Practical Applications of Muscle Stimulationwkdurfee/presentations/muscle-ctr-2007.pdf · Practical...

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Practical Applications of Muscle Stimulation

William DurfeeDepartment of Mechanical Engineering

University of MinnesotaMinneapolis, USA

www.dmdconf.org

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NON-INVASIVE ASSESSMENT OF MUSCLE FUNCTION

External mechanical properties provide window into muscle excitation & contraction mechanismsElectrical stimulation provides controlled inputSystem identification methods reveal muscle parametersRequires mathematical model of muscleNon-invasive

MUSCULOSKELETAL SYSTEMSTIM

u(t)

FORCE/MOTION

y(t)

3

Most common non-invasive muscle force assessment method

Durfee & Iaizzo, Encyclopedia of Medical Devices and Instrumentation, 2006

Encyclopedia of Medical Devices and Instrumentation, 2nd ed . J.G. Webster, ed., Vol6, pp 62-71, Hoboken, John Wiley & Sons, 2006.

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MATHEMATICAL MODELS OF

WHOLE MUSCLE MECHANICS

5

Hill models are still the gold

standard

Proceedings of the Royal Society of London, B. 126(843):136-195, 1938.

SE

PE

CE

Contractile element force depends on several variables

Force = f (neural input, length, velocity)

F

Activation

F

Velocity

F

Length

CE

6

Multiplicative model for CE force

CE Force-Velocity

Fscale

IRC

CE Force-Length

Activation Dynamicsu

V

X X

Model for isolated muscle

X

�

�

PE Force-Velocity

CE Force-Velocity

Fscale

IRC

CE Force-Length

Activation Dynamics (2nd order)

PE Force-Length

u

V

X

V

X

Force

Passive Element

Active Element

∑

∑

Fu

x,v

7

Model OK for isolated muscle

0

5

10

15

20

25

30

35

0 4 8 12 16

Forc

e (N

)

Time (s)

Durfee & Palmer, IEEE Trans. Biomed. Eng., 41(3):205, 1994

Experiment

Model

Identification of intact muscle properties more challenging

1. Skeletal geometry2. Muscle in series with a springy tendon

www.ebookwholesale.co.uk/fatloss.htm?hop=0www.rad.washington.edu/atlas/bicepsbrachii.html

What you want

What you have

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MUSCULOSKELETALSYSTEMSTIM

u(t)

FORCE/MOTION

y(t)

MT GEOM

GEOM-1

u(t)

LDθ(t)τ(t)f(t)

x(t)

Skeletal geometry

Some muscles have significant springs

Tibialis Anterior

http://www.rad.washington.edu/atlas2/tibialisanterior.html

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Tendon spring leads to inaccuracies in estimating muscle force-length curve

Zajac, Crit. Rev. Biomed. Eng., 1989, Figure 13

a(t)LM(t)

VM(t)

CE

SE

PE

muscle

tendon

FM(t)=FT(t)=f(t)

passive

Muscle-tendon model

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WHAT'S WRONG WITH THE MUSCLE MODEL

Invariant F-A, F-L, F-V (no change with activation)Invariant twitch dynamics (uniform fiber types)Time-invariant (no fatigue)

KSE

KPE(θ)

CE Mm

BPE(θ)

MJ(θ)

Full model has muscle-tendon acting against limb load

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KSE

KPE(θ)

CE Mm

BPE(θ)

MJ(θ)

KSE

KPE(θ)

CE Mm

BPE(θ)

MJ(θ)

states excitation, 65

4

3

2

1

=====

qqqq

VqLq

CE

CE

ωθ

)(2

),()(

1)()(

1)()(

1

)(1),,(1

52

66

65

343

33

133

4

43

135212

21

tkuqaaqq

qq

qqfqM

qfqM

qqfqM

q

qq

qqfM

qqqfM

q

qq

PDJ

PEJ

TJ

Tm

CEm

+−−=

=

−−−−=

=

−+=

=

&

&

&

&

&

&

Simulation equations

CE Force-Length

Gordon, J. Physiol., 1966

( )

parameters shape,,

11exp)(

=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎥⎦

⎤⎢⎣

⎡ −+−=

ωρβ

ω

ρβLLFFL

12

CE Force-Velocity

FORCE

VELOCITYSHORTENINGLENGTHENING

LINEAR FIT

( )

( ) *)(

*)(

2

22

1

11

bVVabVF

bVVabVF

FV

FV

+−

=

+−

= shortening

lengthening

Modeling twitch dynamics

Staticnonlinearity

Lineardynamic system

Hammerstein model

stim force

Identify LDS with impulse responseDurfee & Palmer, IEEE TBME, 1994

Identify SL by deconvolutionDurfee & MacLean, IEEE TBME, 1989

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Twitch force varies with stim strength

Recruitment Plot

0

100

200

300

400

500

600

700

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Pulse Width Percentage

020406080

100120140

0 100 200 300 400

Time (mS)

Torq

ue

2)( ask+

FORCE TWITCH

BEST FIT

2nd-order, critically damped linear system fits well enough

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Using nonlinear force twitch

response as a metric

15

0

50

100

150

200

250

300

350

400

450

500

0 50 100 150 200 250 300 350 400

Time (ms)

Torq

ue

Single pulse twitch

0

50

100

150

200

250

300

350

400

450

500

0 50 100 150 200 250 300 350 400

Time (ms)

Torq

ue

Double pulse twitch, if ideal linear system

y 2y

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0

50

100

150

200

250

300

350

400

450

500

0 50 100 150 200 250 300 350 400

Time (ms)

Torq

ue

Double pulse twitch, real

3.2 y

Doublet pulse spacing affects twitch force

0

0.5

1

1.5

2

2.5

3

3.5

1 26 51 76 101 126 151 176 201 226 251 276

Time (ms)

Forc

e

Doublets at 1,2,3,4,5,6,7,8,9,10,20,30,40,50 ms

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Nonlinear summation for TANormalized Peak Torque

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000 40000 50000

Normalized TTI

0

1

2

3

4

5

6

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 20000 30000 40000 50000

Nonlinear summation depends on which muscle

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0 1 2 3 4 5 6 7 8 9 10

IPI (ms)

BicepsQuadricepsTibialis AnteriorMean

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Normalized twitch parameters same for all recruitment levels

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

L1 L2 L3 L4 L5 L6 L7

2.300.640.68X2.180.005.80HDT

2.300.271.29X2.180.006.25HPW

2.300.740.542.180.072.00CT

2.300.101.902.180.062.12ST

2.300.920.282.180.241.34TTI

2.300.590.752.180.700.64PT

Sig.FcritPFSig.FcritPF

L2-L7L1-L7

Metric

WHAT'S NEXT

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Identification strategy

1. Passive length-tension: slowly move2. Twitch dynamics: isometric3. Active length-tension: slowly move

when active4. Force-velocity: apply rich velocity

perturbations about steady-state

Current isometric apparatus

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Improved apparatus

Force, EMG, temp, laptop/USB

Force vs. Acceleration

-15-10-505

1015

-2 -1 0 1 2

Acceleration (g)

Forc

e (lb

-f)

A simple clinical tool to measure limb inertia

KSE

KPE(θ)

CE Mm

BPE(θ)

MJ(θ)

KSE

KPE(θ)

CE Mm

BPE(θ)

MJ(θ)

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Build database of properties for several muscles in non-diseased subjects

F-L, F-V, contraction dynamics, doublet properties

Nash Avery Search for Hope Fund and the Paul and Sheila Wellstone Muscular Dystrophy Center, University of Minnesota.

FES-AIDED GAIT: A NEW APPROACH

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Brain

Spinal Cord

Limb

Stimulator

FEXTERNAL

CONTROL STIMULATORInputs

Measurements

FEXTERNAL

Improve health through weight bearingBrief standing: social and functionalLimited ambulation in vicinity of wheelchairNo balance, no change in neuro function

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Liberson foot-drop system, 1961

Heel switch triggered peroneal n. stimulationCorrection of foot-drop following strokeStarted field of FESSeveral commercial and research embodiments

Medtronic implanted foot-drop system

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STIMULATION PLUS SMART ORTHOTICS

Muscle stimulation

provides power

Brakes for locking and

control

Orthosis provides guidance

and support

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CBO Increases speed and distance

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Without CBO With CBO

Gait Speed

0.09

0.12

Spee

d (m

/s)

0

10

20

30

40

50

60

Without CBO With CBO

Gait Distance

25

50

Dis

tanc

e (m

)

IEEE Trans Rehab Eng, 4(1):13, 1996, IEEE Trans Rehab Neural Eng, 2003

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CBO has better step-to-step repeatability

0

20

40

60

80

100

120

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

20

40

60

80

100

120

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (sec)

With CBO

Time (sec)

Without CBO

Kne

e an

gle

(deg

)

Kne

e an

gle

(deg

)

IEEE Trans Rehab Eng, 4(1):13, 1996, IEEE Trans Rehab Neural Eng, 2003

ENERGY STORING BRACE

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Energy Budget~30 nM over 60 deg of motion31.4 J per extensionExtract 14 J per cycle

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J. Biomechanical Engineering, 127(6):1014-1019, 2005.

ADAMS dynamic model

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Gas springs

Cylinders

Accumulator

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Hip belt

Placeholders for brakes

Knee brace

Prismatic joint

Ab/adductionhinge

Medial hinge

POWEREDHUMAN-ASSIST

TOOLS

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Engineering Research Center for Compact & Efficient Fluid Power

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Compact power sourcesNatural interface and controlPortable and/or wearable

And a few other projects

Replacing muscle

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Muscle metricsShort-stroke, linear actuator

5-20% shortening strokePull force: 30 lbs/sq. in.90 W/lb

180 lb athlete w/ 72 lb of muscle puts out 370 W sustained 5 W/lb for human muscle for continuous use

25% efficientCompliant, back-drivableFatiguesCleanQuiet !

Vogel (2001), "Prime Mover"

Power (W/lb)

0

50

100

150

200

250

Muscle--peak Muscle--sustained

Electric motor Automobileengine

Vogel (2001), "Prime Mover"(Aircraft engine, piston: 700; Aircraft engine, turbine: 2500)

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Miniature free-piston air-compressor

FUTURE MICRO FPAC + 1KPSI TANK

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