observed in TMT

amputees (Dillon, 1995). Despite the delayed initiation of knee flexion, the joint angle

at toe off for subject 3004-1102A was only marginally outside the 95%CI of the normal

population and maximum knee flexion was normally timed (Figure 4.9). This rapid knee

flexion is likely to be aided by concentric activity of biceps femoris long head in a role

similar to that normally associated with the short head of biceps femoris muscle.

Substantial power generation was observed across the knee joint at this time (Figures

4.23-4.24). This power generation peak is typically associated with power generation

across the knee joint due to concentric gastrocnemius activity. However, the atrophy of

the triceps surae and the minimal or absent KP3 power absorption peak typically

associated with controlling the rate of knee rotation due to acceleration of the leg

segment by the triceps surae, would seem to indicate a marginal contribution by the calf

musculature.

Knee flexion into swing phase was delayed in the bilateral Lisfranc amputee

(Figure 4.10). This delay is likely to reflect the increased proportion of stance phase.

For the sound limb, the kinematic patterns observed were virtually identical to

the normal population except increased stance phase knee flexion was observed in

subject 2703-1903A. As previously described, this kinematic pattern modulated the

position of the trunk due to rapid tibial rotation following loading response (Figure

4.11). Although not significant, increased stance phase knee flexion was observed on

the sound limb of many of the Lisfranc and TMT amputee subjects. As previously

described with regard to the pre-swing ankle kinematics of the affected limb, this

pattern of knee motion may be due to the unrestrained fall of the trunk checked by

sound limb initial contact. Increased stance phase knee flexion is likely to absorb the

increased impact and smooth the transfer of weight to the sound limb (Sutherland et al.,

1980; Simon et al., 1978).

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Hip kinematics

At the hip joint, the kinematic pattern of motion was virtually comparable to that

observed in the normal population. Small differences in the timing of maximum hip

extension were observed but these were quite variable and only marginally outside the

tight 95%CI of the normal population and not likely to be of functional significance.

Excessive hip extension was observed on the affected limb of the unilateral

Chopart amputee (Figure 4.7) which, may be an attempt to maintain normal stride

length.

Reductions in static hip extensor range approached significance (13°) in the

bilateral Lisfranc amputee. There seems to be little reason for the reductions in dynamic

hip extension given that gait did not tax the extremes of hip extension (Figure 4.8).

However, given that the majority of power generation causing advancement of the limb

occurred at the hip joint, limiting the available extensor range may put the hip extensor

musculature into at a more advantageous position to generate power during contralateral

toe off.

No significant differences in the swing phase kinematics were evident on the

sound or affected limbs of the amputee subjects compared to the normal population.

Previous investigations into hip kinematics have not reported substantial

differences from normal (Dillon, 1995; Mueller et al., 1998).

Kinetics

Mean kinetic patterns observed at the hip, knee and ankle of the normal

population were comparable to published analyses of normal gait, in terms of both

timing and peak magnitudes (Allard et al., 1997; Winter, 1983). The variability of these

kinetic patterns were also comparable to previous reports of normal gait (Allard et al.,

1997; Winter, 1983; Winter, 1991) except the hip moment CV. The hip moment CV

was exaggerated, reflecting the limitations of the CV technique when the mean of the

signal is close to zero. No differences in the hip moment CMC were observed. Intra-

subject kinematic variability of individuals in the normal cohort were similar to those

reported by Kadaba et al., (1989).

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Interpretation of kinetic parameters are complicated in investigations such as this

where cadence and stride length (the two determinates of walking speed) were not

controlled. Changes in cadence, stride length and thus walking velocity have been

demonstrated to influence the gain of peak joint moments (Winter 1983; Winter 1984;

Winter 1989; White and Lage 1993).

In the present investigation, changes in the gain of peak hip and knee joint

moments were inconsistent with changes expected as a result of decreased walking

speed (Winter 1983; Winter 1984; Winter 1989; White and Lage 1993). The reduced

peak ankle plantarflexor moments observed in the TMT and Lisfranc amputee subjects

(Figures 4.13-4.14) were akin to those changes expected as a result of reductions in

walking velocity. However, reductions in the peak ankle extension moments, observed

uniformly across the TMT and Lisfranc amputee subjects (Figures 4.13-4.14), can not

adequately be explained by the reductions in walking velocity observed in only a few

individuals (Table 4.2).

For example, subjects 2130-2116A and 2803-0410A walked significantly slower

than normal (Table 4.2) but exhibited reductions in the ankle extension moment peak

(Figures 4.13-4.14), comparable to other amputees who walked at the same speed as the

normal population. Moreover, the ankle extension moments were reduced by

approximately 1Nm/kg (Figures 4.13-4.14), which is about five times greater than that

consistent with slow walking (Winter 1983; Winter 1984; Winter 1989; White and Lage

1993). The unilateral Chopart amputee (3004-1102A) who also walked significantly

slower than the normal population (Table 4.2) exhibited an ankle extension moment

peak comparable to the normal population (Figure 4.15).

During loading response, a relatively normal ankle dorsiflexion moment was

observed on both the sound and affected limbs of the amputee subjects except subject

2103-1906A (Figures 4.13-4.14). For this subject, the ankle moved rapidly through a

20° range during loading response from ≈10° dorsiflexion at initial contact to ≈10°

plantarflexion at the initial plantarflexion peak (Figure 4.11). The ankle moment (Figure

4.13) and power (Figure 4.20) profiles reflect the additional eccentric activity of tibialis

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anterior (Figure 4.27) to control the rapid rate of ankle rotation during loading response

(Figure 4.11).

In the preceding discussion on ankle kinematics, the ankle moment profiles of

the affected limbs highlighted reductions in the resistance to ankle dorsiflexion from

loading response through to heel-off (Figures 4.13-4.14). Reductions in the external

moment, and therefore, the internal muscle requirements, are the result of the relatively

fixed lever-arm of the GRF about the ankle (Figures 4.5-4.6). As previously discussed,

it is difficult to ascertain whether the CoP did not progress to avoid substantial force on

the distal residuum or to moderate the trunk position.

During the mid-stance phase, the ankle moment observed on the sound limb of

subject 3004-1102A reflects the varying contributions of the CoP and vertical GRF.

Following loading response, the rapid progression of the CoP dominated the ankle

moment pattern until about 25% of the gait cycle when the progression of the CoP

plateaued (Figure 4.5). At this time, the GRF was located at about 70% of shoe length

(Figure 4.5). The plateau in the ankle moment between 20-40% of the gait cycle reflects

the relatively fixed lever-arm of the GRF about the ankle. The rapid increase in the

ankle moment between 38%GC and 50%GC reflects the increasing magnitude of the

vertical GRF toward the FZ3 peak (Figure 4.3) given that the CoP did not progress

anteriorly during this time (Figure 4.5). Identical variations in the ankle moment pattern

were also observed on the affected limb of subject 3004-1102A and on the right limb of

subject 0904-1924A (Figure 4.15).

A similar plateau in the ankle moment pattern was observed on the sound limb

of subject 2103-2116A. This moment pattern does not seem to be the result of changes

in the external moment given that the magnitude of the vertical GRF was comparable to

normal (Figure 4.3) as was the progression of the CoP (Figure 4.5). As such, the

moment profile is likely to reflect the excessive muscle contributions of, most likely, the

triceps surae however, no substantial increases in EMG activity were observed.

Substantial reductions in the ankle plantarflexion moment were observed across

the TMT and Lisfranc amputees (Figures 4.13-4.14) reflecting the limited progression

of the CoP when the largest vertical GRFs occurred. The CoP had progressed to only

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about 40-50% of its total excursion (Figure 4.5-4.6) when the peak vertical GRFs were

observed (Figure 4.3-4.4). Hence, the negligible peak plantarflexion moments (Figure

4.13-4.14). Substantial progression of the CoP did not occur until double support when

the increasing lever-arm of the GRF was coincident with the rapidly diminishing

vertical force given that the FZ3 peaks occurred prematurely (Figure 4.3). In the

Chopart residuums, the bilateral MTP amputee and the sound limbs of the TMT and

Lisfranc amputees, the timings of the FZ3 peaks were commensurate with substantial

anterior excursion of the CoP. This would explain the normal magnitudes of the

plantarflexion moment peaks observed.

Arguably, these mechanical differences could highlight a limitation of some

prosthetic/orthotic designs to comfortably distribute forces such that maximum forefoot

loading could occur simultaneous to substantial anterior progression of the GRF.

However, as previously discussed, the limited anterior excursion of the CoP may also

serve a role in moderating trunk position due to weak calf musculature. Irrespective of

the prosthetic/orthotic device fitted, the external moments would still need to be

moderated for the CoP to progress substantially forward in unison with increases in the

vertical GRF. It would be difficult for the TMT and Lisfranc amputees to generate

significant internal muscle moments from the calf musculature. Alternatively, the

external moments could be resisted, as in the Chopart amputees, by the

prosthesis/orthosis.

Previous investigations have reported similar reductions in the peak ankle

plantarflexor moments in MTP and TMT amputees (Dillon, 1995; Boyd et al., 1999;

Mueller et al., 1998) and those with metatarsal ray resection or toe amputation (Boyd et

al., 1999).

The ankle power absorption peak (AP1) was substantially delayed on the

affected limbs of the TMT and Lisfranc amputees (Figure 4.20-4.21) commensurate

with the delayed and rapid increase in ankle dorsiflexion observed during terminal

stance (Figure 4.11-4.12).

Significant reductions in power generation across the ankle joint were observed

on the affected limbs of all the amputee subjects except the bilateral MTP amputee

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(Figures 4.20-4.22). For the MTP amputee, reductions in power generation approached

significance and were consistent with reductions in the excursion of the CoP that also

bordered the 95%CI of the normal population (Figure 4.6). No significant reductions in

the joint angular velocity were observed given the normal angular excursion from peak

dorsiflexion to peak plantarflexion during pre-swing (Figure 4.12); confirming that

reductions in power generation were due to changes in the excursion of the CoP.

The generation of work across the ankle was virtually negligible in the TMT and

Lisfranc residuums due to the diminished ankle moment coupled with reductions in the

joint angular velocity. These angular velocity data have not been presented, but such

interpretation may be based on the limited angular excursion of the ankle from

maximum dorsiflexion to maximum plantarflexion (Figures 4.11-4.12). For the Chopart

amputees, where the peak plantarflexion moments were comparable to those observed

in the normal population, reductions in power generation across the ankle reflect the

elimination of ankle motion by the prosthetic socket.

Clinically, reductions in power generation across the ankle reflect the limited

work by ankle plantarflexors to accelerate the leg segment into swing phase (Meinders

et al., 1998; Capozzo et al., 1976; Dillingham et al., 1992), contribute to the forward

kinetic energy of the trunk and maintain the vertical height of the CM of the upper body

(Meinders et al., 1998).

Despite the long-standing controversy in the literature regarding the role of

ankle plantarflexors (Meinders et al., 1998; Sutherland et al., 1980; Simon et al., 1978;

Perry, 1974), more recent and comprehensive evidence suggests that the primary role of

plantarflexor musculature is to accelerate the leg into swing phase and not to contribute

to raising the trunk against gravity (Meinders et al., 1998; Dillingham et al., 1992).

These recent works add new evidence to previous suggestions that the ankle

plantarflexors do not contribute to push-off (Perry, 1974; Mann et al., 1974; Simon et

al., 1978; Sutherland et al., 1980).

Previous investigations have reported similar reductions in power generation

across the ankle in TMT (Mueller et al., 1998, Dillon 1995) and MTP amputees (Dillon,

1995). These findings have been attributed to the shortened plantarflexor lever arm

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(Mueller et al., 1998) and reductions in the total excursion of the CoP (Dillon, 1995) but

have not acknowledged the role of joint angular velocity.

Partial foot amputation affected the knee joint moment profiles during loading

response and the latter portion of the mid-stance phase (Figures 4.16-4.17). In the

bilateral MTP amputee, the knee extension moment during loading response was

significantly larger than normal (Figure 4.17) as was the power absorbed across the

knee (Figure 4.24). These kinetic abnormalities reflect the increased requirement of the

quadriceps musculature to eccentrically control the increased stance phase knee flexion

(Figure 4.10). During the proceeding discussion of knee kinematics, the increased knee

flexion was thought to be a mechanism to control the trunk position in lieu of the

dorsiflexion range through which the ankle operated (Figure 4.12).

On the affected limbs of the unilateral TMT and Chopart amputees reductions in

the knee extension moment (KM2) approached significance (Figure 4.16) and

reductions in the power absorption across the knee (KP1) were significantly different

from normal (Figure 4.23). In the TMT amputee, reductions in power absorption across

the knee reflect reductions in the extension moment about the knee (Figure 4.16) and

the angular velocity of the knee joint given the reduced stance phase knee flexion

(Figure 4.9). Similar findings were also observed in the bilateral Chopart and Lisfranc

amputees that would explain the reductions in work across the knee joint. For the

Chopart amputee, the knee extension moment peak (KM2) was comparable to that

observed in the TMT amputee as was the power absorption peak (KP1) despite a normal

angular excursion of the knee joint (Figure 4.9) which is difficult to explain. The lack of

power absorption (KP1) expected may indicate some energy transfer to another limb

segment. Delays in the timing of the KM2 and KP1 peaks observed in the bilateral

Chopart amputee reflect delays in the peak stance phase knee flexion as previously

discussed (Figure 4.10).

During the latter half of the mid-stance phase, the normal knee flexion moment

was absent on the affected limbs of the TMT and Lisfranc amputees, except subject

2703-1903A (Figure 4.16-4.17). Mechanically, the absence of the normal knee flexion

moment typically reflects the limited carry over ankle plantarflexion moment (Figures

4.13-4.14) that is a primary influence on the knee moment equation during this time.

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Clinically, it is likely that that the tibial angle, and therefore knee position, moved in

unison with the line of action of the GRF in an attempt to reduce the external moment

and the muscular requirement of the weak gastrocnemius musculature. The affect of

muscle activity on the knee moment is likely to be negligible given the atrophied soleus

and gastrocnemius and the absence of other muscle activity and no co-contraction was

observed about the knee joint. The normal power absorption observed across the knee

joint at this time (40%GC) and subsequent power generation prior to the KP3 peak were

equally as puzzling (Figure 4.23) but are the product of the moment profile observed.

For subject 2703-1903A the normal knee flexion moment observed (Figure

4.16) is difficult to explain given that the plantarflexion moment was relatively small

and comparable to the other TMT and Lisfranc amputees (Figure 4.13). It would seem

unlikely that there is substantial triceps surae force in this individual given the atrophy

observed and the subsequent concentric activity of these muscles that would be

indicative of normal function. It is also difficult to explain the normal exchange of

power across the knee between mid-stance and the pre-swing phase (Figure 4.23).

The relatively normal knee flexion moments observed on the affected limbs of

the Chopart amputees were in stark contrast to those of the TMT and Lisfranc amputees.

A substantial external moment is likely to have been observed about the knee joint in

these individuals given the normal magnitude and lever-arm of the GRF (Figure 4.15).

The external moments could be resisted by the clamshell PTB socket assuming

sufficient resistance could be tolerated between the anterior surface of the leg and the

anterior wall of the socket. The external moments seem to have been significantly larger

than normal in subject 3004-1102A and on the left limb of subject 0904-1924A (Figures

4.16-4.17) driving the knee into hyperextension (Figures 4.9-4.10). Resistance to the

external joint moment is likely to have been augmented by the eccentric activity of

biceps femoris long head (Figures 4.23-4.24) in subject 3004-1102A (Figure 4.35) and

on the left limb of subject 0904-1924A (Figure 4.36-4.37). On the right limb of subject

0904-1924A, the knee flexion moment pattern (Figure 4.17) and exchange of work

across the knee (Figure 4.24) were comparable to normal despite the absence of biceps

femoris activity (Figure 4.37). These results may indicate that equilibrium could be

reached without additional muscle activity.

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The kinematic pattern of knee hyperextension observed in the Chopart subjects

3004-1102A and on the left limb of subject 0904-1924A tended to delay knee flexion

into swing phase (Figures 4.9-4.10). This kinematic anomaly seems to have been

resolved by rapid knee flexion into swing phase (Figure 4.9-4.10) and is likely to be due

to concentric activity of biceps femoris (Figures 4.23-4.24) working in a similar manner

to the short head of biceps femoris which is likely to be active at this time. On the right

limb of subject 0904-1924, the same kinematic pattern appears to have been controlled

using more substantial power generation by the hip flexor muscles than observed on the

contralateral limb (Figure 4.26).

Knee joint moment patterns observed in the majority of TMT and Lisfranc

amputees concur with previous reports that a small extension moment was maintained

from foot-flat through to toe-off in TMT amputees (Dillon, 1995; Mueller et al., 1998).

Very little power exchange was observed across the knee during this time (Dillon, 1995;

Mueller et al., 1998), which corroborates findings from the present investigation. The

absorption of power across the knee joint during pre-swing (KP3) was comparable to

previous reports (Muller et al., 1998) however, Dillon (1995) reported substantially less

power absorption at this time. Kinetic patterns for Chopart amputees and the sound limb

have not previously been reported.

The kinetic patterns at the hip were extremely variable across the amputee

subjects compared to those observed at the ankle and knee joints. Unlike the kinetic

patterns observed at the ankle and knee joints, the joint moment and power patterns

observed at the hip were inconsistent with the level of amputation or prosthetic fitting.

A multiplicity of moment and power generation patterns were consistent with

the need to compensate for the lack of power generated across the ankle during terminal

stance (Figures 4.18-4.19). Two basic patterns of power generation across the hip joints

were observed. The first pattern of power generation occurred on the affected hip during

early stance to propel the body forward from the rear. The second pattern also occurred

during early stance, but on the sound limb to provide forward impulse for the pelvis

coincident with the 'push-off' phase on the affected limb.

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The first pattern was observed on the affected limbs of primarily subjects 2703-

1903A, 3004-102A and on the left limbs of the bilateral subjects 2803-0410A and 0904-

1924A where an extension moment was maintained about the hip until just after mid-

stance (Figures 4.18-4.19). Increases in HP1 approached significance in the amputee

subjects except 0704-0403A (Figure 4.25). These hip extension moments were

consistent with significant increases in power generation across the hip during early

stance (HP1) (Figures 4.25-4.26). Prolonged activity of biceps femoris was observed in

several of these individuals, but without EMG of the primary hip extensors like gluteus

maximus it is difficult to establish a concrete relationship. This gait pattern has been

widely reported in both below knee amputees (Winter and Sienko, 1988; Winter, 1991;

Gritter et al., 1991) as well as in above knee amputees (Winter, 1991) to propel the

body forward from the rear.

The second pattern of hip power generation was observed on the sound limb

during early stance (Figure 4.25). This power generation period was coincident with the

pre and initial swing phases on the affected limb. Increased concentric hip extensor

activity was observed in all subjects except subject 0704-0403A (Figure 4.25) and

biceps femoris EMG was also prolonged in many individuals consistent with this type

of gait pattern. This pattern of sound limb power generation has also been observed in

above knee amputees (Seroussi et al., 1996) and provides forward momentum for the

pelvis.

During pre and initial swing phase, the normal power generation associated with

concentric hip flexor activity (HP3) was comparable to normal in all the amputee

subjects (Figures 4.25-4.26). On the sound limbs of the TMT and Lisfranc amputees and

the bilateral Lisfranc amputee, delays in HP3 seemed to coincide with affected limb

HP1 power generation perhaps to drive the body forward in a coordinated bilateral

fashion (Figure 4.25).

A number of interesting relations seem to exist between the hip power

generation peaks HP1 and HP3 which identify a number of different mechanisms to

generate 'sufficient' power to propel the body forward. For example, a substantial power

generation peak (HP1) was observed during early stance on the affected limb of subject

2703-1903A to propel the body forward from the rear (Figure 4.25). The magnitude of

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HP1 must have provided 'sufficient' forward propulsion given that the HP1 peak

observed on the sound limb was substantially smaller than the other TMT and Lisfranc

amputees (Figure 4.25). An alternate pattern of power generation was observed in

subject 3004-1102A where power generation was observed bilaterally during early

stance (HP1) presumably to compensate for the minimal power generated bilaterally

during the HP3 phase (Figure 4.25).

Given the normal power generation observed across the ankle joint of the

bilateral MTP amputee (Figure 4.21) it was not surprising that there were no significant

changes to the hip joint moment (Figure 4.19) and power (Figure 4.26) profiles

compared to the normal population.

For subject 0704-0403A the power generation profiles observed across the hip

joints were comparable to the normal population (Figure 4.25) despite reductions in

power generation across the affected ankle. For the other Lisfranc and TMT amputees,

additional power generation was observed across either the sound or affected hips

during early stance to augment the normal power generation across the sound ankle.

A similarly puzzling scenario was observed for the bilateral Chopart amputee,

where power generation across the ankle was negligible (Figure 4.15) and power

generation across the hip was not commensurately increased above that observed in the

normal population (Figure 4.26). For example, power generation was prolonged until

pre-swing on the left limb of the bilateral Chopart amputee, but the magnitude of this

power generation was relatively small, as was the magnitude of the HP3 peak on both

limbs (Figure 4.26). For the right limb the exchange of work across the hip joint was

comparable to that observed in the normal population (Figure 4.26). This lack of power

generation across the hips and ankles may be explained by the reduced impulse of the

first horizontal GRF peak (FX1) compared to the second (FX2) (Figure 4.2). This

imbalance may tend to cause the limb segment to continually accelerate. Previous

investigators have reported similar reductions in the magnitude of the first horizontal

GRF peak (Dillon, 1995; Hirsch et al., 1996).

For the bilateral Lisfranc and Chopart amputees an extension moment was

dominant across the left hip (Figure 4.19) commensurate with prolonged power

________________________________________________________ Chapter 4. 171

generation and the absence of the normal, HP2 power absorption peak (Figure 4.26). In

these individuals, it appears that only the left limb was responsible for the bulk of power

generation from initial contact through to pre-swing. Similar asymmetries in sagittal

plane energetics have previously been reported for normal individuals (Allard et al.,

1996). Perhaps this gait pattern provided much needed power generation. Reductions in

power generation to advance the body forward with limited compensations in these two

individuals, may be the primary cause of reductions in stride length and walking

velocity (Tables 4.2-4.4).

Previous investigations reporting kinetic patterns for the hip support the variety

of responses observed in the present investigation. Dillon (1995) reported the

maintenance of an extension moment about the hip until after mid stance and a

reduction in the hip flexion moment peak. Similar gait patterns were observed in many

individuals in the present investigation. In contrast, Mueller et al., (1998) reported the

early onset of a flexion moment about the hip which was not corroborated by findings

of the present investigation. Similar variability in the power generation patterns were

also observed, with Dillon (1995) reporting no significant increased in early stance

phase power generation, while Mueller et al., (1998) observed little concentric activity.

Results from the present investigation identified relatively normal power generation

across the hip during early stance in a number of individuals, which would support the

results of Dillon (1995). However, substantial increases in power generation on the

affected limb during early stance were also observed which have not previously been

reported. Previous investigations have not found significant differences in the

magnitude of power generation across the sound hip during pre and initial swing phased

(Dillon, 1995; Mueller et al., 1998). However, Mueller et al., (1998) reported that these

small differences from normal were indicative of a hip flexor gait pattern. Kinetic

patterns for the sound hip or Chopart amputees have not previously been reported with

limited work examining bilateral amputee gait (Dillon, 1995).

Signal processing issues affecting electromyographic data

From the outset of this investigation, the aim of collecting EMG data was,

primarily, to provide quantifiable information about the timing of muscle activity to

augment the interpretation of joint moments and powers. Information about the relative

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intensity of muscle activation was of lesser importance given that many of the muscles

to be analysed in the partial foot population were significantly atrophied. Such

quantifiable information is typically not available using conventional signal processing

techniques, which report either the rectified EMG data or a linear envelope thought to

reflect the pattern of force generation across time.

The simplest technique, which seemed to satisfy the original aim, reported

amplitude normalised EMG using the manual muscle test method (Perry, 1992; Powers

et al., 1998). Periods of muscle activation were determined using a simple threshold

based criteria centred about the 5%MMT level which reflects the equivalent to the

clinically effective grade 2 level of muscle activity (Beasley, 1961 - cited Perry, 1992).

In hindsight, the primary problem with results of the MMT technique proved to

be the level of background noise affecting the quality of the signal and that the level

changed with each electrode placement and person. Much of the EMG signal

characteristic of the noise observed in the present investigation was well in excess of the

5%MMT threshold used to distinguish meaningful muscle activity from the background

noise when the mean of the stable isometric contraction was used (Powers et al., 1998;

Perry, 1992). This lead to the necessity to reduce the level of background noise such

that the clinically meaningful level of 5%MMT could be maintained.

In this investigation, raw EMG data were high-pass filtered at 6Hz to stabilise

the base line signal. Previous investigations have typically utilised a variety of high-pass

cut-off frequencies varying between 10Hz and 40Hz (Hodges and Bui, 1996; Winter,

1991; Basmajian et al., 1985; Murry et al., 1985; Kadaba et al., 1989; Pierotti et al.,

1991; Perry, 1992; Shiavi et al., 1987) to accomplish this goal. However, recent work

suggests that the cut-off frequency should be somewhat less (Nilsson et al., 1993;

Acierno et al., 1998). In the present investigation, high-pass filtering at 6Hz (Acierno et

al., 1998) resulted in marked stabilisation of the baseline signal which was not

improved dramatically with higher cut-off frequencies up to about 20Hz. Cut-off

frequencies above 20Hz, such as the 40Hz utilised by Perry (1992) and Shiavi et al.,

(1987) resulted in a better baseline signal at the expense of affecting the power of the

signal.

________________________________________________________ Chapter 4. 173

The very stable baseline achieved by Perry (1992) and Powers et al., (1998) was

due to the use of fine-wire electrodes and the high-pass filter cut-off frequency of

150Hz. The choice of cut-off frequency while providing a stable base-line signal would

seem to compromise the power of the EMG frequency. The bulk of the power of the

EMG signal lies between 75-102Hz for surface electrodes (Acierno et al., 1998) with a

slightly higher range for indwelling electrodes (Winter, 1990).

Filtering the signal to the point of affecting the power of the signal did not seem

to be a suitable method of resolving the large baseline signal. In order to bring the

baseline signal back within the range needed to utilise the 5%MMT threshold, the

maximum MMT voltage describing 100% muscle activation was determined in a novel

way. Using a stable one-second isometric contraction, the 100% MMT value was given

by the average of the peak voltages of each 10ms interval of the integrated MMT signal.

Determining the maximum MMT voltage in this manner reduced the overall magnitude

of the gait EMG (as a percentage of MMT) and that part of the signal characteristic of

the noise observed was typically below the 5%MMT threshold. The need to modify the

threshold level from 5%MMT suggests that the signal processing technique was not

robust to changes in the level of baseline noise. The variability of the baseline noise was

not well controlled by the signal processing technique used. In some instances, the

baseline noise may have only been 2%MMT, while other times it was above 10%MMT

necessitating that the threshold level be adjusted to give reasonable muscle on/off times.

These variations are likely to reflect factors such as electrode placement and skin

impedance which affected walking EMG as well as the voltage determined to be

100%MMT.

In hindsight, a superior technique would have been to remove the baseline level

of noise. This would have been possible with the collection of a baseline measure of

noise for each electrode placement and offsetting the walking and MMT data by that

level of noise. Determining the 100% MMT value could then utilise the mean of a stable

one-second isometric contraction as described by Powers et al., (1998) and Perry (1992)

without the problems associated with excessive baseline noise. The baseline measure of

noise could have also been used to establish a variable threshold criterion using the

mean and several standard deviations above the baseline signal (Hodges and Bui, 1996;

________________________________________________________ Chapter 4. 174

Studenski et al., 1991; Di Fabio, 1987) to determine an acceptable threshold criteria that

would vary according to the data recorded.

Irrespective of the threshold level used or how the 100%MMT value was

determined, the MMT technique still provided reasonable estimates of muscle on/off

times assuming that the threshold level was adjusted accordingly for each individual

electrode placement. Provided the threshold level utilised was recorded, the results

obtained are reproducible and open for individual interpretation alongside the raw,

filtered and rectified or uncut MMT normalised gait data. The tedious process of

adjusting the threshold level for each muscle of each individual ensured reasonable

muscle on/off times in comparison to previous investigations.

In comparison to previous investigations reporting MMT normalised EMG data

(Perry, 1992) results from the normal population compared favourably in terms of

periods of muscle activation indicating that the estimates of periods of muscle activity

were reasonable. The magnitude of the signals recorded, as a %MMT, were

substantially smaller compared to previous investigation (Perry, 1992). In the present

investigation, peak EMG activity was about one-third that reported elsewhere (Perry,

1992) reflecting differences in the signal processing technique. The mean intensity of

periods of muscle activity proved to be somewhat useless due to fluctuations in the

profile of EMG during lengthy contractions that encompassed more than one phase or

function such as that described in the results section. Moreover, the amplitude

normalisation technique determines each EMG profile relative to the individuals

maximum ability, which does not describe the relative force produced. The relationship

of force production to EMG recorded is further complicated when analysing atrophied

muscle.

In retrospect, a simple linear envelope EMG signal would have provided

sufficient information to identify abnormal periods of muscle activity or gross changes

in amplitude without many of the complications and downfalls of the technique used in

the present investigation.

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4.5 Conclusion

During the last five years, our understanding of the way partial foot amputees

walk has progressed substantially from the static force analysis theories that have

dominated our clinical understanding and treatment practices for some 30 years. Recent

research quantifying the gait of partial foot amputees has highlighted a number of

temperospatial and biomechanical abnormalities. These abnormalities required further

research to identify the causes underpinning the abnormal movement patterns described

in the literature. This study provides new insights into the gait of partial foot amputees

by documenting previously unpublished information such as bilateral electromyography

and mechanical descriptions of the sound limb. These contributions provide much

needed data, which has allowed many of the abnormal movement patterns to be

identified and better understood. Our understanding of the gait of these amputees could

be further enhanced with information documenting kinematic movement of the trunk,

the rise and fall of the centre of mass of the trunk relative to power generation across the

ankle, step length and EMG of the major hip extensors and flexors.

The major findings from this investigation include:

1. Reductions in ankle range of motion in the Lisfranc and Chopart

amputees were consistent with equinus deformity. Reductions in ankle range were

functionally significant for the Lisfranc amputees but not for the Chopart amputees

fitted with clamshell sockets.

2. Temperospatial abnormalities in a few individuals were observed but

were inconsistent with amputation level, age or prosthetic/orthotic fitting.

Reductions in walking velocity were primarily due to reductions in stride length, not

cadence. The proportion of the gait cycle spent in sound limb stance was increased

in these individuals and commensurate reductions in contralateral single support

were observed. The duration of double support (as a percentage of the gait cycle)

was increased in these individuals but differences were inconsistent.

3. No significant reductions in the total excursion of the centre of pressure

were observed, however, substantial progression of the centre of pressure past the

distal residuum did not occur until contralateral heel contact in the TMT and

Lisfranc amputees. These differences seem to reflect requirements to keep the centre

________________________________________________________ Chapter 4. 176

of mass of the trunk within the base of support and have the benefit of protecting the

distal residuum from extreme forces.

4. Ankle kinematic patterns observed in the TMT and Lisfranc amputees

could be characterised by rapid limb loading, poor control of tibial rotation during

the mid-stance and pre-swing phases, reductions in maximum plantarflexion and

variable swing phase trajectories. The ankle kinematic patterns were consistent with

reductions in the effectiveness of soleus and gastrocnemius. During the mid-stance

phase, the tibia seemed to rotate freely over the stance foot and this rotation was

checked by contralateral initial contact. The peak plantarflexion angles observed on

the affected limbs of the TMT and Lisfranc seemed to be related to the ability to

transfer weight to the sound limb and achieve double support stability.

5. Ankle kinematic patterns observed on the affected limb of the Chopart

amputees reflect relative movement of the leg segment within the socket and the

force deflection characteristics of the prosthetic foot. Tibial rotation seemed to be

controlled by an internal moment generated against the anterior wall of the socket,

which was augmented by knee hyperextension during the latter part of the mid-

stance phase.

6. The effects of amputation on stance phase knee flexion were variable and

inconsistent with kinematic patterns commonly seen in individuals with soleus

weakness. In the Chopart amputee, knee flexion into swing phase was delayed as a

result of the knee hyperextension previous described. Concentric activity of biceps

femoris long head was associated with rapid knee flexion, ensuring that the swing

phase knee trajectory was normal.

7. Kinematic patterns of the hip were comparable to normal except in two

individuals where changes in maximum hip extension angle were observed. These

abnormalities may be a mechanism to obtain normal stride length or put the hip

extensor musculature in a more advantageous force/length relationship.

8. Significant reductions in the ankle plantarflexion moment were observed

only in TMT and Lisfranc amputees reflecting changes in both the excursion of the

centre of pressure and premature timing of the terminal vertical force. Reductions in

ankle power generation were consistent with reductions in the external torque in the

TMT and Lisfranc amputee subjects. For the Chopart amputee, reductions in power

generation across the ankle were the result of the elimination of ankle motion.

________________________________________________________ Chapter 4. 177

9. Reductions in ankle power generation were compensated for by

increased concentric activity on both the sound and affected hip joints during early

stance. Increased power generation across both the hip joints provided the missing

work necessary to advance the body forward. Sound limb power generation during

early stance was commensurate with the generation of power across the hip joint

during the pre- and initial swing phases. No significant increases in power

generation were observed during the pre- and initial swing phase. Some individuals

did not seem to generate additional power to compensate for reductions in power

generation across the ankle. Reductions in the impulse of the horizontal ground

reaction force may add acceleration to the limb system as observed in a single

Chopart amputee.

The clinical implications of these results have not been discussed as part of this

chapter. The subsequent chapter focuses on the significant findings of this investigation

and addresses the clinical implications for rehabilitation, prosthetic/orthotic design and

prescription.

_______________________________________________________ Chapter 5. 178

Clinical implications affecting prosthetic design and

rehabilitation practice

5.1 Introduction

Results from the preceding investigation (Chapter 4) highlight that partial foot

amputation results in a number of adaptations to the basic pattern of locomotion

characteristic of triceps surae weakness and the influence of prosthetic and orthotic

design. The purpose of this discussion is to explore some of the clinical implications of

these findings in relation to the design of prosthetic/orthotic devices, rehabilitation

practices for individuals with partial foot amputation and the basis of prescription.

The initial part of this discussion focuses on the gait patterns of Chopart

amputees, describing how prosthetic design and rehabilitation could be altered to reduce

the requirement of the hip extensor musculature to compensate for the lack of power

generated across the affected ankle during early stance. The second part of this

discussion examines the gait patterns of TMT and Lisfranc amputees and demonstrates

how little prosthetic/orthotic design influences the mechanics of locomotion when the

triceps surae musculature is weak. A brief discussion on the merit of current

prescription practices is the final contribution to this discussion chapter.

Chapter 5

_______________________________________________________ Chapter 5. 179

5.2 Clamshell sockets

In light of the gait patterns observed on the affected limb of the Chopart

amputees, a number of novel ideas regarding the design of prostheses, incorporating

clamshell sockets, have come to the fore. These ideas focus on restoring power

generation across the ankle joint to reduce the requirement placed on both sound and

contralateral limb hip extensors during early stance phase and generally improve gait.

Results from the preceding investigation highlighted that power generation

across the ankle was significantly compromised in the Chopart amputees, to the point of

being negligible (Figure 4.22). Reductions in ankle power generation were due to the

effective elimination of ankle motion by the clamshell socket design (Figure 4.12).

Biomechanically, reductions in power generation across the ankle joint were the result

of the restricted joint angular velocity and not the reduced ankle joint moment. The peak

'passive' plantarflexion moments were normally timed and of similar magnitude to those

observed in the normal population (Figure 4.15). These moments are termed 'passive'

because the fixed ankle joint allows the prosthesis to carry the moment without muscle

activity. The abnormal ankle moment pattern observed during the mid-stance phase

would not influence the power generation peak given that by 40% of the gait cycle,

when power generation commenced, the moment patterns were similar to normal

(Figure 4.15).

These gait observations highlight that without a suitable joint in the clamshell

socket it would not be possible to generate power across the ankle. These data also

highlight that prostheses with clamshell sockets enabled the individual to apply body

weight loads (Figures 4.3-4.4) when the GRF was at a substantial lever-arm from the

ankle (Figures 4.5-4.6 and 4.15). Given these observations, if an external ankle joint

could be incorporated into the prosthetic design, would Chopart amputees be able to

generate power across the ankle comparable to that observed in a normal population?

If incorporating an ankle joint into the Clamshell prosthesis did not substantially

alter the ankle kinematic pattern or joint moment from that observed in the normal

population, then it would seem mechanically possible to restore power generation across

the ankle. It would be difficult to demonstrate this clinically given that it is not possible

_______________________________________________________ Chapter 5. 180

to predict how an individual would respond to such radically different prosthetic fitting

given the potential limitations of muscle weakness, difficulties with adequately coupling

the remnant foot and prosthesis to transmit the muscle force develop to the prosthesis.

However, this mechanical principal could be demonstrated mathematically or using a

simple model where the normal ankle kinematic pattern, or joint angular velocity, could

be modelled using a polynomial function. The modelled or 'normal' joint angular

velocity could replace that measured in an amputee subject prior to determining joint

powers using the inverse-dynamic approach. Given that the joint moment and angular

velocity data fed into the joint power calculation would be comparable to normal, then

the calculated ankle power generation would also be comparable to normal.

The inferences able to be gathered from such a model are extremely limited

given the assumptions made with regard to the ankle kinematic pattern and joint

moment profile. While it may be beneficial for an individual to display a 'normal' ankle

kinematic pattern simply by incorporating a joint into the prosthesis, the reality is that

this is an unlikely occurrence given the significant muscle weakness observed in these

amputees and the potential limitation of coupling muscle force to the prosthesis.

Moreover, the 'normal' joint moment could only be carried by the prosthesis because the

ankle joint was fixed and without this mechanism it may not be possible for the weak

calf musculature alone to moderate the external torque. There is little evidence to

suggest that such modifications to the clamshell prosthesis would enable individuals to

adopt a gait pattern commensurate with the ability to moderate the magnitude of the

external torque such that substantial anterior progression of the GRF was commensurate

the peak vertical GRFs during late stance.

The preceding investigation highlights that the 'normal' ankle kinematic pattern

was very much dependant on a number of factors. These factors are likely to include the

strength of the ankle plantarflexor musculature and the ability of these muscles to

generate sufficient internal torque to produce the desired kinematic pattern of motion

against the external torque. Both of these factors, in turn, influence the position of the

trunk over the stance foot. The relationship between the ankle kinematic pattern and

these other factors is worthy of further discussion in the context of designing an ankle

joint for Chopart amputees.

_______________________________________________________ Chapter 5. 181

The weakness of soleus and gastrocnemius would seem to be one limitation to

providing an ankle joint for Chopart amputees. In normal gait, the ankle plantarflexor

musculature not only contribute to the generation of power across the ankle joint during

the pre and initial swing phases, but the role of these muscles during the mid-stance

phase is arguably more important in terms of controlling the kinematic trajectories of

the ankle, knee and trunk.

Throughout the mid-stance phase of normal gait, eccentric activity of soleus

(later augmented by gastrocnemius) contributes to stability of the knee and ankle and

restrains the rate that the tibia rotates over the stance foot. The controlled movement of

the ankle into increasing dorsiflexion is the result of the balance between the intrinsic

muscle and extrinsic joint torques. During the mid-stance phase, the magnitude of the

external joint torque increased linearly and by the end of single limb support is

substantially larger than the internal torque produced by contraction of the ankle

plantarflexors. As such, the ankle dorsiflexion angle increases in a controlled manner.

These actions help control forward movement of the trunk over the stance foot and

prevent excessive ankle dorsiflexion. During the later portion of the mid-stance phase,

the increasing dorsiflexion angle is halted and reversed. These kinematic changes are

affected by substantial activity of the ankle plantarflexors, which increase the magnitude

of the internal torque to match and then exceed the external torque, consequently

moving the ankle toward plantarflexion. In the Chopart amputees where soleus and

gastrocnemius have little effect, the external torque and tibial progression appear to

have been moderated by a counterforce generated across the anterior wall of the

clamshell socket. The ability of the socket alone, to resist the largest external torques

seems unlikely given that hyperextension of the knee (Figures 4.9-4.10) was necessary

to moderate the external torque and the rotation of the leg and foot segment (Figures

4.16-4.17).

If a freely rotating ankle joint were incorporated into a clamshell socket, the

prosthesis would not enable the individual to adopt a gait pattern, which would allow

normal magnitude external torques to be generated. Essentially, the prosthesis would

not be able to resist the external torque and control tibial rotation. Neither would the

weak calf musculature. In all likelihood, the external torque would have to be

substantially reduced to a point where the magnitude of this torque could be managed

_______________________________________________________ Chapter 5. 182

by a combination of the torque developed by the weak ankle plantarflexor musculature

and gait adaptations. The resulting gait pattern could be very similar to that observed in

the TMT and Lisfranc amputees.

In the TMT and Lisfranc amputees, eccentric activity of the triceps surae

seemed unable to control the rate of tibial rotation or halt and reverse the increasing

dorsiflexion angle. Rapid and excessive ankle dorsiflexion was observed during the later

half of the mid-stance phase, which was eventually checked by contralateral heel

contact. The magnitude of the external torque was reduced by limiting the excursion of

the CoP, thus reducing the lever-arm of the GRF about the ankle. The magnitude of the

external torque is likely to have been reduced to a point where it could be controlled by

a combination of muscle activity and gait adaptations. These actions also moderated the

excursion of the CM of the trunk in relation to the base of support until such time that

the trunk could progress outside the base of support in an, arguably, controlled manner.

The resulting gait pattern was described in the preceding investigation as ‘falling over’

the end of the remnant foot.

Many of these potential gait anomalies, which may result by incorporating a

freely rotating ankle joint into the Clamshell prosthesis, could be addressed by

prosthetic design and physical therapy.

Rather than by incorporating a freely rotating ankle joint into the clamshell

prosthesis some mechanism could be incorporated which could moderated tibial rotation

and the increasing ankle dorsiflexion angle during the mid-stance phase. Such an ankle

joint would also allow a portion of the external torque to be carried by the leg shell

given that there would be some degree of controlled coupling, or motion restriction,

between the leg and foot segments. The prosthetic ankle joint may be similar to the

dorsiflex assist ankle joint used in ankle foot orthoses. Ankle dorsiflexion could be

resisted by a tension spring incorporated posterior, or a compression spring anterior, to

the joint axis. The resistance to ankle dorsiflexion would increase linearly with joint

angle in a similar fashion to the external torque if such a spring mechanism were

utilised. The amount of mechanical resistance should be inversely proportional to the

strength of the calf musculature. With physical therapy to strengthen the calf

musculature, the elastic resistance could be reduced as muscle strength increased. The

_______________________________________________________ Chapter 5. 183

device would then augment the remaining muscle activity rather than be the primary

control. However, this relies on research identifying the initial cause of soleus weakness

and thus the muscles potential for rehabilitation.

In the Chopart amputee, soleus weakness and disuse atrophy may be the result of

the elimination of ankle motion due to prosthetic fitting or the result of not developing

force across the ankle joint regularly. Given this scenario, a suitable physical therapy

program in combination with prosthetic fitting that incorporates an ankle joint, could

address the muscular and gait related problems. A suitable physical therapy program

may need to focus on restoring triceps surae strength, ankle joint range of motion in

combination with gait rehabilitation. If the primary cause of triceps surae atrophy is not

disuse, then this type of prosthetic and rehabilitation intervention may fail. However,

alternate explanations for soleus weakness, such as a reluctance or inability to load the

distal residuum or control the position of the trunk seem unconvincing, with

conventional clamshell prosthetic sockets, given that the magnitude and timing of the

external torque was comparable to normal (Figures 4.13,4.15). The normal magnitude

of the net ankle joint torque is a reasonable indicator that the individual could

comfortably apply substantial load the prosthetic forefoot and that the sensitive tissues

are well protected by this socket/prosthetic design.

The transition from peak dorsiflexion to plantarflexion, in the absence of

sufficient muscle strength, would be difficult to achieve using a mechanical joint given

the magnitude of the force required to overcome the substantial external torque during

terminal stance. At best, the stored energy in the ankle joint's spring mechanism would

be returned as the contralateral limb is loaded and the external torque on the affected

limb reduces, forcing the ankle toward a neutral position. However, the timing of rapid

ankle rotation is likely to be delayed if the ankle can not actively halt and reverse the

increasing ankle dorsiflexion until contralateral initial contact. This kinematic pattern

assumes that the torque generated using such a spring mechanism would exceed the

magnitude of the external torque and drive the foot toward plantarflexion. The

continued movement of the ankle into substantial plantarflexion angles, as in normals, is

likely to be a passive occurrence as the magnitude of the external torque is relatively

small, plantarflexor muscle activity has diminished and the vertical and fore-aft forces

are rapidly declining (Sutherland et al., 1980).

_______________________________________________________ Chapter 5. 184

The trailing posture of the limb segment into initial swing relieves concerns

about toe clearance until mid-swing when the effective length of the limb is greatest. In

the Chopart amputees, tibialis anterior is significantly atrophied which would

complicate issues of toe clearance during swing phase. Moreover, the dorsum of the

remnant foot is almost non-existent, almost vertical, and is likely to limit the ability to

gain sufficient purchase of the prosthesis to actively dorsiflex the prosthetic forefoot. A

prosthetic ankle joint would also be required to resolve issues of swing phase toe

clearance. Attaining normal plantarflexion angles during pre and initial swing and rapid

dorsiflexion after toe-off would be difficult to achieve with a simple spring arrangement

such as that described earlier. The likelihood is that any torque designed to move the

foot into neutral during swing phase would also restrict the maximum plantarflexion

angles able to be obtained. A simple, but less than ideal, solution would be for the

spring mechanism to be balanced at a neutral joint angle similar to the position of a

current clamshell socket or ankle foot orthosis. The plantarflexion angles obtained

during pre and initial swing would probably be less than normal in order to obtain

sufficient toe clearance. The simple 'spring-loading' mechanism described here may be

less than ideal, but the number of more complex alternatives are virtually endless.

It is difficult to assess the likely impact an ankle joint would have on the gait

patterns of Chopart amputees described in the preceding chapter. Any such description

would be speculative. Only by understanding how an individual responds to the altered

prosthetic mechanism could mathematical modelling or clinical intervention be used to

improve the design of a suitable ankle joint. Modelling the gait patterns of these

Chopart amputees with a view to designing a suitable joint would require substantial

kinematic and kinetic inputs utilising prototype ankle joints. This type of prosthetic

intervention would rely heavily on physical therapy intervention to improved joint

range, muscle strength and provide gait retraining. Ideally, it would be beneficial to fit

amputees with this style of prosthesis as a primary interim during early rehabilitation.

Thereby, minimising the atrophy of the calf and pre-tibial muscles, minimise muscle

contracture which limits joint range and avoiding extensive physical therapy/gait

retraining.

_______________________________________________________ Chapter 5. 185

It is difficult to know whether these changes would make functionally

significant differences to the power generation observed across the hip joints or merely

alter the ankle kinematic profile to better reflect those observed in non-amputee

populations. Without significant improvement in power generation across the ankle,

striving for kinematic resemblance to normal seems unwarranted. The concept of fitting

Chopart amputees with a functional ankle joint, so that they may benefit from having an

intact ankle and triceps musculature seems worthy of further investigation.

5.3 Below ankle sockets, orthoses and toe fillers

The gait patterns of the TMT and Lisfranc amputee subjects are likely to be

dominated more by the influence of muscle weakness than by prosthetic/orthotic design;

although this was not formally assessed. Given that some subjects were fitted with

below ankle slipper sockets, others with orthoses and toe fillers or had their shoe stuffed

with a sock, it was surprising that the basic pattern of locomotion varied so little once

the metatarsal heads were compromised. This observation was quite surprising given the

author's expectation that below ankle sockets would substantially modify the gait

pattern compared to orthotic interventions or toe fillers given that these devices had a

socket and 'substantial' forefoot replacement.

The basis for this expectation was founded largely on the observations of a

single Chopart amputee (Dillon, 1995) where, as in the Chapter 4, the effective locus of

the CoP was extended and substantial force was applied to the prosthetic forefoot during

terminal stance. The ability of Chopart amputees to demonstrate this loading pattern

during gait reflects the ability of the clamshell socket to comfortably distribute forces

caused by loading the toe lever and the ability to moderate the external torque using the

prosthesis. Of course, without a 'substantial' forefoot lever capable of transmitting these

forces to the socket, the system would not function as observed. The Chopart amputees

moderate the external torque using the anterior leg segment of the clamshell socket in

conjunction with adaptations to the orientation of the leg or thigh segments as evidenced

by the knee hyperextension observed during the mid-stance phase.

The toe fillers and orthoses fitted to some of the Lisfranc and TMT amputees

were unable to function in a similar manner to the Chopart prostheses because orthotic

_______________________________________________________ Chapter 5. 186

management does not incorporate a socket or effective/'substantial' toe lever. An

ineffective toe-lever could be thought of as a material which is unable, or unlikely, to be

able to transmit force to a socket such as plastizote or even polypropylene of a thickness

used in AFOs. The below ankle sockets fitted to some of the Lisfranc amputees did

incorporate a socket and a 'substantial' toe lever. So why were the observed gait patterns

not different from those of other Lisfranc or TMT amputees who were not fitted with

prosthetic style devices?

The gait patterns observed for all the TMT and Lisfranc amputees were limited,

in part, due to soleus and gastrocnemius weakness. For all intents and purposes it would

probably not matter how the orthosis or below ankle socket was designed unless there

was sufficient muscle force to control tibial rotation and trunk position which would

allow individuals to adopt a gait pattern where substantial external torques could be

resisted. Without the ability to match the ‘normal’ magnitude of the external torque, the

individual would adopt an alternate gait pattern to reduce the external torque and

therefore the muscular requirements. If there was sufficient muscle force to resist an

external torque of ‘normal’ magnitude, then a device incorporating a socket and suitable

toe lever would seem to be the most appropriate. For without these two fundamental

aspects of the prosthetic design such torques could not be achieved.

Perhaps the most fundamental question concerning prosthetic/orthotic design for

individuals who do not utilise clamshell style prostheses is what mechanisms cause

weakness of the triceps surae musculature?

Unlike in the Chopart amputees, the initial cause of triceps surae muscle

weakness does not seem to be the result of disuse atrophy due to the elimination of the

available joint range of motion. The preceding investigation highlighted that soleus

weakness may be the result of adopting a gait pattern that reduced the forces applied to

the distal residuum. This seems to have been accomplished, as described in Chapter 4,

by limiting the excursion of the CoP until double support is achieved, when a significant

portion of the superincumbent load could be transferred to the sound limb and

progression of the GRF could then occur with significantly less force transmitted across

the distal residuum. In effect, triceps surae weakness may be the result of inadequacies

in the prosthetic/orthotic design.

_______________________________________________________ Chapter 5. 187

If the devices initially prescribed to people during rehabilitation are unable to

comfortably distribute forces caused by proper loading of the prosthetic forefoot,

individuals may adopt a gait pattern to reduce pain on the distal residuum such as that

just described. Limiting the excursion of the CoP until initial contact of the contralateral

foot, while minimising the force applied to the distal residuum, would decrease the

external torque and forward progression of the CM of the upper body. The long-term

consequence of adopting this gait pattern would be the reduced requirement of the

triceps surae muscles resulting in disuse atrophy. Even if later prosthetic/orthotic

intervention was able to restore the mechanical lever arm of the foot effectively and

distribute forces caused by loading the toe lever in a comfortable fashion, the triceps

surae muscles would be so weak that adopting a more advantageous gait pattern would

not be possible; at least not without prior physical therapy. This hypothesis would seem

to explain the gait patterns of the Lisfranc amputees fitted with below ankle style

prostheses.

Further research needs to identify the initial cause of soleus weakness. If, as

hypothesised here, triceps surae weakness is the result of adopting a gait pattern to

reduce undesirable force on the distal residuum, then primary or interim

prosthetic/orthotic intervention needs to provide devices with suitable forefoot levers

and sockets capable of comfortably distributing forces caused by loading the prosthetic

forefoot. If the devices initially fitted to amputees are not capable of this, then weakness

of the triceps surae is an almost inevitable result. The resulting or long term gait pattern

would then be dominated by muscle weakness even in spite of subsequent prosthetic

fitting which may well have been designed to comfortably distribute forces caused by

loading the forefoot lever.

Reductions in the abnormally high power generated across the hip joint during

early stance phase, on both the sound and affected limbs, are only likely if substantial

power can be produced across the ankle during terminal stance. Again, further research

is warranted to try to provide partial foot amputees with the ability utilise the intact

ankle and triceps surae musculature given that the primary benefit of preserving the

ankle joint is likely to be the ability to use it.

_______________________________________________________ Chapter 5. 188

5.4 Prosthetic prescription

It was surprising that the basic pattern locomotion observed across the TMT and

Lisfranc amputees varied so little, particularly given that subjects were fitted with a

wide variety of devices including below ankle slipper sockets, foot orthoses, toe fillers

or had their shoe stuffed with a sock. This finding is, in its self, a remarkable discovery.

To think that the aforementioned prosthetic and orthotic devices fitted to the TMT and

Lisfranc offered no substantial biomechanical benefit above that which was be achieved

by stuffing a sock in a shoe. So much for prescription criteria based on mechanical

function!

For many decades rehabilitation specialists, podiatrists and prosthetists/orthotists

have prescribed devices such as toe fillers and slipper sockets based largely on clinical

experience in the absence of numerical information describing the biomechanics of

partial foot amputee gait and the influence of prosthetic/orthotic fitting. In light of this

new information, common conceptions about how various prosthetic and orthotic

devices function, such that these devices restore foot length, are brought into question.

So is the mechanical basis upon which each of these devices is prescribed. While there

appears to be little mechanical evidence to support the prescription of toe fillers, slipper

sockets or foot orthoses for the restoration of lost foot length, to aid propulsion or

protect the distal residuum from extreme forces there may be measurable benefits not

identified by this research such as reductions in plantar pressure.

It would be premature to provide an evidence-based approach to the prescription

of prosthetic and orthotic devices given that quantifiable literature is available for only a

small number of amputee subjects and that the insights into the biomechanics of partial

foot amputee gait and the influence of prosthetic/orthotic fittings are theoretical.

5.5 Conclusion

Results from the preceding investigation highlighted that partial foot amputees

typically generate abnormally large power across either or both the sound and affected

hip joints during early stance as a mechanism to compensate for reductions in power

generation across the affected ankle.

_______________________________________________________ Chapter 5. 189

This discussion highlighted the cause of reductions in ankle power generation

and proposed changes to prosthetic/orthotic design and rehabilitation practices aimed at

restoring power generation across the ankle so as to reduce the requirements of the hip

extensor musculature and improve gait in general.

For the Chopart amputee, reductions in affected limb ankle power generation

were due to the elimination of ankle motion resulting from prosthetic fitting. Providing

an ankle joint for the prosthesis would seem to be a simple solution to this problem.

However, the fixed ankle and the clamshell socket design allows the amputee to adopt a

gait pattern commensurate with the ability to moderate the magnitude of the external

torque. Significant improvements in ankle power generation would not be possible

without the inclusion of a custom design ankle joint and the ability to control it. Any

ankle joint would need to augment the available muscle activity and afford the amputee

the ability moderate the external torque in addition to:

1. providing the necessary resistance to control the rate of tibial progression as the

limb rotates over the stance foot;

2. decelerate the rapid anterior rotation of the tibia and allow the individual the

ability to use the existing musculature to drive the foot toward plantarflexion

commensurate the largest ankle joint moments;

3. providing adequate toe clearance during mid-swing given that there is likely to

be an inability to dorsiflex the prosthesis as a result of the shape of the distal

residuum and the poor coupling of the remnant foot and the prosthesis.

For the TMT and Lisfranc amputees, improving strength of the triceps surae

muscles would seem to be the only way of restoring power generation across the ankle.

Sufficient triceps surae strength may allow individuals to adopt a gait pattern that would

capitalise on prosthetic design that incorporates an effective replacement foot lever. The

toe lever would have to be able to transmit forces caused by loading to the prosthetic

socket. The prosthetic socket must be able to comfortably distribute forces caused by

loading the toe lever. A simple clinical test to determine if the prosthesis functions in

this manner may be to see if individuals can 'stand up on their toes'. Individuals with

TMT and Lisfranc amputation who took part in the preceding investigations were

unable to perform this simple test with the prosthesis on. With the prosthesis off, these

_______________________________________________________ Chapter 5. 190

individuals could achieve a reasonable joint range with good muscle strength, which

may have been limited compared to the normal population with the prosthesis on due to

pain or ankle plantarflexor weakness. This test is more limited for Chopart amputees

given the limited range of ankle motion resulting from prosthetic fitting.

Developing a prototype ankle joint for clamshell prostheses would seem like a

logical next stage. Assessment of the resulting gait patterns will provide much

information to guide further development and provide answers or insights to many of

the fundamental questions concerning the efficacy of this concept.

Further research is needed to identify whether the insights discussed regarding

prosthetic design and rehabilitation will result in improved power generation across the

ankle and reductions in the demand on the hip extensor musculature during early stance

and generally improved gait.

________________________________________________________ Chapter 6. 191

Conclusion and indications for further investigation

6.1 Conclusion

This thesis presented a number of discrete investigations, which developed the

central theme of providing accurate mechanical models that could subsequently be

applied to study the effect of amputation and prosthetic/orthotic intervention on gait.

In Chapter 2, a geometric model based on work by Hatze (1979) was developed

to improve the accuracy of anthropometric input data utilised by linked-segment models

used to estimate kinetic parameters of partial foot amputee gait. The model provided

reasonable estimates of foot mass, volume and centre of mass across a wide variety of

intact and partially amputated feet compared to experimentally derived estimates

obtained using incremental immersion. Modelled values of the radius of gyration were

compared to experimental data derived using a trifilar torsional pendulum and the

discrepancies observed, primarily in the amputee population, seem to reflect difficulties

associated with accurately orienting the principle axes of the foot replica on the trifilar.

The discrepancies observed were comparable to those reported for similar models. The

model may be advantageous to investigators of partial foot amputee gait wishing to

acknowledge the unique anthropometry of the remnant foot and improve the accuracy of

kinetic descriptions obtained using linked-segment inverse dynamic models.

Chapter 6

________________________________________________________ Chapter 6. 192

Linked-segment inverse dynamic models were developed in Chapter 3, which

incorporating improved anthropometric descriptions of the remnant foot as well as

accounted for changes in anthropometry of the proximal limb segments and

prosthesis/orthosis and footwear. These modifications to a standard linked segment

model more accurately depicted the amputee’s lower limb, enhancing the kinetic

estimates obtained from these models. These improved linked-segment models

significantly modified the anthropometry of the modelled free body segments and the

influence of changes in segment mass, centre of mass and mass moment of inertia

differed depending on the type of model used. The partial foot models increased the

knee flexion and hip extension moments observed during terminal swing compared to a

standard linked-segment model. These kinetic differences were indicative of a more

accurate portrayal of the activity of the hamstring and gluteus maximums muscles to

decelerate the knee into full extension and the hip into it's initial contact hip flexion

angle. Changes in power generation/absorption across the knee and hip were

commensurate with changes in the joint moments. Previous investigators are likely to

have underestimated the magnitude of moments and powers during terminal swing

phase. Given the substantial work necessary to generate these models and improved

anthropometric input data, many investigators may feel that the additional work is not

warranted by the small absolute differences observed.

Having established an appreciation of the influence these improved

anthropometric and linked-segment models have on the kinetic parameters estimated,

the effect of amputation and prosthetic/orthotic fitting on the gait of a cohort of partial

foot amputees was investigated.

The investigation presented in Chapter 4, reported temperospatial abnormalities

in only a handful of individuals, inconsistent with age, prosthetic/orthotic fitting or level

of amputation. These results indicate that temperospatial abnormalities, such as reduced

walking velocity and stride length or increased proportion of the gait cycle spent in

sound limb stance, were not a direct result of forefoot amputation but could be related to

other measures of function, which were not examined, such as balance. Ankle kinematic

patterns in the transmetatarsal (TMT) and Lisfranc amputees were characterised by poor

control of tibial rotation during the mid-stance phase resulting in an ever increasing

dorsiflexion angle which was eventually checked by contralateral initial contact.

________________________________________________________ Chapter 6. 193

Maximum plantarflexion was substantially reduced in many individuals which seemed

to be related to the ability to transfer weight onto the sound limb and achieve double

support stability. For the Chopart amputee, the ankle kinematic pattern was a reflection

of the force/deflection characteristics of the prosthetic foot and movement of the leg

within the clamshell prosthesis. The centre of pressure did not progress substantially

past the distal residuum until contralateral heel contact in the TMT and Lisfranc

amputees reflecting the requirement to keep the trunk positioned within the base of

support. This gait pattern also has the advantage of protecting the distal residuum from

the peak ground reaction forces. The peak plantarflexion moment observed in the TMT

and Lisfranc amputees was substantially reduced due to the limited anterior excursion of

the centre of pressure commensurate with the peak vertical ground reaction force. This

finding indicates that although the total excursion of the centre of pressure was

comparable to normal, the ability to substantially load the replacement forefoot was

compromised. The inability to load the prosthetic forefoot could reflect inadequacies in

prosthetic design and the inability to control the position of the centre of mass of the

trunk if it progressed outside the base of support. Reductions in power generation

across the ankle of the TMT and Lisfranc amputees were commensurate with reductions

in the joint moment and angular excursion of the ankle. For the Chopart amputees,

reductions in power generation across the ankle were due to the elimination of the ankle

range and not the inability to load the prosthetic forefoot as evidenced by the peak

plantarflexion moment. Reductions in power generation across the ankle resulted in

compensatory increases in concentric hip extensor activity on both the sound and

affected hip joints during early stance. Increased power generation on the affected limb

propelled the body forward from the rear. While power generation across the sound hip

during early stance was commensurate with power generation across affected hip joint

during the pre and initial swing phases associated with concentric work of the hip flexor

musculature.

The substantial work observed across the hip joint could be moderated by

restoring power generation across the affected ankle as discussed in Chapter 5. For the

TMT and Lisfranc amputees, improvements in triceps surae strength may allow

individuals to capitalise on prosthetic design that includes a toe lever and socket capable

of transmitting, and comfortably distributing, forces caused by loading the forefoot.

Shoe inserts or toe fillers do not incorporate a substantial toe lever capable of

________________________________________________________ Chapter 6. 194

transmitting the forces developed by loading the forefoot to the socket nor a socket

capable of comfortably distributing these forces. The ability to load the remnant

forefoot relies on suitable prosthetic design and sufficient calf muscle strength to

moderate the external torque generated by adopting a gait pattern consistent with the

ability to load the replacement forefoot. While the clamshell prosthesis fitted to the

affected limb of the Chopart amputees allowed individuals to generate substantial

external ankle joint torques, improvements in power generation would not be possible

without the ability to utilise the available ankle range. Significant improvements in

power generation across the ankle would not be possible without a suitable ankle joint

and improvements in joint range and muscle strength to control the angular excursion

and moderate the external joint torque. The development of an ankle joint for clamshell

prostheses would pose a substantial design challenge. While mathematically, the merit

of the proposal can be demonstrated, the likelihood is that the internal torques needed to

be generated either by the remnant musculature or a mechanical joint would be too

large.

In conclusion, this thesis provided novel anthropometric and linked-segment

inverse dynamic models that enabled more accurate mechanical descriptions of the

swing phase of partial foot amputee gait. While these models are not likely to be used

routinely, given the small absolute differences in swing phase moments and powers,

they demonstrate the influence of accurate anthropometric modelling on kinetic

descriptions of partial foot amputee gait which may be advantageous to future

investigators.

Results from this thesis also provided exciting new insights into the mechanics

of partial foot amputee gait, which highlighted a number of abnormal movement

patterns and compensatory effects. Previous investigations have not documented kinetic

descriptions of the sound limb or electromyography, which in hindsight proved to be the

keystones explaining how reductions in power generation across the affected ankle were

compensated for. Although previous investigations have documented reductions in

power generation across the affected ankle (Dillon, 1995; Mueller et al., 1998) neither

of these investigations provided substantial insight describing the causes of this

abnormality or the influence of prosthetic and orthotic intervention. This thesis

________________________________________________________ Chapter 6. 195

provided substantial insight into changes in work, satisfying the original objectives of

the thesis.

Results from these investigations challenge common misconceptions about the

gait of partial foot amputees and how prosthetic/orthotic devices function, which have

underpinned our clinical and prescription practices as well as design principles for many

decades. Views concerning the ability of prosthetic/orthotic devices and footwear to

restore the lost lever arm or foot length (Condie, 1970; Rubin, 1984; Rubin, 1985;

Pullen, 1987; Stills, 1987; Condie and Stills, 1988, Weber, 1991; Mueller and Sinacore,

1994; Sanders, 1997; Sobel, 2000) are by and large, not supported by findings from this

research because only Clamshell prostheses were able to restore the 'effective' lever-arm

of the forefoot. Results from this investigation also refute contentions that

prosthetic/orthotic devices aid propulsion or push-off (Rubin and Denisi, 1971; Rubin,

1984; Rubin, 1985; Stills, 1987; Sobel, 2000) or that hallux or toe amputation results in

a loss of push-off or propulsion (Sanders, 1997; Sobel, 2000). Only once the metatarsal

heads were affected was power generation across the ankle negligible irrespective of

foot length. Thus if surgery compromises the metatarsal heads, then more proximal

level selection should be based on criteria (ie: quality of skin coverage) other than trying

to preserve the ability to generate power across the ankle joint by preserving foot length.

This finding also challenges the common belief that preserving foot length should be a

surgical objective necessary to maintain normal gait (Barry et al., 1993; Giurini et al.,

1993; Pinzur et al., 1997; Sobel, 2000). Recent work concluding that partial foot

amputees adopt a hip flexor gait to compensate for a lack of power generation across the

ankle (Mueller et al., 1998) were not supported by results from this work. Results from

this investigation found that the primary compensation for the lack of power generation

across the ankle was an increase in hip extensor work during early stance on both the

sound and affected limb.

While results from this thesis provide substantial insight advancing the

understanding of the gait of partial foot amputees and the influence of

prosthetic/orthotic fitting, it would be beyond the scope of these results to use this data

to provide much needed biomechanical merit to the prescription of prosthetic/orthotic

intervention. A number of subsequent investigations, such as those currently in progress

in the United States (Boyd et al., 1999; Burnfield et al., 1998) may be in a better

________________________________________________________ Chapter 6. 196

position to overcome the limitations of sample size. However, it will be a number of

years before a concrete understanding of partial foot amputee gait can be developed

from studies such as this which offer theoretical insights into causes of abnormal

movement and the influence of prosthetic/orthotic fittings. Only then, can an evidence-

based prescription principle developed.

6.2 Further research

While analysing results from the present investigation, additional information

describing step length, trunk kinematics and displacement of the centre of mass of the

combined head, arms and trunk would have been of tremendous benefit in drawing

more conclusive descriptions of the underlying causes of the abnormal movement

patterns observed. The electromyographic (EMG) patterns of only a small number of

muscles were collected for the hip and knee, which were not sufficient to lead to

conclusive results about the muscles which actually contributed internal work to the

kinetic patterns observed. The major hip extensor muscles should be examined to

provide additional insight supporting kinetic descriptions of power generation across the

hip during early stance phase. Similarly, the EMG profiles of additional knee flexor

muscles should be examined to aid explanation of knee flexion moments which were

largely unexplained in a single Lisfranc amputee and the Chopart amputee subjects.

EMG analysis could also estimate force production through calibrating EMG activity

with muscle activity using a dynamometer.

One aspect of the linked-segment model, which was not exploited in this thesis,

was the ability to extract the measured centre of pressure excursion and replace it with a

modelled norm. The modelled centre of pressure excursion was derived mathematically

using a polynomial function where the coefficients for the function were derived from

normalised centre of pressure excursion measurements of intact feet/normal gait. In this

way the abnormal centre of pressure excursion profile, measured for each amputee

subject, could be replaced with a modelled norm and the influence of restorations of

foot length on kinetic parameters could be assessed. This modelling concept was not

pursued given the unreliability introduced by the assumptions about the timing of peak

ground reaction forces and kinematic profiles, which were necessary. For example, it

would be possible using the centre of pressure excursion model to depict a more normal

________________________________________________________ Chapter 6. 197

progression of the ground reaction force such as would ideally be reconstituted with any

prosthetic design. However, if a prosthetic device, which could restore the effective

centre of pressure was fitted, the amputee would likely adopt an alternate kinematic

pattern. Hence, the joint powers generated would be relatively meaningless unless it was

possible to predict how the kinematic pattern and ground reaction forces would adapt to

improvements in centre of pressure excursion. The centre of pressure excursion model

may provide useful information about prosthetic design and optimal foot length once a

better understanding of how the kinematic profiles vary with changes in the effective

locus of the centre of pressure.

In terms of effecting significant changes to prosthetic/orthotic design, research

needs to focus on determining the mechanisms leading to reductions in ankle power

generation in TMT and Lisfranc amputees. Perhaps, during rehabilitation individuals

learn to adopt a gait pattern, which avoids excessive plantar pressures resulting from the

prosthetic/orthotic device. If subsequent prosthetic/orthotic fitting incorporates a socket

and toe lever suitably designed to effect forefoot loading, these individuals may still not

have sufficient muscle strength to adopt a gait pattern characteristic of the ability to

moderate the external joint torque and ankle kinematic pattern. Alternatively, sockets

and toe levers may not provide the necessary relief of forces as expected thus not permit

the individual to walk in a manner that would maintaining muscle strength. Further

research needs to identify the primary cause of calf atrophy in these amputees so that

suitable rehabilitation programs and prosthetic devices can be designed.

For the Chopart amputee, the inability to generate power across the affected

ankle is the result of the elimination of ankle motion due to prosthetic fitting. The

development of an ankle joint for the clamshell prosthesis poses substantial design

challenges for the engineer and prosthetist given the complexities associated with

maintaining the ability to moderate the external torque and produce a desirable ankle

kinematic pattern. Any ankle joint would need to augment the available muscle strength

to produce a desirable kinematic pattern. A desirable kinematic pattern could be

described as controlled tibial rotation during the mid-stance phase, rapid ankle rotation

from peak dorsiflexion to peak plantarflexion commensurate with the largest joint

moments and safe clearance of the prosthetic foot during swing phase. The development

________________________________________________________ Chapter 6. 198

of such an ankle joint would ideally see Chopart amputees benefit from the intact ankle

joint musculature.

Further research will undoubtedly focus on providing new principles for the

prescription of various prosthetic and orthotic replacements based on biomechanical

merit rather than anecdotal evidence and clinical experience. It will be some time before

the provision of evidenced-based prescription principles becomes a reality given that

our understanding of partial foot amputee gait and the influence of prosthetic and

orthotic design is very much in its infancy. It would be premature for studies such as

this one to provide principles for the prescription of prosthetic/orthotic devices for two

reasons. Firstly, like many studies of amputee gait, the present investigation was based

on a limited sample which will require a number of similar investigations by a number

of investigators to reach a conclusive understanding about the gait of partial foot

amputees and the influence of prosthetic and orthotic fitting. Secondly, many of the

insights into prosthetic design and function highlighted in this thesis are theoretical and

will require ongoing research to either support or refute the understanding attained by

this research.

______________________________________________________ Appendix A. 199

Letter for patient recruitment

This appendix contains a copy of the letter sent to the Queensland Amputee

Limb Service (QALS), definitive prosthetic/orthotic service providers, acute care and

rehabilitation hospitals which these institutions distributed to clients whom were partial

foot amputees.

Appendix A

______________________________________________________ Appendix A. 200

To whom it may concern,

The Queensland Amputee Limb Service has been kind enough to offer me this

opportunity to contact you regarding current research being conducted at Queensland

University of Technology. A PhD study titled “The Biomechanics of Partial Foot

Amputee Gait” is about to commence, however, we need your help to make this

research possible.

Currently there is little data available on the gait or walking patterns of partial foot

amputees. Current literature remains speculative and evidence anecdotal. The purpose

of this study is to gather and document information on the way that partial foot

amputees walk so that prosthetists may have a better understanding of how forefoot

amputation effects the way partial foot amputees walk. The data collected will also be

used to develop a biomechanical model with the view to basing prosthetic design on

biomechanical data rather than anecdotal evidence.

Participants in the study will be required to attend a single testing session of 4-5 hours

duration at a time convenient to them. Queensland University of Technology will

arrange transport for you to attend the testing session and for your return home.

Participants will incur no expense from their involvement.

During the session, I will take your medical history and record some measurements

such as weight, height and foot length. Participants will be required to wear shorts or

bathers during the session so that reflective markers can be placed on the joints of your

leg and foot. Video cameras will record the motion of these markers as you traverse a

10-metre walkway. A platform will be mounted in the floor midway down the walkway

and will collect information about forces during walking. Electromyography (EMG)

______________________________________________________ Appendix A. 201

data, information about the timing and intensity of muscle activation, will also be

collected. All measurements will be taken while you wear your current

prosthetic/orthotic device.

As a participant in the study, you may withdraw your consent to participate at any time.

The information collected during the session will remain confidential, and your name

and personal details will not be associated with the data collected.

If you are interested in participating, or would like further information about the project

or what your involvement would entail, before making a decision please contact me on

3864 -2451.

I thankyou in anticipation for your support.

Kindest regards,

Michael Dillon.

B. Prosthetics and Orthotics (Hons.), PhD Student

Queensland University of Technology

Centre for Rehabilitation Science and Engineering

School of Mechanical, Manufacturing and Medical Engineering

Po Box 2434

Brisbane 4001

______________________________________________________ Appendix B. 202

An Anthropometric Model of the Partial Foot Residuum

B.1 Introduction

Dimensional and inertial characteristics of the partial and normal feet were

derived using a geometric model based on work by Hatze (1979). From first principles,

the model was derived as an assemblage of 103 plates of varying dimensions and

densities. Three trapezoidal plates represent the most inferior portion of the ball of the

foot (S11), the heel (S12), and the sole above these regions (S13) (Figure B.2). The

remaining 100 plates account for the middle and upper part of the foot (S14) which were

described using parabolic (S14P) and trapezoidal (S14

T) plates (Figure B.1-B.2). The

model is symmetrical about the x-axis (Figure B.1).

An exploded view of the foot illustrates the component plates comprising the

model (Figure B.2).

Equations describing the mass (M), volume (V), centre of mass (CM) and mass

moments of inertia about the CM (I) of the model use notations described in Table B.1,

anthropometric measurements described in Table B.2 and constants in Table B.3.

Appendix B

______________________________________________________ Appendix B. 203

Figure B.1 Geometric model of the Metatarsophalangeal residuum of subject 1004-

1307A; including a schematic representation of the input measurements.

See Tables B.1-B.3 for details of the nomenclature and input measurements pictured here.

c

har

b

la

lhf

h2

ha

h1-har

aml

aap

aaphf

½rr

X

Y

Z

S11

S12

S13

S14T

S14P

lk

OS14P

______________________________________________________ Appendix B. 204

Figure B.2 Geometric model of the Metatarsophalangeal residuum of subject 1004-

1307A. Exploded view illustrating the various components comprising the model.

S14T

S13

S11

S12

S14P

S14P

______________________________________________________ Appendix B. 205

Table B.1 Notations

Notation Explanation

S11..14 Numerical depiction of each segment (S) from 11 to 14

according to Hatze, (1979)

M11..14 Mass of each segment of the foot model [kg]

Mfoot Total mass of the foot [kg]

V11..14 Volume of each segment of the foot model [l]

Vfoot Total volume of the foot [l]

X'11..14, Y'11..14, Z'11..14 Coordinates of the mass centroid in the X,Y,Z direction

for each segment of the model [m]

X'foot, Y'foot, Z'foot Coordinates of the mass centroid of the foot in the X,Y,Z

direction [m]

Ixx11..14, Iyy11..14, Izz11..14 Mass moment of inertia about the X,Y,Z axes taken

through the mass centroid for each segment of the model

[kg.m2]

Ixxfoot, Iyyfoot, Izzfoot Mass moment of inertia of the foot about the X,Y,Z axes

taken through the mass centroid of the foot [kg.m2]

kxx11..14, kyy11..14, kzz11..14 Radii of gyration about the X,Y,Z axes taken through the

mass centroid for each segment of the model [m]

kxxfoot, kyyfoot, kzzfoot Radii of gyration of the foot about the X,Y,Z axes taken

through the mass centroid of the foot [m]

γγγγ(i)

γγγγ11..14

Density of the i-th segment; unit kg/m3

Density of each segment of the model [kg/m3]

______________________________________________________ Appendix B. 206

Table B.2 Anthropometric notation and measurement descriptions

Notation Description Measurement

l Intact foot

length

Distance between the most posterior part of the foot

and the end of the hallux taken parallel to the long axis

of the foot. For amputees use sound foot or estimate

using l = stature(m) * 0.15 (Dempster, 1955)

la Amputated foot

length

Distance between the most posterior part of the foot

and the end of the residuum taken parallel to the long

axis of the foot. Is equal to l for normal subjects

lhf Length of the

hind foot

Distance from the most posterior part of the foot, to a

line vertically bisecting the lateral malleolus

b Width across the

distal foot

Width across the 1st to 5th Metatarsal head

perpendicular to the long axis of the foot. If absent,

measure this dimension across the widest portion of the

distal residuum

c Width across the

proximal foot

Width across the calcaneus, perpendicular to the long

axis of the foot in non-weight bearing

h1 Toe height Distance between the floor and superior aspect of the

first phalanx. If absent use contralateral foot or

estimate using h1 = stature(m) * 0.0203 (Chapter 2)

h2 Foot height Distance between the floor and the apex of the lateral

malleolus

ha Amputated foot

height

Distance from the floor to the superior aspect of the

distal end of the residual foot

aap Ankle A-P Anterior-posterior dimension. With one arm of an

anthropometric calliper nestled into the anterior of the

subtalar joint, slide the other arm onto the posterior

surface of the Achilles tendon.

aaphf Ankle A-P of

hind foot only

Distance from the most posterior part of the foot, at the

level of the apex of the lateral malleolus, to a line

vertically bisecting the lateral malleolus

______________________________________________________ Appendix B. 207

aml Ankle M-L Medio-lateral dimension taken across the malleoli

perpendicular to the long axis of the foot

rr Width of the

lateral malleolus

Width of the lateral malleolus at the level of its apex

Table B.3 Constants

Notation Constant value

γγγγ11, γγγγ12 960 kg/m3

γγγγ13, γγγγ100 1001 kg/m3

γγγγ1 1347 kg/m3

har h1/2 when la > 3l/4 [m]

h1/3 when la > 3l/5 and la< 3l/4 [m]

h1/4 when la < 3l/5 [m]

B.2 Determining foot mass

The M of the foot can be determined by calculating and summing the M of each

component plate comprising the foot model. The basic equation describing the M of a

trapezoidal plate was given by

(1)

Hatze, (1979) and is illustrated in Figure B.3.

2

)( cblhM

+= γ

______________________________________________________ Ap

Figure B.3 Basic trapezoid plate

The basic equation describing the M of a parabolic plate was given by

Hatze, (1979) and is illustrated in Figure B.4

Figure B.4 Basic parabolic plate

3

4 abhM

γ=

Z

h a

b

Z

Y X

2

c 2

bThickness, h

l

pendix B.

Y

X

208

(2)

______________________________________________________ Appendix B. 209

The M of the ball of the foot (M11) was given by

(3)

where l11 describes the segment length and the remaining equation notations have been

described in Tables (B.1. and B.3). The derivation of l11 will now be explained in detail.

Modelling the distal foot as an assemblage of trapezoids (S11 and S13) was

mathematically, relatively simple although not anatomically correct. As such, the V of

the distal foot was overestimated relative to a plaster foot replica, which was used to

validate the model. The area of the plaster foot, corresponding to S11, and the area of the

geometric shape of S11, were estimated by tracing these forms on graph paper (Figure

B.4). Using Figure B.4 the area of the plaster foot corresponding to S11 was

approximately 56 cm2 compared to the modelled area of 70.5cm2. The poor anatomical

match between the trapezoid model and the natural arc formed between the hallux and

smaller toes accounted for the bulk of the difference. This could be more accurately

modelled as a separate geometric segment consisting of a parabola or more simply, the

length of the segment could be reduced until the appropriate area was achieved.

Reducing the segment length reduces the V of the modelled foot, which needs to be

balanced against the actual area of the foot depiction and was only possible because the

model was symmetrical about the x-axis.

( )6

5111111

cbhlM

ar += γ

______________________________________________________ Appendix B. 210

Figure B.5 Schematic diagram showing the modelled and anatomical shape of S11

The solid lines represent the modelled shape and the dotted lines the anatomical shape of the distal foot.

The difference between the area of the plaster foot and the model was

approximately 3.5cm2, when the segment length (l11) was given by

(4)

which represents ¾ of the original segment length. When the amputated foot length, la,

was less than ¾ intact foot length, the length of S11 was no longer affected by the shape

of the toes, and could be determined by

(5)

S11 was affected by forefoot amputation such that when the amputated foot length (la)

was less than two thirds of the intact foot length (l), the M of this segment (M11) will

equal zero as amputation has occurred proximal to this segment.

Equation (3) will only be valid when

3

2lla >

4

2311

llal

−=

3

211

llal −=

______________________________________________________ Appendix B. 211

Otherwise equation (3) will yield a negative M. If the M of this segment (M11) is zero

the corresponding CM and I will also be zero hence this simple equation can be used to

govern the dimensional and inertial contributions of S11.

The M of S12 (M12) was given by

(6)

The M of S13 (M13) was given by

(7)

where l13 is also affected, like l11, by the shape of the toes. When

l13 was given by

(8)

Otherwise,

(9)

The M of the top of the foot (M14) was given by summing the M of each of the

100 slices comprising S14. Two parabolic plates were used to independently represent

the hind foot and the fore foot portions of each slice of the proximal section of S14. The

proximal section of S14 extended carniocaudally from the apex of the lateral malleolus

to its inferior edge. The remaining slices of S14 were described using trapezoid plates.

( )18

51212

cblhM

ar += γ

( )2

)( 1131313

cbhhlM

ar +−= γ

1113

3

2l

ll +=

lal =13

4

3lla >

______________________________________________________ Appendix B. 212

The M of the hind foot parabolic plates (M14h) were given by

(10)

and the M of the fore foot parabolic plates (M14f) were given by

(11)

For the remaining slices of S14, inferior to the lateral malleolus, the M of the

these trapezoid plates were given by

(12)

In Equations (10-12), w describes the number of slices of the proximal section of

S14, and was given by

(13)

where, the numerator describes the half height of the lateral malleolus, or that portion of

S14 between the apex of the lateral malleolus and its inferior border. The denominator

( )

∑=

−

=w

i

iii

h

hhclh

M1

12.

14

31002

4γ

( )

∑=

−

=w

i

iii

f

hhblf

M1

12.

14

31002

4γ

( ) ( ) ( )∑

−

+=

+

−+

=w

wi

iiiii cbhh

lhlfM

100

1

12

14

2100

γ

−

= 10012

2hh

rr

w

______________________________________________________ Appendix B. 213

describes the height of S14. The integer value of w was expressed relative to the total

number of slices of S14.

In Equations (10-12), γγγγi describes the density, lhi describes the hind foot length,

ci describes the hind foot width, lfi describes the fore foot length and bi describes the

width of the fore foot; for the i-th segment. The derivation of these parameters shall

now be described in detail.

Density for the i-th segment, γγγγi, was given by

(14)

Hatze, (1979), where γγγγ100 and γγγγ1 were given as constants in Table 2.1.3

The hind foot length for the i-th segment, lh(i) varied linearly and was given by

(15)

and the hind foot width for the i-th segment, c(i) also varied linearly and was given by

(16)

For the intact foot, the anatomical contour of the forefoot length and width was

mathematically depicted by differential equations describing logistic growth with a

maximum limit as defined in its basic form by

where the initial state A(0) was

(17)

)]()[()(' tAMtkAtA −=

MktCe

MtA −+

=1

)(

( )100

iaaphflhfaaphflhi ⋅−+=

( )100

iamlcamlci ⋅−+=

⋅

−−= 2

1

10041 1101 ii

γγγγ

______________________________________________________ Appendix B. 214

Sentilles, (1989). This differential equation describes growth in a limited environment

where M is the upper limit to which A can grow. M-A(t) is a measure of the remaining

capacity for change in A. A(t) is the growth at time (t), K and C are constants. By

substituting the appropriate foot parameters into Equation (17), the minimum foot

height of S14 (h1) at any given foot length (l) was given by

(18)

where, K and C are constants, h1 is the minimum height of the foot at any given length

(l), and h2 is the maximum height of the foot. By solving equation (18) for l, foot length

for each slice of S14 was given as a function of foot height such that

(19)

where h(i) was given by

(20)

C in equation 19, was given by solving equation 18 for C when l = 0

(21)

KlhCe

hh

2

1

21 −+=

1

12

h

hhC

−=

112

)( .100

hihh

h i +

−=

( ) Kh

Ch

h

l

i

i

.001.0

1001.0

log

2

)(

2

)(

+−

−+

=

______________________________________________________ Appendix B. 215

The value of K in Equation 19, was given by the solution of Equation 18 when (l0) gives

the minimum foot height (h1) and, (l100) gives the maximum foot height (h2),

(22)

In Equation 22, 0.001 was added to h2 as there is no solution for the log of zero

and lk was given by

(23)

The length of the forefoot for the i-th segment, (lfi) was given by

(24)

until such time as

After this time, the fore foot length for the remaining i-th segments was given by

(25)

The width of the forefoot for the i-th slice (bi) could be calculated by

substituting the appropriate foot parameters into Equation (17) and the minimum foot

height of S14 (h1), at any given forefoot width (wb), was given by

(26)

( ) klh

Ch

h

K.001.0

1001.0

log

2

2

2

+−

−+

=

( )( )aaphfaaplhfllk −+−= 13

( ) ii laaphfaaplf +−=

lhfllfi −= 13

KwbhCe

hh

2

1

21 −

+=

ii lhlfl +=>13

______________________________________________________ Appendix B. 216

where, K and C are constants, h1 is the minimum height of the foot at any given width

(wb), and h2 is the maximum height of the foot. By solving equation (26) for wb, foot

width for each slice of S14 was given as a function of foot height such that

(27)

where h(i) was given by

(28)

such that when i = 75, the maximum width of the foot (b) will have been reached at the

minimum height of S14 (h1) which is assumed to correspond with the Metatarsal heads.

C in Equation 27, was given by solving Equation 26 for C when wb = 0 and K in

Equation 27, was given by the solution of Equation 27 when (wb0), gives the minimum

foot height (h1) and, (wb100) gives the maximum foot height (h2),

(29)

In Equation 29, 0.001 was added to h2 as there is no solution for the log of zero

and bk was given by

(30)

( ) kbh

Ch

h

K.001.0

1001.0

log

2

2

2

+−

−+

=

( )Kh

Ch

h

wb

i

i

.001.0

1001.0

log

2

)(

2

)(

+−

−+

=

amlbbk −=

112

)( .75

hihh

h i +

−=

______________________________________________________ Appendix B. 217

The width of the forefoot for the i-th segment, (b(i)) was given by

(31)

until such time as the width of the forefoot reached its assumed maximum at the

Metatarsal heads (i=75). After this time, the forefoot width for i-th segment was given

by

(32)

For the amputated foot, the forefoot lengths and widths for the i-th slice of S14

were governed by the proportion of the remnant foot to the intact foot, expressed

relative to the number of slices of S14, such that when

(33)

the forefoot length (lfi) was given by Equation 24, li in Equation 24 was as given by

Equation 19, K in Equation 19 was given by Equation 22 and hi in Equation 19 was

given by

(34)

and the forefoot width (bi) was given by Equation 31, wbi in Equation 31 was given by

Equation 27, K in Equation 27 was given by Equation 29 and hi in Equation 27 was

given by Equation 34.

ii wbamlb +=)(

bb i =)(

<= 100.

l

lai

112

.

100.

hi

l

la

hhhi +

−=

______________________________________________________ Appendix B. 218

Until such time as

then lfi was given by Equation 25 and bi was given by Equation 32.

The M of the foot was given by summation of the M of each component plate

comprising the model such that

(35)

B.3 Determining foot centre of mass

Coordinates for CM of the foot can be determined by calculating the CM of each

component trapezoidal plate comprising the model. The basic equations describing the

CM of a trapezoidal plate were given by Equations 36-38 (Hatze, 1979).

(36)

(37)

(38)

The CM of a parabolic plate were given by Equations 39 and 40 (Hatze, 1979)

(39)

(40)

hffoot MMMMMMM 141414131211 +++++=

( ))(3

2'

cb

cblZ

++=

0' =X

2'

hY =

> 100.

l

lai

aX 4.0' −=

0'' == ZY

______________________________________________________ Appendix B. 219

The coordinate system utilised by Hatze (1979) has been modified to match the

coordinate system of the kinematic and kinetic data. The X', Y', Z' coordinate system

used in Equations 36-40 is that of Hatze (1979) and does not represent the coordinate

system utilised in this model. The coordinate system illustrated in Figures (1) and (2)

demonstrates the local coordinate system utilised for this model and governs all

subsequent equations. Coordinates of the CM were given from the origin, located at lhf,

from the most posterior portion of the foot.

CM of S11 was given by,

(41)

(42)

(43)

CM of S12 was given by

(44)

(45)

(46)

1111

1111

)8(3

)5(2

3

2M

cb

cbllhfl

lCMx

++−

−

+=

11211

2M

hhCMz

ar

+−=

011 =CMy

1212

)5(9

)8(

3M

cb

cbllhf

lCMx

++−+

−=

12212

2M

hhCMz

ar

−= −

012 =CMy

______________________________________________________ Appendix B. 220

CM of S13 was given by

(47)

(48)

(49)

The CM of the hindfoot parabolic plates of S14 were given by

(50)

(51)

(52)

The CM of the forefoot parabolic plates of S14 were given by

(53)

(54)

(55)

( ) 1313

1313

)(3

)2(M

cb

cbllhflCMx

++−−=

131

213

2M

hhhhCMz

arar

−++−=

013 =CMy

( )[ ]∑=

−=w

i

hiih MlhCMx1

1414 4.0

∑=

−−=

w

i

hih Mhh

iCMz1

1412

14

100

014 =hCMy

∑=

−−=

w

i

fif Mhh

iCMz1

1412

14

100

014 =fCMy

( )[ ]∑=

=w

i

fiif MlfCMx1

1414 4.0

______________________________________________________ Appendix B. 221

For the remaining slices of S14, inferior to the lateral malleolus, the CM of the

these trapezoid plates were given by

(56)

(57)

(58)

CM of the foot was given by

(59)

(60)

(61)

+++++=

foot

fhfoot

M

CMzCMzCMzCMzCMzCMzCMz

141414131211

+++++=

foot

fhfoot

M

CMxCMxCMxCMxCMxCMxCMx

141414131211

0=footCMy

( )( )( )∑

+=

+++−=

100

1

1414

3

2

wi

i

ii

iiiii M

cb

cblhlflfCMx

014 =CMy

∑+=

−−=

100

1

1412

14

100.

wi

iMhh

iCMz

______________________________________________________ Appendix B. 222

B.4 Determine mass moment of inertia of the foot

Calculating and summing the value of I, about the CM, of each trapezoid and

parabolic plate comprising the foot model, can determine values of I of the foot, about

the CM. The basic equations describing the value of I of a trapezoid plate were given by

Equations 62-64 (Hatze, 1979).

(62)

(63)

(64)

The value of Iyy given by the sum of Ixx and Izz (Equation 65) seems to be an

approximation to the true value of Iyy derived from first principles (IyyP) (Equation 66).

(65)

(66)

( )

+

++= 2

222

18

..4..

cb

ccbblMIxx

+=24

22cb

MIzz

IzzIxxIyy +=

( )

+

++++++=).(24

)..(12..4)..(2..222223

cb

MlclbhcbcbcbbIyy

P

Mcb

lcbcbIzzIxxIyy .

)(

).3.(4.

24

12

22

+

+++=+=

______________________________________________________ Appendix B. 223

The approximation of Iyy (Equation 65) seems a useful alternative to the true

value of Iyy (Equation 65) given its numerical simplicity. This approximation can be

used when the trapezoidal plate is 'thin', or when the height, h, is much smaller than b, c

or l. The error associated with this approximation is;

Hatze (1979) did not acknowledge the approximation of Iyy or the error

associated with adopting this approximation. Given the current application, the error

associated with approximating Iyy seems negligible given the thinness of the slices of

S14. As such the approximation of Iyy shall be used for its numerical simplicity.

The basic equations describing the value of I of a parabolic plate, were given by

Equations 67-69 (Hatze, 1979).

(67)

(68)

(69)

12

.2

Mh

+=

125

22hb

MIxx

+=

12175

1222

haMIyy

+=

5175

1222

baMIzz

______________________________________________________ Appendix B. 224

The value of I for S11 about the CM was given by,

(70)

(71)

(72)

( )

( )

11

2

1111

2

2

2

22

211

11

)8(3

)5.(.2

3

2

...2

...

3

2.18

3

2

3

2.4

.

M

CMxcb

cbllhfl

l

CMzh

h

cbb

cbcbbb

l

Iyy

foot

footar

−

++−

−

++

+

−+

++

++

++

=

( )

−

++−

−

+

+

++

+

++

+

++

=

11

2

1111

2

111122

2211

11

)8(3

)5).(.2(

3

2

3

218

..3

24

3

2

24

MCMxfcb

cbllhfl

l

cbb

Mlccb

bb

cbb

M

Izz

oot

11

2

2

22

11

2243

2

MCMzfh

h

cbb

Ixx ootar

+

−+

++

=

______________________________________________________ Appendix B. 225

The value of I for S12 about the CM was given by;

(73)

(74)

+

++−+

−+

+

−+

+

+

++

+

=

2

2

2

2

22

2

12

)5(9

)8(

3

...2

...

3

5.18

3

2.4

3

2

.3

foot

footar

CMxcb

cbllhf

l

CMzh

h

cb

ccb

ccb

l

Iyy

+

++−+

−+

+

+

+

++

+

+

+

+

=

12

2

2

12

22

2

22

12

12

)5(9

)8(

3

...

3

218

.3

.3

24

3

2

...3

2

24

MCMxcb

cbllhf

l

ccb

Ml

cccbcb

ccbM

Izz

foot

______________________________________________________ Appendix B. 226

(75)

The value of I for S13 about the CM was given by

(76)

(77)

12

2

2

2

12

224

3

2

MCMzh

h

ccb

Ixx footar

+

−+

+

+

=

( ) ( )

( ) ( )

13

2

1313

2

12

2

22

213

13

)(3

2.

2

.18

..4.

M

CMxcb

cbllhfl

CMzhh

hh

cb

ccbbl

Iyy

foot

footar

ar

−

++−−

+

+

−−−

+

+

++

=

( ) ( )( )( )

( )

−

+

+

−−+

+

+++

+

=

13

2

13

13

2

132

1322

2213

13

)(33

2.

...18

..4

24

MCMxcb

cbl

lhfl

cb

Mlcbcbcb

M

Izz

foot

______________________________________________________ Appendix B. 227

(78)

The value of I for the hindfoot and forefoot parabolic plates, of the proximal

section, of S14 were given by

(79)

(80)

(81)

13

2

12

22

13

224MCMz

hhhh

cbIxx foot

arar

+

−−−+

+=

( )

∑=

−−+

+

−

+

−

+

=w

i

hi

ifootfoot

i

h M

lhCMxCMzhh

i

hhlh

Iyy1

14

2

2

12

212

2

14

4.0100

...12

100175

12

( )

∑=

−+

+

−

+

−

+

=w

i

fi

ifootfoot

i

f M

lfCMxCMzhh

i

hhlf

Iyy1

14

2

2

12

212

2

14

4.0100

...12

100175

12

( )∑=

−−+

+

=

w

i

hiifootii

h MlhCMxclh

Izz1

142

22

14 4.05175

12

______________________________________________________ Appendix B. 228

(82)

(83)

(84)

The value of I for the remaining trapezoid plates of S14 were given by

(85)

( )( )

∑+=

−

+

++−+

+

−

+

++++

=100

1

2

2

12

14

2

14222

14

)(3

)2.(

...100

.

...)(18

....4

wi

foot

ii

iiii

i

foot

i

ii

iiiiiii

CMxcb

cblhlflf

CMzhh

i

M

cb

Mlhlfccbb

Iyy

∑=

+

−+

−

+

=

w

i

hifooti

h MCMzhh

i

hhc

Ixx1

14

2

12

212

2

14

10012100

5

∑=

+

−+

−

+

=

w

i

fifooti

f MCMzhh

i

hhb

Ixx1

14

2

12

212

2

14

10012100

5

( )∑=

−+

+

=

w

i

fiifootii

f MlfCMxblf

Izz1

142

22

14 4.05175

12

______________________________________________________ Appendix B. 229

(86)

(87)

The value of I for the foot was given by

(88)

(89)

(90)

( )

( )( )( )

( )( )

∑+=

−

+++−

+

+

+++

+

+

=100

1

14

2

2

14222

2214

14

)(3

2.

18

..4

24

wi

ifoot

ii

iiiii

ii

iiiiiii

iii

MCMxcb

cblhlflf

cb

Mlhlfccbb

cbM

Izz

∑+=

+

−+

+=100

1

14

2

1222

14

10024wi

ifootii

MCMzhh

icb

Ixx

[ ]141414131211 IyyIyyIyyIyyIyyIyyIyy fhfoot +++++=

[ ]141414131211 IxxIxxIxxIxxIxxIxxIxx fhfoot +++++=

[ ]141414131211 IzzIzzIzzIzzIzzIzzIzz fhfoot +++++=

______________________________________________________ Appendix B. 230

B.5 Determining foot volume

Calculating and summing the V of each component plate of the foot model

determined the V of the foot. Hatze (1979) described the basic equation for determining

foot V from pre-determined foot M (Equation 91).

(91)

The V of S11..13 was given by,

(92)

V of S14 is given by,

(93)

(94)

B.6 An example of the effect of errors in anthropometric input data

A comprehensive error analysis would in its self be a substantial piece of work

given the mathematical complexity of the model and the number of cross correlations.

For example, while it may be possible to take a single input parameter such as intact

foot length (l) and add/subtract a given error margin, it is not easy to identify how this

single change will affect the many calculations that include this input parameter.

However, in an attempt to determine how robust the model is likely to be to errors in

anthropometric input data a very basic error analysis was undertaken.

Input anthropometric measurements were taken on each of three intact feet on

two consecutive days. The author was blind to the measurements taken on the first day.

The maximum error for each input parameter across the two days was determined as the

∑=i

i

iMV

γ.1000

13..11

13..1113..11 .1000

γM

V =

∑=i

i

iMV

14

1414 .1000

γ

1413..11 VVVfoot +=

______________________________________________________ Appendix B. 231

largest error in any one of the three intact feet studied (Table B.4). The parameters of

heel width (c), medio-lateral width of the ankle (aml) and width of the lateral malleolus

(rr) had the smallest error across the two days with a maximum difference of 1mm

(Table B.4). The length of hind foot (lhf) and the ankle anterioposterior dimension of

the hind foot only (aaphf) had the largest maximum error, which was 4mm (Table B.4).

Table B.4 Maximum errors in anthropometric input data

N/A - parameters of la and ha were not measured because only intact feet were studied. The value of la

was equal to the value of l for all conditions and the value of ha was equal to zero.

Subject 1 Subject 2 Subject 3Parameter

Day 1 Day 2 Day 1 Day2 Day1 Day2

Maximum

error (∝)

b (m) 0.106 0.103 0.100 0.102 0.095 0.093 ±0.003

c (m) 0.064 0.063 0.057 0.057 0.054 0.054 ±0.001

l (m) 0.264 0.262 0.246 0.246 0.242 0.243 ±0.002

la (m) 0.264 0.262 0.246 0.246 0.242 0.343 N/A

h2 (m) 0.074 0.077 0.070 0.071 0.066 0.065 ±0.003

h1 (m) 0.035 0.032 0.034 0.033 0.024 0.025 ±0.003

ha (m) 0 0 0 0 0 0 N/A

aml (m) 0.074 0.075 0.070 0.070 0.068 0.068 ±0.001

aap (m) 0.089 0.089 0.083 0.080 0.078 0.077 ±0.003

lhf (m) 0.060 0.058 0.058 0.059 0.048 0.052 ±0.004

aaphf (m) 0.050 0.048 0.047 0.050 0.040 0.044 ±0.004

rr (m) 0.032 0.031 0.029 0.028 0.029 0.030 ±0.001

As an example of the effect of errors in anthropometric input data, each

anthropometric input parameter for subject 1 (Day 1) was independently manipulated by

subtracting/adding the maximum error associated with each input parameter and

recording the BSP calculated. These results were compared to baseline BSP data

calculated using input parameters obtained on day 1 for subject 1. Results have been

presented for each parameter in Tables B.5-B.14.

______________________________________________________ Appendix B. 232

These data highlight that errors in h2 and h1 resulted in the largest differences in

the prediction of BSP data and as such should be measured with greatest care. A ±3mm

error associated with the measurement of either h2 or h1 resulted in a 30ml change in

foot V (3.4%), 40g change in foot M (3.8%) and 2mm change in CMz (4.3%) for subject

1 (Tables B.8 and B.9). Errors in the measurement of lhf of ±4mm resulted in ±3mm

changes (6.3%) in the location of the mass centroid along the z-axis (Table B.12). No

other significant differences were observed.

Table B.5 Errors in BSP data caused by errors in parameter b

V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes

the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes

maximum errors described in Table B.4.

Condition Differences Condition DifferencesBaseline

b-∝ Absolute % b+∝ Absolute %

V (l) 0.970 0.956 -0.014 1.5 0.984 0.014 -1.5

M (kg) 1.032 1.017 -0.015 1.4 1.047 0.015 -1.4

CMx (m) 0.050 0.049 -0.001 1.2 0.050 0.000 0.0

CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0

CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0

Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0

Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

kxx (m) 0.032 0.031 -0.001 1.0 0.032 0.000 0.0

kyy (m) 0.069 0.069 0.000 0.0 0.070 0.001 -0.1

kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0

______________________________________________________ Appendix B. 233

Table B.6 Errors in BSP data caused by errors in parameter c

V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes

the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes

maximum errors described in Table B.4.

Condition Differences Condition DifferencesBaseline

c-∝ Absolute % c+∝ Absolute %

V (l) 0.970 0.965 -0.005 0.5 0.975 0.005 -0.5

M (kg) 1.032 1.027 -0.005 0.5 1.037 0.005 -0.5

CMx (m) 0.050 0.050 0.000 0.0 0.050 0.000 0.0

CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0

CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0

Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0

Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0

kyy (m) 0.069 0.070 0.001 -0.1 0.069 0.000 0.0

kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0

______________________________________________________ Appendix B. 234

Table B.7 Errors in BSP data caused by errors in parameter l,la

V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes

the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes

maximum errors described in Table B.4. Differences in both l and la were assesses simultaneously

because when an intact foot is studies, the amputated foot length, la, is equal to intact foot length, l.

Condition Differences Condition DifferencesBaseline

l,la-∝ Absolute % l,la+∝ Absolute %

V (l) 0.970 0.964 -0.006 0.6 0.976 0.006 -0.6

M (kg) 1.032 1.026 -0.006 0.6 1.039 0.006 -0.6

CMx (m) 0.050 0.049 -0.001 1.6 0.051 0.001 -1.4

CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0

CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0

Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0

Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0

kyy (m) 0.069 0.069 0.000 0.0 0.070 0.001 -0.9

kzz (m) 0.072 0.071 -0.001 0.7 0.073 0.001 -0.8

______________________________________________________ Appendix B. 235

Table B.8 Errors in BSP data caused by errors in parameter h2

V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes

the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes

maximum errors described in Table B.4.

Condition Differences Condition DifferencesBaseline

h2-∝ Absolute % h2+∝ Absolute %

V (l) 0.970 0.937 -0.033 3.4 1.003 0.033 -3.4

M (kg) 1.032 0.993 -0.039 3.8 1.072 0.040 -3.8

CMx (m) 0.050 0.051 0.001 -2.2 0.049 -0.001 2.4

CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0

CMz (m) -0.041 -0.039 0.002 4.4 -0.043 -0.002 -4.2

Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0

Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

Izz (kg.m2) 0.005 0.005 0.000 1.9 0.006 0.001 -3.8

kxx (m) 0.032 0.031 0.000 1.3 0.032 0.000 0.0

kyy (m) 0.069 0.070 0.001 -0.3 0.069 0.000 0.0

kzz (m) 0.072 0.072 0.000 -0.6 0.072 0.000 0.0

______________________________________________________ Appendix B. 236

Table B.9 Errors in BSP data caused by errors in parameter h1

V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes

the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes

maximum errors described in Table B.4.

Condition Differences Condition DifferencesBaseline

h1-∝ Absolute % h1+∝ Absolute %

V (l) 0.970 0.937 -0.033 3.4 1.003 0.033 -3.4

M (kg) 1.032 0.993 -0.039 3.8 1.072 0.040 -3.8

CMx (m) 0.050 0.051 0.001 -2.2 0.049 -0.001 2.4

CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0

CMz (m) -0.041 -0.039 0.002 4.4 -0.043 -0.002 -4.2

Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0

Iyy (kg.m2) 0.005 0.005 0.000 0 0.005 0.000 0.0

Izz (kg.m2) 0.005 0.006 0.001 -9.8 0.006 0.000 0.0

kxx (m) 0.032 0.031 -0.001 1.3 0.032 0.000 0.0

kyy (m) 0.069 0.070 0.001 -0.3 0.069 0.000 0.0

kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0

______________________________________________________ Appendix B. 237

Table B.10 Errors in BSP data caused by errors in parameter aml

V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes

the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes

maximum errors described in Table B.4.

Condition Differences Condition DifferencesBaseline

aml-∝ Absolute % aml+∝ Absolute %

V (l) 0.970 0.968 -0.002 0.2 0.972 0.002 -0.2

M (kg) 1.032 1.030 -0.002 0.2 1.035 0.002 -0.2

CMx (m) 0.050 0.050 0.000 0.0 0.050 0.000 0.0

CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0

CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0

Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0

Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

kxx (m) 0.032 0.031 -0.001 0.3 0.032 0.000 0.0

kyy (m) 0.069 0.069 0.000 0.0 0.069 0.000 0.0

kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0

______________________________________________________ Appendix B. 238

Table B.11 Errors in BSP data caused by errors in parameter aap

V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes

the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes

maximum errors described in Table B.4.

Condition Differences Condition DifferencesBaseline

aap-∝ Absolute % aap+∝ Absolute %

V (l) 0.970 0.965 -0.005 0.6 0.975 0.005 -0.6

M (kg) 1.032 1.026 -0.007 0.6 1.039 0.007 -0.6

CMx (m) 0.050 0.050 0.000 0.0 0.050 0.000 0.0

CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0

CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0

Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0

Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0

kyy (m) 0.069 0.070 0.001 -0.3 0.069 0.000 0.0

kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0

______________________________________________________ Appendix B. 239

Table B.12 Errors in BSP data caused by errors in parameter lhf

V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes

the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes

maximum errors described in Table B.4.

Condition Differences Condition DifferencesBaseline

lhf-∝ Absolute % lhf+∝ Absolute %

V (l) 0.970 0.968 -0.002 0.2 0.972 0.002 -0.2

M (kg) 1.032 1.030 -0.003 0.3 1.035 0.003 -0.3

CMx (m) 0.050 0.053 0.003 -6.2 0.047 -0.003 6.4

CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0

CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0

Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0

Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

Izz (kg.m2) 0.005 0.006 0.001 -3.8 0.005 0.000 0.0

kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0

kyy (m) 0.069 0.070 0.001 -1.4 0.069 -0.001 1.2

kzz (m) 0.072 0.073 0.001 -1.3 0.071 -0.001 1.1

______________________________________________________ Appendix B. 240

Table B.13 Errors in BSP data caused by errors in parameter aaphf

V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes

the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes

maximum errors described in Table B.4.

Condition Differences Condition DifferencesBaseline

aaphf-∝ Absolute % aaphf+∝ Absolute %

V (l) 0.970 0.973 0.003 -0.3 0.967 -0.003 0.3

M (kg) 1.032 1.035 0.003 -0.3 1.029 -0.003 0.3

CMx (m) 0.050 0.051 0.001 -1.4 0.049 -0.001 1.6

CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0

CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0

Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0

Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0

kyy (m) 0.069 0.069 0.000 0.0 0.070 0.001 -0.7

kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0

______________________________________________________ Appendix B. 241

Table B.14 Errors in BSP data caused by errors in parameter rr

V denotes volume. M denotes mass. CMx, CM,y, CM,z denotes the centre of mass estimate for the x, y and

z directions. kxx, kyy, kzz denotes the radius of gyration estimate about the x, y and z axes. Ixx, Iyy, Izz denotes

the mass moment of inertia estimate about the x, y and z axes through the centre of mass. ∝ denotes

maximum errors described in Table B.4.

Condition Differences Condition DifferencesBaseline

rr-∝ Absolute % rr+∝ Absolute %

V (l) 0.970 0.971 0.001 -0.1 0.969 -0.001 0.1

M (kg) 1.032 1.034 0.002 -0.1 1.031 -0.002 0.1

CMx (m) 0.050 0.050 0.000 0.0 0.050 0.000 0.0

CMy (m) 0.000 0.000 0.000 0.0 0.000 0.000 0.0

CMz (m) -0.041 -0.041 0.000 0.0 -0.041 0.000 0.0

Ixx (kg.m2) 0.001 0.001 0.000 0.0 0.001 0.000 0.0

Iyy (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

Izz (kg.m2) 0.005 0.005 0.000 0.0 0.005 0.000 0.0

kxx (m) 0.032 0.032 0.000 0.0 0.032 0.000 0.0

kyy (m) 0.069 0.069 0.000 0.0 0.069 0.000 0.0

kzz (m) 0.072 0.072 0.000 0.0 0.072 0.000 0.0

______________________________________________________ Appendix C. 242

Validation of the incremental immersion technique for

determining volume and centre of volume.

C.1 Introduction

The incremental immersion technique has been widely used in many forms

(Clauser et al., 1969; Contini, 1972; Drillis and Contini, 1966) however the accuracy of

the technique does not seem to have been reported. Given the many forms of the

technique, the experimental error for the technique used in the present investigation was

assessed by determining the volume (V) or centre of volume (CV) of objects of known

dimensions where these same anthropometric descriptions could be determined

theoretically.

During the pilot investigation, the volume of liquid held in the immersion tank

before the test was deemed an important predictor of the volume displaced during

immersion of the foot replica. Once the tank appeared full, it was possible to add more

liquid creating a meniscus on the surface of the tank. For this reason, it was decided to

assess the effect of surface tension on experimentally derived V and CV estimates

under two experimental conditions; a water only condition and water with soap

condition.

Appendix C

______________________________________________________ Appendix C. 243

The aim of this investigation was to:

1. determine the error of the incremental immersion technique by comparing

experimentally derived V and CV data against theoretically derived values for

an object of known dimensions;

2. determine whether surface tension of the immersion liquid, affected

experimentally derived V and CV estimates.

C.2 Method

Subject

A steel calibration block was milled and the dimensions of the block recorded,

in metres, as 0.1849 x 0.0900 x 0.3970 m3.

Apparatus

All equipment used for these experiments has been described in Chapter 2.

Procedure

Prior to immersion of the calibration block, immersion increments were marked

every 4cm along the 0.1849m face (x-axis) and every 2cm along the 0.0900m face (z-

axis). The last segment for each axis accommodated the remnant portion.

Two experiments were conducted to investigate the effect of water surface

tension on the prediction of V and CV. The first experiment was set up and executed as

previously described in Chapter 2 for both the z and x-axes using the water only

condition. The second experiment used the water/soap mixture to decrease surface

tension. V and CV of the steel calibration block were calculated using standard

geometric equations and comparisons were made between this benchmark data and the

experimentally derived V and CV values under both experimental conditions.

The weight of water in the immersion containers was measured pre- and post-

experiment to assess how much liquid was lost as a result of the experiment as the

accuracy of the later immersion increments in the experiment would not be accurate if

substantial water loss was observed. The immersion increments were randomised to

avoid potential effects water loss.

______________________________________________________ Appendix C. 244

C.3 Results

Mathematically derived and experimental V and CV data describing the steel

calibration block has been presented in Tables C.1 and C.2 for the water only and water

with 0.25% soap conditions.

The weight of liquid in the immersion containers pre- and post experiment has

been presented for the water only and water with 0.25% soap conditions in Tables C.3

and C4.

Table C.1 Comparison of theoretical and experimentally derived V and CV of the steel

calibration block for the water only condition.

Standard errors are reported in brackets.

Theoretical Experimental Difference

Water only % Abs

Volume (litres)

X axis 0.6606 0.6179

(0.00358)

6.46 0.0427

Z axis 0.6606 0.6262

(0.00480)

5.21 0.0344

CV (m)

X axis 0.0925 0.0895

(0.00016)

3.24 0.0030

Z axis 0.045 0.0400

(0.000006)

11.11 0.005

______________________________________________________ Appendix C. 245

Table C.2 Comparison of theoretical and experimentally derived V and CV of the steel

calibration block for the water plus soap condition.

Standard errors are reported in brackets.

Theoretical Experimental Difference

Water/soap % Abs

Volume (litres)

X axis 0.6606 0.6386

(0.00176)

3.33 0.022

Z axis 0.6606 0.6599

(0.00074)

0.00 0.0007

CV (m)

X axis 0.0925 0.0943

(0.00008)

-1.95 -0.0018

Z axis 0.045 0.0431

(0.00015)

4.22 0.0019

Table C.3 Weight of liquid in the immersion container pre and post experiment for the

water only condition.

Experiment Difference

Pre Post % Abs

Weight of water in immersion container (kg)

X axis 2.7138 2.7014 0.46 0.0124

Z axis 5.7830 5.7627 0.35 0.0203

______________________________________________________ Appendix C. 246

Table C.4 Weight of liquid in the immersion container pre and post experiment for the

water plus soap condition.

Experiment Difference

Pre Post % Abs

Weight of water in immersion container (kg)

X axis 2.7232 2.7065 0.61 0.0167

Z axis 5.7986 5.7749 0.41 0.02369

C.4 Discussion

V and CV were mathematically calculated for the steel calibration block and

compared to experimentally derived values using two experimental conditions; water

only and water plus 0.25% soap.

Results from these experiments demonstrated that the V and CV of the

calibration object could best be experimentally determined when the water/soap mixture

was used. The water only condition resulted in larger absolute and percentage

differences when compared with the water/soap condition.

This observation my be due to the reduced surface tension, caused by the

addition of soap to the water, resulting in a smaller meniscus on the surface of the

immersion container. The overflow volume measured, more accurately represented the

actual volume of the immersion object resulting in more accurate V and CV

measurements.

To account for the effect of water loss, the amount of water in the immersion

containers were recorded pre- and post- experiment. Less than 1% of the water weight

was lost as a result of the experimental process across the water only and water/soap

conditions. More water was lost in the water/soap condition than the water only

condition again perhaps due to the reduced surface tension.

______________________________________________________ Appendix C. 247

C.5 Conclusion

The error associated with the prediction of V and CV, when 0.25% soap was

used in the immersion water was greatly reduced possibly due to a decrease in water

surface tension. 0.25% soap should be added to water in the immersion container to

improve the accuracy of V and CV predicted using this the incremental immersion

method. Randomisation of immersion increments was believed to overcome any

systematic errors due to water loss.

______________________________________________________ Appendix D. 248

Subject consent form

This appendix contains a copy of the subject consent form as required by the

University Human Research Ethics Committee for subjects.

Appendix D

______________________________________________________ Appendix D. 249

CONSENT TO PARTICIPATE IN RESEARCH PROJECT

BIOMECHANICAL MODELLING OF PARTIAL FOOT AMPUTEEGAIT

Chief Investigators: Michael Dillon (Postgraduate student)

Dr. Timothy Barker (School of Mechanical, Manufacturingand Medical Engineering) Dr. Michael McDonald (School of Human Movement Studies)

Current information of the biomechanics of partial foot amputee gait is scarce. Thepurpose of this study is to document data on the way partial foot amputees walk, so thatprosthetists have a better understanding of how prosthetic devices function and the waythat it affects the performance of subjects whilst walking. This data will also be used toexamine current treatment principles.

Subjects will be required to attend a single testing session of approximately 5 hoursduration, or two sessions of approximately 2.5 hours, and will be required to wearbathers during this session. All measurements will be taken while you wear yourprosthesis or orthosis.

During the session, a patient history will be documented and measurements of weight,height and foot length, leg circumferences and joint range of motion and musclestrength will be taken. A plaster cast of both your feet will be made. Reflective markerswill then be placed upon the joints of the leg and foot and video cameras will record thetrajectory of these markers during walking. Electromyography information will becollected simultaneously, and will require small pads to be places on muscle groups ofyour leg to record electrical activity of your muscles while you walk. Participants willbe required to walk along a 10 metre walkway and contact the force platform with eithertheir right or left foot. Several practice trials may be required so that the subject cancontact the platform while walking at a constant speed and in a normal fashion.

This project is being conducted by a research Postgraduate student as part of a Doctor ofPhilosophy program.

I acknowledge that the nature, purpose and contemplated effects of the examination sofar as it affects me have been fully explained to my satisfaction by the investigator andmy consent is given voluntarily.

______________________________________________________ Appendix D. 250

The details of the procedure proposed has been explained to me, including theanticipated length of time it will take, and an indication of any effects which may beexperienced during the examination.

Although I understand that the purpose of this research is to improve the quality ofmedical care, it has been explained to me that my involvement may not be of directbenefit to me.

I am informed that no information regarding my medical history will be divulged andthe results of any tests involving me will not be published so as to reveal my identify.

I understand that my involvement in the project will not affect my relationship with mymedical advisers in the management of my health.

I also understand that I am free to withdraw from the project at any time.

Feedback to the participants involved in this study will be provided, where this isrequested by the participants and is practicable.

If you have any complaints about this project or any questions which the investigatorsare unable to answer, you may also contact the Chairperson of the University ResearchEthics Committee.

SecretaryUniversity Research Ethics CommitteeQueensland University of TechnologyTelephone (07) 3864 2902

I, ________________________________ the undersigned have read and understood theinformation above, and any questions I have had, have been answered to mysatisfaction. I agree to my involvement in the research project on Biomechanicalmodelling of Partial Foot Amputee Gait.

Signatures: _____________________________________ Date _________Chief Investigator

_____________________________________ Date _________ Participant

______________________________________________________ Appendix E. 251

Software to process and report kinematic and kinetic data

E.1 Introduction

Information in this appendix describes, in detail, how kinematic, force and

kinetic data were processed through various pieces of software. The titles of individual

programs have been underlined through out this text. The actual Matlab 5.3

programming scripts are lengthy and as such have been included on CD. A detailed

description of the workings of some minor scripts and functions have not been included

in this appendix. However, programs have been commented.

E.2 Processing force plate data

Raw force plate data, recorded in volts, were imported into force4.m. The raw

voltage data were filtered using a zero lag, 4th order Butterworth digital filter with

125Hz cut-off frequency to remove unwanted electrical noise affecting the signal. A

Fast Fourier Transform (FFT) and power spectral density analysis revealed an array of

high frequency components affecting the signal. There were no specific frequencies

affecting the quality of the signal. With this in mind, the choice of cut-off frequency

was assessed in two ways.

Appendix E

______________________________________________________ Appendix E. 252

Firstly, the raw and filtered data were overlayed to observe any unwanted effects

of the filtering process with specific attention to attenuation of the signal at heel contact,

toe-off and the heel strike transient. The cut-off frequency and filter order were

systematically altered, on a small sample of data, until the voltage data were unduly

attenuated. The heel strike transient was affected before the heel contact and toe-off

times and as such, the cut-off frequency was selected to avoid unwanted filtering of this

component of the signal.

Secondly, heel contact and toe-off times were susceptible to small changes in the

filter order as evidenced in the time domain. To ensure the accuracy of both the filter

cut-off frequency and filter order, heel contact and toe-off times were compared

between the raw and filtered voltage data on a small sample of data. Differences in the

timing of these events were negligible with the filter characteristics specified.

Force and moment voltage data were converted to Newtons using the force

plate's calibration matrix, the amplifier's bridge excitation voltage and gain. Processing

the signal in this manner accounted for cross talk caused by the mechanical orientation

of the strain gauges within the force plate.

Small offsets in force and moment data, from absolute zero, were observed and

seemed to be due to the inherent inaccuracies of balancing the bridge excitation voltages

on the force platform amplifier. Each amplifier channel has its own pair of Light

Emitting Diodes (LED), D1 and D2. When D1 was lit the amplifier output was less than

-0.05V and when D2 was lit the output was greater than 0.05V (AMTI, 1991). By

adjusting the balance potentiometer until both LEDs went out, the voltage could be set

to approximately zero. To overcome this inaccuracy, force and moment data were offset

by the mean of a one-second sample of data, obtained prior to initial contact, for each

channel of force or moment data (Dillon and Frossard, 1999).

Force platform data were then sub-sampled from 1000Hz to match the kinematic

sampling rate of 50Hz. The difference between the sampling rates was not optimal but

unavoidable because the electromyographic data had to be sampled at 1000Hz, and all

analog data had to be sampled at the same rate. It was not necessary to filter data

following sub-sampling as evidenced in the time domain.

______________________________________________________ Appendix E. 253

Stance phase and the events of heel contact and toe-off were determined using a

threshold-based criterion. Stance phase was defined as the period when the magnitude

of the vertical force (Fz) exceeded 10N (Hreljac and Marshall, 2000). Previous

investigations have utilised a 5N vertical force threshold (Hennig and Milani, 1995;

Hennig et al., 1993). Irrespective of the threshold criterion chosen, initial contact times

were comparable to those obtained from footswitch data given the rapid rise in the

vertical force with time. Small differences in toe-off times were evident between the

two threshold based techniques. These differences in toe-off times were not of concern

given that the resolution of determining contact times at 50Hz is 20ms, which was

substantially larger than the error caused by differences in toe-off times determined

using either a 5N or 10N threshold.

The choice of threshold criterion was also a primary influence on the accuracy

of the centre of pressure (CoP), during initial and terminal stance. During these times,

when the magnitude of the vertical force is very small (<2% body mass), errors in the

vertical force represent large percentage errors in the CoP (Winter, 1990) because the

vertical force is the denominator of the CoP equation. The 10N-threshold criterion

resulted in practically no errors in the excursion of the CoP compared with the lower

threshold criterion.

CoP excursion were calculated as described by Winter (1990) and accounted for

the offset between the true and geometric origin of the force plate in the vertical

direction (AMTI, 1999). Offsets between the true and geometric origin of the force

platform in the horizontal directions were less than 1mm (AMTI, 1999) and were

therefore not of concern. The total excursion of the CoP was determined as the

difference between the two end-points selected manually using a set of mouse driven

crosshairs. Manual intervention was preferable to the automated systems trialed, which

were unable to accurately identify errors in the CoP during initial or terminal stance.

These problems have received little attention in the literature probably because errors in

the excursion of the CoP are coincident with very small ground reaction forces and

therefore, do not greatly influence the accuracy of joint moments or powers.

______________________________________________________ Appendix E. 254

Shear force data were inverted to account for differences in the direction of

approach during analysis of the right of left limbs.

Force and CoP data were then cut to the stance phase using the predetermined

heel contact and toe off times. Data were displayed on screen for visual inspection and

stored to file for further analysis.

Footswitch data were utilised to determine the duration of single and double

support phases and the second initial contact of the stride (the first having been

determined from the force platform). Initial contact times determined using the

footswitches were comparable to those determined from the force platform. Typically,

the registered onset of stance is delayed by about 2% with the use of footswitches

compared to force platform derived recordings (Perry, 1992). In the present

investigation, no systematic errors were observed, however initial contact times

obtained from the footswitches differed, on average, by approximately 0.5% compared

to the force platform derived values. These errors did not seem to be due to the

sensitivity of the footswitches necessary to prevent inadvertent activation as described

by Perry (1992) given that no systematic differences were observed. However, these

errors seem to be the result of differences in determining initial contact times using

footswitch data sampled at 1000Hz compared to force platform data sampled at 50Hz.

These differences were accounted for by determining the difference between

initial contact times obtained using the force platform and footswitches and adjusting

footswitch data such that the initial contact times matched the force platform derived

initial contact times. Subsequent initial contact times were adjusted bilaterally to

preserve the temporal relationship.

Footswitch data consistently resulted in delayed toe-off compared to

simultaneous force platform recordings by up to 70ms. These errors are likely to be an

artefact of the compression closing footswitches, which seem to respond poorly when

the force time profile is not steep, as it is during initial contact. The toe-off times

obtained from the footswitches were replaced with those determined from the force

platform. For the contralateral limb, where no force platform was available, the data

______________________________________________________ Appendix E. 255

were unable to be utilised. However, the periods of single and double support could still

be calculated.

For example, if the right stride included stance on the force platform, then the

initial contact and toe-off times could be derived from the force platform. The

subsequent right initial contact, concluding the right stride, could be determined from

the footswitch data. Single support for the left side, was simply the difference between

the second initial contact of the right stride, obtained from the footswitch and the toe-off

time obtained from the force platform for the right stride (Figure E.1).

Figure E.1 Schematic of support phase calculation using a combination of force

platform and footswitch derived event times.

Superscript FP denotes force platform derived variables while superscript FS denotes footswitch derived

parameters. Subscript R denotes right and L denotes left limb. HC denotes heel contact and TO denotes

toe-off. The blue section of the left stance phase indicates a period of double support.

______________________________________________________ Appendix E. 256

Only one double support phase could be determined at any time without

accurate bilateral toe-off times. Using the previous example, the double support phase

following initial contact for the left limb could be determined as the duration between

the right toe-off and left initial contact (Figure E.1). Similarly, when the stride from the

left limb contacted the force platform, the double support period subsequent to the right

initial contact could be determined.

The timing of the contralateral heel contact was also determined from the

adjusted footswitch data. Utilising the current example, the left or contralateral initial

contact could be expressed as a percentage of the right or ipsilateral gait cycle given the

difference between the first initial contact for the left and right strides divided by the

right gait cycle time.

E.3 Processing kinematic data

Reconstructed and interpolated 3D marker coordinate data were imported into

angles4.m to calculate joint angles of rotation for the hip, knee and ankle.

Raw XYZ marker displacement data were then filtered using a zero-lag, 4th

order low pass Butterworth digital filter with 6Hz cut-off frequency. The filter

characteristics were selected by analysing the frequency components of the heel and toe

markers on a small sample of subjects. These marker displacement data have been

demonstrated to have the highest harmonics (Winter et al., 1974) and as such the

frequency components of these markers were assessed using a FFT and power spectral

density analysis.

Heel marker displacement data had higher frequency components than those

observed for the toe displacement data. For the bulk of the toe displacement data it was

possible to filter the data with a cut-off frequency as low as 3Hz without unduly

attenuating the signal as evidenced in the time domain. However, for the displacement

data of the heel marker a 5Hz cut-off frequency was necessary to avoid unwanted

attenuation of the signal.

______________________________________________________ Appendix E. 257

It appears that the bulk of the power of the signal was below the 6th harmonic

(5Hz) with much of the signal after this point being characteristic of the noise observed

at higher frequencies. Given the uncertainty in the small sample of displacement data

analysed, a slightly higher cut-off frequency of 6Hz was selected as advocated by

Winter et al., (1974) who performed such an analysis on a larger number of subjects.

This cut-off frequency did not appear to increase the noise level in the time domain.

Marker displacement data were transformed to account for the direction of

approach during analysis of the right of left limbs.

Segment angles describing the orientation of the pelvis, thigh, leg and foot

relative to the horizontal axis of the global coordinate system (GCS) were determined

using an arc tangent function (Winter, 1990).

Neutral segment angle data were established in quiet standing and processed as

for the dynamic segment angle data. Neutral segment angle data were averaged and

used to account for errors in marker placement affecting the description of the neutral

joint position.

Joint angles were then determined as the difference between adjacent segment

angles (Winter, 1990).

Joint angle data were displayed to screen for visual inspection to determine if the

gait cycle to be analysed was representative of the subject’s normal pattern. In this way

it was possible to see if subjects altered their gait pattern or coordination to target the

force platform.

Dynamic joint angle data were cut to the gait cycle using the heel contact times

(derived during force4.m), normalised to 100 data points and displayed for visual

inspection. Unrepresentative joint angle data were excluded from further analysis at this

stage. The following data were then exported for further analysis: normalised joint angle

data, uncut joint angle data, dynamic and neutral marker displacement data as well as

the coordinates for the marker located on the walkway.

______________________________________________________ Appendix E. 258

E.4 Processing kinetic data

Kinetic parameters such as joint moments and powers were calculated using

moments4.m. A large number of input data were required to calculate joint moments

and powers such as body segment parameter (BSP) data, joint and limb segment

rotations, linear and angular velocities/accelerations of the centre of mass (CM) and

ground reaction forces.

A program called bspinput.m was used to either enter body segment parameters

measured from a subject or load an existing set of measurements describing the physical

characteristics of the foot, leg and thigh segments as well as general characteristics of

age, height, weight and sex. Mathematical models of the foot (bspfoot.m), leg

(bspleg.m) and thigh (bspthigh.m) were used to compute the volume, mass (M), centre

of mass (CM ) and mass moment of inertia (I) of each limb segment. Experimental

measurements were used to obtain these anthropometric descriptions of the

prosthesis/orthosis and shoes.

If partial foot model- B was selected the M, CM and I of the lumped leg, foot

and prosthesis/shoe segment were computed (Appendix F) and described the

characteristics of a 'lumped' leg, foot and prosthesis/shoe segment relative to the knee

joint. If partial foot model-A was selected the combined M, CM and I of the foot and

prosthesis/orthosis (if any) and shoe were computed (Appendix F) and described the

characteristics of the 'lumped' segment relative to the ankle joint. These input BSP data

and computed anthropometric descriptions were displayed for visual inspection and

stored to disk.

Filtered XYZ marker coordinates describing the position of the marker on the

walkway relative to the kinematic/global coordinate system (GCS) were imported. A

transformation between the origin of the force platform and the GCS was then

computed.

Filtered XYZ marker coordinates describing the displacement of each limb

segment were imported and angles of the pelvis, thigh, leg and foot segments were

calculated relative to the GCS in radians (Winter, 1990). Limb segment velocities and

______________________________________________________ Appendix E. 259

accelerations were then computed (Winter, 1990). Limb segment velocity data were low

pass filtered, using a 4th order Butterworth digital filter with 6Hz cut-off frequency,

prior to calculating limb segment accelerations.

Filtered XYZ marker coordinates describing the neutral limb position were

imported. Coefficients describing the position of the CM relative to these kinematic data

were computed (Appendix F). Displacements of the CM of the thigh, leg and foot

segments were calculated (Appendix F) as were linear and angular velocities of the CM

(Winter, 1990). Again, linear velocity data were low pass filtered, prior to calculating

linear accelerations of the CM.

Joint angle and force platform data, which had previously calculated in

angles4.m and force4.m respectively, were imported. The force platform data had

previously been cut such that only the stance phase was considered. The remaining data

were padded with zeros such that all matrices feeding into the joint moment equations

were of equal length. Force platform data collected prior to and following the stance

phase of interest were equal to zero.

CP data were expressed relative to the GCS using the previously determined

transformation between the origin of the force platform and kinematic/GCS. All

kinematic and force platform data were now expressed relative to the origin of the

kinematic/GCS.

Net joint moments were then calculated by resolving joint reaction forces prior

to calculating moments about the joint (Appendix F) and adjusted for the sign

convention such that all extension moments were positive (Ounpuu, 1994). Joint powers

were calculated as the scalar product of the moment and angular velocity and accounted

for power transfer across joints (Winter, 1990). Power generation across the joint was

considered to be positive on the y-axis (Ounpuu, 1994). The resultant joint moments

and powers were then normalised by body mass, cut to the gait cycle using the events of

heel contact derived from force4.m, and normalised to 100 data points (Ounpuu, 1994).

______________________________________________________ Appendix E. 260

Joint angle, moment and power data were displayed to screen for visual

inspection and stored to file. Padded force platform data were also cut to the gait cycle

and normalised to 100 data points prior to being stored to file.

E.5 Processing Temperospatial data

Temporal and spatial parameters were calculated using tempero.m. Parameters

describing the duration and proportions of the gait cycle were determined using the

initial contact and toe-off times obtained from force4.m according to the definitions of

Ounpuu (1994). Measurements of stride length and walking velocity utilised

displacement data of the ankle marker. During processing of the force platform data

(force4.m), the total excursion of the CP was obtained, as was the timing of the

contralateral initial contact. The total excursion of the CP was normalised by the

individuals shoe length and expressed as a percentage. The timing of contralateral initial

contact was expressed as a percentage of the ipsilateral gait cycle.

E.6 Reporting kinematic and kinetic data

Gait data were synthesised into a report for the right and left limbs of each

subject (Appendix I). Multiple trials of joint angle, moment and power data were

imported together with temperospatial, support phase and ground reaction force data to

form a matrix for each gait parameter. The CP data were offset such that initial contact

for each trial comprising the matrix was represented by a zero, indicating no excursion

of the CP. The CP data were subsequently normalised by shoe length to reduce

variability. The mean, standard deviation, range as well as the maximum and minimum

values were reported for the temperospatial and support phase data. For the joint angle,

moment, power and ground reaction force data, the multiple trials were averaged and a

time-based standard deviation was calculated for each parameter. The coefficient of

variation (CV) was calculated for each parameter as described by Winter (1983). The

variability of these data were also reported using the adjusted coefficient of multiple

determination (CMC) as described by Kadaba et al., (1989).

A number of figures portraying a variety of aspects of gait including variability

and average kinematic and kinetic data were generated. Of these figures, a number were

______________________________________________________ Appendix E. 261

used to elicit information about the timing and magnitude of specific mean joint angles,

moments, powers and ground reaction forces using a set of mouse driven crosshairs.

The exact x and y-axis values of the data point currently in the centre of the crosshair

were displayed on the top of the figure so that the true maximum/minimum could be

easily determined (Figure E.2). The crosshair location and the actual data values were

matched by scaling the figure so that there were the same number of pixels along each

axis. The actual data point had the smallest Euclidean distance, from the pixel currently

in the centre of the crosshair.

All data and figures generated from reportkin.m were stored to disk for future

reference and including in gait reports such as that presented in Appendix I.

______________________________________________________ Appendix E. 262

Figure E.2 Mean joint powers for the control sample plotted against ±2 standard

deviations of the control sample.

The circles show previously selected data points. The crosshair is placed on the ankle power generation

peak (AP2) and the corresponding x and y-axes values appearing in the boxes on the top of the figure.

The solid vertical line identifies toe-off at 60%GC.

10 20 30 40 50 60 70 80 90 100-1

0

1

2

Hip Power

(W/k

g) G

en

.

10 20 30 40 50 60 70 80 90 100

-2

-1

0

1

2Knee Power

(W/k

g) G

en

.

10 20 30 40 50 60 70 80 90 100-2

0

2

4

6Ankle Power

(W/k

g) G

en

.

Gait Cycle

HP2

HP3

HP4

KP1

KP2

KP3KP4

AP1

AP2

_______________________________________________________ Appendix F. 263

Linked-segment inverse dynamic models for the analysis

of partial foot amputee gait: implementation

F.1 Introduction

Implementation of these two partial foot inverse dynamic models (Chapter 3)

was mathematically relatively simple, although somewhat involved. The process used to

implement these models and calculate kinetic parameters involved:

• obtaining anthropometric descriptions of the partial foot residuum, leg and

thigh segment of the amputee as well as anthropometric descriptions of any

prosthetic/orthotic intervention and footwear

• combining the individual anthropometric characteristics of each of these

segments (ie: foot, leg, thigh, prosthesis, shoe) such that only one set of body

segment parameter (BSP) data reflects the contributions of all of the

individual segments

• creating a time series describing the location of the CM of each segment

relative to the global coordinate system

• deriving the remainder of the moment equation input data in the usual

fashion ie: calculate joint angles, linear and angular velocities and

accelerations, transpose force plate derived data into the global coordinate

system etc…

• calculating joint moments and powers

Appendix F

_______________________________________________________ Appendix F. 264

F.2 Obtaining the necessary anthropometric descriptions

Anthropometric characteristics of the normal and partial foot were determined

using the anthropometric model, and measurement techniques described in Chapter 2.

Anthropometric characters of the leg and thigh segments were obtained as described in

Chapter 3 as were these descriptions of the prosthesis/orthosis and footwear.

The anthropometric measurements obtained directly from the subject were

entered into software developed to geometrically model the residual foot, leg and thigh

segment and calculate body segment parameter (BSP) data including the mass (M),

centre of mass (CM) and mass moment of inertia (I) of these limb segments (Appendix

3.3). The M of the prosthesis/orthosis/shoe and the location of the mass centroid were

obtained directly and the value of I was calculated from the period of oscillation values

obtained (Chapter 3). With these input measurements the software returned a cell matrix

with BSP data such as that presented of a single individual with Chopart amputation and

clamshell prosthetic socket (3004-1102A) (Table F.1). The location of the mass centroid

for all limb segments including the prosthesis/orthosis/shoe were given in x, y, z

coordinates from the proximal end of the segment (joint centre) commensurate with the

laboratory coordinate system. The location of the CM of the prosthesis/shoe was given

relative to the knee joint as described in the assumptions of partial foot model-B (Table

F.1). The value of I was taken through the CM of the 'lumped' or modelled limb

segment.

Table F.1 Anthropometric data of the remnant foot, leg, thigh and prosthesis/shoe

stored in cell matrix format

Anthropometric characteristics of the isolated foot segment (anth.foot), leg segment (anth.leg), thigh

segment (anth.thigh) and combined prosthesis/shoe (anth.pros) were described. N/O denotes parameters

not obtained.

anth. Volume

(l)

Mass

(kg)

CMx

(m)

CMy

(m)

CMz

(m)

Ixx

(kg.m2)

Iyy

(kg.m2)

Izz

(kg.m2)

foot 0.4045 0.4434 -0.0127 0 -0.0364 0.0003 0.0006 0.0006

leg 2.4370 2.6728 0.0000 0 -0.1584 0.0394 0.0398 0.0031

thigh 9.9998 10.6541 0.0000 0 -0.1803 0.1518 0.1583 0.0403

pros N/O 1.5890 0.0280 0 -0.3750 N/O 0.0339 N/O

_______________________________________________________ Appendix F. 265

F.3 Combining the individual anthropometric descriptions

Given the individual anthropometric descriptions of the remnant foot, leg, thigh

and prosthesis/shoe it was necessary to combine these so that only one set of BSP data

reflects the contributions of all of the individual segments.

In continuing with the example using the Chopart amputee, the M of the leg,

residual foot and prosthesis/shoe (LFP) (Table F.1) were added together to yield the M

of the combined segment (Mlfp) which would be 4.7052kg.

The location of the mass centroid of the LFP, from the knee joint centre, was

given by the parallel axis theorem. The M of each segment comprising the LFP has

been represented by M123 and the distance from the segment origin to the segment CM,

has been represented by X123 in a pictorial representation (Figure F.1). This pictorial

representation depicts the various body segments, which need to be considered to

describe the anthropometry of a Chopart amputee wearing a clamshell PTB prosthesis

(Figure F.1).

The location of the CM of the LFP was given, from the knee joint centre, along

the z-axis by

(1)

where the length of the leg segment (l) was 0.41m.

Using the same method, the location of the CMlfp along the x-axis, from the knee

joint centre, was determined to be 0.0083m. The location of the mass centroid of the

LFP in x, y, z coordinates from the knee joint centre as [0.004 0 -0.259], assuming the

CM was located in the x-z plane (y=0).

( ) ( )( ) ( )( )

+++−+=321

332211 ...

MMM

XMlXMXMCM

z

lfp

( ) ( )( ) ( )

++−+−−+−=

589.1443.0673.2

375.0.589.1410.0036.0.443.0159.0.673.2z

lfpCM

mCMz

lfp 259.0−=

_______________________________________________________ Appendix F. 266

Figure F.1 Schematic illustrating how anthropometric characteristics of each limb

segment were combined to yield one set of characteristics describing the 'lumped' leg,

foot and prosthesis (LFP) of a chopart amputee.

From left to right, the leg and remnant foot, exploded view of the leg and remnant foot, Clamshell PTB

prosthesis and combined leg, remnant foot and prosthesis. The orthogonal axes sets describe the knee and

ankle joint local coordinate systems. X1,2,3,lfp is the distance from the proximal joint centre to the segment

CM. M1,2,3,lfp is the mass of the leg, foot and prosthesis and lumped limb segment, respectively.

Using the parallel axis theorem, the value of I of the foot, leg and prosthesis,

through the CM of that segment, was expressed relative to the mass centroid of the LFP

(CMlfp). As an example, the value of I of the leg segment taken through the CM of the

leg about the yy-axis (Iyyleg) was expressed relative to the CM of the LFP (Iyyleg_CMlfp)

by

(2)

( ) ( )( )( )222

2587.01584.00083.00.6728.20398.0_ +−+−+=lfpleg CMIyy

2.0669.0_ mkgCMIyy lfpleg =

( ) ( )( ) 222

._

++= −−ZZXX

lfpleglfpleglegleglfpleg CMCMCMCMMIyyCMIyy

_______________________________________________________ Appendix F. 267

where Mleg denotes the M of the leg, CMleg and CMlfp denote the location of the

mass centroid of the leg and LFP respectively. Superscript x and z denotes the x and z-

axes. Numeric values were for these variables were obtained from Table F.1.

Using the same method, the value of Iyy of the foot and prosthesis/shoe

segments through the CM of the LFP was determined to be 0.0376 kg.m2 and 0.0560

kg.m2, respectively.

The value of I of the LFP through the mass centroid was given by the sum of the

values of I of the foot, leg and prosthesis through the CM of the LFP. The value of I of

the 'lumped' leg, foot and prosthesis through the mass centroid of the LFP was 0.1605

kg.m2.

A complete set of anthropometric characteristics of the combined leg, residual

foot and prosthesis/shoe for this Chopart amputee using partial foot model-B are given

in Table F.2.

Table F.2. A complete set of anthropometric characteristics of the 'lumped' leg, foot,

prosthesis and shoe for the affected limb of a single Chopart amputee

The CM of the LFP was expressed relative to the knee joint local coordinate system and the value of I

about the yy axis through the mass centroid of the LFP. N/O denotes parameters not obtained.

anth. Volume

(l)

Mass

(kg)

CMx

(m)

CMy

(m)

CMz

(m)

Ixx

(kg.m2)

Iyy

(kg.m2)

Izz

(kg.m2)

lfp N/O 4.7052 0.0083 0 -0.2587 N/O 0.1605 N/O

F.4 Transformation of the mass centroid location between the local/joint

and global coordinate systems

To this point, the location of the mass centroid of each isolated limb segment

and of the 'lumped' segments has been described in x, y, z coordinates relative to the

joint or local coordinate systems (LCS). Prior to calculating joint moments,

transformations between the LCS and the global or laboratory coordinate system (GCS)

_______________________________________________________ Appendix F. 268

were undertaken using two different methods depending on whether the segment's CM

was located in the sagittal mid-line between the segment's end points, or in some other

location not on the sagittal mid-line.

For example, the thigh segment's CM is located in x, y, z coordinates from the

hip joint's LCS (0, 0, -0.1803) indicating that CM is located in the sagittal mid-line of

the segment (x = 0 and y = 0) but displaced inferiorly along the segment's z-axis (z = -

0.1803). The location of the thigh segment's CM in the GCS can be calculated by firstly,

expressing the location of the CM as a proportion of the segment length. So if the thigh

segment was 0.41m in length, the location of the mass centroid could be expressed as a

coefficient of the segment length given by the location of the CM in along the z-axis

divided by the segment length, which would equal 0.4398. Thus indicating that the

location of the thigh segment's CM was 43.98% of the length of the segment from the

proximal joint centre. The location of the thigh segment's centre of mass in the GCS can

then given by

(3)

where CMthighX,Z described the position of the CM of the thigh segment in the CGS

along the X and Z-axes. Hx,z and Kx,z describe the position of the hip and knee joint

along the X and Z-axes in the GCS. i is the increment of time

When the segment's CM is not located along the segment's mid-line, as would be

the case for the LFP or the foot segment, then the location of the segment's CM in the

GCS was calculated using a simple transformation matrix. Whereby the location of the

mass centroid was referenced to the LCS and in turn, was referenced back to the GCS.

The only additional information required was the angle of the segment with respect to

the horizontal (GCS).

As an example, the CM of the LFP previously calculated of the Chopart

amputee was located in x, y, z coordinates from the knee joint's LCS at (0.0083, 0, -

0.2587) and is depicted in Figure F.2.

( ) ( ) ( ) ( )( )( )iKiHiHiCM xxxX

thigh −−= .4389.0

( ) ( ) ( ) ( )( )( )iKiHiHiCM zzzZ

thigh −−= .4389.0

_______________________________________________________ Appendix F. 269

If the angle of the LFP segment was 106.46 degrees from the horizontal (Figure

F.2.) then the CM of the LFP in terms of the GCS could be calculated as follows

(4)

where CMlfpX,Z describes the location of the segment's mass centroid with

respect to the GCS and CMlfpx,z describes the location of the segment's mass centroid of

the LFP with respect to the LCS. The value of θθθθ describes the rotation of the LCS with

respect to the GCS and was given by the segment angle, with respect to the horizontal,

less 90 degrees. The segment angle was 106.46 θθθθ = 16.46. KX,Z describes the 2D

coordinates of the knee joint in the GCS (Figure F.2).

F.5 Deriving the remaining input data necessary to calculate joint moments

and powers

With the location of the mass centroid expressed relative to the GCS, linear

velocities and accelerations of the mass centroid could now be calculated in the normal

fashion (Winter, 1990). It has been assumed that the remaining input data necessary to

calculate joint moments and powers have been derived and do not require detailed

explanation.

+

−=

Z

X

zlfp

xlfp

Zlfp

Xlfp

K

K

CM

CM

CM

CM.

cossin

sincos

θθ

θθ

( ) ( )( ) ( )

−+

−

−=

5256.0

0196.0

2587.0

0083.0.

46.16cos46.16sin

46.16sin46.16cos

Zlfp

Xlfp

CM

CM

=

2799.0

0616.0

Zlfp

Xlfp

CM

CM

_______________________________________________________ Appendix F. 270

Figure F.2. Depiction of a frame of the gait cycle shortly after heel contact for a

Chopart amputee.

The figure illustrates the LFP segment with the segment's CM described with reference to the knee LCS.

The angle of the LFP segment from the horizontal was 106.46 degrees. GCS denotes the global

coordinate system, LCS the local coordinate system of the knee joint. X,Z are the X and Z-axes in the

GCS. x,z are these axes in the LCS and x',z' when the LCS was rotated back to match the GCS (see knee

joint denoted by K). The location of the knee was given in X and Z coordinates from the GCS.

F.6 Calculating joint moments and powers

A complete inverse dynamic link-segment analysis yields the net muscle

moment at every joint during the time course of movement by analysing each free body

segment typically from the most distal to the most proximal segment. Each free body

segment acts independently under the influence of reaction forces and muscle moments,

which act at either end, plus the forces due to gravity. Of these influences, several are

_______________________________________________________ Appendix F. 271

known including kinematics, anthropometrics and reaction forces at the distal end of the

segment. The unknown influences include the reaction forces at the proximal joint and

the net muscle moment acting on the segment at the proximal joint and are represented

mathematically using the following notation

Known

m mass of the segment

CMx, CMz location of the mass centroid

Io mass moment of inertia taken through the CM

Jxd , Jzd kinematic coordinates describing the location of the distal end of the free

body segment. For the foot segment, these describe the location of the

centre of pressure

Jxp , Jzp kinematic coordinates describing location of the proximal end of the free

body segment

αααα angular acceleration of the segment in the plane of movement

ax, az acceleration of the segment centre of mass

Rxd, Rzd reaction forces acting at the distal end of the segment, usually determined

from a prior analysis of the proximal forces acting on distal segment or for

the foot segment, usually the ground reaction forces

Md net muscle moment acting at distal joint, usually determined from an

analysis of the proximal muscle acting on distal segment

Unknown

Rxp, Rzp reaction forces acting at proximal joint

Mp net muscle moment acting on segment at proximal joint

Several equations are necessary to calculate net joint moments. Proximal

joint reaction forces were given by

(5)xxdxp

xx

amRR

amF

.

.

=−

=∑

_______________________________________________________ Appendix F. 272

(6)

and the proximal joint moment can be derived using

(7)

where equation 7 was taken about the segment mass centroid.

It is valuable to illustrate how the reaction force data from the force plate are

combined with the segment anthropometric and kinematic data to calculate muscle

moments and joint reaction forces. The best way of illustrating this would be through an

example calculation for each of the partial foot models used.

For the 'lumped' foot segment of a Transmetatarsal amputee during mid-stance

(Figure F.3) the following data were obtained using partial foot model-A: αααα = 1.6686

rad/s2 and the value of I through the CM was 0.0096 kg.m2. The remaining input data

has been described in Figure F.3.

zzdzp

zz

amgmRR

amF

..

.

=−−

=∑

∑ = α.IoM

_______________________________________________________ Appendix F. 273

Figure F.3 Free body diagram of a Transmetatarsal amputee at mid-stance modelled

using partial foot model-A .

The centre of pressure (CP) is acting at the floor level. The joint reaction forces (Fx,Fz), linear

accelerations (ax,az), joint moment (Mp), inertia (I), angular acceleration (α), segment mass (m) and

gravity (g) represented, describe the sign convention, where these values are positive, not the actual data

values for this example. The value 'K' denotes the knee joint and values in brackets describes the

kinematic coordinates along the x and z -axes.

_______________________________________________________ Appendix F. 274

The muscle moment at the proximal end of the segment can be calculated by

solving equations 5-7 and substituting the algebraic terms for data described in Figure

F.3. Resolving equations 5-6 yields the proximal joint reaction forces Rxp and Rzp which

were given by

(8)

Using equation 7, the net muscle moment at the proximal (Mp) or ankle moment

(MA) end of the segment was given by

(9)

( )( ) ( )( ) ( )( )( )( ) α

α

..

......

.

opxpxzp

zzpxpxxdzdzdzxd

IMJCMR

CMJRCMJRJCMR

IoM

=+−−

−−−+−

=∑

( )( ) ( )( )( )( ) ( )( )xpxzpzzpxp

xxdzdzdzxdop

JCMRCMJR

CMJRJCMRIM

−+−+

−−−−=

..

......α

( ) ( )( )( )( ) ( )( )

( )( )NmM

M

A

A

9852.38

2274.01975.0.9817.589

...0745.01146.0.5890.141975.02274.0.7447.607

...0745.0.7147.156686.1.0096.0

=

−−+

−+−−

−−=

( ) ( )

( ) ( ) ( )NR

R

NR

R

zp

zp

xp

xp

9817.589

4777.60781.9.8019.11001.0.8019.1

5890.14

7147.156247.0.8019.1

−=

−+−=

=

−−−=

zdzzp

xdxxp

RgmamR

RamR

−+=

−=

..

.

_______________________________________________________ Appendix F. 275

The proximal joint reaction forces (Rxp and Rzp) and the proximal joint muscle

moment (Mp) calculated could then be used as the distal reaction forces (Rxd and Rzd)

and distal joint moment (Md) for the more proximal segment. The distal joint reaction

forces and moment act in the opposite direction on the more proximal segment. As such

a sign change would be required.

For the 'lumped' foot, leg and prosthesis/shoe segment of a Chopart amputee

(Figure F.4) the following data were obtained using partial foot model-B: αααα = -40.2086

rad/s2 and the value of I through the CM of the LFP was 0.1605 kg.m2. The remaining

input data has been described in Figure F.4. The knee joint reaction forces for the

chopart amputee were computed using equations 8 as described by

For the Chopart amputee, the knee joint moment was given by

( ) ( )NR

R

xp

xp

0635.74

3481.253524.10.7052.4

−=

−−=

xdxxp RamR −= .

zdzzp RgmamR −+= ..

( ) ( ) ( )NR

R

zp

zp

1202.119

3053.16281.9.7052.46319.0.7052.4

−=

−+−=

( )( ) ( )( )( )( ) ( )( )xpxzpzzpxp

xxdzdzdzxdop

JCMRCMJR

CMJRJCMRIM

−+−+

−−−−=

..

......α

( ) ( )( )( )( ) ( )( )

( )( )( )NmM

M

K

K

2650.49

0481.00434.0.1202.119

...2859.05280.0.0635.740434.00849.0.3053.162

...02859.0.3481.252086.40.1605.0

−=

−−−+

−−+−−

−−−=

_______________________________________________________ Appendix F. 276

Again these joint reaction force and muscle moment data would be carried over

to the proximal limb segment in the same manner as described in the example using

partial foot model-A.

Figure F.4. Free body diagram of the 'lumped' foot, leg, prosthesis and shoe of a

Chopart amputee just after heel contact modelled using in partial foot model-B.

The centre of pressure (CP) is acting at the floor level. The joint reaction forces (Fx,Fz), linear

accelerations (ax,az), joint moment (Mp), inertia (I), angular acceleration (α), segment mass (m) and

gravity (g) represented, describe the sign convention, where these values are positive, not the actual data

values for this example. The value 'K' denotes the knee joint and values in brackets describes the

kinematic coordinates along the x and z -axes.

______________________________________________________ Appendix G. 277

Physical assessment forms

This appendix contains a copy of the anthropometric measurement forms, joint

range of motion assessment forms and muscle strength test assessment forms used in

this investigation.

Appendix G

______________________________________________________ Appendix G. 278

Data storage and filenames

Path: __________________________

Right: *.anth - ________________ Left: *.anth - _______________

Right: *.bsp - ________________ Left: *.bsp - _______________

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

General

Stature (m): _____ Weight (kg): _____ Age: _____

Affected side: ❏ Right ❏ Left

Anthropometric Measurement Form Subject ID:

______________________________________________________ Appendix G. 279

Prosthesis/Orthosis Characteristics

Mass (kg): _____

Position of the CoM (m) - X: _____ Y: _____ Z: _____

Time for 10 cycles (s) - X: _____ Y: _____ Z: _____

Calculated Inertia (kg.m2) - X: _____ Y: _____ Z: _____

Shoe Characteristics

Shoe length (m): _____

Shoe mass (kg): _____

Position of the CoM (m) - X: _____ Y: _____ Z: _____

Time for 10 cycles (s) - X: _____ Y: _____ Z: _____

Calculated Inertia (kg.m2) - X: _____ Y: _____ Z: _____

Combined prosthesis/orthosis and shoe characteristics

Mass (kg): _____

Position of the CoM (m) - X: _____ Y: _____ Z: _____

Time for 10 cycles (s) - X: _____ Y: _____ Z: _____

Calculated Inertia (kg.m2) - X: _____ Y: _____ Z: _____

Anthropometric Measurement Form Subject ID:

______________________________________________________ Appendix G. 280

Right Foot Characteristics

Met. head width (m): _____ Heel width (m): _____________(Include WB and NWB measurements)

Intact foot length (m): _____ Amp. foot length (m): _____(for normal use intact foot length )

Lat. Malleolus height (m): _____ Metatarsal height (m): _____

Amp. residuum height (m): _____ Radius of lat. malleolus (m): ____(for normal use 0 )

Ankle A-P (m): _____ Ankle M-L (m): _____

Length of hind foot (m): ______ Length of hind foot AP (m): ____

Left Foot Characteristics

Met. head width (m): _____ Heel width (m): _____(Include WB and NWB measurements)

Intact foot length (m): _____ Amp. foot length (m): _____(for normal use intact foot length )

Lat. Malleolus height (m): _____ 1st Metatarsal height (m): _____

Amp. residuum height (m): _____ Radius of lat. malleolus (m): ____(for normal use 0 )

Ankle A-P (m): _____ Ankle M-L (m): _____

Length of hind foot (m): ______ Length of hind foot AP (m): ____

Anthropometric Measurement Form Subject ID:

______________________________________________________ Appendix G. 281

Right Leg Characteristics

Leg circumferences (m):

_____, _____, _____, _____, _____, _____, _____, _____, _____, _____

Leg M-L measurements (m):

_____, _____, _____, _____, _____, _____, _____, _____, _____, _____

Leg length (m): _____ Malleolus width (m): _____

Left Leg Characteristics

Leg circumferences (m):

_____, _____, _____, _____, _____, _____, _____, _____, _____, _____

Leg M-L measurements (m):

_____, _____, _____, _____, _____, _____, _____, _____, _____, _____

Leg length (m): _____ Malleolus width (m): _____

Anthropometric Measurement Form Subject ID:

______________________________________________________ Appendix G. 282

Right Thigh Characteristics

Thigh circumferences (m):

_____, _____, _____, _____, _____, _____, _____, _____, _____, _____

Thigh M-L measurements (m):

_____, _____, _____, _____, _____, _____, _____, _____, _____, _____

Thigh length to GT (m): _____ Thigh length to pubis (m): _____

Width across GT (m) - Soft tissue: _____ No soft tissue: _____

Sex of subject ( Males -1 Females - 0 ) : _____

Left Thigh Characteristics

Thigh circumferences (m):

_____, _____, _____, _____, _____, _____, _____, _____, _____, _____

Thigh M-L measurements (m):

_____, _____, _____, _____, _____, _____, _____, _____, _____, _____

Thigh length to GT (m): _____ Thigh length to pubis (m): _____

Anthropometric Measurement Form Subject ID:

________

Left

Subject ID:

ROM assessment form

______________________________________________ Appendix G. 283

Right

Hip

Flexion (0-120°)

Extension (0-30°)

Abduction (0-45°)

Adduction (0-30°)

Internal rotation (0-45°)

External rotation (0-45°)

Comments:

Knee

Flexion (0-135°)

Comments:

Ankle

Dorsiflexion (0-20°)

Plantarflexion (0-50°)

Inversion (0-35°)

Eversion (0-15°)

Comments:

___

Le

Muscle strength assessment form

_______________________________________

ft

Hip

Flexion

Extension

Adduction

Abduction

Internal rotation

External rotation

Knee

Flexion

Extension

Ankle

Dorsiflexion

Plantarflexion

Internal rotation

External rotation

Subject ID:

____________ Appendix G. 284

Right

_______________________________________________________Appendix H. 285

Additional results and discussion

Chapter 2: Additional results

H2.1 Bland and Altman plots for assessing agreement between two methods of

measurement

In Chapter 2, paired two tailed t-tests and linear regression analyses comparing

the slope of the regression line to the theoretical line of identity were used to assess the

similarity of body segment parameter (BSP) predicted using the geometric model and

experimental techniques. While these tests provide information about differences

between paired observations and describe the linearity of changes in BSP predicted

using these two techniques, the magnitude of the differences observed is not obvious.

To augment the interpretation of the two basic statistical techniques presented in

Chapter 2, the mean differences between BSP data predicted using the model and

experimental techniques have been presented in Figures H2.1-H2.7 according the

method described by Bland and Altman (1986).

Appendix H

_______________________________________________________Appendix H. 286

Figure H2.1 Differences between modelled and experimentally derived foot mass for

both the normal and amputee samples

Figure H2.2 Differences between modelled and experimentally derived foot volume for

both the normal and amputee samples

-0.25

-0.15

-0.05

0.05

0.15

0 0.5 1 1.5 2

Average foot mass by model and experimental techniques (kg)

Diff

ere

nce

be

twe

en

m

odelle

d a

nd e

xperim

enta

lly

de

rive

d f

oo

t m

ass

(kg

)

Intact sample

Amputee sample

-0.25

-0.15

-0.05

0.05

0.15

0 0.5 1 1.5

Average foot volume by model and experimental techniques (l)

Diff

ere

nce

be

twe

en

m

od

elle

d a

nd

exp

eri

me

nta

lly

de

rive

d f

oo

t vo

lum

e (

l)

Intact sample

Amputee sample

_______________________________________________________Appendix H. 287

Figure H2.3 Differences between modelled and experimentally derived foot CM in the

x direction for both the normal and amputee samples

Figure H2.4 Differences between modelled and experimentally derived foot CM in the

z direction for both the normal and amputee samples

-0.004

-0.002

0

0.002

0.004

0.006

-0.02 0 0.02 0.04 0.06 0.08

Average foot CMx by model and experimental techniques (m)

Diff

ere

nce

be

twe

en

mo

de

lled

and e

xperim

enta

lly d

eriv

ed

CM

x (m

)

Intact sample

Amputee sample

-0.015

-0.01

-0.005

0

0.005

0.01

-0.06 -0.04 -0.02 0

Average foot CMz by model and experimental techniques (m)

Diff

ere

nce

be

twe

en

mo

de

lled

a

nd

exp

eri

me

nta

lly d

eri

ved

C

Mz

(m)

Intact sample

Amputee sample

_______________________________________________________Appendix H. 288

Figure H2.5 Differences between modelled and experimentally derived k about the x-

axis through the CM for both the normal and amputee samples

Figure H2.6 Differences between modelled and experimentally derived k about the y-

axis through the CM for both the normal and amputee samples

-0.06

-0.04

-0.02

0

0.02

0 0.02 0.04 0.06 0.08

Average foot kxx by model and experimental techniques (m)

Diff

ere

nce

be

twe

en

mo

de

lled

and e

xperim

enta

lly d

eriv

ed

k xx (

m)

Intact sample

Amputee sample

-0.06

-0.04

-0.02

0

0.02

0 0.02 0.04 0.06 0.08 0.1

Average foot kyy by model and experimental techniques (m)

Diff

ere

nce

be

twe

en

mo

de

lled

and e

xperim

enta

lly d

eriv

ed

k yy (

m)

Intact sample

Amputee sample

_______________________________________________________Appendix H. 289

Figure H2.7 Differences between modelled and experimentally derived k about the z-

axis through the CM for both the normal and amputee samples

Chapter 3: Additional results and discussion

H3.1 Peak moments and powers observed during stance phase

Peak joint moment and powers generated using a standard and the partial foot

linked-segment models were presented for only swing phase in Chapter 3. These same

data were not presented for stance phase or for the ankle joint given that there were no

significant differences observed between the different linked-segment models. To

augment the results presented in Chapter 3, Tables H3.1-H3.6 describe the magnitude of

peak joint moments and powers observed during both stance and swing phase for the

hip, knee and ankle.

H3.2 Influence of anthropometry on joint moments and powers

Clinical interpretations of the joint moment profiles provide useful information

about the causes of movement. However, their usefulness for observing how

-0.04

-0.02

0

0.02

0 0.02 0.04 0.06 0.08 0.1

Average foot kzz by model and experimental techniques (m)

Diff

ere

nce

be

twe

en

mo

de

lled

and e

xperim

enta

lly d

erive

d k

zz

(m)

Intact sample

Amputee sample

_______________________________________________________Appendix H. 290

anthropometric changes affect the net joint moments are limited because only changes

caused by differences in anthropometric data as a whole can be observed. This appendix

detail how the moment equations were manipulated to determine the individual

influences of mass, centre of mass and mass moment of inertia.

Table H3.1 Mean hip joint moment peaks for both the standard and partial foot linked-

segment models

HM denotes hip moment. Standard deviation reported in brackets.

Inverse Dynamic Model Differences

Standard Partial foot absolute %

Sample A - with ankle motion

HM1 (Nm/kg) 1.107

(0.376)

1.144

(0.366)

0.037 -3.3

HM2 (Nm/kg) -0.430

(0.118)

-0.443

(0.114)

-0.013 -3.0

HM3 (Nm/kg) 0.208

(0.041)

0.301

(0.032)

0.093 -44.7

Sample B - without ankle motion

HM1 (Nm/kg) 0.953 0.981 0.028 -2.9

HM2 (Nm/kg) -0.271 -0.249 0.022 8.1

HM3 (Nm/kg) 0.188 0.242 0.054 -28.7

_______________________________________________________Appendix H. 291

Table H3.2 Mean knee joint moment peaks for both the standard and partial foot

linked-segment models

KM denoted knee moment. Standard deviation reported in brackets.

Inverse Dynamic Model Differences

Standard Partial foot absolute %

Sample A - with ankle motion

KM1 (Nm/kg) -0.585

(0.230)

-0.618

(0.240)

-0.033 -5.6

KM2 (Nm/kg) 0.630

(0.248)

0.628

(0.246)

-0.002 0.3

KM3 (Nm/kg) -0.120

(0.019)

-0.129

(0.192)

-0.009 -7.5

KM4 (Nm/kg) 0.116

(0.034)

0.120

(0.034)

0.004 -3.5

KM5 (Nm/kg) -0.195

(0.024)

-0.256

(0.026)

-0.061 -31.3

Sample B - without ankle motion

KM1 (Nm/kg) -0.453 -0.473 -0.020 -4.4

KM2 (Nm/kg) 0.297 0.296 -0.001 0.3

KM3 (Nm/kg) -0.790 -0.798 -0.008 -1.0

KM4 (Nm/kg) 0.040 0.066 0.026 -65.0

KM5 (Nm/kg) -0.181 -0.222 -0.041 -22.7

_______________________________________________________Appendix H. 292

Table H.3 Mean ankle joint moment peaks for both standard and partial foot linked-

segment models

AM denotes ankle moment. For the Chopart amputee (Sample-B), ankle moment was not calculated due

to the assumptions of the linked-segment model Standard deviation reported in brackets.

Inverse Dynamic Model Differences

Standard Partial foot absolute %

Sample A - with ankle motion

AM1 (Nm/kg) -0.218

(0.166)

-0.215

(0.166)

0.003 1.4

AM2 (Nm//kg) 0.846

(0.238)

0.848

(0.238)

0.002 -0.2

Table H3.4 Mean hip joint power peaks for both the standard and partial foot linked-

segment models

HP denotes hip power. Standard deviation reported in brackets.

Inverse Dynamic Model Differences

Standard Partial foot absolute %

Sample A - with ankle motion

HP1 (W/kg) 0.894

(0.550)

0.887

(0.546)

-0.007 0.8

HP2 (W/kg) -0.188

(0.126)

-0.175

(0.122)

0.013 6.9

HP3 (W/kg) 0.843

(0.278)

0.919

(0.294)

0.076 -9.0

HP4 (W/kg) 0.079

(0.080)

0.132

(0.160)

0.053 -67.1

Sample B - without ankle motion

HP1 (W/kg) 0.948 0.943 -0.005 3.8

HP2 (W/kg) -0.177 -0.161 0.016 9.0

HP3 (W/kg) 0.431 0.460 0.029 -7.0

HP4 (W/kg) -0.013 -0.016 -0.003 -23.1

_______________________________________________________Appendix H. 293

Table H3.5 Mean knee joint power peaks for both the standard and partial foot linked-

segment models

KP denoted knee power. Standard deviation reported in brackets.

Inverse Dynamic Model Differences

Standard Partial foot absolute %

Sample A - with ankle motion

KP1 (W/kg) -0.817

(0.480)

-0.814

(0.474)

0.003 0.4

KP2 (W/kg) 0.462

(0.210)

0.459

(0.208)

-0.003 0.6

KP3 (W/kg) -0.675

(0.232)

-0.697

(0.234)

-0.022 -3.3

KP4 (W/kg) -0.831

(0.176)

-1.070

(0.278)

-0.239 -28.8

Sample B - without ankle motion

KP1 (W/kg) -0.179 -0.179 0.000 0.0

KP2 (W/kg) 0.147 0.148 0.001 -0.7

KP3 (W/kg) 1.391 1.426 0.035 -2.5

KP4 (W/kg) -0.665 -0.797 -0.132 -19.8

_______________________________________________________Appendix H. 294

Table H3.6 Mean ankle joint power peaks for both standard and partial foot linked-

segment models

AP denotes ankle power. For the Chopart amputee (Sample-B), ankle power was not calculated due to the

assumptions of the linked-segment model Standard deviation reported in brackets.

Inverse Dynamic Model Differences

Standard Partial foot absolute %

Sample A - with ankle motion

AP1 (W/kg) -0.991

(0.480)

-0.993

(0.482)

-0.002 -0.2

AP2 (W/kg) 0.800

(0.296)

0.804

(0.290)

0.004 -0.5

By dissecting the joint moment equations into their component parts it was

possible to gather more information about how the moment equations were affected by

individual changes in segment mass (M), centre of mass (CM) and mass moment of

inertia (I). Joint moments were taken about the proximal end of the free body segments,

to better illustrate the mass-acceleration products of the moment equation. As an

illustrative example, a knee joint moment equation (Eq. 1) has been dissected into its

component parts (Eq 2).

(1)

where Ip is the mass moment of inertia about the sagittal plane axis through the

proximal joint, αααα is the angular acceleration, Ma is the carried over moment about the

ankle, Fzd and Fxd are the carry over forces from the distal segment in the z and x

directions, m is the mass of the leg, g is the acceleration due to gravity, ax and az are

the linear accelerations in the x and z directions, CMx and CMz describe the location of

( )( ) ( )( )( )( ) ( )( )( )( )KxCMxazm

CMzKzaxmKxCMxgm

AzKzFxKxAxFzMIM ddapk

−−

−−−+

−−−−−=

..

.......

......α

_______________________________________________________Appendix H. 295

the mass centroid in the x and z directions, x and z describe the kinematic coordinates of

the ankle and knee markers along the x and z axes in the GCS, and A and K denote the

ankle and knee joints respectively.

(2)

Each of the 7 components or 'terms' of the moment equation (Eq 2), allow the

contributions of I and angular acceleration (term 1), the forces acting at the distal end of

the free body (terms 2 and 4), the carry over moment from the distal segment (term 3),

the acceleration of the segment's mass due to gravity (term 5) and the mass-linear

accelerations (terms 6 and 7) to be independently described.

Joint moments were calculated about the proximal end of the segments using a

standard linked-segment model and the partial foot models, to illustrate how individual

changes in M, CM and I contributed to the differences observed in the swing phase knee

and hip joint moments described in Tables H3.1-H3.6. Data for one illustrative

individual in each sample has been presented and discussed.

Sample-A / Partial foot model-A

The knee extension moment peak observed during initial swing (KM4) was

larger with the use of partial foot model-A, than with the standard model due to small

increases in terms 2 and 4 (Figure H3.1). These terms describe the contributions of the

α.1_ ptermk IM =

( )( )KxAxFzM dtermk −−= .2_

atermk MM −=3_

( )( )AzKzFxM dtermk −−= .4_

( )( )KxCMxgmM termk −+= ..5_

( )( )CMzKzaxmM termk −−= ..6_

( )( )KxCMxazmM termk −−= ..7_

_______________________________________________________Appendix H. 296

joint reaction forces, which were carried over from the ankle joint. These reaction forces

merely reflect the mass-acceleration products of the foot segment, which have changed

due to the increased M of the modelled foot segment (Table 3.6). The linear acceleration

terms were not particularly susceptible to changes in the position of the CM such as that

observed between a standard linked-segment model and partial foot model-A.

Partial foot model-A increased the knee flexion moment peak (KM5)

significantly compared with the standard model (Table H3.2) due to an increased

contribution provided by the ankle joint reaction force in the x direction (term 4). The

ankle joint reaction forces were carried over from the foot to the leg segment and

thereby influenced the knee joint moment. The ankle joint reaction forces were

dominated during swing phase by the linear acceleration profiles due largely to there

being no ground reaction force (Figure H3.1). The increased M of the modelled foot

segment amplified these linear acceleration profiles.

During terminal swing, partial foot model-A increased the hip joint extension

moment peak (HM3) compared to a standard linked-segment model (Table H3.1). The

increased hip extension moment was due to an increase in the knee flexion moment

peak (KM5) (term 3) and the knee joint reaction force (term 4) (Figure H3.2). Changes

in knee flexion moment peak have previously been described. The knee joint reaction

force (in the x direction) is, in part, the product of the M and linear acceleration of the

segment (in the x direction). These parameters were not significantly affected by

changes in modelling approaches. Therefore, changes in the knee joint reaction forces

were due to the increase in the ankle joint reaction forces which was carried over to the

distal end of the leg segment free body. As previously described changes in the ankle

joint reaction force, which inturn affected the knee joint reaction force, were due largely

to an increase in the M of the modelled foot segment.

_______________________________________________________Appendix H. 297

Figure H3.1 Contributions to the knee joint moment equation using a standard linked-

segment model (red lines) and partial foot model - A (blue lines)

Aside from the joint moment, the other terms of the moment equation are in relative units not Nm. Terms

in the legend describe contributions listed in Equation 2.

5 10 15 20 25-20

-15

-10

-5

0

5

10

Components of the knee joint moment for subject 2103-2116A

Swing phase (frames @ 50Hz)

Kne

e M

om

ent

(N

m)

Ext

. >C

om

po

nent

s: R

ela

tive

uni

ts

Knee momentTerm 1 Term 2 Term 3 Term 4 Term 5 Term 6 Term 7

Standard model (red dashed), partial foot model-A (blue solid

_______________________________________________________Appendix H. 298

Figure H3.2 Contributions to the hip joint moment equation using a standard linked-

segment model (red lines) and partial foot model-A (blue lines)

Aside from the joint moment, the other terms of the moment equation are in relative units not Nm. Terms

in the legend describe contributions listed in Equation 2.

5 10 15 20 25-25

-20

-15

-10

-5

0

5

10

15

20

25Components of the hip joint moment for subject 2103-2116A

Swing phase (frames @ 50Hz)

Hip

Mo

me

nt (

Nm

) E

xt. >

Co

mp

one

nts:

Re

lativ

e u

nits

Hip MomentTerm 1 Term 2 Term 3 Term 4 Term 5 Term 6 Term 7

Standard model (red dashed), Partial foot model-A (blue solid)

_______________________________________________________ Appendix H. 300

Sample-B / Partial foot model-B

The knee joint moment peaks (KM4 and KM5) were significantly different

between a standard linked-segment model and partial foot model-B (Table 3.8). The

increased knee extension moment peak observed during initial swing (KM4) was due to

the increased value of I of the lumped leg, foot and prosthesis/shoe with partial foot

model-B compared to the leg only segment in the standard linked-segment model

(Figure H3.3). The increase increased value of I was offset by a reduction in the

contributions provided by terms 4-7 (Figure H3.3).

The reduced contributions of terms 5, 6 and 7 toward the knee extension

moment peak (KM4) were largely the result of increased M of the lumped leg, foot and

prosthesis/shoe segment compared to the leg only segment in the standard model.

However, for terms 6 and 7, there were increases in the linear accelerations of the

modelled leg, foot and prosthesis/shoe segment compared to the standard segment as

well as small increases in the moment lever-arms (< 1 cm).

The changes observed in term 4 were the result of differences in the way the

segments were modelled with partial foot model-B compared to a stanrard model. In a

standard linked-segment model, the ankle joint reaction forces provide the input at the

distal end of the leg segment free body, however, for partial foot model-B the leg, foot

and prosthesis were modelled as a single segment and the ground reaction forces act at

the distal end of this free body. For partial foot model-B, the impact of term 4 was

negligible during swing phase when there is no ground reaction force. In the standard

model, when the ground reaction force is zero, term 4 is dominated by the mass-

acceleration terms.

The knee flexion moment peak observed during terminal swing (KM5) was

largely the result of an increase in the value of I of modelled leg segment. However

decreases in the contributions provided by terms 4, 5 and 6 were also evident

(FigureH3.3). The mechanisms by which these terms affect the knee flexion moment

have previously been described with reference to the swing phase knee extension

moment peak (KM4).

_______________________________________________________ Appendix H. 301

Figure H3.3 Contributions to the knee joint moment equation using a standard linked-

segment model (red lines) and partial foot model - B (blue lines)

Aside from the joint moment, the other terms of the moment equation are in relative units not Nm. Terms

in the legend describe contributions listed in Equation 2.

5 10 15 20 25-30

-20

-10

0

10

20

30Components of the knee joint moment for subject 3004-1102A

Swing phase (frames @ 50Hz)

Mo

me

nt: (

Nm

) E

xt. >

Co

mp

one

nts

: Re

lativ

e u

nits

Knee momentTerm 1 Term 2 Term 3 Term 4 Term 5 Term 6 Term 7

Standard model (red dashed), Partial foot model -B (blue solid)

_______________________________________________________ Appendix H. 302

Figure H3.4 Contributions to the hip joint moment equation using a standard linked-

segment model and partial foot model - B

Aside from the joint moment, the other terms of the moment equation are in relative units not Nm. Terms

in the legend describe contributions listed in Equation 2.

5 10 15 20 25-20

-15

-10

-5

0

5

10

15

20

25Components of the hip joint moment for subject 3004-1102A

Swing phase (frames @ 50Hz)

Hip

Mo

me

nt (

Nm

) E

xt. >

Co

mp

one

nts

: Re

lativ

e u

nits

Hip momentTerm 1 Term 2 Term 3 Term 4 Term 5 Term 6 Term 7

Standard model (red dashed), partial foot model-B (blue solid)

_______________________________________________________ Appendix H. 303

The hip joint extension moment peak (HM3) observed during terminal swing

phase reflects the increased flexion moment observed at the knee during this time

(Figures H3.3 and H3.4). The influence of the knee joint moment are exerted distally on

the free body of the thigh segment by way of the carry over of the knee joint moment

(term 3).

The joint moment profiles calculated using partial foot model-A, were

dominated by the additional M of the modelled foot segment and in terms of the

moment equation, the additional M was reflected in the mass-acceleration products. In

turn, these joint reaction forces affected the knee and hip joint moment calculations. The

small differences in the location of the mass centroid and value of I between modelling

approaches seemed to be of little consequence. Hence, only the M of the modelled

segment would be of major concern with this modelling approach (partial foot model-

A).

The knee joint moment patterns, observed with partial foot model-B compared

to the standard linked-segment model, reflected not only changes in the M of the

modelled segments but the influence of I proved dominant during both initial and

terminal swing. Differences in the location of the segment's mass centroid were also

evident. Differences in the hip extension moments observed during terminal swing were

exclusively due to the carry over knee joint moments. With this modelling approach it

seems imperative that not only the M, but also the location of the mass centroid and the

value of I be adequately depicted.

The differences in joint powers were due to changes in the joint moment

profiles. There were no differences evident in the angular velocities of the 'lumped'

segments used in the partial foot models compared to the standard model.

_______________________________________________________ Appendix I. 304

Gait reports

This appendix contains a gait report for the left limb of subject 1004-1307A as

an illustration of the reports generated bilaterally for each subject. The remaining gait

reports have been included on CD.

Appendix I

____

Da

Ca

Am

Af

Gait Analysis Reporting Form

______________________________________

te of amputation: 4 December 1987

use of amputation: ❏❏❏❏ PVD ❏❏❏❏ Trauma ❏❏❏❏

Other: Gangrene secondary to Frostbite

putation Level: MTP ❏❏❏❏ TMT ❏❏❏❏Lisfr

Other:

fected side : Right Left

Subject ID: 1004-1307A

DM Gangrene other

anc ❏❏❏❏ Chopart ❏❏❏❏ other

Skin Condition: Intact ❏❏❏❏ Lesions :

Sensation : Intact ❏❏❏❏ Impaired :

Footware: ❏❏❏❏ Boots ❏❏❏❏ Dress shoes Runners ❏❏❏❏ other

Other:

Gait aids: None ❏❏❏❏ 1 x single point stick ❏❏❏❏ 2 x single point stick ❏❏❏❏ other

Other:

Device category : ❏❏❏❏ Prosthesis Orthosis

Device type: ❏❏❏❏ Clamshell PTB ❏❏❏❏ Below ankle socket

❏❏❏❏ AFO ❏❏❏❏ Toe filler other

Other: Bilateral shoe inserts

Describe device: Full length shoe insert with polypropylene sole, EVA upper andtoe block, silicone pad under the Metatarsal ends. Orthosis covered in leather.

_____________ Appendix I. 305

____

Amp

Left

Degs

136

20

39

22

37

33

147

20

45

20

8

Gait Analysis Reporting Form

______________________________________

utated limb: Right Left

Joint range of motio

.Hip

Flexion (0-120°)

Extension (0-30°)

Abduction (0-45°)

Adduction (0-30°)

Internal rotation (0-45°)

External rotation (0-45°)

Comments:

Knee

Flexion (0-135°)

Comments:

Ankle

Dorsiflexion (0-20°)

Plantarflexion (0-50°)

Inversion (0-35°)

Eversion (0-15°)

Comments:

Subject ID: 1004-1307A

_____________ Appendix I. 306

n Right

Degs.

135

20

42

21

39

30

146

22

50

22

5

____

Amp

Left

5

5

5

5

5

5

5

5

5

5

5

5

Gait Analysis Reporting Form

______________________________________

utated limb: Right Left

Oxford Manual Muscle

Hip

Flexion

Extension

Adduction

Abduction

Internal rotation

External rotation

Knee

Flexion

Extension

Ankle

Dorsiflexion

Plantarflexion

Internal rotation

External rotation

Subject ID: 1004-1307A

_____________ Appendix I. 307

strength test Right

5

5

5

5

5

5

5

5

5

5

5

5

____

00

50

100

00

50

100

EM

G a

mpl

itude

(%

MM

T)

00

50

100

Gait Analysis Reporting Form

______________________________________

20 40 60 80 100

Biceps Femoris (-)

Active

20 40 60 80 100

Tibialis Anterior (-)

20 40 60 80 100

Gastrocnemius medial head (-)

Gait Cycle [%]

Threshold = 2.5%MMT

Threshold = 2.5%MMT

Subject ID: 1004-1307A

_____________ Appendix I. 308

Event Active period(% GC)

Mean(MMT%)

BF1 1-5 5.7791BF2 78-100 7.0493

TA1 1-6 12.9584TA2 56-79 4.7813TA3 88-100 10.7459

GM1 20-45 15.2594

____

5

10

5

10

EM

G a

mpl

itude

(%

MM

T)

5

10

Gait Analysis Reporting Form

______________________________________

0 20 40 60 80 1000

0

0Vastus Lateralis (-)

Active

0 20 40 60 80 1000

0

0Gastrocnemius Lateral Head (-)

0 20 40 60 80 1000

0

0Soleus (-)

Gait Cycle [%]

Subject ID: 1004-1307A

_____________ Appendix I. 309

Event Active period(% GC)

Mean(MMT%)

VL1 1-14 10.2401VL2 90-100 9.5480

GL1 24-46 11.4716GL2 90-100 4.8562

SOL1 1-46 9.3923SOL2 95-100 7.7363

____

n =

SoleuGastGastTibiaBiceVast

00

20

40

60

00

10

20

30

40

EM

G -

Nor

mal

ised

to

100%

MM

T

00

5

10

15

20

25

Gait Analysis Reporting Form

______________________________________

❏❏❏❏4 ❏❏❏❏5 6 ❏❏❏❏7 ❏❏❏❏ Other(n = _ )

CV(%) s 59.7517

rocnemius Lateral Head 82.9666rocnemius Medial Head 75.0217lis Anterior 64.6902

ps Femoris Long Head 77.2593us Lateralis 73.8389

0

10

20

30

40

50

0

10

20

30

40

50

EM

G -

Nor

mal

ised

to

100%

MM

T

20 40 60 80 100

Gastrocnemius Medial head (-)

Gait Cycle [%]

20 40 60 80 100

Tibialis Anterior (-)

20 40 60 80 100

Biceps Femoris (-)

0

10

20

30

40

Subject ID: 1004-1307A

_____________ Appendix I. 310

Variability CMC

0.65880.59270.76450.71740.71890.7009

0 20 40 60 80 100

Soleus (-)

Gait Cycle [%]

0 20 40 60 80 100

Gastrocnemius lateral head (-)

0 20 40 60 80 100

Vastus Lateralis (-)

EMG

____

n =

Side

Notefromdeterprese

00

20

40

60

80

100

00

20

40

60

80

100

EM

G a

mpl

itude

(%

MM

T)

00

20

40

60

80

100

Gait Analysis Reporting Form

______________________________________

❏❏❏❏4 ❏❏❏❏5 6 ❏❏❏❏7 ❏❏❏❏ Other(n = _ )

analysed : ❏❏❏❏Right Left

: The threshold for Biceps Femoris Long Head 5% MMT to 2.5% MMT so that reasonamined in line with those expected from visuanted.

0

20

40

60

80

100

0

20

40

60

80

100

EM

G a

mpl

itude

(%

MM

T)

20 40 60 80 100

Gastrocnemius medial head (-)

Gait Cycle [%]

20 40 60 80 100

Tibialis Anterior (-)

20 40 60 80 100

Biceps Femoris (-)

0

20

40

60

80

100Threshold = 2.5%MMT

Threshold = 2.5%MMT

Subject ID: 1004-1307A

_____________ Appendix I. 311

and Tibialis Anterior were reducedble muscle on/off times could bel inspection of multiple MMT data

0 20 40 60 80 100

Soleus (-)

Gait Cycle [%]

0 20 40 60 80 100

Gastrocnemius lateral head (-)

0 20 40 60 80 100

Vastus Lateralis (-)

Active

____

-2

2

4

(Deg

.) F

lex.

>

-2

2

4

6

8

(Deg

.) F

lex.

>

-4

-2

2

(Deg

.) F

lex.

>

Gait Analysis Reporting Form

______________________________________

0 20 40 60 80 100

0

0

0

0

Hip Angle (-)

0 20 40 60 80 1000

0

0

0

0

0Knee Angle (-)

0 20 40 60 80 1000

0

0

0

Ankle Angle (-)

Gait Cycle [%]

Subject ID: 1004-1307A

_____________ Appendix I. 312

Event Time(% GC)

Angle(Deg.)

HA1 1 29.1522HA2 52 -16.9413HA3 60 -9.0434HA4 88 29.8551HA5 100 29.2131

KA1 1 7.6548KA2 14 25.0611KA3 60 38.7125KA4 72 66.2778KA5 100 6.8935

AA1 1 4.6722AA2 8 -5.5039AA3 48 14.5531AA4 60 -3.7889AA5 65 -10.9731AA6 100 3.5277

____

Gait Analysis Reporting Form

______________________________________

0 20 40 60 80 100-1

0

1

2

Hip Moment (-)

(Nm

/kg)

Ext

. >

0 20 40 60 80 100

-1

0

1

Knee Moment (-)

(Nm

/kg)

Ext

. >

0 20 40 60 80 100

0

1

2

Ankle Moment ()

Gait Cycle [%]

(Nm

/kg)

Ext

. >

Subject ID: 1004-1307A

_____________ Appendix I. 313

Event Time(% GC)

Moment(Nm/kg)

HM1 3 1.1345HM2 50 -0.5050HM3 93 0.2786

KM1 2 -0.5330KM2 13 0.8806KM3 45 -0.5023KM4 59 0.0535KM5 93 -0.2547

AM1 6 -0.1699AM2 49 1.5198

____

-

(W/k

g) G

en.

>

-

-

(W/k

g) G

en.

>

-

(W/k

g) G

en.

>

Gait Analysis Reporting Form

______________________________________

0 20 40 60 80 1001

0

1

2

Hip Power (-)

0 20 40 60 80 100

2

1

0

1

2Knee Power (-)

0 20 40 60 80 1002

0

2

4

6Ankle Power ()

Gait Cycle [%]

Subject ID: 1004-1307A

_____________ Appendix I. 314

Event Time(% GC)

Power(W/kg)

HP1 15 0.2380HP2 47 -0.4099HP3 62 0.7440HP4 93 0.0645

KP1 10 -1.3152KP2 18 0.7839KP3 59 -0.3139KP4 90 -1.2004

AP1 43 -1.0329AP2 54 2.5126

____

0

-2

0

2

(N/k

g)

0

0

5

10

(N/k

g)

0

0

50

100

(%IF

L)

Gait Analysis Reporting Form

______________________________________

E

20 40 60 80 100

Fx (-)

20 40 60 80 100

Fz (-)

20 40 60 80 100

Ax (-)

Gait Cycle [%]

Subject ID: 1004-1307A

_____________ Appendix I. 315

vent Time(%GC)

Force(N/kg)

CoP(%SL)

FX1 12 -2.4817FX2 52 2.1960

FZ1 14 11.8505FZ2 27 6.9045FZ3 47 11.2067

AX1 1 0AX2 59 95.01

____

S

In

PFL

Gait Analysis Reporting Form

______________________________________

Anthropometric d

tature (m) : 1.744 Weight (kg): 64.85

verse dynamic model: ❏ Chopart

Centre of MassVolume

(ltrs.)

Mass

(kg.) X

(m)

Y

(m)

Z

(m)

Foot 0.7036 0.7653 0.0411 0 -0.03

Leg 2.7722 3.0208 0 0 -0.16

Thigh 7.1794 7.6754 0 0 -0.19

PS - 0.5640 0.0720 0 -0.06

FPS - 1.3293 0.0542 0 -0.04

LFPS - - - - -

S : Prosthesis or orthosis and shoePS : combined foot, prosthesis/orthosis and shoe aFPS : combined leg, foot, prosthesis/orthosis and sh

Subject ID: 1004-1307A

_____________ Appendix I. 316

ata

Age (years): 40

Normal / Orthotic

Mass moment of Interia

X

(kg.m2)

Y

(kg.m2)

Z

(kg.m2)

63 0.0007 0.0025 0.0057

83 0.0377 0.0383 0.0038

17 0.1115 0.1144 0.0201

00 - 0.0050 -

63 - 0.0080 -

- - -

s a lumped segmentoe as a lumped segment

____

0

-2

0

2

(N/k

g)

0

0

50

100

(%IF

L)

Gait Analysis Reporting Form

______________________________________

Variability

CV(%) CMCFx 1481.2 0.9866Fy 60.1833 0.9283Fz 9.1150 0.9903

CV(%) CMCAx 18.5937 0.968

50 100

Fx (.)

Gait Cycle [%]0 50

-1

0

1

Fy(.)

Gait Cycle [%]

(N/k

g)

50 100

Ax (-)

Gait Cycle [%]0 50

-0.2

0

0.2

0.4

0.6

Ax (.)

Gait Cycle [%]

(M)

Subject ID: 1004-1307A

_____________ Appendix I. 317

7

100 0 50 100

0

5

10

Fz (.)

Gait Cycle [%]

(N/k

g)

100

____

Gait Analysis Reporting Form

______________________________________

Vari

Angle

CV(%) CMC CV(

Ankle 34.6081 0.9546 18.00

Knee 6.7996 0.9925 816.6

Hip 10.8250 0.9948 327.2

Subject ID: 1004-1307A

ability

Moment Power

%) CMC CV(%) CMC

40 0.9861 476.8895 0.9406

160 0.9686 213.3956 0.9336

473 0.9496 114.4886 0.9166

_____________ Appendix I. 318

____

Gait

Stanc

Swin

Stanc

Swin

Cont

Strid

Strid

Walk

Walk

Cade

CoP

CoP

Sing

Sing

Doub

Doub

Gait Analysis Reporting Form

______________________________________

Mean SD

cycle (s) 1.1517 0.0075

e time (s) 0.6933 0.0103

g time (s) 0.4583 0.0075

e time (%GC) 60.2014 0.6908

g time (%GC) 39.7986 0.6908

ralateral HC (%GC) 49.9014 0.4137

e length (m) 1.5591 0.0106

e length / stature 0.8939 0.0060

ing velocity (m/s) 1.3538 0.0089

ing velocity/stature 0.7762 0.0051

nce (steps/minute) 104.2005 0.6821

excursion (m) 0.3021 0.0024

excursion (%SL) 102.0608 0.8153

le support (s) 0.4762 0.0118

le support (%GC) 40.9823 0.8212

le support (s) 0.1099 0.0095

le support (%GC) 9.4651 0.8510

Subject ID: 1004-1307A

_____________ Appendix I. 319

Range Min Max

0.0200 1.1400 1.1600

0.0200 0.6800 0.7000

0.0200 0.4500 0.4700

1.7392 59.1304 60.8696

1.7392 39.1304 40.8696

1.2122 49.3976 50.6098

0.0252 1.5446 1.5698

0.0144 0.8857 0.9001

0.0243 1.3431 1.3674

0.0139 0.7701 0.7840

1.8149 103.4483 105.2632

0.0065 0.2993 0.3058

2.1959 101.1149 103.3108

0.0296 0.4601 0.4897

1.9555 39.6619 41.6174

0.0247 0.1021 0.1268

2.2548 8.6785 10.9333

_____

-20

0

20

40

(Deg

.) F

lex.

>

-20

0

20

40

60

80

(Deg

.) F

lex.

>

-40

-20

0

20

(Deg

.) F

lex.

>

Gait Analysis Reporting Form

_____________________________________

20 40 60 80 100

Hip Angle (-)

20 40 60 80 100

Knee Angle (-)

20 40 60 80 100

Ankle Angle (-)

Gait Cycle [%]

20 40 60-1

0

1

2

Hip Moment (-)

(Nm

/kg)

Ext

. >

20 40 60

-1

0

1

Knee Moment (-)

(Nm

/kg)

Ext

. >

20 40 60

0

1

2

Ankle Moment (-)

(Nm

/kg)

Ext

. >

Gait Cycle [%]

Subject ID: 1004-1307A

Gait cycle (sec) : 1.1517 Side analysed : ❏❏❏❏Right Left

Stance time (sec) : 0.6933 Stance time (%GC) : 60.2014Swing Time (sec) : 0.4583 Swing time (%GC) : 39.7986

Single support (sec) : 0.4762 Single support (%GC) : 40.9823Double support - HC (sec) : 0.1099 Double support - HC (%GC) : 9.4651

Cadence (Steps/min) : 104.2005 Contralateral HC (%GC) : 49.9014

Stride length (m) : 1.5591 Stride length / Stature : 0.8939Walking velocity (m/s) : 1.3538 Walking velocity/ Stature: 0.7762CoP excursion (m): 0.3021 CoP (%SL): 102.0608

Ensembled average n = ❏❏❏❏4 ❏❏❏❏5 6 ❏❏❏❏7 ❏❏❏❏ Other (n = _ )

_____________ Appendix I. 320

80 100

80 100

80 100

20 40 60 80 100-1

0

1

2

Hip Power (-)

(W/k

g) G

en.

>

20 40 60 80 100

-2

-1

0

1

2Knee Power (-)

(W/k

g) G

en.

>

20 40 60 80 100-2

0

2

4

6Ankle Power (-)

Gait cycle [%]

(W/k

g) G

en.

>

________________________________________________________ References. 321

Acierno, S.P., Baratta, R.V. and Solomonow, M. (1998) A practical guide to

electromyography. Tutorial from the Gait and Clinical Movement Analysis Conference,

San Diego. Published by LSU Bioengineering Laboratory, Louisiana

Ackland, T.R., Henderson, P.W., and Bailey, D.A. (1988) The uniform density

assumption: its effect upon the estimation of body segment inertial parameters.

Inernational Journal of Sports Biomechanics 4,146-155.

Allard, P., Lachance, R., Aissaoui, R. and Duhaime, M. (1996) Simultaneous bilateral

3-D gait analysis. Human Movement Science 15,327-346.

Allard, P., Lachance, R., Aissaoui, R., Sadeghi, H., Duhaime, M. (1997) Able-bodied

gait in men and women. In Allard, P., Capozzo, A., Lundberg, A., Vaughan, C. Editors

of Three-dimensional analysis of human locomotion. John Wiley and Sons Ltd.

Chichester West Sussex. pp. 307-334.

AMTI (1991) Biomechanics platform set instruction manual. Advanced Mechanical

Technologies Inc. Waterton Massachusetts USA.

Bach, T. (1994) A computer simulation of the swing phase in human walking with

application to optimisation of inertial characteristics of transfemoral prosthetic limbs.

PhD thesis. La Trobe University. Melbourne.

References

________________________________________________________ References. 322

Barry, D.C., Sabacinski, K.A., Habershaw, G.M., Giurini, J.M. and Chrzan, J.S. (1993)

Tendo achillis procedures for chronic ulcerations in diabetic patients with

transmetatarsal amputations. Journal of the American Podiatric Medical Association

83,96-100.

Basmajian, J.V. and Deluca, D.J. (1985) Muscles alive: Their functions revealed by

electromyography. 5th Ed. Williams and Wilkins, Baltimore. pp19-64.

Beasley, W.C. (1961) Quanttitative muscle testing: principles and applications to

research and clinical services. Archives of Physical Medicine and Rehabilitation 42,398-

425.

Birkie , J.A. and Sims, D.S. (1988) The insensitive foot. In Hunt, G.C. Editors of

Physical Therapy of the foot and ankle. Churchill Livingston Inc, New York. pp 143-

164.

Bobbert, M.F. and Schamhardt, H.C. (1990) Accuracy of determining the point of force

application with piezoelectric force plates. Journal of Biomechanics 23,705-710.

Boyd, L.A., Rao, S. and Burnfield, J. (1999) Forefoot rocker mechanics in individuals

with partial foot amputation. In Proceedings of the Clinical Gait and Movement

Analysis Society. Dallas, Texas.

Boyd, L.A., Roa, S.S., Burnfield, J.M., Mulroy, S.J. Perry, J. (1999) Forefoot rocket

mechanics in individuals with partial foot amputation. In Proceedings of the Clinical

Gait and Movement Analysis Society. Dallas, Texas.

Brand, P.W. (1983) The Diabetic Foot. In Ellenburg, M. and Rifkin, H. Editors of

Diabetes Mellitus. Theory and Practice. 3rd Ed. Medical Examination Publishing Co.

Inc., New Hyde Park, New York. pp 829-849.

Burkett, B. J. (1998) A biomechanical analysis for Transfemoral amputees. PhD thesis.

Queensland University of Technology. Brisbane.

________________________________________________________ References. 323

Burnfield, J.M., Boyd, L.A., Roa, S., Mulroy, S.J. and Perry, J. (1998) The effect of

partial foot amputation on sound limb loading force during barefoot walking. Gait and

Posture 7,178-79.

Capozzo, A. and Berme, N. (1990) Subject specific segment inertial parameter

determination - a survey of current methods. In Berme, N and Capozzo, A. Editors of

Biomechanics of Human Movement, Applications in Rehabilitation, Sports and

Ergonomics. Bertec, Washington. pp 179-185.

Capozzo, A., Cataini, F. and Leardini, A. (1993) Skin movement artifacts in human

movement photogrammetry. In Proceedings of the XIVth Congress of the International

Society of Biomechanics, Paris. pp 238-239

Capozzo, A., Figura, F and Marchetti, M. (1976) The interplay of muscular and external

forces in human ambulation. Journal of Biomechanics 9,35-43

Cappozzo, A. Figura, F., Leo, T. and Marchetti, M. (1976) Biomechanical evaluation of

above-knee prostheses. In Komi, P.V. Editor of Biomechanics V: Proceedings of the

fifth International Congress on Biomechanics. University Park Press, Baltimore.

Chrzan, J., Giurini, J. and Hurchik, J. (1993) A biomechanical model for the

transmetatarsal amputation. Journal of the American Podiatric Medical Association. 83,

82-86.

Clarkson, H.M. and Gilweich, G.B. (1989) Musculoskeletal assessment. Joint range of

motion and manual muscle strength. Williams and Wilkins, Baltimore.

Clauser, C.E., McConville, J.T. and Young, J.W. (1969) Weight, volume and centre of

mass of segments of the human body. Technical report AMRL-TR-69-70, Wright-

Patterson Air Force Base, Ohio.

Condie, D.N. (1970) Biomechanics of the partial-foot amputations. In Prosthetics and

Orthotics Practice. Edward Arnold Publishers Ltd., London. pp 149-160.

________________________________________________________ References. 324

Condie, D.N. and Stills, M.L. (1988) Biomechanics and Prosthetic/Orthotic solutions. In

Murdoch, G. Editor of Amputation Surgery and Lower limb prosthetics. Blackwell

Scientific Publications Inc., Boston. pp 105-113

Contini, R. (1970) Body segment parameters (pathological). Technical report 1584.03

School of Engineering and Science, New York University, New York.

Contini, R. (1972) Body segment parameters, part II. Artifical Limbs 16,1-19.

Craik, R.B. and Dutterer, L. (1995) Spatial and temporal characteristics of foot fall

patterns. In Craik, R.B. and Oatis, C.A. Editors of Gait Analysis: Theory and

Application. Mosby, St. Louis. pp143-158.

Czerniecki, J.M., Gitter, A. and Munro, C. (1991) Joint moment and muscle power

output characteristics of below knee amputees during running: the influence of energy

storing prosthetic feet. Journal of Biomechanics 24,63-75.

Davis, B.L. (1992) Uncertainty in calculating joint moments during gait. In Proceedings

of the VII meeting of the European Society of Biomechanics. Rome. pp 276

Das, R.N. and Ganguli, S. (1979) Preliminary observations on parameters of human

locomotion. Ergonomics 22,1231-1242.

Dean, C.A. (1965) An analysis of energy expenditure in level and grade walking.

Ergonomics 8,31-48.

De Looze, M.P., Bussmann, J.B., Kingma, I. and Toussaint, H.M. (1992a) Different

methods to estimate total power and its components during lifting. Journal of

Biomechanics 25,1089-1095

De Looze, M.P., Kingma, I., Bussmann J.B. and Toussaint, H.M. (1992b) Validation of

a dynamic linked segment model to calculate joint moments during lifting. Clinical

Biomechanics 7,161-69

________________________________________________________ References. 325

Dempster, W.T. (1955) Space requirements for the seated operator. WADC Technical

Report 55-159. Wright-Patterson Air Force Base, Ohio.

Di Fabio, R.P. (1987) Reliability of computerised surface electromyography for

determining the onset of muscle activity. Physical Therapy 67,43-48.

Dillingham, T.R., Lehmann, J.F., Price, R. (1992) Effect of lower limb on body

propulsion. Archives of Physical Medicine and Rehabilitation 73,647-51

Dillon, M. (1995) The biomechanics of partial foot amputee gait. Honours thesis. La

Trobe University. Melbourne.

Dillon, M. and Frossard, L. (1999) Influences of A/D multiplexing and offsets in force

plate data on the accuracy of centre of pressure excursion. Internal report for the Centre

for Rehabilitation Science and Engineering. Queensland University of Technology,

Brisbane.

Dorostkar, M., Ayyappa, E., Perry, J., Chambers, R., Burnfield, J., Boyd, L., Bontrager,

E., Roa, S. and Mulroy,S. (1997) Gait mechanics of the partial foot amputee. In

Rehabilitation Research and Development progress reports. Veterans Affairs, Seattle.

pp 17-18.

Drillis, R. and Contini, R. (1966) Body segment parameters. Technical report 1166.03,

New York University, School of Engineering Science. New York.

Drillis, R.; Contini, R. and Bluestein, M. (1964) Body Segment Parameters: a survey of

measurement techniques. Artifical Limbs 8,44-66.

Eng, J.J. and Winter, D.A. (1995) Kinetic analysis of the lower limbs during walking:

what information can be gained from a three dimensional model? Journal of

Biomechanics 28,753-758.

Fernie, G.R. and Holliday, P.J. (1982) Volume fluctuations in the residual limbs of

lower limb amputees. Archives of Physical Medicine and Rehabilitation 63,162-165

________________________________________________________ References. 326

Frossard, L. and Dillon, M. (1999A) Impact of camera positions on the collection and

reconstruction of 3D kinematic data with the Peak-Motus system. Internal report for the

Centre for Rehabilitation Science and Engineering. Queensland University of

Technology, Brisbane.

Frossard, L. and Dillon, M. (1999B) Accuracy of the force-plates and three-dimensional

motion analysis systems. Internal report for the Centre for Rehabilitation Science and

Engineering. Queensland University of Technology, Brisbane.

Garabolsa , J.C., Cavanagah, P.R., Wu, G., Ulbrecht, J.S., Becker, M.B., Alexander, I.J.

and Campbell, J.H. (1996) Foot function in diabetic patients after partial amputation.

Foot and Ankle International 17,43-48.

Giurini, J.M., Basile, P., Chrzan, J.S., Habershaw, G.M. and Rosenblum, B.I. (1993)

Panmetatarsal head resection: a viable alternative to the transmetatarsal amputation.

Journal of the American Podiatric Medical Association 83,101-107

Grabiner, M.D. (1997) Locomotion in healthy older adults. In Allard, P., Capozzo, A.,

Lundberg, A., Vaughan, C. Editors of Three-dimensional analysis of human locomotion.

John Wiley and Sons Ltd. Chichester West Sussex. pp. 363-373.

Grieve, D.W. and Gear, R.J. (1966) The relationship between length of stride, step

frequency, time of swing and speed of walking for children and adults. Ergonomics

5,379-399.

Gritter, A., Czerniecki, J.M. and DeGroot, D.M. (1991) Biomechanical analysis of the

influence of prosthetic feet on below-knee amputee walking. Archives of Physical

Medicine and Rehabilitation 70,142-148.

Habershaw, G.M., Gibbons, G.W. and Rosenblum, B.I. (1993) A historical look at the

transmetatarsal amputation and its changing indications. Journal of the American

Podicatic Medical Association 83,79-81

________________________________________________________ References. 327

Hanavan, E.P. (1964) A mathematical model of the human body. Technical report

AMRL-TR-64-102. Wright-Patterson Air Force Base. Ohio.

Hatze, H. (1979) A mathematical model for the computational determination of

parameter values of anthropometric segments. Technical report TWISK 79, National

Research Institute of Mathematical Sciences, Periota.

Hatze, H. (1980) A mathematical model for the computational determination of

parameter values of anthropometric segments. Journal of Biomechanics 13,833-843.

Heim, M. (1994) A new orthotic device for Chopart amputees. Orthopaedic Review,

249-252.

Henning, E.M. and Milani, T.L. (1995) In-shoe pressure distribution for running in

various types of footwear. Journal of Applied Biomechanics 11,299-310.

Henning, E.M., Milani, T.L. and Lafortune, M.A. (1993) The use of ground reaction

force parameters for the prediction of peak tibial accelerations in running with different

footwear. Journal of Applied Biomechanics 9,306-314.

Henning, E.M. and Lafortune, M.A. (1997) Technology and application of force,

acceleration and pressure distribution measurements in biomechanics. In Allard, P.,

Capozzo, A., Lundberg, A., Vaughan, C. Editors of Three-dimensional analysis of

human locomotion. John Wiley and Sons Ltd. Chichester West Sussex. pp 109-127.

Hirsch, G., Mc Bride, M., Murry, D., Sanderson, D., Dukes, I. and Menard, M. (1996)

Chopart prosthesis and semirigid foot orthosis in traumatic forefoot amputation.

American Journal of Physical Medicine and Rehabilitation 75,283-291.

Hodge, M.J., Peters, T.G. and Efird, W.G. Amputation at the distal portion of the foot.

Southern Medical Journal 82,1138-1142.

________________________________________________________ References. 328

Hodges, P.W. and Bui, B.H. (1996) A comparison of computer-based methods for the

determination of onset of muscle contraction using electromyography.

Electroencephalography and Clinical Neurophysiology 101,511-519.

Hreljac, A. and Marshall, R.N. (2000) Algorithms to determine event timing during

normal walking using kinematic data. Journal of Biomechanics 33,783-786.

Imler, L.D. (1985) Imler partial foot prosthesis. IPFP -"The Chicago Boot". Orthotics

and Prosthetics 39,53-56.

Inman, V.T., Ralston, H.J and Todd, J. (1981) Human Walking. Willins and Wilkins,

Baltimore.

Jensen, R.K. (1986) Body segment mass, radius and radius of gyration proportions of

children. Journal of Biomechanics 19,359-368.

Kadaba, M.P., Ramakrishnan, H.K. Wooten, M.E., Gainey, J., Gorton, G. and Cochran,

G.V.B. (1989) Repeatability of kinematic, kinetic and electromyographic data in normal

adult gait. Journal of Orthopaedic Research 7,849-860.

Kendall, F.P. and McCreary, E.K. (1983) Muscles: testing and function. 3rd Ed.

Williams and Wilkins, Baltimore.

Kingma, I., Toussaint, H., De Looze, M. and Van Dieen, J. (1996) Segment inertial

parameter evaluation in two anthropometric models by application of a dynamic linked

segment model. Journal of Biomechanics 29, 693-704.

Krouskop, T.A., Dougherty, D., Yalcinkaya, M.I. and Muilenburg, A. (1988) Measuring

the shape and volume of an above knee amputee stump. Prosthetics and Orthotics

International 12,136-142.

Lange, L.R. (1985) The Lange silicone partial foot prosthesis. Journal of Prosthetics

and Orthotics 4,56-61.

________________________________________________________ References. 329

Lavery, L.A., Lavery, D.C. and Quebedeax-Farnham, T. (1995) Increased foot pressures

after great toe amputation in diabetics. Diabetes Care 18,1460-1462.

Lee, J.S., Lu, M., Lee, V.S., Russell, D., Bahr, C. and Lee. E.T. (1993) Lower extremity

amputation: incidence, risk factors and mortality in the Oklahoma Indian Diabetes

Study. Diabetes 42,876-82.

Lehmann, J.F., Concon, S.M., de Lateur, B.J. and Smith, J.C. (1985) Gait abnormalities

in tibial nerve paralysis: a biomechanical study. Archives of Physical Medicine and

Rehabilitation 66,80-85.

Lieberman, J.R., Jacobs, R.L., Goldstock, L., Durham, J. and Fuchs, M.D. (1993)

Chopart amputation with percutaneous heel cord lengthening. Clinical Orthopaedics

and Related Research 296,86-91

Maltbaek, J.C. (1988) Dynamics in engineering. Halsted Press. Chichester, West

Sussex.

Mann, R.A., Hagy, J.L. and Simon, S.R. (1974) Push-off phase of gait. Abbott Proc

5:85-

McConville, J.T., Churchill, T.D., Kaleps, I., Clauser, C.E. and Cuzzi, J. (1980)

Anthropometric relationships of body and body segment moments of inertia. Report No

AFAMRL-TR-80-119. Wright-Patterson Air Force Base. OH.

McKittrick, L.S., McKittrick, J.B., Risley, T.S. (1949) Transmetatarsal amputation for

infection or gangrene in patients with diabetes mellitus. Annals of Surgery 130,826-.

Reprinted Journal of the American Podiatric Medical Association 83,62-76

Meinders, M., Gritter, A., and Czerniecki, J. (1998) The role of ankle plantarflexor

muscle work during walking. Scandanivian Journal of Rehabilitation Medicine. 30,39-

46.

________________________________________________________ References. 330

Middleton, J., Sinclair, P. and Patton, R. (1999) Accuracy of centre of pressure

measurement using piezoelectric force platform. Clinical Biomechanics 14,357-360.

Miller, D.I. (1987) Resultant lower extremity joint moments in below-knee amputees

during running stance. Journal of Biomechanics 20,529-541.

Mueller, M.J., Allen, B.T. and Sinacore, D.R. (1995) Incidence of skin breakdown and

higher amputation after transmetatarsal amputation: Implications for rehabilitation.

Archives of Physical Medicine and Rehabilitation 76,50-54

Muller, M.J, Strube, M.J and Allen, B.T. (1997) Therapeutic footwear can reduce

plantarpressures in patients with diabetes and transmetatarsal amputation. Diabetes

Care 20,637-41.

Muller, M.J. and Sinacore, D.R. (1994) Rehabilitation factors following Transmetatarsal

amputation. Physical Therapy 74,1027-1033.

Muller, M.J., Salisch, G.B. and Bastian, A.J. (1998) Differences in gait characteristics

of people with diabetes and transmetatarsal amputation compared with aged match

controls. Gait and Posture 7,200-206

Murry, M.P., Drought, A.B. and Kory, C.R. (1964) Walking patterns of normal men.

Journal of Bone and Joint Surgery. 64A,335-360

Murry, M.P., Kory, R.C. and Clarkson, B,H. (1969) Walking patterns in healthy old

men. Journal of Gerontology 24,169-178

Murry, M.P., Guten, G.N., Sepic, S.B., Gardiner, G.M. and Baldwin, J.M. (1978)

Function of the triceps surae during gait. Compensatory mechanism for unilateral loss.

Journal of Bone and Joint Surgery 60A,473-476.

Murry, M.P., Spurr, G.B., Sepic, S.B. Gardiner, G.M. and Mollinger, L.A. (1985)

Treadmill vs. floor walking: kinematics electromyogram and heart rate. Journal of

Applied Physiology 59,87-91.

________________________________________________________ References. 331

Nilsson, J. Panizza, M. and Hallet, M. (1993) Principles of digital sampling of a

physiologic signal. Electroencephelogram and Clinical Neurophysiology 89,349-58.

Norkin, C.C. and Levangie, P.K. (1992) Joint structure and function: a comprehensive

analysis. 2nd Ed. Davis, F.A., Philadelphia

Nubar, Y. (1962) Rotating platform method for determining moments of inertia of body

segments, Unpublished Report, Research Division, College of Engineering, New York

University. New York.

Ounpuu, S. (1994) Terminology for clinical gait analysis Draft#2. AACPDM Gait lab

committee.

Parziale, J. and Hahn, K. (1988) Functional considerations in partial foot amputations.

Orthopaedic Review XVII,262-266

Perotto, A. (1994) Anatomical guide for the electromyographer: the limbs and trunk. 3rd

Ed. Thomas, C.C., Illinois.

Perry, J. (1974) Kinesiology of lower extremity bracing. Clinical Orthopaedics and

related research 102,18-31

Perry, J. (1992) Gait analysis: normal and pathological function. SLACK Inc.

Thorofare, New Jersey.

Pierotti, S.E., Brand, R.A., Gabel, R.H., Pedersen, D.R. and Clarke, W.R. (1991) Are

leg electromyogram profiles symmetrical? Journal or Orthopaedic Research. 9,720-

729.

Pinzur, M.S., Wolf, B. and Havey, R.M. (1997) Walking pattern of midfoot and ankle

disarticulation amputees. Foot and Ankle International 18,635-638

________________________________________________________ References. 332

Plagenhoef, S. (1971) Pattern of human motion: a cinematographic analysis. Prentice-

Hall. New Jersey.

Plagenhoef, S. (1983) Anatomical data for analysing human motion. Res. Quart.

Exercise Sports 54,169-178

Pomoselli, F.B., Basile, P., Campbell, D.R. and LoGerfo, F.W. (1993) Salvaging the

ischemic transmetatarsal amputation through distal arterial reconstruction. Journal of

the American Podiatric Medical Association 83,87-90.

Powers, C.M., Roa, S. and Perry, J. (1998) Knee kinetics in trans-tibial amputee gait.

Gait and Posture 8,1-7.

Pullen, J.J. (1987) A low profile paediatric partial foot. Prosthetics and Orthotics

International 11,137-138.

Quebedeaux, T.L., Lavery, L.A. and Lavery, D.C. (1996) The development of foot

deformities and ulcers after great toe amputation in diabetics. Diabetes Care 19,165-

167.

Quigley, F.G., Faris, I.B. and Xiouruppa, H. (1995) Transmetatarsal amputation for

advanced forefoot tissue loss in elderly patients. Australian and New Zealand Journal of

Surgery 65,339-341

Reid, J.G. and Jensen, R.K. (1990) Human body segment inertial parameters: A survey

and status report. Exercise and Sport Science Reviews 18, 225-241

Roebuck, J.A. (1975) Engineering anthropometry methods. Wiley-Interscience, New

York.

Rubin, G.R. and Danisi, M. (1971) A functional Chopart prosthesis. Bulletin Prosthetics

Research 8,149-152.

________________________________________________________ References. 333

Rubin, G. (1984) The partial foot amputation. Journal of the American Podiatry

Association 74,518-522.

Rubin, G. (1985) Indications for variants of the partial foot prosthesis. Orthopaedic

Review 14,49-53.

Sadeghi, H., Allard, P. and Duhaime, M. (1997) Functional gait asymmetry in able-

bodied subjects. Human Movement Science 16,243-258.

Sage, R., Pinzur, M., Cronin, R., Preuss, F. and Osterman, H. (1989) Complications

following midfoot amputation in Neuropathic and dysvascular feet. Journal of the

American Podiatric Medical Association 79,277-280.

Sanders, L.J. (1997) Transmetatarsal and midfoot amputations. Clinics in Podiatric

Medicine and Surgery 14,741-761.

Sanders, L.J. and Dunlap, G. Transmetatarsal amputation: a successful approach to limb

salvage. Journal of the American Podiatric Medical Association 82,129-35.

Santini, M.D., Thoma, B.J. and Chambers, R.B. (1993) Survivorship of healed partial

foot amputations in dysvascular patients. Clinical Orthopaedics and Related Research

292,245-249.

Schneider, K. and Zernicke, R.F. (1992) Mass, centre of mass and moment of inertia

estimates for infant limb segments. Journal of Biomechanics. 25,145-148.

Schneider, K., Zernicke, R.F., Ulrich, B.D., Jensen, J.L., Thelen, E. (1990)

Understanding motor control in infants through the analysis of limb intersegmental

dynamics. Journal of Motor behaviour 22,493-520.

Schwindt, C.D., Lulloff, R.S. and Rogers, S.C. (1973) Transmetatarsal amputations.

Orthopaedic Clinics of North America 4,31-42

________________________________________________________ References. 334

Sentilles, D. (1989) Applying calculus in economic and life sciences. Wadsworth

Publishing Company. Belmont, California. pp 451-453.

Seroussi, R.E., Gritter, A., Czerniecki, J.M. and Weaver, K. (1996) The mechanical

work adaptations of above-knee amputee ambulation. Archived of Physical Medicine

and Rehabilitation 77,1209-1214

Shiavi, R.; Bugle, H.J. and Limbird, T. (1987) Electromyographic gait assessment, part

1: Adult EMG profiles and walking speed. Journal of Rehabilitation Research and

Development 24,13-23.

Simon, S.R., Mann, R.A., Hagy, J.L. and Larsen, L.J. (1978) Role of the posterior calf

muscles in normal gait. Journal of Bone and Joint Surgery 60A,465-472

Simonsen, E.B., Dyhre-Poulsen, P., Voigt, M, Aagaard, P. and Fallentin, N. (1997)

Mechanisms contributing to different joint moments observed during human walking.

Scand J Med Sci Sports. 7:1-13.

Sobel, E.C. (1995) Advances in foot prosthetics. In Kominsky, S.J. Editor of Advances

in Podiatric Medicine and Surgery, Volume 1. Mosby-Year Book Inc. St Louis,

Missouri. pp 213-289

Sobel, E.C. (2000) Prosthetic management of the partially amputated foot.

www.podiatrymgt.com/cme/sob-02.htm accessed 12.12.2000

Solomonow, M., Baten, C., Smit, J. Baratta, R., Hermens, H. and D'Ambrosia, R.

(1990) EMG power spectral frequencies associated with motor unit recruitment

strategies. Journal of Applied Physiology 68,1177-1185.

Stills, M.L. (1987) Partial foot prostheses/orthoses. Clinical prosthetics and orthotics

12,14-18.

Stuck, R.M., Sage, R., Pinzur, M. and Osterman, H. (1995) Amputations in the diabetic

foot. Clinicas in Podiatric Medicine and Surgery 12,141-155.

________________________________________________________ References. 335

Studenski, S. Duncan, P.W. and Chandler, J. (1991) Postural responses and effector

factors in persons with unexplained falls: results and methodological issues. Journal of

the American Geriatrics Society. 39,229-234.

Sutherland, D.H. (1966) An electromyographic study of the plantarflexors of the ankle

in normal walking on the level. Journal of Bone and Joint Surgery 48A,66-71.

Sutherland, D.H., Cooper, L. and Daniel, D. (1980) The role of ankle plantarflexors in

normal walking. Journal of Bone and Joint Surgery. 62A,354-363

Torburn, L., Perry, J., Ayyappa, E., Shanfield, S.L. (1990) Below-knee amputee gait

with dynamic elastic response prosthetic feet: A pilot study. Journal of Rehabilitation

Research and Development 27,369-384.

Vaughan, C., Davis, B. and O'Connor, J. (1992) Dynamics of human gait. Human

Kinetics Publishers. Champaign, Illinois. pp 15-43

Walters, R.L., Perry, J., Antonelli, D. and Hislop, H. (1976) Energy cost of walking of

amputees: The influence of level of amputation. Journal of Bone and Joint Surgery

58,42-46.

Weber, D. (1991) Partial foot amputation. In Weber, D and Agro, M. Editors of Clinical

aspects of lower extremity prosthetics. Elgan Enterprises, Oakville Ontario. Co-

published with Canadian Association of Prosthetics and Orthotics. Winnipeg, Manitoba.

pp 197-209

Whittle, M. (1991) Gait analysis - An introduction. Butterworth-HeinemannLtd.,

Oxford.

Whittle, S.C. and Lage, K.J. (1993) Changes in joint moments due to independent

changes in cadence and stride length during gait. Journal of Human Movement Science

12,461-474

________________________________________________________ References. 336

Winter, D.A. (1983) Biomechanical motor patterns in normal walking. Journal of Motor

Behaviour 15,302-330.

Winter, D.A. (1983b) Energy generation and absorption at the ankle and knee during

fast, natural and slow cadences. Clinical Orthopaedics 175,147-157.

Winter, D.A. (1984) Kinematic and kinetic patterns in human gait: variability and

compensating effects. Human Movement Science 3,51-76.

Winter, D.A. (1989) Biomechanics of normal and pathological gait: Implications for

understanding human locomotor control. Journal of Motor Behaviour 21,337-355

Winter, D.A. (1990) Biomechanics and Motor Control of Human Movement. 2nd Ed.

John Wiley & Sons Inc. New York.

Winter, D.A (1991) The biomechanics and motor control of human gait: normal,

elderly and pathological. Waterloo Biomechanics, Waterloo.

Winter, D.A. (1993) Biomechanical motor patterns in normal walking. Journal of Motor

Behaviour 15, 302-330.

Winter, D.A. and Robertson, D.G. (1978) Joint torque and energy patterns in normal

gait. Biol Cybern 29,137-142.

Winter, D.A. and Sienko, S.E. (1988) Biomechanics of below-knee amputee gait.

Journal of Biomechanics 21,361-367.

Winter, D.A., Sidwall, H.G. and Hobson, D.A. (1974) Measurement and reduction of

noise in kinematics of locomotion. Journal of Biomechanics 7,157-159

Winter, D.A., Quandbury, A.O., Hobson, D.A., Sidwall, H.G., Reimer, G., Trenholm,

B.G., Steinkle, T., Shlosser, H. (1974) Kinematics of normal locomotion - a statistical

study based on T.V. data. Journal of Biomechanics 7,479-486.

________________________________________________________ References. 337

Yang, J.F. and Winter, D.A. (1984) Electromyographic amplitude normalisation

methods: Improving their sensitivity as diagnostic tools in gait analysis. Archives of

Physical Medicine and Rehabilitation 65,517-521

Zar, J.H. (1984) Biostatistical Analysis. Prentice Hall Inc. Englewood Cliffs. New

Jersey. pp 261-292

Zatsiorsky, V. and Seluyanov, V. (1985) Estimation of the mass and inertial

characteristics of the human body by means of the best predictive regression equations.

In Winter, D.A., Norman, R., Wells, R.P., Hayes, K.C. and Patla, A.E. Editors of

Biomechanics IX-B. Human Kinetics Publishers, Champaign. Illinois. pp. 233-239.

Zatsiorsky, V., Seluyanov, V. and Chugunova, L. (1990) In vivo body segment inertial

parameter determination using a gamma-scanner method. In Berme, N and Capozzo, A.

Editors of Biomechanics of human movement: Applications in rehabilitation, sports and

ergonomics. Bertec, Washington. pp.186-202