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ESTIMATION OF THE MUSCULOTENDON GEOMETRY DURING MOTIONS USING PHYSICS-

BASED APPROACH

YM Tang*, PPY Lui*, PSH Yung*, KM Chan*, KC Hui**

*Department of Orthopaedics and Traumatology, The Chinese University of Hong Kong, Hong Kong SAR

**Department of Automation and Computer-Aided Engineering, The Chinese University of Hong Kong, Hong

Kong SAR

INTRODUCTION

The musculotendon geometry is essential for predicting the muscle’s ability to generate forces and joint

moments in biomechanics and biomedical engineering. Accurate musculotendon geometry is particularly important

in the study of tendon injury and the effect of the joint movement after injury. However, acquiring accurate

musculotendon geometry during human movement is not simple. Clinically, the musculotendon geometry of human

is usually obtained from a set of magnetic resonance (MR) images. The images are collected with the subject in

static position. The process of obtaining musculoskeletal geometry from MR images is labor intensive and time-

consuming. Computer model is useful for studying the dynamic changes of the musculotendon geometry. In this

paper, a physics-based approach is adopted to estimate the musculotendon geometry during human movement. The

method can estimate and visualize the change in musculotendon geometry interactively with a computer.

METHODS

The musculotendon geometry was defined by an axial curve. The mass-spring system was adopted to compute

the updated axial curve during human movement. The musculotendon geometry was usually modeled by a series of

line segments. The geometrical constrains of the path were defined through the “via points”. We proposed to model

the geometrical path of tendon models by representing it using a B-spline axial curve through the “via points”. To

estimate the musculotendon geometry using the mass-spring system (Miller 88),

],1[, Ii

i∈p

is denoted as the ith

mass point (“via point”) with mass

i

m

that define the axial curve c(t), where I is the total number of the mass points.

Each mass point is connected with at least one massless spring in its natural position. The structural and flexion

springs are usually adopted in the mass-spring system. Springs linking the ith and (i+1)th mass points are referred to

as the structural springs. Springs linking the ith and (i+2)th mass points are referred to as the flexion springs. Given

the motion of the model, the updated positions

1

p′

and

I

p′

are known, we update

]1,2[, −∈ Ii

i

p

using the mass-

spring system. The mass-spring system is governed by the fundamental law of dynamics

iii

mpF

=

, where

i

F

is the

total force exerted on

i

p

and

i

p

is the acceleration of the ith mass point.

i

F

is composed of four major forces:

internal spring force,

int

i

F

, external force,

ext

i

F

, damping force,

damp

i

F

and gravitational force,

grav

i

F

such that

grav

i

damp

i

ext

iii FFFFF +++= int

. Given the total forces exerted on the mass point at time

0

t

, the objective is to

determine the position of the mass point at time

tt ∆+

0

which can be determined by the expression

() ( )

∫∫

=∆+ dtdtt

m

tt

i

i

i00

1Fp

. Then the estimated axial curve

)(t

new

c

that define the musculotendon geometry is

computed by fitting a curve through the updated mass points

i

p′

.

RESULTS

Experiments were performed to visualize the estimated geometry of the tendons of the extensor hallucis longus,

extensor digitorum longus and extensor pollicis longus. Experiments have demonstrated that the musculotendon

geometry could be estimated in real-time. For a tendon model with 46 systems, the time required for estimating the

musculotendon geometry for each frame of motion was only twenty milliseconds.

DISCUSSION

This paper adopted the physics-based technique to estimate the musculotendon geometry during motions in

computer. The technique could compute deformation as well as the force exhibited on the tendon models. It was

particularly useful for studying the effect of different mechanical load characteristics such as direction, distribution,

duration and loading rate on tendon deformation, which are important variables in the study of tendon injury by

external loads and preventive strategies interactively with a computer.

REFERENCES

Miller, G. (1988). The Motion Dynamics of Snakes and Worms. Computer Graphics, 22: 169-178.