31th

Danubia-Adria Symposium, Kempten University, Germany, 2014

EMPIRICAL DESCRIPTION OF KNEE ROTATION SEGMENTS

Gábor Katona1, Gusztáv Fekete

2, Béla M. Csizmadia

1

1 Szent István University, Faculty of Mechanical Engineering, Páter Károly u. 1, 2100 Gödöllő,

HUNGARY. E-mails: katona.gabor@gek.szie.hu, csizmadia.bela@gek.szie.hu

2 University of West Hungary, Faculty of Natural Sciences, Károlyi Gáspár tér 4, 9700, Szombathely,

HUNGARY. E-mail: fekete.gusztav@ttk.nyme.hu

1. Introduction

Probably the most significant relative motion of

the knee joint is the rotation; therefore a new

aspect of this type of movement is presented in this

current paper which can contribute to the

qualification methods of different, commercial

prostheses.

As a novelty, the rotation curve is described as

a trilinear function. This special description is

based on the fact that the movement of the knee

extension and flexion has been divided up to two

segments: the first segment from 0 to 20˚ of

flexion angle is called ‘screw-home’ segment,

where the rotation is constrained, governed by the

contact surfaces, while the segment between 20˚ to

120˚ is called ‘active functional arc’ and this

motion is unconstrained [1]. Between these

segments exists an intermediate section, where the

transition, from constrained to unconstrained

motion, takes place. The determination and

presentation of this intermediate segment, which

has not yet been discussed, is on of the aims of this

paper.

An additional aim is to present a method which

allows translating the initial point of any rotation-

flexion function into a zero initial rotational point.

This question is well-founded since some authors

provided rotation functions starting from zero

initial rotation [2, 3], while other authors published

these functions from different, non-zero, initial

points [4]. However, no indication has been given

about how, or with what method, the above

mentioned authors translated these functions into

the initial zero rotational point.

2. Methods

In order to achieve these goals, experimental

investigations was carried out with the help of an

adequately designed and manufactured test rig [5].

These experiments were carried post mortem on 6

cadaver subjects, involving 9 knee joints. The

obtained kinematical data was processed in

accordance of a coordinate system defined by

Grood et al. [6] and the project VAKHUM [7].

The process was followed by making a matrix

connection between the coordinate system used for

the experiments and the anatomical coordinate

system [8]. By this matrix equation, the rotation,

flexion and abduction values can be determined in

the anatomical coordinate system. Based on the

obtained experimental results, it was concluded

that the ideal, rotation-flexion function of the

human knee joint can be adequately approximated

with a trilinear curve (Fig. 1).

-30

-25

-20

-15

-10

0 20 40 60 80 100

Flexion angle [°]

Rota

tion

[°]

Experimental data

Trilinear function

Fig. 1. Experimental data and the trilinear function

The domain of the trilinear function is given

between φ = 0˚ - 90˚. The breakpoint of the first

and second segments is threshold of the

constrained (screw-home) motion (1), while the

breakpoint of the second and third segments is the

unconstrained motion (2). The equations of the

functions in case of any knee joints:

20233

10122

011

)()(

)()(

)(

jjj

jjj

jjj

a

a

a

(1)

The unknown threshold points have been

determined by the use of theory of sample

variance. According to the theory, the fitted

variance of the variables (1, 2), on the complete

domain, has to be minimum.

Therefore the extremity (minimums) of the

sj(1,2) function must be found (Fig.2).

31th

Danubia-Adria Symposium, Kempten University, Germany, 2014

Fig. 2. Minimum of the function

The extreme point was calculated by means of

numerical methods, which provides the threshold

breakpoints of the variables (1, 2). After deriving

the results, the trilinear function has been fitted on

the threshold breakpoints. This is followed by the

simple translation of the experimentally gained

data by j0. It has to be noted, that this simple

translation is exclusively applicable on rotation,

since this is the last, third angle defined in the

anatomical coordinate system. Finally, a so-called

reference function can be fitted on the

experimental data (3):

20233

10122

11

)()(

)()(

)(

CCC

CCC

CC

a

a

a

(3)

3. Results

Finally the threshold breakpoints between the

constrained (1), and the intermediate section (2),

with 95% probability have been determined based

on the theorem of least squares with regard of all

the nine empirical functions:

86,075,172111 s , (4)

84,328,422222 s . (5)

Based on the sufficient number of cadavers and the

natural difference between human knee joints, the

following, rounded, numbers have been appointed

for further use for threshold breakpoints: 1 = 20°

and 2 = 40°. By the use of these threshold

breakpoints, if the earlier determined trilinear

curve-system (3) should be fitted on any arbitrary

experimental data set, then the constants of the

fitted reference functions, regardless of their

anatomical coordinate systems, can be determined

as well.

0

5

10

15

20

0 30 60 90

Flexion angle [°]

Ro

tati

on

[°]

Reference function Cadaver 2

Fig. 2. Reference function

References

[1] Moglo, K.E., Shirazi-Adl, A., Cruciate

coupling and screw-home mechanism in

passive knee joint during extension-flexion. J

Biomech, 38, 2005, pp. 1075-1083.

[2] Wilson, D.R., Feikes, J.D., Zavatsky, A.B.,

O'Connor J.J., The components of passive knee

movement are coupled to flexion angle, J

Biomech, 33, 2000, pp. 465-473.

[3] Akalan, N.E., Ozkan, M., Temelli, Y., Three-

dimensional knee model: Constrained by

isometric ligament bundles and experimentally

obtained tibio-femoral contacts, J. Biomech

41, 2008, pp. 890–896.

[4] Bull, A.M.J., Kessler, O., Alam, M., Amis A.

A., Changes in Knee Kinematics Reflect the

Articular Geometry after Arthroplast, Clin

Orthop Relate R, 466, 2008, pp. 2491–2499.

[5] Katona, G., Csizmadia, B.M., Andrónyi, K.

Determination of reference function to knee

prosthesis rating. Biomech Hung, 6, 2013, pp.

293-301.

[6] Grood, E.S. and W.J. Suntay, A joint

coordinate system for the clinical description

of 3-dimensional motions application to the

knee. J Biomech Eng-T ASME, 105, 1983, pp.

136-144.

[7] Hilal, I., Van Sint Jan, S., Leardini, A., Della

Croce, U., D3.2. Technical Report on Data

Collection Procedure ANNEX I. 20. p. In:

Virtual Animation of the Kinematics of the

Human for Industrial, Educational and

Research Purposes. Information Societies

Technology Programme.

[8] Bíró, I., Csizmadia, B. M., Katona, G.,

Determination of instantaneous axis of rotation

of tibia and its role in the kinematical

investigation of human knee joint. Proc. 3rd

Hung Conf Biomech, 2008, pp. 57-62.