Citation
Predicted Changes in the Knee Adduction Torque due to Gait Modifications

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Title:
Predicted Changes in the Knee Adduction Torque due to Gait Modifications
Creator:
ROONEY, KELLY L. ( Author, Primary )
Copyright Date:
2008

Subjects

Subjects / Keywords:
Axes of rotation ( jstor )
Gait ( jstor )
Kidnapping ( jstor )
Kinematics ( jstor )
Kinetics ( jstor )
Knee joint ( jstor )
Knees ( jstor )
Pelvis ( jstor )
Rotational dynamics ( jstor )
Torque ( jstor )

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University of Florida
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University of Florida
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Copyright Kelly L. Rooney. Permission granted to University of Florida to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
5/1/2005
Resource Identifier:
71279535 ( OCLC )

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PREDICTED CHANGES IN THE KNEE ADDUCTION
TORQUE DUE TO GAIT MODIFICATIONS
















By

KELLY L. ROONEY


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2005

































Copyright 2005

by

Kelly L. Rooney















ACKNOWLEDGMENTS

I would like to thank my committee chair, Dr. B.J. Fregly, for his guidance and

support. I would also like to thank my other committee members, Dr. Raphael Haftka and

Dr. Malisa Sarntinoranont, for their suggestions and time.

I greatly appreciate all of the support and friendship provided by the other students

in the Computational Biomechanics Lab. Specifically, I appreciate Jeff for contributions

to my research, Zhao Dong and Yi-chung for Chinese lessons, and Langston and Carlos

for moral support and encouragement.

I would also like to thank my friends from the Tri-Gators and Roller Hockey Team

for providing me with an athletic escape from the academic world.

Finally, I would like to thank Bemd for his personal support throughout the years.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ......... .................................................................................... iii

LIST OF TABLES ........ ...................................... ................. ........ vi

L IST O F F IG U R E S .... ...... ................................................ .. .. ..... .............. vii

A B ST R A C T .......... ..... ...................................................................................... x

CHAPTER

1 B A C K G R O U N D ................................................................ ....... ................ .

O osteoarthritis ......................................... 1
K n ee A ddu action T orqu e ............................................................... .......................... 1
H igh Tibial O steotom y ................................................. ... ......... .... .............. .. 1
M option Capture ................................. ............................... ...............
D ynam ic Sim ulations .......................................................................................... 2
O ptim ization .................................................................2

2 IN TR O D U C T IO N ................................................................... .............................4

3 M E TH O D S .................................................................7

E xperim mental D ata C ollection........... .... ....................................... ...... ..............
Dynamic Gait Model Development.......................................................... ............... 7
Dynamic Model Parameter Tuning ...................... ...... ...............8
Movement Prediction via Inverse Dynamic Optimization .......................................9

4 R E SU L T S ................................. .................. .. ........................ ........................14

Optimizations without Experimental Leg Torque Tracking.................................. 14
Optimizations with Experimental Leg Torque Tracking .........................................15

5 D ISCU SSIO N ...................................................................... .......... 32

O b se rv a tio n s ...............................................................................................................3 2
L im itatio n s ......................................................................................3 3



iv










6 CONCLUSIONS AND FUTURE WORK....... ........ ....................................35

APPENDIX

A DESRIPTION OF OPTIMIZATION FILES.................. ....................36

B DESCRIPTION OF MATLAB FILES...................................... ....................... 38

L IST O F R E FE R E N C E S ............................................................................. .............. 40

B IO G R A PH IC A L SK E TCH ...................................................................... ..................42














































v
















LIST OF TABLES

Table pge

1 RMS errors between the Fourier fit curves and experimental data...........................9

2 Various foot path cases tested for effect on knee adduction..................................12















LIST OF FIGURES


Figure page

1 The 3D, 14 segment, 27 DOF full-body kinematic model linkage joined by a set
of gim bal, universal, and pin joints. ....................................................................... 13

2 Comparison of left knee abduction/adduction torques achieved without
matching experimental leg torques, where positive torque represents abduction
and negative torque represents adduction. .................................... .................16

3 Comparison of left hip flexion/extension motion achieved without matching
experimental leg torques, where positive angle represents flexion and negative
angle represents extension ............ .......................................... 16

4 Comparison of left knee flexion/extension motion achieved without matching
experimental leg torques, where positive angle represents flexion and negative
angle represents extension ......................................................................... .........17

5 Comparison of left ankle dorsiflexion/planarflexion motion achieved without
matching experimental leg torques, where positive angle represents dorsiflexion
and negative angle represents planarflexion. ................................... ..................... 17

6 Comparison of pelvis longitudinal axis rotation motion achieved without
matching experimental leg torques, where positive angle represents rotation to
left and negative angle represents rotation to right. ............................. ............... 18

7 Comparison of pelvis anterior/posterior axis rotation motion achieved without
matching experimental leg torques, where positive angle represents tilt to left
and negative angle represents tilt to right ............................................. ............... 18

8 Comparison of pelvis horizontal axis rotation motion achieved without
matching experimental leg torques, where positive angle represents forward tilt
land negative angle represents backward tilt .............. .............................................19

9 Comparison of left hip internal/external rotation motion achieved without
|matching experimental leg torques, where positive angle represents internal
and negative angle represents external .................................................................. 19

10 Comparison of left hip abduction/adduction motion achieved without matching
experimental leg torques, where negative angle represents abduction and angle
torque represents adduction ........... ..... ......... ................... 20









11 Comparison of left subtalar inversion/eversion motion achieved without
matching experimental leg torques, where positive angle represents inversion
and negative angle represents version. ...................................... ............... 20

12 Comparison of left knee flexion/extension torques achieved without matching
experimental leg torques, where positive torque represents flexion and negative
torque represents extension. ............................................ ............................. 21

13 Comparison of left subtalar inversion/eversion torques achieved without
matching experimental leg torques, where positive torque represents inversion
and negative torque represents version ................................ ............ ............. 21

14 Comparison of left hip internal/external rotation torques achieved without
matching experimental leg torques, where positive torque represents internal
and negative torque represents external. ...................................... ............... 22

15 Comparison of left hip abduction/adduction torques achieved without
matching experimental leg torques, where negative torque represents abduction
and positive torque represents adduction. ..................................... ............... 22

16 Comparison of left hip flexion/extension torques achieved without matching
experimental leg torques, where positive torque represents flexion and negative
torque represents extension. ............................................ ............................. 23

17 Comparison of left ankle dorsiflexion/planarflexion torques achieved without
matching experimental leg torques, where positive torque represents
dorsiflexion and negative torque represents planarflexion...........................23

18 Comparison of left hip flexion/extension motion achieved with matching
experimental leg torques, where positive angle represents flexion and negative
angle represents extension ......................................................................... .........24

19 Comparison of left knee flexion/extension motion achieved with matching
experimental leg torques, where positive angle represents flexion and negative
angle represents extension ......................................................................... .........24

20 Comparison of left ankle dorsiflexion/planarflexion motion achieved with
matching experimental leg torques, where positive angle represents dorsiflexion
and negative angle represents planarflexion. ................................ ..................25

21 Comparison of pelvis horizontal axis rotation motion achieved with matching
experimental leg torques, where positive angle represents forward tilt and
negative angle represents back ard tilt ........... .............................. ...... ............. 25

22 Comparison of pelvis anterior/posterior axis rotation motion achieved with
matching experimental leg torques, where positive angle represents tilt to left
and negative angle represents tilt to right ............................................................ 26









23 Comparison of left hip internal/external rotation motion achieved with
matching experimental leg torques, where positive angle represents internal
and negative angle represents external ..........................................................26

24 Comparison of pelvis longitudinal axis rotation motion achieved with matching
experimental leg torques, where positive angle represents rotation to left and
negative angle represents rotation to right. ................................... ............... 27

25 Comparison of left subtalar inversion/eversion motion achieved with matching
experimental leg torques, where positive angle represents inversion and negative
angle represents version. ............................................................. .....................27

26 Comparison of left hip abduction/adduction motion achieved with matching
experimental leg torques, where negative angle represents abduction and angle
torque represents adduction ........... ..... ......... ................... 28

27 Comparison of left knee abduction/adduction torques achieved with matching
experimental leg torques, where positive torque represents abduction and
negative torque represents adduction. ........................................... ............... 28

28 Comparison of left knee flexion/extension torques achieved with matching
experimental leg torques, where positive torque represents flexion and negative
torque represents extension. ............................................ ............................. 29

29 Comparison of left subtalar inversion/eversion torques achieved with matching
experimental leg torques, where positive torque represents inversion and
negative torque represents version. ............................................. ............... 29

30 Comparison of left hip abduction/adduction torques achieved with matching
experimental leg torques, where negative torque represents abduction and
positive torque represents adduction .......................................................................30

31 Comparison of left hip internal/external rotation torques achieved with matching
experimental leg torques, where positive torque represents internal and negative
torque represents external............................................... .............................. 30

32 Comparison of left hip flexion/extension torques achieved with matching
experimental leg torques, where positive torque represents flexion and negative
torque represents extension. ............................................ ............................. 31

33 Comparison of left ankle dorsiflexion/planarflexion torques achieved with
matching experimental leg torques, where positive torque represents
dorsiflexion and negative torque represents planarflexion...........................31















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

PREDICTED CHANGES IN THE KNEE ADDUCTION
TORQUE DUE TO GAIT MODIFICATIONS

Kelly L. Rooney

May 2005

Chair: Benjamin J. Fregly
Major Department: Biomedical Engineering

Dynamic optimizations capable of predicting novel gait motions have great

potential for addressing clinically significant problems in orthopedics and rehabilitation.

This study evaluates gait modifications as an alternative to surgery for treating medial

compartment knee osteoarthritis. Researchers developing forward dynamic optimizations

of gait for such applications face significant challenges that may be resolved by

implementing an inverse dynamic approach. This study used Fourier coefficients, which

defined the motion and ground reaction torque curves, as kinematic design variables with

an inverse dynamics optimization to predict novel motions. The cost function, minimized

by a nonlinear least squares optimization function, included the left knee adduction

torque and several reality constraints. Two sets of prediction optimizations were

performed to evaluate the effect of foot placement on the knee adduction torque. The first

set of prediction optimizations, which allowed leg torques to change without limit,

resulted in motions with similar kinematic changes that reduced the knee adduction

torque (72% average decrease) regardless of the foot path. The second set, which tracked









experimental leg torques, also resulted in the knee adduction torque being reduced for all

cases (45% average decrease), but to a lesser degree. The optimizations suggest that

novel movement modifications can have a significant effect (more than a high tibial

osteotomy surgery) on reducing the peak knee adduction torque during gait.














CHAPTER 1
BACKGROUND

Osteoarthritis

The most common type of arthritis, known as osteoarthritis, affects 15 million

people in the United States today according to the 2004 National Arthritis Meeting

Report. This degenerative disease occurs when the cartilage, or cushioning, between

bones breaks down due to uneven loading and excessive wear. Over time, cartilage in a

joint may be completely worn away leaving painful bone on bone contact. Osteoarthritis

is most common in the large weight bearing joints such as the hips and knees.

Knee Adduction Torque

Most patients who suffer from knee osteoarthritis have loss of cartilage in the

medial compartment of the knee joint. This is due to the knee adduction torque, which

results from the way the human body is constructed. When a person is standing on one

leg, their center of mass falls medially, or inside, of the standing leg. The weight of the

body acts to adduct the knee. Adduction causes the medial compartment of the knee to be

forced together and the lateral knee compartment to be pulled apart. As a person walks,

the knees repeatedly go through cycles of this uneven loading. Over time this will cause

breakdown of the medial compartment cartilage. These effects are multiplied in patients

with a varus (bow-legged) alignment.

High Tibial Osteotomy

In order to stop this breakdown of essential cartilage, a patient may undergo a high

tibial osteotomy surgery. This procedure removes a wedge of bone from the tibia, or shin









bone, in order to correct a varus, or bow-legged, alignment. The forces in the knee are

shifted laterally in order to move the pressure from the damaged cartilage to the healthy

tissue.

Motion Capture

The motion data of a patient is collected in a gait lab using high-speed, high-

resolution cameras. Spheres covered with reflective tape are placed on all segments of the

patient's body. The cameras record the location of these markers over time. The marker

data is used to create a computer model by calculating the location and orientation of the

joints with respect to the markers. The movement of the markers throughout the gait

cycle is used to calculate the motion of the joints.

Dynamic Simulations

The computer model of the patient's gait, or walking, cycle, is used to perform

dynamic simulations. The modeling software creates the equations of motion based on

the model structure and joint motions provided. These equations are used to solve

dynamic simulations. Two types of dynamic simulations are discussed in this paper.

Inverse dynamics, as the name suggests, occurs in the opposite order of real life events.

Given the motion of a model, inverse dynamics is used to calculate the forces and torques

that would produce that motion. Forward dynamics on the other hand occurs in the

natural order. Forces and torques are input to calculate the resulting motions.

Optimization

An optimization is a mathematical method used to find the best solution to a

problem. The important components of an optimization are design variables, a cost

function, and constraints. The design variables are the values that are changed in order to

search for the solution. The optimizer seeks to find the values of the design variables that






3


will minimize or maximize a cost function. Constraints are boundaries that cannot be

crossed while searching for the optimal solution.














CHAPTER 2
INTRODUCTION

Dynamic optimizations capable of predicting novel gait motions have great

potential for addressing clinically significant problems in orthopedics and rehabilitation

(Delp et al., 1990; Delp et al., 1996; Pandy, 2001). In orthopedics, an optimization may

be valuable to predict the outcome of certain procedures given various combinations of

surgical parameters. For example, Cerebral Palsy patients often have muscles lengthened

or redirected to improve gait coordination (Arnold et al., 2001). A predictive model may

demonstrate how such changes affect the entire body rather than just one or two joints

spanned by the altered muscle. As another example, tibial osteotomy patients may have

lower leg alignment corrected to relieve knee pain due to osteoarthritis. Researchers have

investigated the relationship between dynamic gait measurements and clinical outcome,

with the peak knee adduction moment being identified as an important clinical marker

(Andriacchi, 1994; Hurwitz etal., 1998; Prodromos etal., 1985;Sharma etal., 1998;

Wang et al., 1990). A model could help define the optimal amount of correction by

predicting the post surgery knee forces and torques throughout the entire gait cycle. In

rehabilitation, a predictive gait model could permit the development of novel

rehabilitation procedures that may be difficult to identify experimentally.

Researchers developing forward dynamic optimizations of gait for such

applications face two significant challenges. The first problem is instability of the

repeated forward simulations performed during the optimization process. During gait, the

body can be viewed as an inverted pendulum where the mass of the upper body swings









over a foot fixed to the ground. Without constraints or feedback control, the torso will

quickly fall over in forward dynamic simulations driven only by torque actuators (Winter,

1990). Others have used muscles to overcome this instability (Gerristen et al., 1998).

Muscles act as inherent stabilizers due to their force-length and force-velocity properties.

The second obstacle is large computational cost associated with repeated numerical

integration of the equations of motion for full-body, three-dimensional (3D) gait models.

Previous investigations required parallel processing to complete such large-scale

optimizations (Anderson and Pandy, 2001).

Both problems associated with a forward dynamic optimization may be resolved by

implementing an inverse dynamic approach. With forward dynamic optimization, design

variables are placed on the torques and the equations of motion are integrated to predict

motion. However, if the design variables are instead placed on the motion, an inverse

dynamics approach can be used to predict the resulting motion and loads similar to

forward dynamic optimization. Contrary to forward dynamics, the inverse approach does

not have stability problems nor does it require costly numerical integration.

This study evaluates gait modifications as an alternative to surgery for treating

medial compartment knee osteoarthritis. The specific goal was to predict the influence of

foot position (i.e., toe out and wider stance) on the peak knee adduction moment. The

predictions were developed using inverse dynamic optimization of a 27 degree-of-

freedom (DOF), full-body gait model. The optimizations sought to minimize the peak

knee adduction moment and were performed under two conditions. The first allowed the

optimizer to vary the joint torques without limit, while the second sought to change the






6


nominal torques as little as possible. Novel movement modifications may have a

significant affect on reducing the peak knee adduction moment during gait.














CHAPTER 3
METHODS

Experimental Data Collection

Gait data were collected from a single adult male using a HiRes Expert Vision

System (Motion Analysis Corp., Santa Rosa, CA) with institutional review board

approval. Surface marker data of a modified Cleveland Clinic marker set were collected

at 180Hz for static and dynamic trials. The static trials were used to define segment

coordinate systems and the locations of the markers within those coordinate systems.

Dynamic joint trials were used to define the location and orientations of the joints.

Dynamic gait trials provided the marker location data for an entire gait cycle. Two force

plates (Advanced Mechanical Technology, Inc., Watertown, MA) recorded the ground

reaction forces and torques of each foot about the electrical center of the respective force

plate. The raw data were filtered using a fourth-order, zero phase-shift, low pass

Butterworth Filter with a cutoff frequency of 6 Hz.

Dynamic Gait Model Development

Identical 3D, full body dynamic models were developed using Autolev (Online

Dynamics, Inc., Sunnyvale, CA), a symbolic manipulator for engineering and

mathematical analysis, and Software for Interactive Musculoskeletal Modeling (SIMM,

Motion Analysis Corporation, Santa Rosa, CA). The Autolev model was designed for

patient specific motion analysis and provides direct access to the equations of motion.

The SIMM model provided visualization of the motion, and allows for the computation

of muscle forces. Two models were necessary to validate the inverse dynamic approach









did not contain programming flaws. The models consist of 14 segments linked by 27

DOFs including gimbal, universal, and pin joints. Similar to Pandy's (2001) model

structure, 3 translational and 3 rotational DOFs express the movement of the pelvis in a

Newtonian reference frame. The remaining lower body DOFs include 3 DOF hip joints, 1

DOF knee joints, and 2 DOF ankle joints. The upper body DOFs include a 3 DOF back

joint, 2 DOF shoulder joints, and 1 DOF elbowjoints. (Error! Reference source not

found.).

Inverse dynamic analysis was performed on both full-body models using the state-

space form of the equations of motion. Consequently, 27 control forces and torques were

calculated from the experimentally determined joint kinematics and ground reaction

quantities. All forces and torques calculated by the two models were identical to within

round-off error, providing a check on the dynamical equation formulation. An additional

degree of freedom in the model, prescribed to produce no motion, was used to calculate

the left knee adduction torque. External forces and torques acting on the pelvis were also

calculated, since the model's position and orientation with respect to the ground frame

are defined by a 6 DOF joint between the ground and pelvis. In reality there are no

external forces or torques acting on the pelvis segment. Any non-zero force and/or torque

found at this joint represents error in the model and/or data.

Dynamic Model Parameter Tuning

A nonlinear least squares optimization was performed using Matlab (The

Mathworks, Natick, MA) to find model parameters, joint kinematics, and ground

reactions to create a nominal data set consistent with the dynamical equations and the

experimental gait data. The goal of this optimization was to alter the experimental data as

little as possible while adjusting selected model parameters, smoothing the inverse









dynamic torques, and driving the external pelvis forces and torques close to zero. The

optimization design variables were selected joint parameters (positions and orientations

in the body segments), body segment parameters (masses, mass centers, and moments of

inertia), and parameters defining the joint trajectories. A penalty was placed on changes

to the body segment parameters in order to minimize the differences between the

optimized data and the experimental data.

Movement Prediction via Inverse Dynamic Optimization

Motion and ground reaction torque curves were parameterized by a combination of

polynomial and Fourier terms. The coefficients served as design variables for an inverse

dynamics optimization used to predict novel motions. To accurately match the

experimental data (Table 1), 8 harmonics and a cubic polynomial were needed for each

DOF and ground reaction. The motion curves were differentiated to calculate velocities

and accelerations. The right and left ground reaction forces and torques measured in the

ground frame were applied to the respective feet. The resulting kinematics were used to

calculate the corresponding joint forces and torques.

Table 1: RMS errors between the Fourier fit curves and experimental data.
Ground Reaction Forces (N) Ground Reaction Torques (Nm) Translations (cm) Rotations (deg)

4.13 0.750 0.0257 0.173

The inverse dynamic optimization used the Matlab nonlinear least squares

algorithm "lsqnonlin" and minimized the left knee adduction torque subject to several

reality constraints implemented via a penalty method (Equation 1):









100 3 2 2
10 T2I+ f(r)+I(Ar )+ (Ar J + (



J=1 s -1 J=1 J=1







refers to time frame (1 through 100)

j refers to translational or rotational joint axis number (maximum value depends on

number of prescribed joint axes for the specified anatomic joint)

s refers to side (1 for left, 2 for right)

WKinemahc = 2, WKinech = 2, and Wcop = 20 are weight factors determined by trial and

error

TAdd is left knee adduction torque

Aqrunk is change in trunk x, y or z rotation ( = 1 to 3) away from its nominal value

measured with respect to the lab frame

Aqpels is change in pelvis x or z translation ( = 1, 2) away from its nominal value

measured with respect to the lab frame

Aq0oo is change in foot x, y or z translation or rotation (/= 1 to 6) away from its

nominal value measured with respect to the lab frame

ATpelv, is change in external pelvis x, y or z force or torque ( = 1 to 6) away from its

nominal value (close to zero) expressed in the lab frame

AT,, is change in hip flexion/extension, abduction/adduction, or inertial/external

rotation torque ( = 1 to 3) away from its nominal value









ATKnee is change in knee flexion/extension torque away from its nominal value

ATAnke is change in ankle flexion/extension or inversion/eversion torque ( = 1, 2)

away from its nominal value

ecp is error in the center of pressure x or z location ( = 1, 2) beyond the outer edge

of the foot

The predicted motion was forced to follow a prescribed foot path. This constraint

allowed for the evaluation of various foot placements by altering the foot path to be

matched. The trunk orientations were constrained to match the experimental orientations

in order to avoid a motion where the model leaned over unrealistically. The transverse

plane translations were also constrained to match the experimental translations. This

constraint prevented the model from swinging a hip out laterally in such a way that an

actual person may lose balance. The pelvis residual forces and torques were minimized

because any non-zero residual would be an error. Because the ground reaction torques

were design variables, the centers of pressure of the resultant right and left ground

reaction forces were constrained to pass through the respective feet.

Two sets of prediction optimizations were performed to evaluate the effect of foot

placement on the knee adduction torque. The first set allowed the leg torques to change

without limit (i.e., AT7, AT7ne, and ATAnkle were removed from Eq. (1)), while the

second set minimized the difference between the experimental and optimized leg torques.

Five cases were run within each set to evaluate the combinations of toeing out or

changing stance width. The first case sought to match the experimental foot path. The

remaining cases included all combinations of toeing out +150 and changing the stance







12


width by +5 cm (Table 2). For each combination of foot path within each set of

prediction optimization, the kinematic and kinetic changes were compared.

Table 2. Various foot path cases tested for effect on knee adduction.
Foot Path Changes
Case Toe Out (degrees) Stance Width (cm)
1 0 0
2 15 5
3 15 -5
4 -15 5
5 -15 -5
















-" 26
q25


q27








q14


I




q2
I





q3
L-- ---------.-


% Y
(superior)

q1 '

Z
(lateral)
Lab


Figure 1. The 3D, 14 segment, 27 DOF full-body kinematic model linkage joined by a set
of gimbal, universal, and pin joints.


t'


s,


Joint Types


Pin


Universal





Gimbal


N
'75q1


q7










q1













q12


2 '


q17


q18
9,


(anterior)


2 23
q 22














CHAPTER 4
RESULTS

Optimizations without Experimental Leg Torque Tracking

The first set of prediction optimizations allowing leg torques to change without

limit resulted in motions with similar kinematic changes that reduced the knee adduction

torque (72% average decrease) regardless of the foot path (Figure 2). The kinematic

changes included greater hip flexion (Figure 3), knee flexion (Figure 4), and ankle

dorsiflexion (Figure 5) angles throughout the gait cycle. The pelvis noticeably rotated

about the longitudinal axis (Figure 6) and the anterior-posterior axis (Figure 7) to position

the left hip more anterior and inferior during left foot stance. The pelvis rotation about the

horizontal axis remained consistent throughout all cases (Figure 8). The hips were more

externally rotated and abducted for the toeing out cases and internally rotated and

adducted for the toeing in cases (Figure 9 and Figure 10). The subtalar joint angle was

generally more inverted in each case compared to the experimental data (Figure 11).

The inverse dynamic analyses resulted in similar kinetic changes that correspond to

the kinematic changes. The resulting kinetic changes included larger knee extensor

(Figure 12) and subtalar inversion (Figure 13) torques. The hip torques showed greater

internal rotation (Figure 14) and adduction (Figure 15) torques compared to the

experimental data. The hip flexion torque increased with toeing in and decreased with

toeing out for the wider stance cases only (Figure 16). The ankle flexion torque changes

did not show significant correlation to individual cases (Figure 17).









Optimizations with Experimental Leg Torque Tracking

Similar changes, but to a lesser degree, resulted when the experimental torques

were tracked. The model again flexed the hip (Figure 18), knee (Figure 19), and ankle

(Figure 20) more than the experimental motion. The pelvis horizontal axis and

anterior/posterior axis rotations (Figure 21 and Figure 22) along with the hip

internal/external rotations (Figure 23) were similar to the prediction optimization without

torque tracking. However, the pelvis longitudinal axis rotations significantly increased to

aid the hip internal/external rotations (Figure 24). The subtalar motion was inverted for

toeing in and everted for toeing out (Figure 25). The hip abduction/adduction motion

showed a similar trend by reduced magnitude compared to the previous set (Figure 26).

Again the reduction in the knee adduction torque (Figure 27) was not greatly

affected by the foot path, but was reduced for all cases (45% average decrease).

However, the reduction was not as dramatic due to the limits placed on the leg torque

changes. The knee flexion (Figure 28), subtalar inversion (Figure 29), and hip adduction

(Figure 30) torques all increased as in the previous set. The only difference in the kinetic

changes was that where the hip had a greater internal rotation torque in the previous set

(Figure 14), the torque tracking set produced motions with greater hip external rotation

torque (Figure 31). The hip flexion/extension and ankle torques were virtually identically

in all cases including the experimental data (Figure 32 and Figure 33).






























Percent of Gait Cycle (%)
Figure 2. Comparison of left knee abduction/adduction torques achieved without
matching experimental leg torques, where positive torque represents
abduction and negative torque represents adduction.

On-E
-10











wU
LI
-j



-T15S 5

20 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 3. Comparison of left hip flexion/extension motion achieved without matching
experimental leg torques, where positive angle represents flexion and negative
angle represents extension.


































Percent of Gait Cycle (%)
Figure 4. Comparison of left knee flexion/extension motion achieved without matching
experimental leg torques, where positive angle represents flexion and negative
angle represents extension.

90 ,I



.TS



0 40 50 60 70 80 90 100






30 -





0 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 5. Comparison of left ankle dorsiflexion/planarflexion motion achieved without
matching experimental leg torques, where positive angle represents
dorsiflexion and negative angle represents planarflexion.























61



-10.1 TExp

-186 "T ,
TI. 45
-188- T -T15S -
-8-T_15S5
1900 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 6. Comparison of pelvis longitudinal axis rotation motion achieved without
matching experimental leg torques, where positive angle represents rotation to
left and negative angle represents rotation to right.

10


VT 155

T _15 95
TS












IL


-1 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 7. Comparison of pelvis anterior/posterior axis rotation motion achieved without
matching experimental leg torques, where positive angle represents tilt to left
and negative angle represents tilt to right.
































Percent of Gait Cycle (%)
Figure 8. Comparison of pelvis horizontal axis rotation motion achieved without
matching experimental leg torques, where positive angle represents forward
tilt and negative angle represents backward tilt.









0













0 0 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 9. Comparison of left hip internal/external rotation motion achieved without
matching experimental leg torques, where positive angle represents internal
and negative angle represents external.



































Figure 10. Comparison of left hip abduction/adduction motion achieved without
matching experimental leg torques, where negative angle represents abduction
and angle torque represents adduction.

T15S 30 I
Exp
ELu
a- ,-




10 T-1T 55
5 -:: ]'T15S5





























0- 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 11. Comparison of left subtalar inversion/eversion motion achieved without
matching experimental leg torques, where positive angle represents inversion
and negative angle represents version.
30)








'E











-1 10 20 30 40 0 60 70 80 90 101






























-Exp
SLSo

U-

C T-,__S


T S
+T-15S5

-10 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 12. Comparison of left knee flexion/extension torques achieved without matching
experimental leg torques, where positive torque represents flexion and
negative torque represents extension.




i~l4- -
I, ,







: T S







Er-









0 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 13. Comparison of left subtalar inversion/eversion torques achieved without
matching experimental leg torques, where positive torque represents inversion
and negative torque represents version.












1,5I I Ii


--Exp
SVT15S5



T 15S5


E TS

.2
I

E
L I









Percent of Gait Cycle (%)
Figure 14. Comparison of left hip internal/external rotation torques achieved without
matching experimental leg torques, where positive torque represents internal
and negative torque represents external.










T -S






-4-

215S





ST-15'-5
10 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 15. Comparison of left hip abduction/adduction torques achieved without
matching experimental leg torques, where negative torque represents
abduction and positive torque represents adduction.

















4-

2MI




a
0



I-


dV
-Exp
S
X

.LL --

+T 15S5
C T



0 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 16. Comparison of left hip flexion/extension torques achieved without matching
experimental leg torques, where positive torque represents flexion and
negative torque represents extension.


* 4

r-



13

A,


C-

E



m .-F
a-

I _

aIin


'~~AmC net _.A#. ,r


-Exp



T,,S5

e T-15S5
.3-


0 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Comparison of left ankle dorsiflexion/planarflexion torques achieved without
matching experimental leg torques, where positive torque represents
dorsiflexion and negative torque represents planarflexion.


Figure 17.

















P
g



S 10 20 30 40 50 60 70 80 90 100










angle represents extension.
aoi i--,-I--.
2 T1.S




I0- T :S
.U









-0 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 18. Comparison of left hip flexion/extension motion achieved with matching
experimental leg torques, where positive angle represents flexion and negative
angle represents extension.




80









.2
-n-








-10-

S 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 19. Comparison of left knee flexion/extension motion achieved with matching
experimental leg torques, where positive angle represents flexion and negative
angle represents extension.






















4T 51-J



W
')t, -Exp

301




S 10 20 30 40 5 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 20. Comparison of left ankle dorsiflexion/planarflexion motion achieved with
matching experimental leg torques, where positive angle represents
dorsiflexion and negative angle represents planarflexion.

5 5





















^"0 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 21. Comparison of pelvis h horizontal axis rotation motion achieved with matching








experimental leg torques, where positive angle represents forward tilt and
negative angle represents backward tilt.
T15S 5


0 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 21. Comparison of pelvis horizontal axis rotation motion achieved with matching
experimental leg torques, where positive angle represents forward tilt and
negative angle represents backward tilt.
















I6

S4 10 20 30 60 70 80 90 100




.2









C I I- I -I



























-1 T-
0 10 20 30 40 50 60 70 80 90 100

Figure 23. Comparison of left hip interiornal/exposterior axis rotation motion achieved with
matching experimental leg torques, where positive angle represents tilt to leftrnal
and negative angle represents extilt to right.
0


0












0 in 20 30 40 50 60 70 0 9 100
Percent of Gait Cycle (%)
Figure 23. Comparison of left hip interiornal/exposterior axis rotation motion achieved with
matching experimental leg torques, where positive angle represents tilt to leftrnal
and negative angle represents extilt to right.
cm Inr

.22 0 40 fD 6 0 0 9 D
16cn o atCyl #



Fiue23 opaio o et i ntra/xtra rttonmtoCLhevdwt
matcingexprimnta le stores whre osiiveangl reresntsintrnT




























o -190- -Exp
T o

-3 T9.0[5T -

2I I I

-2000 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 24. Comparison of pelvis longitudinal axis rotation motion achieved with
matching experimental leg torques, where positive angle represents rotation to
left and negative angle represents rotation to right.


-Exp

20 VT15S5
iF r-





.0














-100 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 25. Comparison of left subtalar inversion/eversion motion achieved with matching
experimental leg torques, where positive angle represents inversion and
negative angle represents version.























r-4





T




"1 -T 15 S
10 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 26. Comparison of left hip abduction/adduction motion achieved with matching
experimental leg torques, where negative angle represents abduction and angle
torque represents adduction.








1 r 1 I I I r




-






C- -T S




o-T 5 -5

0 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 27. Comparison of left knee abduction/adduction torques achieved with matching
experimental leg torques, where positive torque represents abduction and
negative torque represents adduction.
I-- 1
(-I















negative torque represents adduction.




























-Exp
0-1 5- eTO O
I-










-2 0 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 28. Comparison of left knee flexion/extension torques achieved with matching
experimental leg torques, where positive torque represents flexion and
negative torque represents extension.
W -Exp



.C +T-15S5






S
-


















0- 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 29. Comparison of left subtalar inversion/eversion torques achieved with matching
experimental leg torques, where positive torque represents inversion and
negative torque represents version.
10 20 30 4 7 0 9
Percent of Gait Cycle (%)
Figure 29. Comparison of left subtalar inversion/eversion torques achieved with matching
experimental leg torques, where positive torque represents inversion and
negative torque represents version.
























-2-



'-4






0 10 20 ]Q 40 0 X 7.0 K) 10
Percent of Gait Cycle ('Y)

Figure 30. Comparison of left hip abduction/adduction torques achieved with matching
experimental leg torques, where negative torque represents abduction and
positive torque represents adduction.




1 .
I














ne.




S -1 T5
-V

















S 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 31. Comparison of left hip internal/external rotation torques achieved with
matching experimental leg torques, where positive torque represents internal
and negative torque represents external.













2-
r2










2
-Exp

LV T d9T

+T 15S5
I I I I I I

0 10 20 30 40 50 60 70 80 90 100
Percent of Gait Cycle (%)
Figure 32. Comparison of left hip flexion/extension torques achieved with matching
experimental leg torques, where positive torque represents flexion and
negative torque represents extension.







C-Z2







.2
)-4

-Exp






10 20 30 40 50 60 70 90 100
9a T1 45




Percent of Gait Cycle (%)
Figure 33. Comparison of left ankle dorsiflexion/planarflexion torques achieved with
matching experimental leg torques, where positive torque represents
dorsiflexion and negative torque represents planarflexion.














CHAPTER 5
DISCUSSION

Observations

This study used a predictive gait model to evaluate the effects of gait modifications

on the knee adduction moment. An inverse dynamics optimization approach was used

rather than the traditional forward dynamic approach, because of two main advantages.

There are no stability problems with an inverse dynamics optimization, and inverse

dynamic simulations do not require integration. Two sets of prediction optimizations

were performed to determine the effect of foot placement on the knee adduction torque.

The optimizations were successful in predicting novel motions that reduced the knee

adduction torque, although foot placement was not a key component.

Common kinematic changes regardless of foot placement were found in all cases of

the first set of optimizations that allowed unlimited torque changes. The combinations of

these changes drove the left knee inward such that the ground reaction force passed

through the knee more laterally resulting in a lower left knee adduction torque. The

resulting kinetic changes including larger knee extensor, subtalar inversion, hip

adduction, and hip internal rotation torques may not be physically possible within these

joints.

The second set of prediction optimizations minimized the changes in the leg

torques to avoid physically impossible solutions. Again the results for all combinations of

toe out and stance width changes were similar. As in the first set of optimizations, this set

also drove the left knee inward in order to reduce the adduction moment. The difference









being that many of the kinematic and kinetic changes were of a lesser degree due to the

torque constraint with the exception of the pelvis longitudinal axis rotations and hip

internal/external rotation torques. The combinations of kinematic changes in the second

set of predication optimizations were different to allow for better tracking of the

experimental torques.

Although the flexed knee motion predicted by the model was effective in reducing

the adduction moment, it may be problematic for osteoarthritis patients. This motion is

less energetically efficient that regular gait due to the additional knee extensor strength

required to maintain the slight crouch throughout gait. Osteoarthritis patients tend to have

weak knee flexors and may not be able to produce the energy required for this motion.

The resulting knee adduction torque reductions suggest that gait modifications are

capable of reducing the peak knee adduction torque more than a high tibial osteotomy

surgery. The average post surgery decrease for a group of 25 high tibial osteotomy

patients was 34% (Prodromos et al., 1985). The optimizer reduced the peak knee

adduction torque an average of 72% without experimental torque tracking, and 45% with

torque tracking. These results are limited by the fact that this study analyzed only one

patient whose experimental data showed a peak knee adduction torque close classified as

normal (3% body weight height) by Prodromos et al. (1985). However, the general

movement modifications predicted by the optimizations suggest mechanics principles

that should be applicable to any subject.

Limitations

Without including reality constraints in the cost function, the optimizer found three

ideal near zero knee adduction torque results with undesired kinematics or kinetics. First,

if the ground reaction forces and torques are allowed to change, the medial-lateral force









will shift more laterally. This causes the total ground reaction force to pass through the

knee more laterally thus reducing the knee adduction torque without changing the

motion. However, this change may not be physically realistic, because the ratio of

medial-lateral to vertical forces tripled in value in order to create these ground reaction

force changes. Second, if the pelvis translations are free to change, lateral pelvis swinging

will result. The optimizer predicts a motion where it shifts the body's center of mass

laterally by swinging the pelvis back and forth similar to a "hula" dance. As a result, the

center of mass was shifted directly above the knee so that the adduction moment was near

to zero. Third, if the foot path was allowed to change, the model would cross the legs

during gait so as to pass one tibia through the other. As a result, the knee moved under

the body's center of mass, rather than the center of mass over the knee. The runway

"model walk" has the same affect on the adduction torque as the "hula walk." The "hula

walk" is disadvantageous, because it is energetically inefficient. While the "model walk"

does not compromise efficiency as much, there is a loss in stability by bringing the feet

closer together and is not physically realizable.














CHAPTER 6
CONCLUSIONS AND FUTURE WORK

The optimizations suggest that novel movement modifications can have a

significant effect on reducing the peak knee adduction torque during gait. Gait

modification has a greater influence on internal knee loads than previously shown. It is

interesting to note the number of different realistic motions that are able to reduce the

knee adduction torque. This approach has many possibilities of clinical applications,

especially for medial compartment knee osteoarthritis patients. The optimizations

highlight the importance of knee extensor strength for avoiding osteoarthritis problems.

As was explored in this study, these patients may be able to relieve their osteoarthritis

symptoms simply by modifying their gait. Experimental evaluation of the hypothesis

presented in this paper would be valuable in determining the feasibility of implementing

the predicted gait modifications.















APPENDIX A
DESCRIPTION OF OPTIMIZATION FILES

MATLAB FILES (See descriptions in Appendix B)

Call_optimizer_stance_toe.m

ChangeFootPathMain.m

ChangeFootPath.m

Opt_min_add_grf.m

Cost_func_min_add_grf.m

PolyFourierFitNew.m

CenterOfPressure fourier.m

Complete.m

TEXT FILES

Qcoefs_Final.txt: Fourier coefficients describing the experimental 27 DOFs.

Grf_coefs.txt: Fourier coefficients describing the experimental right and left
ground reaction forces and torques.

Kinetics_final_no_header.ktx: A SIMM input file, which contains the
experimental positions, velocities, accelerations, and ground reactions.

Invdyn_foot_exp_final.txt: The foot, trunk and pelvis path calculated by the
executable with the experimental data.

Invdyn_trq_exp_final.txt: The inverse dynamic torques calculated by the
executable with the experimental data.

Params.txt: A text file read by the executable where the user must specify the
name if the input kinetics file and desired step size for output data.






37


OTHER

Simulation.exe: The executable that performs inverse dynamics given an input
kinetics file.

Msvcr71d.dll: A library file needed to run the executable















APPENDIX B
DESCRIPTION OF MATLAB FILES
















Matlab Files Called by Inputs Outputs Description
Call_optimizer User None Coefficients_guess Calls the optimization function. Change the
stancetoe.m.m .txt foot placement values here to predict a
Kinetics_guess.ktx different motion.

ChangeFootPathMai Calloptimizer Foot placement variables, Invdyn footchan Calculates the changes in the x,y,z foot
stancetoe.m invdynexpfinal.txt ged.txt translations and rotations with respect to
kinetics final no header.ktx the ground frame.

ChangeFootPath.m ChangeFootPat Old translations and rotations and changed New foot Calculates the new x,y,z foot translations
hMain.m to foot path translations and rotations, translations and and rotations with respect to the ground
rotations. frame.
Opt min add_grf.m Calloptimizer invdynfootexp final.txt, None Loads experimental values.
stancetoe.m invdyn foot changed.txt, Creates initial conditions matrix.
invdyntrq_expfinal.txt, Calls the Matlab optimizer, "lsqnonlin."
kinetics final no header.ktx,
QCoefsFinal.txt
grf coefs.txt
Costfuncmin Opt min add Current guess of design variables, Cost function error Reads in the current guess of the design
addgrf.m grf.m invdyntrq.txt matrix, to be variables. Writes a kinetics file based on
invdynfoot.txt squared and that guess. Calls simulation.exe. Reads in
cop_error.txt summed by the inverse dynamic results. Calculates cost
optimizer. function.
PolyFourierFitNew. Cost funcmin Fourier coefficients, omega, time, degree Values of the Creates motion and ground reaction curves
addgrf.m of polynomial, derivative flag curves at the based on the Fourier coefficients.
specified time
points.
CenterOfPressure_ Costfuncmin Ground reaction forces and torques in the Center of pressure Calculates the left and right centers of
fourier.m _addgrf.m ground reference frame, locations in the pressure in the ground reference frame.
ground reference
frame.

Complete.m Optmin_ None None Alerts user when an optimization has
addgrf.m terminated.















LIST OF REFERENCES


Anderson, F.C., Pandy, M.G. (2001). Dynamic Optimization of Human Walking. Journal
of Biomechanical Engineering 123, 381-390.

Andriacchi, T.P. (1994). Dynamics of Knee Malalignment. Orthopedic Clinics of North
America 25, 395-403.

Arnold, A.S., Blemker, S.S., Delp, S.L. (2001). Evaluation of a Deformable
Musculoskeletal Model for Estimating Muscle-Tendon Lengths During Crouch
Gait. Annals of Biomedical Engineering 29, 263-274.

Delp, S.L., Loan, J.P., Hoy, M.G., Zajac, F.E., Topp E.L., Rosen, J.M. (1990). An
Interactive Graphics-based Model of the Lower Extremity to Study Orthopaedic
Surgical Procedures. IEEE Transactions on Biomedical Engineering 37, 757-767.

Delp, S.L., Arnold, A.S., Speers, R.A., Moore, C.A. (1996). Hamstrings and Psoas
Lengths During Normal and Crouch Gait: Implications for Muscle-Tendon
Surgery. Journal of Orthopaedic Research 14, 144-151.

Gerristen, K.G.M., van den Bogert, A.J., Hulliger, M., Zemicke, R.F. (1998). Intrinsic
Muscle Properties Facilitate Locomotor Control A Computer Simulation Study.
Motor Control 2, 206-220.

Hurwitz, D.E., Ryals, A.R., Block, J.A., Sharma, L., Shcnitzer, T.J., Andriacchi, T.P.
(2000). Knee Pain and Joint Loading in Subjects with Osteoarthritis of the Knee.
Journal of Orthopaedic Research 18, 572-579.

Pandy, M.G. (2001). Computer Modeling and Simulation of Human Movement. Annual
Reviews in Biomedical Engineering 3, 245-273.

Prodromos, C.C., Andriacchi, T.P., Galante, J.O. (1985). A Relationship between Gait
and Clinical Changes following High Tibial Osteotomy. The Journal of Bone and
Joint Surgery 67A, 1188-1194.

Sharma, L., Hurwitz, D.E., Thonar, E.J-M.A., Sum, J.A., Lenz, M.E., Dunlop, D.D.,
Schnitzer, T.J., Kirwan-Mellis, G., Andriacchi, T.P. (1998). Knee Adduction
Moment, Serum Hyaluronan Level, and Disease Severity in Medial Tibiofemoral
Osteoarthritis. Arthitis & Rheumatism 41, 1233-1240.






41


Wang, J.W., Kuo, K.N., Andriacchi, T.P., Galante, J.O. (1990). The Influence of Walking
Mechanics and Time on the Results of Proximal Tibial Osteotomy. Journal of Bone
and Joint Surgery 72A, 905-913.

Winter, D.A. (1990). Biomechanics and Motor Control of Human Movement, 2nd
Edition. Wiley, New York.















BIOGRAPHICAL SKETCH

Kelly Rooney was born in Michigan in 1979. She moved to Palm Harbor, Florida,

with her family in 1986 and remained there through the completion of her high school

education. She graduated valedictorian from East Lake High School in 1997 and began

her studies at The University of Florida that fall. Kelly graduated with a Bachelor of

Science degree in engineering science in May of 2002. In addition to her major studies,

she also received minors in biomechanics, French and music. She continued her

education at the University of Florida as a graduate student in the Department of

Biomedical Engineering in August 2002. Throughout her stay at the University of

Florida, Kelly has been very active in three sport clubs. She has served as the president

and captain of the Women's Roller Hockey Club, and competed nationally with Team

Florida Cycling and the Tri-Gators triathlon club.




Full Text

PAGE 1

PREDICTED CHANGES IN THE KNEE ADDUCTION TORQUE DUE TO GAIT MODIFICATIONS By KELLY L. ROONEY A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2005

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Copyright 2005 by Kelly L. Rooney

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iii ACKNOWLEDGMENTS I would like to thank my committee chair, Dr. B.J. Fregly, for his guidance and support. I would also like to thank my other committee members, Dr. Raphael Haftka and Dr. Malisa Sarntinoranont, for their suggestions and time. I greatly appreciate all of the support and friendship pr ovided by the other students in the Computational Biomechanics Lab. Speci fically, I appreciate Jeff for contributions to my research, Zhao Dong and Yi-chung for Chinese lessons, and Langston and Carlos for moral support and encouragement. I would also like to thank my friends from the Tri-Gators and Roller Hockey Team for providing me with an athletic escape from the academic world. Finally, I would like to thank Bernd for his personal support throughout the years.

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iv TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iii LIST OF TABLES.............................................................................................................vi LIST OF FIGURES..........................................................................................................vii ABSTRACT....................................................................................................................... ..x CHAPTER 1 BACKGROUND..........................................................................................................1 Osteoarthritis................................................................................................................. 1 Knee Adduction Torque...............................................................................................1 High Tibial Osteotomy.................................................................................................1 Motion Capture.............................................................................................................2 Dynamic Simulations....................................................................................................2 Optimization.................................................................................................................2 2 INTRODUCTION........................................................................................................4 3 METHODS...................................................................................................................7 Experimental Data Collection.......................................................................................7 Dynamic Gait Model Development..............................................................................7 Dynamic Model Parameter Tuning..............................................................................8 Movement Prediction via Inverse Dynamic Optimization...........................................9 4 RESULTS...................................................................................................................14 Optimizations without Experime ntal Leg Torque Tracking.......................................14 Optimizations with Experimental Leg Torque Tracking............................................15 5 DISCUSSION.............................................................................................................32 Observations...............................................................................................................32 Limitations..................................................................................................................33

PAGE 5

v 6 CONCLUSIONS AND FUTURE WORK.................................................................35 APPENDIX A DESRIPTION OF OPTIMIZATION FILES..............................................................36 B DESCRIPTION OF MATLAB FILES.......................................................................38 LIST OF REFERENCES...................................................................................................40 BIOGRAPHICAL SKETCH.............................................................................................42

PAGE 6

vi LIST OF TABLES Table page 1 RMS errors between the Fourier fi t curves and experimental data............................9 2 Various foot path cases tested for effect on knee adduction....................................12

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vii LIST OF FIGURES Figure page 1 The 3D, 14 segment, 27 DOF full-body kine matic model linkage joined by a set of gimbal, universal, and pin joints..........................................................................13 2 Comparison of left knee abduction/ adduction torques achieved without matching experimental leg torques, where positive torque represents abduction and negative torque represents adduction................................................................16 3 Comparison of left hip flexion/exte nsion motion achieved without matching experimental leg torques, where positiv e angle represents flexion and negative angle represents extension........................................................................................16 4 Comparison of left knee flexion/exte nsion motion achieved without matching experimental leg torques, where positiv e angle represents flexion and negative angle represents extension........................................................................................17 5 Comparison of left ankl e dorsiflexion/planarflexio n motion achieved without matching experimental leg torques, wher e positive angle represents dorsiflexion and negative angle represents planarflexion............................................................17 6 Comparison of pelvis longitudinal ax is rotation motion achieved without matching experimental leg torques, where positive angle represents rotation to left and negative angle repr esents rotation to right..................................................18 7 Comparison of pelvis anterior/posteri or axis rotation motion achieved without matching experimental leg torques, where positive angle represents tilt to left and negative angle represents tilt to right.................................................................18 8 Comparison of pelvis horizontal ax is rotation motion achieved without matching experimental leg torques, wher e positive angle represents forward tilt |and negative angle represents backward tilt............................................................19 9 Comparison of left hip internal/ext ernal rotation moti on achieved without |matching experimental leg torques, wher e positive angle represents internal and negative angle represents external.....................................................................19 10 Comparison of left hip abduction/ad duction motion achieved without matching experimental leg torques, where negativ e angle represents abduction and angle torque represents adduction......................................................................................20

PAGE 8

viii 11 Comparison of left subtalar invers ion/eversion motion achieved without matching experimental leg torques, wher e positive angle represents inversion and negative angle represents eversion....................................................................20 12 Comparison of left knee flexion/exte nsion torques achieved without matching experimental leg torques, where positive torque represents flexion and negative torque represents extension......................................................................................21 13 Comparison of left subtalar invers ion/eversion torques achieved without matching experimental leg torques, where positive torque represents inversion and negative torque represents eversion...................................................................21 14 Comparison of left hip internal/exter nal rotation torques achieved without matching experimental leg torques, where positive torque represents internal and negative torque represents external...................................................................22 15 Comparison of left hip abduction/ adduction torques ach ieved without matching experimental leg torques, where negative torque represents abduction and positive torque represents adduction.................................................................22 16 Comparison of left hip flexion/exte nsion torques achieved without matching experimental leg torques, where positive torque represents flexion and negative torque represents extension......................................................................................23 17 Comparison of left ankl e dorsiflexion/planarflexio n torques achieved without matching experimental leg torques, where positive torque represents dorsiflexion and negative torque represents planarflexion.......................................23 18 Comparison of left hip flexion/ex tension motion achieved with matching experimental leg torques, where positiv e angle represents flexion and negative angle represents extension........................................................................................24 19 Comparison of left knee flexion/ex tension motion achieved with matching experimental leg torques, where positiv e angle represents flexion and negative angle represents extension........................................................................................24 20 Comparison of left ankl e dorsiflexion/planarflexio n motion achieved with matching experimental leg torques, wher e positive angle represents dorsiflexion and negative angle represents planarflexion............................................................25 21 Comparison of pelvis horizontal axis rotation motion achieved with matching experimental leg torques, where positiv e angle represents forward tilt and negative angle represen ts backward tilt....................................................................25 22 Comparison of pelvis anterior/posteri or axis rotation motion achieved with matching experimental leg torques, where positive angle represents tilt to left and negative angle represents tilt to right.................................................................26

PAGE 9

ix 23 Comparison of left hip internal/ext ernal rotation motion achieved with matching experimental leg torques, wher e positive angle represents internal and negative angle represents external.....................................................................26 24 Comparison of pelvis longitudinal axis rotation motion achieved with matching experimental leg torques, where positive angle represents rotation to left and negative angle represents rotation to right...............................................................27 25 Comparison of left subt alar inversion/eversion mo tion achieved with matching experimental leg torques, where positive angle represents inversion and negative angle represents eversion.........................................................................................27 26 Comparison of left hip abduction/ad duction motion achieved with matching experimental leg torques, where negativ e angle represents abduction and angle torque represents adduction......................................................................................28 27 Comparison of left knee abduction/a dduction torques achieved with matching experimental leg torques, where posi tive torque represents abduction and negative torque repr esents adduction.......................................................................28 28 Comparison of left knee flexion/exte nsion torques achieved with matching experimental leg torques, where positive torque represents flexion and negative torque represents extension......................................................................................29 29 Comparison of left subtal ar inversion/eversion tor ques achieved with matching experimental leg torques, where positiv e torque represents inversion and negative torque represents eversion.........................................................................29 30 Comparison of left hip abduction/ad duction torques achieved with matching experimental leg torques, where nega tive torque represents abduction and positive torque represents adduction........................................................................30 31 Comparison of left hip internal/externa l rotation torques achieved with matching experimental leg torques, where positive torque represents internal and negative torque represents external.........................................................................................30 32 Comparison of left hip flexion/exte nsion torques achieved with matching experimental leg torques, where positive torque represents flexion and negative torque represents extension......................................................................................31 33 Comparison of left ankle dorsiflexio n/planarflexion torques achieved with matching experimental leg torques, where positive torque represents dorsiflexion and negative torque represents planarflexion.......................................31

PAGE 10

x Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science PREDICTED CHANGES IN THE KNEE ADDUCTION TORQUE DUE TO GAIT MODIFICATIONS Kelly L. Rooney May 2005 Chair: Benjamin J. Fregly Major Department: Biomedical Engineering Dynamic optimizations capable of pred icting novel gait motions have great potential for addressing clini cally significant problems in or thopedics and rehabilitation. This study evaluates gait modifications as an alternative to surgery for treating medial compartment knee osteoarthritis. Researcher s developing forward dynamic optimizations of gait for such applications face signif icant challenges that may be resolved by implementing an inverse dynamic approach. Th is study used Fourier coefficients, which defined the motion and ground reac tion torque curves, as kinematic design variables with an inverse dynamics optimization to predic t novel motions. The cost function, minimized by a nonlinear least squares optimization function, included the left knee adduction torque and several reality constraints. Tw o sets of prediction optimizations were performed to evaluate the effect of foot pl acement on the knee adducti on torque. The first set of prediction optimizations, which allo wed leg torques to change without limit, resulted in motions with similar kinema tic changes that reduced the knee adduction torque (72% average decrease) regardless of the foot path. The second set, which tracked

PAGE 11

xi experimental leg torques, also resulted in the knee adduction torque being reduced for all cases (45% average decrease), but to a lesse r degree. The optimizations suggest that novel movement modifications can have a si gnificant effect (mor e than a high tibial osteotomy surgery) on reducing the p eak knee adduction torque during gait.

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1 CHAPTER 1 BACKGROUND Osteoarthritis The most common type of arthritis, known as osteoarthritis, affects 15 million people in the United States today accord ing to the 2004 National Arthritis Meeting Report. This degenerative dis ease occurs when the cartilag e, or cushioning, between bones breaks down due to uneven loading and ex cessive wear. Over time, cartilage in a joint may be completely worn away leaving painful bone on bone cont act. Osteoarthritis is most common in the large weight bear ing joints such as the hips and knees. Knee Adduction Torque Most patients who suffer from knee osteoa rthritis have loss of cartilage in the medial compartment of the knee joint. This is due to the knee adduction torque, which results from the way the human body is cons tructed. When a person is standing on one leg, their center of mass falls medially, or in side, of the standing leg. The weight of the body acts to adduct the knee. Adduction causes th e medial compartment of the knee to be forced together and the lateral knee compartm ent to be pulled apart. As a person walks, the knees repeatedly go through cy cles of this uneven loadin g. Over time this will cause breakdown of the medial compartment cartilage These effects are multiplied in patients with a varus (bow-legged) alignment. High Tibial Osteotomy In order to stop this breakdown of essent ial cartilage, a patient may undergo a high tibial osteotomy surgery. This procedure rem oves a wedge of bone from the tibia, or shin

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2 bone, in order to correct a varus, or bow-le gged, alignment. The forces in the knee are shifted laterally in order to move the pressu re from the damaged car tilage to the healthy tissue. Motion Capture The motion data of a patient is collec ted in a gait lab using high-speed, highresolution cameras. Spheres covered with reflec tive tape are placed on all segments of the patientÂ’s body. The cameras reco rd the location of these ma rkers over time. The marker data is used to create a co mputer model by calculating the location and orientation of the joints with respect to the markers. The movement of the markers throughout the gait cycle is used to calculate the motion of the joints. Dynamic Simulations The computer model of the patientÂ’s gait, or walking, cycle, is used to perform dynamic simulations. The modeling software creates the equations of motion based on the model structure and joint motions provi ded. These equations are used to solve dynamic simulations. Two types of dynamic simu lations are discussed in this paper. Inverse dynamics, as the name suggests, occurs in the opposite order of real life events. Given the motion of a model, inverse dynamics is used to calculate th e forces and torques that would produce that motion. Forward dyna mics on the other hand occurs in the natural order. Forces and torques are i nput to calculate the resulting motions. Optimization An optimization is a mathematical met hod used to find the best solution to a problem. The important components of an op timization are design variables, a cost function, and constraints. The de sign variables are the values that are changed in order to search for the solution. The optimizer seeks to fi nd the values of the design variables that

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3 will minimize or maximize a cost function. C onstraints are boundaries that cannot be crossed while searching for the optimal solution.

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4 CHAPTER 2 INTRODUCTION Dynamic optimizations capable of pred icting novel gait motions have great potential for addressing clini cally significant problems in or thopedics and rehabilitation (Delp et al ., 1990; Delp et al ., 1996; Pandy, 2001). In orthopedi cs, an optimization may be valuable to predict the outcome of certain procedures given vari ous combinations of surgical parameters. For example, Cerebral Palsy patients often have muscles lengthened or redirected to improve gait coordination (Arnold et al. 2001). A predictive model may demonstrate how such changes affect the entire body rather than just one or two joints spanned by the altered muscle. As another ex ample, tibial osteotomy patients may have lower leg alignment corrected to relieve knee pain due to oste oarthritis. Researchers have investigated the relationshi p between dynamic gait measurem ents and clinical outcome, with the peak knee adduction moment being id entified as an important clinical marker (Andriacchi, 1994; Hurwitz et al. 1998; Prodromos et al. 1985;Sharma et al. 1998; Wang et al. 1990). A model could help define the optimal amount of correction by predicting the post surg ery knee forces and torques thr oughout the entire gait cycle. In rehabilitation, a predictive gait model could permit the development of novel rehabilitation procedures that may be difficult to identify experimentally. Researchers developing forward dynamic optimizations of gait for such applications face two signifi cant challenges. The first problem is instability of the repeated forward simulations performed duri ng the optimization process. During gait, the body can be viewed as an inverted pendul um where the mass of the upper body swings

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5 over a foot fixed to the ground. Without constrai nts or feedback cont rol, the torso will quickly fall over in forward dynamic simulations driven only by torque actuators (Winter, 1990). Others have used muscles to ov ercome this instab ility (Gerristen et al ., 1998). Muscles act as inherent stabi lizers due to their force-length and force-velocity properties. The second obstacle is large computational co st associated with repeated numerical integration of the equations of motion for full-body, three-dimensional (3D) gait models. Previous investigations required parallel processing to complete such large-scale optimizations (Anderson and Pandy, 2001). Both problems associated with a forwar d dynamic optimization may be resolved by implementing an inverse dynamic approach. With forward dynamic optimization, design variables are placed on the torques and the equa tions of motion are integrated to predict motion. However, if the design variables are instead placed on the motion, an inverse dynamics approach can be used to predic t the resulting motion and loads similar to forward dynamic optimization. Contrary to forward dynamics, the inverse approach does not have stability problems nor does it require costly numer ical integrations. This study evaluates gait modifications as an alternative to surgery for treating medial compartment knee osteoarthritis. The sp ecific goal was to pred ict the influence of foot position (i.e., toe out and wider stan ce) on the peak knee adduction moment. The predictions were developed using invers e dynamic optimization of a 27 degree-offreedom (DOF), full-body gait model. The optimizations sought to minimize the peak knee adduction moment and were performed und er two conditions. The first allowed the optimizer to vary the joint torques without limit, while the second sought to change the

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6 nominal torques as little as possible. Novel movement modifications may have a significant affect on reducing the peak knee adduction moment during gait.

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7 CHAPTER 3 METHODS Experimental Data Collection Gait data were collected from a single adult male using a HiRes Expert Vision System (Motion Analysis Corp., Santa Rosa CA) with institutional review board approval. Surface marker data of a modified Cleveland Clinic marker set were collected at 180Hz for static and dynamic trials. The st atic trials were used to define segment coordinate systems and the locations of the markers within those coordinate systems. Dynamic joint trials were used to define the location and orientat ions of the joints. Dynamic gait trials provided the marker locati on data for an entire gait cycle. Two force plates (Advanced Mechanical Technology, Inc., Watertown, MA) recorded the ground reaction forces and torques of each foot about the electrical center of the respective force plate. The raw data were filtered using a fourth-order, zero phase-shift, low pass Butterworth Filter with a cutoff frequency of 6 Hz. Dynamic Gait Model Development Identical 3D, full body dynamic models were developed using Autolev (Online Dynamics, Inc., Sunnyvale, CA), a symbo lic manipulator for engineering and mathematical analysis, and Software for In teractive Musculoskeletal Modeling (SIMM, Motion Analysis Corporation, Santa Rosa, CA). The Autolev model was designed for patient specific motion analysis and provide s direct access to th e equations of motion. The SIMM model provided visua lization of the motion, and a llows for the computation of muscle forces. Two models were necessary to validate the inverse dynamic approach

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8 did not contain programming flaws. The mode ls consist of 14 segments linked by 27 DOFs including gimbal, universal, and pin jo ints. Similar to PandyÂ’s (2001) model structure, 3 translational and 3 rotational DOFs express the mo vement of the pelvis in a Newtonian reference frame. The remaining lower body DOFs include 3 DOF hip joints, 1 DOF knee joints, and 2 DOF ankle joints. The upper body DOFs include a 3 DOF back joint, 2 DOF shoulder joints, and 1 DOF elbow joints. ( Error! Reference source not found. ). Inverse dynamic analysis was performe d on both full-body models using the statespace form of the equations of motion. Consequently, 27 control forces and torques were calculated from the experimentally determined joint kinematics and ground reaction quantities. All forces and torques calculated by the two models were identical to within round-off error, providing a check on the dynamical equation formulation. An additional degree of freedom in the model, prescribed to produce no motion, was used to calculate the left knee adduction torque. External forces and torques acting on the pelvis were also calculated, since the modelÂ’s position and orientation with respect to the ground frame are defined by a 6 DOF joint between the gr ound and pelvis. In reality there are no external forces or torques ac ting on the pelvis segment. Any non-zero force and/or torque found at this joint re presents error in th e model and/or data. Dynamic Model Parameter Tuning A nonlinear least squares optimization was performed using Matlab (The Mathworks, Natick, MA) to find model parameters, joint kinematics, and ground reactions to create a nominal data set consistent with the dynamical equations and the experimental gait data. The goal of this optimi zation was to alter the experimental data as little as possible while adjusting selected model parameters, smoothing the inverse

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9 dynamic torques, and driving the external pe lvis forces and torques close to zero. The optimization design variables were selected joint parameters (positions and orientations in the body segments), body segment parameters (masses, mass cente rs, and moments of inertia), and parameters defining the joint tr ajectories. A penalty was placed on changes to the body segment parameters in order to minimize the differences between the optimized data and the experimental data. Movement Prediction via In verse Dynamic Optimization Motion and ground reaction torque curves we re parameterized by a combination of polynomial and Fourier terms. The coefficients served as design variables for an inverse dynamics optimization used to predict novel motions. To accurately match the experimental data (Table 1), 8 harmonics a nd a cubic polynomial were needed for each DOF and ground reaction. The motion curves were differentiated to calculate velocities and accelerations. The right and left ground reac tion forces and torques measured in the ground frame were applied to the respective f eet. The resulting kinematics were used to calculate the corresponding jo int forces and torques. Table 1: RMS errors between the Fourie r fit curves and experimental data. Ground Reaction Forces (N) Ground Reaction Tor ques (Nm) Translations (cm) Rotations (deg) 4.13 0.750 0.0257 0.173 The inverse dynamic optimization used the Matlab nonlinea r least squares algorithm “lsqnonlin” and minimized the left knee adduction torque subject to several reality constraints implemented via a penalty method (Equation 1):

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10 min T+wqqq wTTTT weKinematicj j j j sj j s f Kineticjsjssj j j s j CoPCoPsj L AddTrunkPelvisFoot PelvisHipKneeAnkle 22 1 3 2 1 2 2 1 6 1 2 1 100 2222 1 2 1 3 1 2 1 6 2()()() ()()()() () j s 1 2 1 2 (1) where f refers to time frame (1 through 100) j refers to translational or rotational join t axis number (maximum value depends on number of prescribed joint axes for the specified anatomic joint) s refers to side (1 for left, 2 for right) w, w, wKinematicKineticCoP 2220 and are weight factors determined by trial and error TL Add is left knee adduction torque qTrunk is change in trunk x y or z rotation ( j = 1 to 3) away from its nominal value measured with respect to the lab frame qPelvis is change in pelvis x or z translation ( j = 1, 2) away from its nominal value measured with respect to the lab frame qFoot is change in foot x y or z translation or rotation ( j = 1 to 6) away from its nominal value measured with respect to the lab frame TPelvis is change in external pelvis x y or z force or torque ( j = 1 to 6) away from its nominal value (close to zero) expressed in the lab frame THip is change in hip flexion/extension, abduction/adduction, or inertial/external rotation torque ( j = 1 to 3) away from its nominal value

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11 TKnee is change in knee flexion/extension torque away from its nominal value TAnkle is change in ankle flexion/extens ion or inversion/eversion torque (j = 1, 2) away from its nominal value eCoP is error in the center of pressure x or z location (j = 1, 2) beyond the outer edge of the foot The predicted motion was forced to follow a prescribed foot path. This constraint allowed for the evaluation of various foot placements by altering th e foot path to be matched. The trunk orientations were constrained to match th e experimental orientations in order to avoid a motion where the model leaned over unrealistically. The transverse plane translations were also constrained to match the experimental translations. This constraint prevented the model from swinging a hip out laterally in such a way that an actual person may lose balance. The pelvis residual forces and torques were minimized because any non-zero residual would be an error. Because the ground reaction torques were design variables, the cen ters of pressure of the re sultant right and left ground reaction forces were constrained to pass through the respective feet. Two sets of prediction optimizations were pe rformed to evaluate the effect of foot placement on the knee adduction torque. The firs t set allowed the leg torques to change without limit (i.e., THip, TKnee, and TAnkle were removed from Eq. (1)), while the second set minimized the difference between th e experimental and optimized leg torques. Five cases were run within each set to ev aluate the combinations of toeing out or changing stance width. The first case sought to match the experimental foot path. The remaining cases included all combinations of toeing out + 15 and changing the stance

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12 width by + 5 cm (Table 2). For each combination of foot path with in each set of prediction optimization, the kinematic and kinetic changes were compared. Table 2. Various foot path cases te sted for effect on knee adduction. Foot Path Changes Case Toe Out (degrees) Stance Width (cm) 1 0 0 2 15 5 3 15 -5 4 -15 5 5 -15 -5

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13 Figure 1. The 3D, 14 segment, 27 DOF full-body ki nematic model linkage joined by a set of gimbal, universal, and pin joints.

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14 CHAPTER 4 RESULTS Optimizations without Experimental Leg Torque Tracking The first set of prediction optimizations allowing leg torques to change without limit resulted in motions with similar kinematic changes that reduced the knee adduction torque (72% average decrease) regardless of the foot path (Figure 2). The kinematic changes included greater hip flexion (Figur e 3), knee flexion (Figure 4), and ankle dorsiflexion (Figure 5) angles throughout the gait cycle. The pelvis noticeably rotated about the longitudinal axis (Figure 6) and the an terior-posterior axis (Figure 7) to position the left hip more anterior and inferior during left foot stance. The pelvis rotation about the horizontal axis remained consistent throughout all cases (Figure 8). The hips were more externally rotated and abducted for the to eing out cases and inte rnally rotated and adducted for the toeing in cases (Figure 9 a nd Figure 10). The subtal ar joint angle was generally more inverted in each case compar ed to the experimental data (Figure 11). The inverse dynamic analyses resulted in similar kinetic changes that correspond to the kinematic changes. The resulting kine tic changes included larger knee extensor (Figure 12) and subtalar inve rsion (Figure 13) torques. Th e hip torques showed greater internal rotation (Figure 14) and adducti on (Figure 15) torques compared to the experimental data. The hip flexion torque in creased with toeing in and decreased with toeing out for the wider stance cases only (Fi gure 16). The ankle flexion torque changes did not show significant correlati on to individual cases (Figure 17).

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15 Optimizations with Experimental Leg Torque Tracking Similar changes, but to a lesser degree, resulted when the experimental torques were tracked. The model again flexed the hi p (Figure 18), knee (Fi gure 19), and ankle (Figure 20) more than the experimental motion. The pelvis horizontal axis and anterior/posterior axis rotations (Fig ure 21 and Figure 22) along with the hip internal/external ro tations (Figure 23) were similar to the prediction optimization without torque tracking. However, the pelvis longitudina l axis rotations signifi cantly increased to aid the hip internal/external rotations (Figur e 24). The subtalar motion was inverted for toeing in and everted for toeing out (Figur e 25). The hip abduction/adduction motion showed a similar trend by reduced magnitude co mpared to the previous set (Figure 26). Again the reduction in the knee adduction torque (Fi gure 27) was not greatly affected by the foot path, but was reduced for all cases (45% average decrease). However, the reduction was not as dramatic due to the limits placed on the leg torque changes. The knee flexion (Figure 28), subt alar inversion (Figur e 29), and hip adduction (Figure 30) torques all increased as in the prev ious set. The only difference in the kinetic changes was that where the hip had a greater in ternal rotation torque in the previous set (Figure 14), the torque track ing set produced motions with greater hip external rotation torque (Figure 31). The hip flexion/extension and ankle torques were virtually identically in all cases including the experiment al data (Figure 32 and Figure 33).

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16 Figure 2. Comparison of left knee abductio n/adduction torques achieved without matching experimental leg torques, where positive torque represents abduction and negative tor que represents adduction. Figure 3. Comparison of left hip flexion/ extension motion achieved without matching experimental leg torques, where positiv e angle represents flexion and negative angle represents extension.

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17 Figure 4. Comparison of left knee flexion/ex tension motion achieved without matching experimental leg torques, where positiv e angle represents flexion and negative angle represents extension. Figure 5. Comparison of left ankle dorsifle xion/planarflexion motion achieved without matching experimental leg torques, where positive angle represents dorsiflexion and negative angl e represents planarflexion.

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18 Figure 6. Comparison of pelvis longitudina l axis rotation motion achieved without matching experimental leg torques, wher e positive angle represents rotation to left and negative angle repres ents rotation to right. Figure 7. Comparison of pelvis anterior/poste rior axis rotation motion achieved without matching experimental leg torques, where positive angle represents tilt to left and negative angle represents tilt to right.

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19 Figure 8. Comparison of pelvis horizontal axis rotation motion achieved without matching experimental leg torques, wh ere positive angle represents forward tilt and negative angle represents backward tilt. Figure 9. Comparison of left hip interna l/external rotation motion achieved without matching experimental leg torques, wher e positive angle represents internal and negative angle represents external.

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20 Figure 10. Comparison of left hip abduc tion/adduction motion achieved without matching experimental leg torques, wher e negative angle represents abduction and angle torque represents adduction. Figure 11. Comparison of left subtalar i nversion/eversion motion achieved without matching experimental leg torques, wher e positive angle represents inversion and negative angle represents eversion.

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21 Figure 12. Comparison of left knee flexion/ex tension torques achieved without matching experimental leg torques, where posi tive torque represents flexion and negative torque repres ents extension. Figure 13. Comparison of left subtalar i nversion/eversion torques achieved without matching experimental leg torques, wher e positive torque represents inversion and negative torque represents eversion.

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22 Figure 14. Comparison of left hip internal/e xternal rotation tor ques achieved without matching experimental leg torques, wher e positive torque represents internal and negative torque represents external. Figure 15. Comparison of left hip abductio n/adduction torques achieved without matching experimental leg torques, where negative torque represents abduction and positive torque represents adduction.

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23 Figure 16. Comparison of left hip flexion/ex tension torques achieved without matching experimental leg torques, where posi tive torque represents flexion and negative torque repres ents extension. Figure 17. Comparison of left ankle dorsiflexi on/planarflexion torques achieved without matching experimental leg torques, where positive torque represents dorsiflexion and negative torque represents planarflexion.

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24 Figure 18. Comparison of left hip flexion/ extension motion achieved with matching experimental leg torques, where positiv e angle represents flexion and negative angle represents extension. Figure 19. Comparison of left knee flexion/ extension motion achieved with matching experimental leg torques, where positiv e angle represents flexion and negative angle represents extension.

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25 Figure 20. Comparison of left ankle dorsif lexion/planarflexion motion achieved with matching experimental leg torques, where positive angle represents dorsiflexion and negative angl e represents planarflexion. Figure 21. Comparison of pelvis horizontal axis rotation mo tion achieved with matching experimental leg torques, where posi tive angle represents forward tilt and negative angle represents backward tilt.

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26 Figure 22. Comparison of pelvis anterior/poste rior axis rotation mo tion achieved with matching experimental leg torques, where positive angle represents tilt to left and negative angle represents tilt to right. Figure 23. Comparison of left hip internal /external rotation motion achieved with matching experimental leg torques, wher e positive angle represents internal and negative angle represents external.

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27 Figure 24. Comparison of pelvis longitudi nal axis rotation mo tion achieved with matching experimental leg torques, wher e positive angle represents rotation to left and negative angle repres ents rotation to right. Figure 25. Comparison of left subtalar inve rsion/eversion motion achieved with matching experimental leg torques, where posi tive angle represents inversion and negative angle represents eversion.

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28 Figure 26. Comparison of left hip abduction/ adduction motion achieved with matching experimental leg torques, where negativ e angle represents abduction and angle torque represents adduction. Figure 27. Comparison of left knee abduction/ adduction torques achie ved with matching experimental leg torques, where posi tive torque represents abduction and negative torque repr esents adduction.

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29 Figure 28. Comparison of left knee flexion/ extension torques achieved with matching experimental leg torques, where posi tive torque represents flexion and negative torque repres ents extension. Figure 29. Comparison of left s ubtalar inversion/eversion to rques achieved with matching experimental leg torques, where posi tive torque represents inversion and negative torque re presents eversion.

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30 Figure 30. Comparison of left hip abduction/ adduction torques achieved with matching experimental leg torques, where nega tive torque represents abduction and positive torque represents adduction. Figure 31. Comparison of left hip internal /external rotation to rques achieved with matching experimental leg torques, wher e positive torque represents internal and negative torque represents external.

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31 Figure 32. Comparison of left hip flexion/ex tension torques achieved with matching experimental leg torques, where posi tive torque represents flexion and negative torque repres ents extension. Figure 33. Comparison of left ankle dorsifle xion/planarflexion torques achieved with matching experimental leg torques, where positive torque represents dorsiflexion and negative torque represents planarflexion.

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32 CHAPTER 5 DISCUSSION Observations This study used a predictive gait model to evaluate the effects of gait modifications on the knee adduction moment. An inverse dyna mics optimization approach was used rather than the traditional forward dynamic approach, because of two main advantages. There are no stability problems with an inverse dynamics optimization, and inverse dynamic simulations do not require integrat ion. Two sets of prediction optimizations were performed to determine the effect of foot placement on the knee adduction torque. The optimizations were successful in pred icting novel motions that reduced the knee adduction torque, although foot pl acement was not a key component. Common kinematic changes regardless of f oot placement were found in all cases of the first set of optimizations that allowed un limited torque changes. The combinations of these changes drove the left knee inward such that the ground reaction force passed through the knee more laterally resulting in a lower left knee adduction torque. The resulting kinetic changes including larger knee extensor, subtal ar inversion, hip adduction, and hip internal rota tion torques may not be physically possible within these joints. The second set of prediction optimizati ons minimized the changes in the leg torques to avoid physically impossible solutions Again the results for all combinations of toe out and stance width changes we re similar. As in the first set of optimizations, this set also drove the left knee inward in order to reduce the adduction moment. The difference

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33 being that many of the kinematic and kinetic changes were of a lesser degree due to the torque constraint with the exception of the pelvis longitudinal axis rotations and hip internal/external rotation tor ques. The combinations of ki nematic changes in the second set of predication optimizations were diffe rent to allow for be tter tracking of the experimental torques. Although the flexed knee motion predicted by the model was effective in reducing the adduction moment, it may be problematic fo r osteoarthritis patients. This motion is less energetically efficient that regular gait due to the additional kne e extensor strength required to maintain the slight crouch throughout gait. Osteoarthritis patients tend to have weak knee flexors and may not be able to produce the energy required for this motion. The resulting knee adduction torque reductions suggest th at gait modifications are capable of reducing the peak knee adduction torque more than a high tibial osteotomy surgery. The average post surgery decreas e for a group of 25 high tibial osteotomy patients was 34% (Prodromos et al., 1985). The optimizer reduced the peak knee adduction torque an average of 72% without experimental torque tracking, and 45% with torque tracking. These results are limited by the fact that this study analyzed only one patient whose experimental data showed a p eak knee adduction torque close classified as normal (3% body weight height) by Prodromos et al. (1985). However, the general movement modifications predicted by the opt imizations suggest mechanics principles that should be applicable to any subject. Limitations Without including reality constraints in th e cost function, the optimizer found three ideal near zero knee adduction torque results with undesired kinematics or kinetics. First, if the ground reaction forces a nd torques are allowed to chan ge, the medial-lateral force

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34 will shift more laterally. This causes the total ground reaction force to pass through the knee more laterally thus reducing the kn ee adduction torque without changing the motion. However, this change may not be phys ically realistic, because the ratio of medial-lateral to vertical for ces tripled in value in order to create these ground reaction force changes. Second, if the pelvis translatio ns are free to change, lateral pelvis swinging will result. The optimizer predicts a motion where it shifts the body’s center of mass laterally by swinging the pelvis back and forth similar to a “hula” dance. As a result, the center of mass was shifte d directly above the knee so that the adduction moment was near to zero. Third, if the foot path was allowed to change, the model would cross the legs during gait so as to pass one tibia through the other. As a result, the knee moved under the body’s center of mass, rather than th e center of mass over the knee. The runway “model walk” has the same affect on the adduc tion torque as the “hula walk.” The “hula walk” is disadvantageous, because it is energe tically inefficient. While the “model walk” does not compromise efficiency as much, there is a loss in stability by bringing the feet closer together and is not physically realizable.

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35 CHAPTER 6 CONCLUSIONS AND FUTURE WORK The optimizations suggest that novel movement modifications can have a significant effect on reducing the peak knee adduction torque during gait. Gait modification has a greater influence on intern al knee loads than prev iously shown. It is interesting to note the number of different re alistic motions that are able to reduce the knee adduction torque. This approach has ma ny possibilities of clin ical applications, especially for medial compartment knee os teoarthritis patients. The optimizations highlight the importance of knee extensor st rength for avoiding osteoarthritis problems. As was explored in this study, these patients may be able to relieve their osteoarthritis symptoms simply by modifying their gait. Experimental evaluation of the hypothesis presented in this paper would be valuable in determining the feasibility of implementing the predicted gait modifications.

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36 APPENDIX A DESRIPTION OF OPTIMIZATION FILES MATLAB FILES (See descriptions in Appendix B) Call_optimizer_stance_toe.m ChangeFootPathMain.m ChangeFootPath.m Opt_min_add_grf.m Cost_func_min_add_grf.m PolyFourierFitNew.m CenterOfPressure_fourier.m Complete.m TEXT FILES Qcoefs_Final.txt : Fourier coefficients describi ng the experimental 27 DOFs. Grf_coefs.txt : Fourier coefficients describing the experimental right and left ground reaction forces and torques. Kinetics_final_no_header.ktx : A SIMM input file, which contains the experimental positions, velocities, accelerations, and ground reactions. Invdyn_foot_exp_final.txt : The foot, trunk and pelvis path calculated by the executable with the experimental data. Invdyn_trq_exp_final.txt : The inverse dynamic torques calculated by the executable with the experimental data. Params.txt: A text file read by the executable where the user must specify the name if the input kinetics file a nd desired step size for output data.

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37 OTHER Simulation.exe : The executable that performs inverse dynamics given an input kinetics file. Msvcr71d.dll : A library file needed to run the executable

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APPENDIX B DESCRIPTION OF MATLAB FILES

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39 Matlab Files Called by Inputs Outputs Description Call_optimizer_ stance_toe.m.m User None Coefficients_guess .txt Kinetics_guess.ktx Calls the optimization function. Change the foot placement values here to predict a different motion. ChangeFootPathMaiCall_optimizer _stance_toe.m Foot placement variables, invdyn_exp_final.txt kinetics_final_no_header.ktx Invdyn_foot_chan ged.txt Calculates the changes in the x,y,z foot translations and rotations with respect to the ground frame. ChangeFootPath.m ChangeFootPat hMain.m Old translations and rotations and changed to foot path translations and rotations. New foot translations and rotations. Calculates the new x,y, z foot translations and rotations with respect to the ground frame. Opt_min_add_grf.m Call_optimizer _stance_toe.m invdyn_foot_exp_final.txt, invdyn_foot_changed.txt, invdyn_trq_exp_final.txt, kinetics_final_no_header.ktx, QCoefs_Final.txt grf_coefs.txt None Loads experimental values. Creates initial conditions matrix. Calls the Matlab optimizer, “lsqnonlin.” Cost_func_min_ add_grf.m Opt_min_add_ grf.m Current guess of design variables, invdyn_trq.txt invdyn_foot.txt cop_error.txt Cost function error matrix, to be squared and summed by the optimizer. Reads in the current guess of the design variables. Writes a kinetics file based on that guess. Calls simulation.exe. Reads in inverse dynamic results. Calculates cost function. PolyFourierFitNew.Cost_func_min _add_grf.m Fourier coefficients, omega, time, degree of polynomial, derivative flag Values of the curves at the specified time points. Creates motion and ground reaction curves based on the Fourier coefficients. CenterOfPressure_ fourier.m Cost_func_min _add_grf.m Ground reaction forces and torques in the ground reference frame. Center of pressure locations in the ground reference frame. Calculates the left and right centers of pressure in the ground reference frame. Complete.m Opt_min_ add_grf.m None None Alerts user when an optimization has terminated.

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40 LIST OF REFERENCES Anderson, F.C., Pandy, M.G. (2001). Dynamic Optimization of Human Walking. Journal of Biomechanical Engineering 123, 381-390. Andriacchi, T.P. (1994). Dynamics of Knee Malalignment. Orthopedic Clinics of North America 25, 395-403. Arnold, A.S., Blemker, S.S., Delp, S.L. (2001). Evaluation of a Deformable Musculoskeletal Model for Estimatin g Muscle-Tendon Lengths During Crouch Gait. Annals of Biomed ical Engineering 29, 263-274. Delp, S.L., Loan, J.P., Hoy, M.G., Zajac, F.E., Topp E.L., Rosen, J.M. (1990). An Interactive Graphics-based Model of th e Lower Extremity to Study Orthopaedic Surgical Procedures. IEEE Transactions on Biomedical Engineering 37, 757-767. Delp, S.L., Arnold, A.S., Speers, R.A., M oore, C.A. (1996). Hamstrings and Psoas Lengths During Normal and Crouch Gait: Implications for Muscle-Tendon Surgery. Journal of Orthopaedic Research 14, 144-151. Gerristen, K.G.M., van den Bogert, A.J., Hu lliger, M., Zernicke, R.F. (1998). Intrinsic Muscle Properties Facilitate Locomoto r Control – A Computer Simulation Study. Motor Control 2, 206-220. Hurwitz, D.E., Ryals, A.R., Block, J.A., Sharma, L., Shcnitzer, T.J., Andriacchi, T.P. (2000). Knee Pain and Joint Loading in Subj ects with Osteoarthritis of the Knee. Journal of Orthopaedic Research 18, 572-579. Pandy, M.G. (2001). Computer Modeling and Simulation of Human Movement. Annual Reviews in Biomedical Engineering 3, 245-273. Prodromos, C.C., Andriacchi, T.P., Galante, J.O. (1985). A Relationship between Gait and Clinical Changes following High Tibi al Osteotomy. The Journal of Bone and Joint Surgery 67A, 1188-1194. Sharma, L., Hurwitz, D.E., Thonar, E.J-M.A., Sum, J.A., Lenz, M.E., Dunlop, D.D., Schnitzer, T.J., Kirwan-Mellis, G., Andriacchi, T.P. (1998). Knee Adduction Moment, Serum Hyaluronan Level, and Dis ease Severity in Medial Tibiofemoral Osteoarthritis. Arthit is & Rheumatism 41, 1233-1240.

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41 Wang, J.W., Kuo, K.N., Andriacchi, T.P., Galant e, J.O. (1990). The Influence of Walking Mechanics and Time on the Results of Proxi mal Tibial Osteotomy. Journal of Bone and Joint Surgery 72A, 905-913. Winter, D.A. (1990). Biomechanics and Motor Control of Human Movement, 2nd Edition. Wiley, New York.

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42 BIOGRAPHICAL SKETCH Kelly Rooney was born in Michigan in 1979. She moved to Palm Harbor, Florida, with her family in 1986 and remained ther e through the completion of her high school education. She graduated valedictorian from East Lake High School in 1997 and began her studies at The University of Florida that fall. Kelly graduated with a Bachelor of Science degree in engineering science in May of 2002. In addition to her major studies, she also received minors in biomechanics, French and music. She continued her education at the University of Florida as a graduate student in the Department of Biomedical Engineering in August 2002. Th roughout her stay at the University of Florida, Kelly has been very active in three sport clubs. She has served as the president and captain of the WomenÂ’s Roller Hockey Club, and competed nationally with Team Florida Cycling and the Tr i-Gators triathlon club.