UNDERSTANDING BIOMECHANICAL CAUSES AND FUNCTIONAL

MECHANISM OF TREATMENT FOR STIFF-KNEE GAIT IN CEREBRAL

PALSY

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Melanie Diane Fox

May 2011

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/vk276ss2747

© 2011 by Melanie Diane Fox. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Scott Delp, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Thomas Andriacchi

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Jessica Rose

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

iv

ABSTRACT

Many children with cerebral palsy walk with a stiff knee gait, or a reduction

and delay in swing phase knee flexion, which causes tripping or energy-inefficient

compensatory movements. Since over-activity of the rectus femoris muscle is

frequently implicated as the cause, a common treatment is transfer of the distal end of

the rectus femoris from its insertion on the patella to a location behind the knee.

Outcomes, though positive on average, vary among individuals, with some patients

demonstrating unimproved or worsened knee flexion postoperatively. This variability

is due in part to insufficient understanding of the biomechanical causes of stiff-knee

gait and the functional effects of surgical treatment. The goal of this dissertation was

to clarify the causes of stiff-knee gait and examine the biomechanical mechanism of

improvement following rectus femoris transfer surgery.

Swing-phase rectus femoris activity is commonly thought to cause of stiff-knee

gait, despite evidence that many patients have excessive knee extension moments in

preswing rather than swing phase. We compared the effects of preswing to swing

phase activity of the rectus femoris on peak knee flexion in swing by creating and

analyzing musculoskeletal simulations of subjects with stiff-knee gait. We found that

in six out of ten subjects preswing rectus femoris activity had at least a 90% higher

effect on peak knee flexion than swing phase rectus femoris activity, suggesting that

preswing rectus femoris activity is an important factor limiting knee flexion in some

subjects and should be examined to better determine the factors leading to stiff-knee

gait.

v

To understand how other muscles, besides rectus femoris, may limit knee

flexion in stiff-knee gait, it is first necessary to understand how muscles coordinate

successful swing phase knee flexion in unimpaired gait and how muscle contributions

change with walking speed, since many stiff-knee subjects walk slowly. We analyzed

simulations of unimpaired subjects walking at different speeds to determine the

muscles that accelerated and decelerated knee flexion prior to swing. We found that

preswing knee flexion acceleration was achieved primarily by the hip flexor muscles

with help from biceps femoris short head, suggesting that weakness in these muscles

may contribute to stiff-knee gait. Vasti and soleus decelerated knee flexion, suggesting

over-activity in these muscles may contribute to stiff-knee gait.

We also investigated the mechanism of improvement following rectus femoris

transfer surgery. We altered the geometry of rectus femoris and simulated the

dynamics of the swing phase of subjects with stiff-knee gait after different surgical

procedures. Analysis of the simulations demonstrated that knee flexion may be

improved with a reduction of the knee extension moment generated by the rectus

femoris, even if the muscle is not converted to a knee flexor.

This dissertation clarifies preswing rectus femoris activity as a cause of stiff-

knee gait, demonstrates the functional mechanism of improvement following transfer

surgery, and informs future research investigating other potential contributors to stiff-

knee gait.

vi

ACKNOWLEDGEMENTS

I have been indescribably blessed to have had the guidance, support, and

collaboration of so many talented and wonderful people during my time at Stanford.

First, I am incredibly grateful to my advisor, Scott Delp, whose excellent guidance,

genuine concern, and infectious confidence make him an outstanding mentor. It has

truly been a privilege to work with him.

I am also extremely thankful for the collaborations of my co-authors, Allison

Arnold, Sylvia Ounpuu, and Jeffrey Reinbolt, who made this work possible and

contributed to the high quality of research. I owe a particular debt of gratitude to

Jeffrey Reinbolt, not only for his vital contributions to the work presented here, but

also for his early guidance and patience and his continued support. I am appreciative

of the excellent work done by Mike Schwartz and May Liu, who collected the data

and created the simulations which we analyzed in Chapter 5 of this dissertation. I am

also thankful for the generosity of my NMBL labmates who have always been willing

to give excellent feedback and ask tough questions on presented research. The NMBL

group is full of remarkable talent, and I am grateful to have had the chance to learn in

this environment. I am especially grateful to Kat Steele, Jen Hicks, and Chand John

for their valuable input, brainstorming, and research help.

I would like to acknowledge the funding sources that made this research

possible. A National Science Foundation Graduate Fellowship and grants from the

National Institutes of Health, including R01 HD046814, T32GM63495, and

T15LM7033 funded this research. The musculoskeletal images used in Chapter 2 are

vii

taken with permission from the University of Washington Musculoskeletal Atlas: A

Musculoskeletal Atlas of the Human Body by Carol Teitz, M.D. and Dan Graney,

Ph.D.

My time at Stanford would not have been nearly as fun or fulfilling without

Mandy Koop, Melinda Cromie, and Ariel Dowling. I could always count on these

ladies for everything from late night robot building sessions to crazy adventure races

to spiritual support. Finally, I am exceedingly grateful to my parents, Art and Mary,

and my sisters, Cristina and Lisa, for their love and support. I appreciate their endless

supply of encouragement, as well as their discernment in recognizing those times

when not to ask how research was going. Though over 3000 miles away, they stood

beside me throughout this journey.

viii

CONTENTS Abstract .......................................................................................................................... iv 

Acknowledgements ....................................................................................................... vi 

List of Tables .................................................................................................................. x 

List of Figures ................................................................................................................ xi 

1 Introduction ................................................................................................................. 1 

1.1 Focus of the Dissertation ...................................................................................... 3 

1.2 Significance .......................................................................................................... 4 

1.3 Thesis Overview ................................................................................................... 8 

2 Background ................................................................................................................ 10 

2.1 Knee Flexion in Normal Gait .............................................................................. 10 

2.2 Stiff-Knee Gait in Children with Cerebral Palsy: Causes and Treatments ......... 11 

2.2.1 Rectus femoris over-activity ........................................................................ 12 

2.2.2 Vasti over-activity ........................................................................................ 30 

2.2.3 Ankle mechanics .......................................................................................... 32 

2.2.4 Insufficient hip flexion moment ................................................................... 35 

2.2.5 Hamstrings over-activity .............................................................................. 36 

2.2.6 Crouch gait ................................................................................................... 39 

2.2.7 Other potential causes .................................................................................. 42 

2.3 Methodology: Using Simulation to Understand Muscle Function .................... 43 

2.3.1 Simulation of Gait ........................................................................................ 44 

2.3.2 Analysis of Simulations ............................................................................... 46 

3 Importance of Preswing Rectus Femoris Activity in Stiff-knee Gait ........................ 49 

3.1 Abstract ............................................................................................................... 49 

3.2 Introduction ......................................................................................................... 50 

3.3 Methods .............................................................................................................. 52 

3.4 Results ................................................................................................................. 59 

3.5 Discussion ........................................................................................................... 60 

4 Mechanisms of Improved Knee Flexion After Rectus Femoris Transfer Surgery .... 67 

4.1 Abstract ............................................................................................................... 67 

ix

4.2 Introduction ......................................................................................................... 68 

4.3 Methods .............................................................................................................. 70 

4.4 Results ................................................................................................................. 77 

4.5 Discussion ........................................................................................................... 79 

5 Contributions of Muscles and Passive Dynamics to Swing Initiation Over a Range of Walking Speeds ............................................................................................................ 83 

5.1 Abstract ............................................................................................................... 83 

5.2 Introduction ......................................................................................................... 84 

5.3 Methods .............................................................................................................. 86 

5.4 Results ................................................................................................................. 90 

5.5 Discussion ........................................................................................................... 94 

6 Preliminary work: rectus femoris velocities before and after rectus femoris lengthening surgery ...................................................................................................... 99 

6.1 Introduction ......................................................................................................... 99 

6.2 Methods .............................................................................................................. 99 

6.3 Results ............................................................................................................... 103 

6.4 Discussion ......................................................................................................... 106 

7 Conclusion ............................................................................................................... 110 

7.1 Summary ........................................................................................................... 110 

7.2 Future work ....................................................................................................... 112 

8 References ............................................................................................................... 114 

x

LIST OF TABLES Table 3.1 Descriptive values for stiff-knee and able-bodied subjects......................... 53

Table 3.2 Rectus femoris electromyography deviations among subjects................... 55

Table 6.1 Multivariate model predicting change in knee range of motion after surgery.........................................................................................................................105

xi

LIST OF FIGURES Figure 2.1 Rectus femoris muscle…………………………………. ……………..... 13

Figure 3.1 Simulation of gait during preswing through early swing ……………..... 56

Figure 3.2 Method used to determine increase in peak knee flexion when rectus femoris activity was eliminated during preswing or early swing………………….… 58

Figure 3.3 Bar graph of increases in peak knee flexion caused by eliminating rectus femoris activity during preswing or early swing …………........................................ 60

Figure 3.4 EMG from two subjects with varying levels of preswing and early swing rectus femoris activity.……………………………………………………………….. 62

Figure 4.1 Knee flexion over gait cycle of stiff-knee subjects ……………..........… 72

Figure 4.2 Illustrations and moment arms of musculoskeletal models of rectus femoris transfer………………………………………………………………………. 75

Figure 4.3 Illustrations of peak knee flexion resulting from simulations of rectus femoris transfers………………………………………….......................................... 76

Figure 4.4 Bar graph of increase in peak knee flexion after simulated rectus femoris transfers……………………………………………………….................................... 78

Figure 4.5 Bar graph of change in peak knee flexion due to hip and knee moments of rectus femoris……………………………………………………………………..….. 78

Figure 5.1 Comparison of experimental and simulated knee kinematics and depiction of superposition of perturbation analysis for one subject……………………………. 89

Figure 5.2 Change in knee kinematics with walking speed……………..………….. 91

Figure 5.3 Bar graph of contributions of leg muscles and passive dynamics to knee flexion acceleration…………………………………………...................................... 93

Figure 5.4 Bar graph of contributions of individual muscle on preswing leg to knee flexion acceleration ...……………………………………….......................................94

Figure 6.1 Average knee flexion angles of subject and control groups ...................100

Figure 6.2 Estimated rectus femoris musculotendon lengths and velocities for a representative subject compared to average of controls ……....................................102

Figure 6.3 Preoperative peak rectus femoris lengthening velocities versus change in peak rectus femoris lengthening velocities after surgery ...........................................104

Figure 6.4 Preoperative peak rectus femoris lengthening velocities versus change in knee range of motion after surgery .……………………………...............................104

1

1 INTRODUCTION

Walking is an important skill of daily living that enables independent mobility

in diverse environments and provides myriad health benefits. Particularly for children,

ambulation plays an important role in social development. Walking is also indicative

of general health. In fact, walking speed is predictive of mortality in older adults

(Studenski et al., 2011).

Gait pathologies limit or impair mobility, which can reduce quality of life and

lead to secondary health problems. Left untreated, gait pathologies can become worse

over time and result in the inability to ambulate due to prohibitive energy cost or

intolerable pain.

Determining effective treatment of gait abnormalities is challenging.

Currently, treatment plans are typically based on interpretation of gait and physical

exam data and clinical intuition. These data are often insufficient to identify the

underlying causes of gait impairments. Patients frequently exhibit many gait

abnormalities simultaneously, and it is not always possible to determine which

abnormal findings are primary pathologies and which are secondary compensations.

The functional mechanisms of treatments are not well understood. As a result,

treatment outcomes are highly variable. Many available treatments for children with

cerebral palsy target muscles, such as strengthening, surgical lengthening, and surgical

transfer, but without rigorous understanding of how individual muscles contribute to

whole body movement, treatment may target the wrong muscles or alter them

inappropriately. Understanding the biomechanics of impaired gait and the functional

2

effects of treatments will help clinicians match appropriate treatments to individual

patients, leading to improved and more consistent outcomes.

Computer simulation is a powerful tool for understanding muscle function

during walking. Simulation of walking allows estimation of quantities that cannot be

measured, such as how much a muscle contributes to motion at all joints. It is also

valuable in elucidating cause and effect relationships, such as determining whether

inappropriate activity of a particular muscle could cause an observed gait abnormality.

This dissertation uses computer simulation to examine stiff-knee gait, a

common abnormal gait pattern among children with spastic cerebral palsy. Cerebral

palsy is a neuromuscular disorder resulting from non-progressive damage to the

developing brain which can lead to impaired motor control, abnormal muscle

physiology, and bone deformities. Stiff-knee gait is the inability to properly flex the

knee during the swing phase of gait. This makes it difficult to clear the toe from the

ground and frequently results in tripping or energy-inefficient compensatory motions,

which may make walking unsafe or exceedingly difficult (Mattsson and Brostrom,

1990; Lage et al., 1995; Abdulhadi et al., 1996). The cause is generally thought to be

inappropriate activity of the rectus femoris muscle (Sutherland et al., 1975; Waters et

al., 1979; Perry, 1987; Sutherland et al., 1990; Renshaw et al., 1995); however, it is

unclear at what point in the gait cycle activity from this muscle most impacts swing

phase knee flexion. The most common treatment for stiff-knee gait is surgical transfer

of the rectus femoris muscle in an effort to convert it from a knee extensor to a knee

flexor. However, outcomes of the surgery are variable and the mechanism by which

the surgery causes improvement in some subjects is unclear. Additionally, it is not

3

known whether other biomechanical factors may contribute to stiff-knee gait, since it

has been difficult to determine how muscles coordinate successful swing phase in

unimpaired gait.

1.1 FOCUS OF THE DISSERTATION

The first goal of this dissertation was to identify the biomechanical factors

contributing to stiff-knee gait in children with cerebral palsy. We clarified the

understanding of a currently accepted cause of stiff-knee gait by creating subject-

specific simulations of subjects with stiff-knee gait and altering the simulated muscle

excitations of rectus femoris during preswing and early swing. We demonstrated that

rectus femoris activity during preswing, though not traditionally recognized as a cause,

contributed to stiff-knee gait in many subjects. We also analyzed simulations of eight

unimpaired subjects walking at four speeds to quantify how muscles and passive

dynamics coordinate successful preparation for swing phase. This identified other

potential causes of stiff-knee gait in children with cerebral palsy.

The second goal of this dissertation was to reconcile conflicting experimental

evidence about the functional effect of surgical transfer of the rectus femoris. We

modeled the transferred geometry of the muscle and simulated its effect on knee

flexion in subjects with stiff-knee gait to show that even if the muscle is not converted

to a knee flexor, as intended, substantial improvement in knee flexion may be attained

through reduction of the muscle’s hindering knee extension effect.

4

1.2 SIGNIFICANCE

The work presented in this dissertation contributes significantly to both the

clinical and biomechanical communities. To the clinical community, this work further

clarifies the causes of stiff-knee gait. It provides modified clinical indications for

surgical transfer of rectus femoris and it proposes other possible causes of stiff-knee

gait in cerebral palsy to direct future research. Additionally, this work clarifies the

mechanism of improvement following rectus femoris transfer surgery. This informs

surgical technique and postoperative rehabilitation that could lead to improved

outcomes.

This work also contributes to the biomechanical community. It provides a

comprehensive understanding of how muscles and passive dynamics contribute to

coordinating a successful swing phase in unimpaired gait at different walking speeds.

This adds to the general understanding of muscle function in normal gait.

Additionally, we have provided new computational tools and methods for

investigating human walking.

The primary contributions of the research presented in this dissertation are:

• Creation of ten muscle-actuated simulations that accurately represent the

dynamics of children with cerebral palsy walking with a stiff-knee gait

We created some of the first muscle-actuated simulations of impaired gait. These

simulations allowed us to compare the effects of preswing and early swing rectus

femoris activity on swing phase knee flexion in stiff-knee gait. They also allowed

us to simulate the effects of different types of rectus femoris transfer surgery on

5

knee flexion. Additionally, they provide a resource for future investigation of

muscle function and compensations in stiff-knee gait and are available at

https://simtk.org/home/stiffknee.

• Identification of preswing rectus femoris activity as a contributor to stiff-knee

gait

Swing phase rectus femoris activity has classically been implicated as the cause of

stiff-knee gait. However, investigation of joint moments in individuals with

cerebral palsy walking in a stiff-knee gait showed that many patients had high

knee extension moments in preswing rather than the swing phase of gait (Goldberg

et al., 2006). Our study demonstrated that preswing rectus femoris activity can

contribute to stiff-knee gait and in many subjects, had a more limiting effect on

knee flexion in swing than swing phase rectus femoris activity. This finding helps

to clarify surgical indications for rectus femoris treatment. Traditionally, only

swing phase EMG has been considered an indication for rectus femoris treatment,

but our results suggest that preswing rectus femoris activity may also be an

indication for rectus femoris treatment. Additionally, comparing patient rectus

femoris EMG to speed-matched unimpaired EMG may assist in diagnosing

improper preswing rectus femoris activity since unimpaired individuals typically

exhibit preswing rectus femoris activity at free and fast speeds, while patients with

stiff-knee gait tend to walk at slower speeds. It should, however, be noted that

surface EMG may be subject to cross-talk from the vasti (Barr et al., 2010).

6

• Development of musculoskeletal models of three different types of rectus

femoris transfer

Modeling the transferred geometry of the rectus femoris muscle allowed

evaluation of the mechanism of knee flexion improvement following surgery.

These models offer the opportunity to answer a broad range of questions of clinical

interest regarding biomechanical effect of the surgery. For example, they could be

used to investigate other aspects of transfer surgery, such as effect on the muscle’s

force-length relationship, they could be combined with models of surgical

treatment to other muscles to investigate multilevel surgery, and they could be

combined with a finite element approach and a model of scar tissue to investigate

force transmission in scarred transfers as well as the role fascial connections play

in force transmission.

• Quantitative evidence that the mechanism of improved swing phase knee

flexion following rectus femoris transfer is reduction of the muscle’s knee

extension moment

Rectus femoris transfer was developed with the intention of converting the

muscle’s knee extension moment, which hinders swing phase knee flexion, to a

knee flexion moment by relocating its insertion behind the knee (Perry, 1987).

However, experimental evidence has shown that the transferred muscle still

generated an extension moment in many subjects (Riewald and Delp, 1997;

Asakawa et al., 2002). We modeled the transferred muscle and simulated the effect

on swing phase knee flexion to determine that the mechanism of improved swing

7

phase knee flexion following transfer was reduction of the muscle’s knee

extension moment. This is clinically significant because it suggests that less

invasive methods of reducing the muscle’s knee extension moment, such as

lengthening surgery, may be comparably effective. It also suggests that

mechanisms of reducing scar tissue formation between the rectus femoris and the

underlying vasti has the potential to improve surgical efficacy.

• Modification of an existing algorithm to quantify contributions of Coriolis

and centrifugal accelerations to joint motion

An existing algorithm allowed quantification of joint accelerations induced by

forces from muscles and gravity while accounting for the portion of the ground

reaction force generated by each (Liu et al., 2006a). We modified this algorithm to

enable quantification of joint accelerations induced by Coriolis and centrifugal

accelerations along with their contributions to the ground reaction force. With this

addition, all system forces were accounted for allowing confidence in the analysis

by summing all contributors to knee angular acceleration and comparing the total

to the measured knee angular acceleration. Furthermore, since our analysis

quantified the contributors at different speeds, calculation of velocity-dependent

terms was an important factor.

• Generation of a quantitative comprehensive understanding of how muscles

and passive dynamics accelerate the knee into flexion during preswing

8

While rectus femoris over-activity is the most commonly accepted cause of stiff-

knee gait, variability in treatment outcomes and research in the stroke population

suggest that other factors may contribute to stiff-knee gait. Understanding how

muscles and passive dynamics contribute to swing initiation in unimpaired gait is

necessary to identifying possible causes of an individual’s stiff-knee gait.

Additionally, it is necessary to understand how these contributions may change

with speed, since many subjects with stiff-knee gait tend to walk at slower speeds.

This analysis provides a framework for investigating other possible causes of stiff-

knee gait. It also adds to the understanding of muscle function in normal gait.

1.3 THESIS OVERVIEW

This dissertation is comprised of five subsequent chapters. Chapter 2 presents a

summary of the literature surrounding stiff-knee gait and presents the key clinical

questions. It also contains an explanation of the perturbation technique used to analyze

muscle function. Chapters 3 through 5 are self-contained journal articles, resulting in

some redundant presentation of introduction and methodology. Chapter 3 (Reinbolt et

al. (2009), published in the Journal of Biomechanics) presents a study using muscle-

actuated simulations of stiff-knee gait to demonstrate that rectus femoris activation in

preswing contributes to stiff-knee gait. Chapter 4 (Fox et al. (2009), published in the

Journal of Biomechanics) describes the creation of musculoskeletal models of

transferred rectus femoris and simulation of resulting knee flexion to identify

reduction of the muscle’s knee extension moment as the mechanism of improvement

following surgery. Chapter 5 (Fox et al. (2010), published in the Journal of

9

Biomechanics) details the use of a modified perturbation algorithm to quantify

contributions from muscles and passive dynamics to knee flexion acceleration during

double support at different walking speeds. Chapter 7 summarizes the main

conclusions of the research and suggests future directions for study.

In appreciation of the invaluable contributions of my collaborators to this research, I

use the pronoun “we” throughout this dissertation to refer to the multiple coauthors of

each study. The principle contributors to each of the presented studies include:

Chapter 3: Jeffrey Reinbolt, Allison Arnold, Sylvia Ounpuu, Scott Delp

Chapter 4: Jeffrey Reinbolt, Sylvia Ounpuu, Scott Delp

Chapter 5: Scott Delp

10

2 BACKGROUND

2.1 KNEE FLEXION IN NORMAL GAIT

The gait cycle is divided into phases defined by foot contact with the ground.

Each leg undergoes a period of stance, in which the foot is in contact with the ground,

and a period of swing, in which the foot is off of the ground. At the beginning of

single limb stance, the foot contacts the ground and the knee undergoes mild flexion,

to approximately 20 degrees, absorbing energy from the impact. The leg extends

during mid-stance, acting as a strut while the weight of the body passes over it. As the

opposite leg comes into contact with the ground at approximately 50% of the gait

cycle, the double support phase begins, an important period in preparation for swing

phase. During the double support, or preswing, phase the leg flexes rapidly reaching a

maximum knee flexion velocity around toe-off at 60% of the gait cycle, as the foot

leaves the ground, of approximately 340 degrees per second (Goldberg et al., 2006).

The knee reaches maximum flexion of approximately 60 degrees during swing phase

at approximately 10% of the gait cycle after toe-off. Sufficient knee flexion velocity at

toe-off is required for the knee to achieve adequate flexion to clear the toe from the

ground without stubbing the toe or necessitating out-of-plane compensatory motions.

Rectus femoris is normally active briefly at toe-off in normal gait which is

thought to prevent excess knee flexion in swing at free and fast walking speeds and to

contribute to hip flexion (Perry, 1992). Nene et al. (1999) found a linear relationship

between the angular acceleration of the shank and the amount of rectus femoris

activity in unimpaired gait.

11

2.2 STIFF-KNEE GAIT IN CHILDREN WITH CEREBRAL PALSY: CAUSES AND

TREATMENTS

Cerebral palsy is diagnosed in approximately 3 out of every 1,000 children

each year (CDC, 2004). This condition is a result of damage to the motor control areas

of the brain during development. Children with cerebral palsy commonly exhibit loss

of selective motor control, muscle weakness, exaggerated muscle stretch reflexes,

shortened muscle-tendon units, and subsequent bone deformities, which can make

walking very difficult. One of the most common walking abnormalities among

individuals with cerebral palsy is “stiff-knee gait,” or the inability to properly flex the

knee during the swing phase of gait (Wren et al., 2005a). Though precise kinematic

definitions differ stiff-knee gait has been identified by abnormal swing phase knee

kinematics including diminished and delayed peak knee flexion, reduced knee range

of motion, and difficulty with toe-clearance (Gage et al., 1987; Sutherland et al., 1990;

Kerrigan et al., 1991; Sutherland and Davids, 1993; Kerrigan et al., 1999; Rodda et al.,

2004; Wren et al., 2005a). This condition can lead to injury from tripping or energy-

inefficient compensatory movements such as circumduction, vaulting, upward pelvis

tilt, and pelvic lag to clear the stiff leg from the floor (Mattsson and Brostrom, 1990;

Lage et al., 1995; Abdulhadi et al., 1996). Stiff-knee gait is common not only in

cerebral palsy, but also in stroke, spinal cord injury, and traumatic brain injury

populations. Much of the literature investigating causes of stiff-knee gait has studied

these other populations. Stiff-knee gait is one of the most common gait abnormalities

in ambulatory children with spastic cerebral palsy (Wren et al., 2005a), making it a

valuable area of research aimed at improving treatments outcomes.

12

There has been much investigation into stiff-knee gait aimed at characterizing

the condition, probing the causes, investigating functional effects of treatments, and

assessing clinical treatment outcomes. Yet, the question of how to improve treatment

outcomes of patients with stiff-knee gait remains unanswered. Why do some knees

remain stiff after treatment? Failed treatment outcomes are either due to inaccurate

identification of the cause or ineffective treatment. To improve outcomes we must

understand more thoroughly both the causes of stiff-knee gait and the functional

effects of treatments.

2.2.1 RECTUS FEMORIS OVER-ACTIVITY

Rectus femoris over-activity has been considered historically to be the cause of

stiff-knee gait and remains the most commonly cited and treated cause of stiff-knee

gait (Sutherland et al., 1975; Waters et al., 1979; Perry, 1987; Sutherland et al., 1990;

Renshaw et al., 1995). In unimpaired gait, the rectus femoris is active briefly at toe-

off, which is thought to prevent excess knee flexion in swing and flex the hip (Perry,

1987; Perry, 1992; Nene et al., 1999; Schwartz et al., 2008). Nene et al. (1999)

showed that in unimpaired gait, the magnitude of rectus femoris activity was linearly

related to the angular acceleration of the shank in early swing. It is thought that

inappropriate activity of the rectus femoris, either in magnitude or in timing, could

result in an excessive knee extension moment and restrict knee flexion in swing

(Perry, 1987). Over-activity of the rectus femoris may be due to a spastic reflex

response triggered by rapid knee flexion near toe-off (Jonkers et al., 2006). Others

have suggested that the spastic response of the rectus femoris could be triggered when

13

the hip reaches maximum extension near terminal stance (Silfverskiold, 1923). In

stroke patients, others have suggested that a multi-joint, heteronymous stretch reflex

triggered by extension of hip extensors may result in inappropriate activation of the

knee extensors (Lewek et al., 2007). These authors found that imposed hip extension

resulted in greater reflex responses of the rectus femoris and vatus lateralis in subjects

with stroke as compared to controls and was correlated with decreased knee flexion

during swing (Lewek et al., 2007).

Figure 2. 1 Rectus femoris, part of the quadriceps muscle group, is a bi-articular muscle generating a hip flexion moment and a knee extension moment. (Copyright 2003-2004, University of Washington. All rights reserved including all photographs and images. No re-use, re-distribution or commercial use without prior written permission of the authors and the University of Washington.)

14

The timing of rectus femoris activity in preswing has been identified as a

contributor to stiff-knee gait. However, rectus femoris over-activity during swing is

generally cited as the cause of stiff-knee gait and is considered as an indication for

surgical treatment (Sutherland et al., 1990; Chung et al., 1997; Miller et al., 1997;

Yngve et al., 2002; Saw et al., 2003; Kay et al., 2004; Muthusamy et al., 2008). Rectus

femoris activity during preswing, before toe-off, has not historically been considered

to cause stiff-knee gait because the rectus femoris is active during this time in

unimpaired subjects at self-selected walking speeds (Perry, 1992; Nene et al., 1999;

Schwartz et al., 2008). However, many subjects with stiff-knee gait walk at slow

speeds and the rectus femoris is not typically active during preswing in unimpaired

subjects walking at slow speeds (Schwartz et al., 2008). Additionally, a recent study

has shown that many subjects with cerebral palsy who walk with a stiff-knee gait

exhibit excessive knee extension moments during preswing, not swing (Goldberg et

al., 2006). Also, it has been observed clinically that inappropriate swing phase rectus

femoris activity exists in patients who do not exhibit a stiff-knee gait (DeLuca et al.,

1997).

Musculoskeletal simulation has provided evidence that preswing rectus

femoris activity can contribute to stiff-knee gait. Simulations of unimpaired gait

demonstrated that sufficient knee flexion velocity at toe-off is necessary to achieve

adequate knee flexion during swing (Piazza and Delp, 1996; Anderson et al., 2004).

Reduced knee flexion velocity at toe-off is exhibited in many individuals with stiff-

knee gait (Goldberg et al., 2006) and can be caused by preswing rectus femoris

activity (Goldberg et al., 2004). Finally, simulations of stiff-knee gait have suggested

15

that restoring knee flexion velocity at toe-off to normal values can restore peak knee

flexion in swing (Goldberg et al., 2003) and that preswing rectus femoris activity is at

least as influential as early swing rectus femoris activity in limiting knee flexion in

swing (Reinbolt et al., 2008, chapter 3 of this dissertation).

Experimental evidence has also demonstrated that preswing rectus femoris

activity can contribute to stiff-knee gait. Electrical stimulation of the rectus femoris

during treadmill walking in unimpaired subjects demonstrated that excessive rectus

femoris activity during preswing caused greater reduction in swing phase peak knee

flexion than excessive rectus femoris activity during swing (Hernandez et al., 2010).

Following injection of botulinum toxin injection into the rectus femoris in adults with

stiff knee gait due to stroke or traumatic brain injury, subjects showed an increase in

knee flexion velocity at toe-off suggesting that preswing rectus femoris activity had

been contributing to stiff-knee gait by limiting knee flexion velocity at toe-off

(Robertson et al., 2009). A group of subjects with cerebral palsy with rectus femoris

activity in preswing demonstrated improved peak knee flexion after rectus femoris

transfer surgery leading the authors to suggest that either rectus femoris activity in

preswing was contributing to stiff-knee gait, or another concomitant surgery had

improved stiff-knee gait (Miller et al., 1997). Collectively, this research suggests that

rectus femoris over-activity during preswing can limit peak knee flexion in swing.

Rectus femoris transfer

Rectus femoris transfer, proposed by Perry (1987) and Gage et al. (1987), is

the most common treatment for stiff-knee gait (Chambers, 2001). The surgical

16

procedure consists of release of the distal end of the muscle with its component of the

quadriceps tendon, dissection away from the underlying vasti, displacement of the

distal end either medially or laterally (depending on intended transfer site), and

reattachment (Gage et al., 1987; Sutherland et al., 1990; Patrick, 1996; Chambers et

al., 1998). Common transfer sites are medial to sartorius, gracilis, or semitendinosus or

lateral to the iliotibial band.

Mechanism of surgical effect

Rectus femoris transfer was developed with the intention of converting the

rectus femoris to a knee flexor while preserving its hip flexion moment (Perry, 1987;

Sutherland et al., 1990). Experimental study of transfer in cadavers combined with

musculoskeletal modeling showed that rectus femoris had a knee flexion moment arm

after transfer to semitendinosus, gracilis, or sartorius, and an insignificant moment arm

after transfer to the iliotibial band (Delp et al., 1994). However, further investigation

of rectus femoris after transfer has suggested that it is not converted to a knee flexor.

Riewald and Delp (1997) stimulated the transferred muscle in four subjects and found

that it generated a knee extension torque in all subjects. A dynamic imaging study

(Asakawa et al., 2002) measured the motion of the transferred muscle during passive

knee movement and found that the transferred rectus femoris displaced with the knee

extensors, meaning that it still acted as a knee extensor after transfer, though its

velocity relative to the knee extensors, signifying its capacity for knee extension, was

diminished by the surgery. A static imaging study (Asakawa et al., 2004; Gold et al.,

2004) found evidence of scar tissue between rectus femoris and the underlying vasti.

17

They also found that the transferred rectus femoris muscle path from origin to

insertion showed an angular deviation, greater than 35 degrees, in most cases. Force

generated by the rectus femoris may be transferred to the vasti through the scar tissue

connection, resulting in a knee extension moment. Finally, a simulation study

demonstrated that if scarred transfer of rectus femoris reduces its knee extension

capacity by half, improvements in peak knee flexion in swing similar to clinically

reported improvement following isolated rectus femoris transfer (Hemo et al., 2007)

may still be achieved (Fox et al., 2009, chapter 4 of this dissertation). These

simulations also showed that simulated force output of rectus femoris after transfer to

the knee flexors, assuming no scarring, was reduced due to the muscle’s conversion

from operating eccentrically to concentrically, since it was stretched when anterior to

the knee but shortened when posterior to the knee during knee flexion at toe-off (Fox

et al., 2009, chapter 4 of this dissertation).

Though it is clear that reducing scar tissue formation is helpful in achieving

good outcomes following rectus femoris transfer, it is unclear how surgical technique

and postoperative rehabilitation affect the formation of scar tissue . Lipaphayom and

Prasongchin (2011) intra-operatively examined the transferred rectus femoris in three

knees during subsequent surgery 7 – 60 months following the rectus femoris transfer.

In contrast to the previously described imaging studies, they observed minimal scar

tissue formation and a smoothly gliding muscle path and elicited knee flexion by

manual pull on the rectus femoris tendon, which they attributed to surgical technique.

In contrast, surgical revision of rectus femoris transfer presented as a case study for a

single patient found significant scar tissue formation after 4 years (Johnson et al.,

18

2011). Improvement in swing phase knee flexion was achieved in this patient after

release of scar tissue and lengthening of the rectus femoris. Some advocate the use of

continuous passive movement machines and early mobilization postoperatively, but

there are no studies comparing the effects of different postoperative rehabilitation

strategies.

Outcomes

Outcomes following rectus femoris transfer surgery are positive on average,

but variable among individuals. As rectus femoris transfer may be performed to treat

diminished peak knee flexion in swing or to prevent a reduction in peak knee flexion

following hamstrings treatment for crouch gait (DeLuca et al., 1997), knee range of

motion is a relevant outcome metric to compare outcomes from studies with and

without concomitant hamstrings surgeries. All rectus femoris outcome data available

for review reported an average improvement in knee range of motion, with the

exception of Carney et al. (2006) which reported no significant difference on average

in 29 limbs. Among the subject groups that showed an average significant

postoperative improvement, the average amount of improvement in knee range of

motion during gait was 12.8 degrees with a range of 4 degrees to 36 degrees. Other

outcome metrics, though less commonly reported, included decreased mean knee

extensor moment in stance (Adolfsen et al., 2007) and increased knee flexion velocity

surrounding toe-off (Hadley et al., 1992; Muthusamy, 2006).

Different effects were observed following rectus femoris transfer with versus

without concomitant hamstrings lengthening. On average among studies in which

19

hamstrings lengthening was performed with rectus femoris transfer, peak knee flexion

in swing was retained while knee extension in stance was increased, resulting in

improved knee range of motion during gait. Following rectus femoris transfer without

hamstrings lengthening, on average peak knee flexion in swing was increased while

knee extension in stance was decreased to a lesser extent or unchanged, resulting in

improved knee range of motion during gait (Miller et al., 1997; Carney et al., 2006;

Hemo et al., 2007). In addition, Miller et al. (1997) reported an increase in knee

flexion at initial contact when rectus femoris transfer was performed without

hamstrings lengthening.

Change in the timing of peak knee flexion in swing is also an important metric

of the success of rectus femoris transfer surgery. All group averages reported in the

studies examined showed either improvement in timing in peak knee flexion in swing

or no significant change. Among the studies that reported a significant improvement,

the average improvement in timing of peak knee flexion was 3.5% of the gait cycle.

Timing of peak knee flexion in swing has been reported as percent of gait cycle or

percent of swing phase. Van der Linden et al. (2003) have suggested reporting the

outcome as percent of gait cycle since the duration of swing phase may change

following treatment. For the studies reporting timing of peak knee flexion as a

percentage of swing phase, these outcomes have been converted to percent of gait

cycle assuming a swing phase duration of 40% of the gait cycle to allow comparison

across all studies.

Reports of long term outcomes following rectus femoris transfer are few and

varied. The largest study of long-term rectus femoris transfer outcomes reported that

20

peak knee flexion and knee range of motion in swing were relatively stable from years

1 to 3 postoperatively in 50 limbs (Moreau et al., 2005). Similarly, Adolfsen et al.

(2007) found improvements after one year to be maintained after 4 years in 9 limbs.

Saw et al. (2003) also reported maintained improvement in swing phase knee flexion

after 4.6 years in 26 limbs, but reported a decrease in total knee range of motion

during gait. In this study, 9 limbs of 5 subjects developed crouch and required

subsequent hamstrings lengthening; many subjects in this study did not receive

concomitant hamstrings lengthening with the original rectus femoris transfer.

Early investigation hypothesized that the choice of rectus femoris transfer site

may provide additional benefit by correcting transverse plane rotational deformities

(Gage et al., 1987). In specific, rectus femoris transfer medially to sartorius or

semimembranosus was hypothesized to create an external rotation moment at the knee

which would improve excessive internal rotation, while lateral transfer to the iliotibial

band was hypothesized to improve excessive external rotation. No significant

rotational effect has been observed after transfer either medially or laterally (Gage et

al., 1987; Nene et al., 1993; Ounpuu et al., 1993a). In the sagittal plane, no significant

difference in transfer sites has been reported comparing changes in peak knee flexion

in swing, knee range of motion, and knee extension at in stance (Ounpuu et al., 1993a;

Chambers et al., 1998). Some studies have reported differences in a single outcome

metric among transfer sites (peak knee flexion in swing or knee extension in stance),

but have suggested that this may be due to disparate proportions of concomitant

hamstrings lengthenings among the different groups (Muthusamy, 2006; Hemo et al.,

2007; Muthusamy et al., 2008). One study, with relatively equal proportions of

21

hamstrings lengthenings in each group, reported greater improvement in peak knee

flexion after transfer to gracilis compared to sartorius (Chung et al., 1997). They

suggest that this improvement may be a result of their revised technique in transferring

rectus femoris to gracilis, although average improvement in knee range of motion in

this study is less than that reported by Ounpuu et al. (1993a).

Limitations with current outcome studies following rectus femoris transfer

include that many studies do not correct for inclusion of data from two limbs per

subject, many studies do not account for differences in walking speed, some studies

statistically evaluate postoperative values without statistically comparing preoperative

values, and some studies do not take into account changes in height in evaluating

temporal-spatial parameters.

Although rectus femoris spasticity is often considered an indication for rectus

femoris surgery, there have been few studies investigating whether rectus femoris

spasticity actually decreases following rectus femoris surgery. The few studies that

have been conducted have used the Duncan Ely test, rather than a more quantitative

measurement, to assess spasticity. Subjects undergoing rectus femoris transfer did not

all have positive preoperative Duncan Ely tests (86%, Kay et al., 2004; 100%, Hemo

et al., 2007; 42%,Koca et al., 2009). The studies that have reported change in Duncan

Ely scores after surgery report variable results between 43% and 85% rates of

spasticity improvement (50%, Kay et al., 2004; 51%, Adolfsen et al., 2007; 85%,

Hemo et al., 2007; 34%, Koca et al., 2009), suggesting that spasticity, as measured by

Duncan Ely test, may improve in some but not all patients after rectus femoris

transfer. Kay et al. (2004) found that in a group that maintained positive Duncan Ely

22

tests before and after surgery, spasticity decreased, measured by Ashworth scale and

angle at which hip rise occurred during Duncan Ely test. More quantitative

measurements of changes in spasticity following surgery and correlation with surgical

outcome are warranted.

Clinical indications

Surgical indications for rectus femoris transfer differ by institution, but

generally include diminished peak knee flexion, delayed peak knee flexion, reduced

knee range of motion, and impaired foot clearance. Abnormal rectus femoris activity,

such as prolonged activity into swing, or continuous activity throughout the gait cycle,

and rectus femoris spasticity, measured during physical exam by a Duncan Ely test

(Bleck, 1987) are also taken into account.

There are limitations to the current clinical indicators. First, clinical measures

of spasticity may be unreliable. The most common clinical measure of rectus femoris

spasticity is the Duncan Ely test. In this test, the patient lies prone with the hips

extended while the knee is gradually flexed to 130 degrees. If the hip flexes, causing

the buttocks to rise from the table, the rectus femoris is considered spastic. There is

concern that the Ely test may not isolate rectus femoris activity, as iliopsoas activity

may also result in a positive test (Sutherland et al., 1975; Perry et al., 1976). Chambers

et al. (1998) found that the Duncan Ely test had no predictive value for abnormal

rectus femoris activity during gait. Marks et al. (2003) also questioned the relationship

between the Duncan Ely test and kinematic and electromyographic indicators of stiff-

knee gait, though they caution that the high prevalence of rectus femoris dysfunction

23

in their subject population may have affected their results. Another limitation of

current assessment for spasticity during clinical exam is that it may not correlate with

spasticity during gait. Sutherland et al. (1975) noticed anecdotally that a large number

of spastic patients demonstrated a positive Duncan Ely test yet did not exhibit

functional limitations during gait. Kerrigan et al. (1999) observed patients with

quadriceps spasticity on static evaluation that had normal activity during walking. One

possible explanation is that subjects may walk slowly enough to avoid eliciting a

spastic rectus femoris response during gait.

A more useful evaluation of the utility of Duncan Ely may be its predictive

value of outcome after treatment. Some studies have found Duncan Ely to have no

predictive value for surgical outcome (Goldberg et al., 2006; Muthusamy, 2006;

Muthusamy et al., 2008). In contrast, Kay et al. (2004) found Duncan Ely may be a

helpful predictor of outcome after rectus femoris transfer since knee range of motion

and timing of peak knee flexion improved on average only in the group of subjects

with a positive Duncan Ely tests. However, these are average improvements, and

outcomes may vary for individual patients. Other measures of spasticity, including the

Ashworth and modified Ashworth scales, the Tardieu scale, and the pendulum test, do

not isolate rectus femoris spasticity. Better measures of spasticity are required to

evaluate the effects of rectus femoris spasticity on stiff-knee gait and outcomes after

rectus femoris transfer.

Another limitation of current clinical indicators for rectus femoris transfer is

that the usefulness of preoperative rectus femoris activity, measured by EMG, is

unclear. Rectus femoris activity during swing has been observed in conjunction with

24

normal knee kinematics (DeLuca et al., 1997). Several studies reported that rectus

femoris EMG does not have predictive value for surgical outcomes (Chambers et al.,

1998; Saw et al., 2003; Muthusamy, 2006; Muthusamy et al., 2008). In contrast,

Miller et al. (1997) suggested that rectus femoris EMG does have predictive value

since a group with swing phase rectus femoris EMG had greater average improvement

in peak knee flexion than a group with normal rectus femoris EMG; however, they did

not report differences in preoperative peak knee flexion between the groups, and there

was a small number of subjects in each group. Barr et al. (2010) has cautioned using

surface EMG to measure rectus femoris activity, as it can be subject to crosstalk from

the vasti, particularly during a crouch gait at fast speeds.

Additional clinical indicators have been explored to identify subjects that need

rectus femoris transfer. Reduced preoperative knee range of motion during gait has

been suggested as a predictor for positive outcomes after rectus femoris transfer

(Ounpuu et al., 1993b; Chung et al., 1997; Niiler et al., 2007), though Chambers et al.

(1998) found no relationship between preoperative and postoperative knee range of

motion. Knee flexion velocity at toe-off has been suggested as a possible indicator for

rectus femoris surgery (Muthusamy et al., 2008), though some report greater

improvements in subjects with low knee flexion velocities (Muthusamy, 2006), while

others report greater improvement with high knee flexion velocities (Reinbolt et al.,

2009). Neither of these studies accounted for confounding variables, such as overall

severity, in their analyses, which may contribute to the discrepancy. Goldberg et al.

(2006) found that increases in knee flexion velocity at toe-off were associated with

improvements in stiff-knee gait. Vasti over-activity has been investigated as a

25

contraindication for rectus femoris transfer. Chambers et al. (1998) and Sutherland et

al. (1990) found no difference in outcomes among subjects with cerebral palsy with

and without concomitant abnormal vasti activity. In contrast, Waters et al. (1979)

reported that the amount of improvement in stroke patients with stiff-knee gait

following release of rectus femoris, and vastus intermedius in some subjects, was

dependent on the component of the quadriceps that showed inappropriate EMG in

swing.

Rectus femoris release

Rectus femoris release was developed before rectus femoris transfer as a

treatment for stiff-knee gait, with the intent of improving knee flexion in swing

(Silfverskiold, 1923; Sutherland et al., 1975). It was originally performed as a

treatment for hip flexion contracture (Duncan, 1955; Cottrell, 1963; McMulkin et al.,

2005), and secondarily knee flexion deformity (Duncan, 1955; Cottrell, 1963). Rectus

femoris release may be performed distally or proximally. Concern over the negative

effects of proximal release on hip and pelvis motion (Sutherland et al., 1975) led to the

adoption of distal release (Perry, 1987). The surgery involves dissection of the rectus

femoris away from the underlying vasti, and dissection of the tendon from its

insertion, either proximally or distally. Gage et al. (1987) proposed that inferior results

following rectus femoris release may be due to the muscle retaining its ability to

generate a knee extension moment, possibly due to reattachment to the quadriceps

through scar tissue formation.

26

Outcomes following rectus femoris release are inferior to rectus femoris

transfer. Studies of outcomes after distal rectus femoris release, with many subject

receiving concomitant hamstring lengthening, have reported no changes in knee range

of motion during gait (Ounpuu et al., 1993b; Chambers et al., 1998) and either no

change (Chambers et al., 1998) or a decrease (Ounpuu et al., 1993b) in peak knee

flexion after lengthening. Sutherland et al. (1975) reported increased knee flexion in

swing in six of eight subjects following proximal rectus femoris release, though

outcomes were variable and improvements limited. After distal rectus femoris release

without hamstring lengthening, Sutherland et al. (1990) reported an average increase

in peak knee flexion in swing and knee range of motion during gait, though both were

smaller than improvements after rectus femoris transfer. Studies reported no

improvement on average in timing of peak knee flexion in swing following release

(Sutherland et al., 1990; Ounpuu et al., 1993b; Chambers et al., 1998). Some studies

report that release was accompanied by an increase in crouch (Sutherland et al., 1975),

though others have not observed this (Sutherland et al., 1990; Chambers et al., 1998).

In an adult stroke population undergoing proximal rectus femoris release without

hamstrings lengthening (Waters et al., 1979), average improvement in peak knee

flexion (9.6 degrees) was comparable to rectus femoris distal release combined with

hamstrings lengthening in patients with cerebral palsy (9.1 degrees, Chambers et al.,

1998). The degree of improvement in this stroke population was dependent on the

component of quadriceps that showed inappropriate EMG in swing (i.e., if rectus

femoris was the only active head, improvements were greater).

27

Rectus femoris lengthening

The literature describing rectus femoris lengthening to treat stiff-knee gait is

sparse. Others have described rectus femoris lengthening in an effort to treat hip or

knee flexion deformities (Matsuo et al., 1987; Guerado and de la Varga, 2001), but

there is no journal article describing rectus femoris lengthening to treat stiff-knee gait.

In rectus femoris intramuscular lengthening surgery, incisions are made into the

aponeurosis, the portion of the tendon connected to the muscle fibers. The intended

effect is reduction of muscle spasticity by decreasing the lengthening velocity of the

muscle fibers. The procedure is less invasive than rectus femoris transfer and requires

less dissection, potentially allowing reduced postoperative pain, earlier postoperative

mobilization, and reduction of complications.

The effectiveness of this surgery on the treatment of stiff-knee gait is currently

unclear as there has been only a preliminary report of outcomes. A conference abstract

has reported outcomes following rectus femoris intramuscular lengthening in 72 knees

of 43 subjects, most of which received concomitant hamstrings lengthening (Cruz et

al., 2009). The authors conclude that outcomes are similar to rectus femoris transfer

with an average 2% of gait cycle improvement in timing of peak knee flexion and an

average 2-degree improvement in knee range of motion during gait, though there was

variability among subjects. Rectus femoris lengthening may be an attractive

alternative to rectus femoris transfer if it proves to be as effective, but additional study

is needed to quantify its effectiveness.

28

Neuromuscular block

Injection of neuromuscular toxins into the rectus femoris may be used for

temporary evaluation of treatment options or for longer-term treatment. Temporary

treatments, such as lidocaine, are injected into the vicinity of the target nerve to block

activation of the muscle. For more long term treatment, phenol may be used to destroy

the nerve fibers or botulinum toxin may be injected to inhibit the release of

acetylcholine from the neuromuscular junction (Burgen et al., 1949).

Almost all outcome studies of nerve or motor point block of rectus femoris

have been conducted in the adult population. The only study reporting outcomes after

botulinum toxin injection to rectus femoris in subjects with cerebral palsy found no

appreciable change in dynamic knee range of motion in eight subjects (Chambers,

2001). In stroke, early reports of nerve block to treat stiff-knee gait were generally

unsuccessful in improving knee flexion and left some patients too unstable to walk

(Mooney and Goodman, 1969; Treanor, 1969). More recently, Albert et al. (2002)

performed femoral nerve block in 12 subjects with stiff-knee gait due to CNS injury

and also reported no improvement in gait parameters. However, the majority of

outcome reports following nerve block of rectus femoris report positive impact on

stiff-knee gait. Average improvement in peak knee flexion has been reported

following lidocaine (15 degrees, Sung and Bang, 2000; 11 degrees, Robertson et al.,

2009), phenol (9 degrees, Sung and Bang, 2000) , and botulinum toxin injections (5

degrees, Stoquart et al., 2008; 8 degrees, Robertson et al., 2009). Chantraine et al.

(2005) found an average 5 degree increase in knee range of motion among 6 subjects

after motor branch block with lidocaine. Caty et al. (2008) reported increased peak

29

knee flexion by an average of 5 deg in 20 stroke subjects after botulinum toxin into a

combination of rectus femoris, semitendinosus, and triceps surae.

Most studies report average improvements in knee flexion velocity at toe-off

after injection of lidocaine (0.9 degrees per percent gait cycle, Sung and Bang, 2000;

43 degrees per second, Stoquart et al., 2008), phenol (0.47 degrees per percent gait

cycle, Sung and Bang, 2000), and botulinum toxin (30 degrees per second, Stoquart et

al., 2008; 53 degrees per second, Robertson et al., 2009). In contrast, Chantraine et al.

(2005) found no improvement on average in knee flexion velocity at toe-off among six

subjects after motor branch block with lidocaine. No improvement was measured in

maximum preswing knee moment among subjects (Chantraine et al., 2005) or peak

moments at hip, knee, or ankle (Robertson et al., 2009). However, Robertson et al.

(2009) described two subjects who had excessive preoperative knee extension

moments in preswing that were maintained following botulinum toxin injection, yet

they were able to attain normal peak knee flexion. Duncan Ely scores improved after

nerve block in stroke subjects (Chantraine et al., 2005; Caty et al., 2008; Stoquart et

al., 2008).

Some undesired secondary effects after injection of neuromuscular blocks,

though infrequent, have been reported including weakness of quads or knee buckling

during stair climbing (Sung and Bang, 2000), and one subject whose gait changed

from crouch to jump knee with no improvement in swing phase knee flexion

(Chantraine et al., 2005). Another secondary effect reported after Botulinum toxin

injection into rectus femoris was a reduction in vastus lateralis and biceps femoris

activity (Stoquart et al., 2008). There is debate over whether results of nerve block of

30

rectus femoris depend on activity present in other heads of the quadriceps. Sung and

Bang (2000) reported preswing to midswing quadriceps EMG activity confined to

rectus femoris seemed to result in more improved outcomes in 31 subjects, while

Chantraine et al. (2005) found no relationship in 6 subjects. Severity of quadriceps

spasticity, measured by Ashworth scale, did not influence nerve block effect (Sung

and Bang, 2000). There is also disagreement over whether preoperative knee range of

motion influences outcome following nerve block. Stoquart et al. (2008) reported 4

out of 19 subjects who had less than 10 degrees of knee range of motion before

injection did not improve, whereas Caty et al. (2008) found that higher dosage

injection of botulinum toxin into multiple muscles improved swing phase knee flexion

in subjects with less than 10 degrees of knee range of motion.

2.2.2 VASTI OVER-ACTIVITY

Over-activity of the vasti is a less commonly proposed cause of stiff-knee gait

in patients with cerebral palsy. In cerebral palsy, rectus femoris is more frequently

over-active during gait than the vasti (Csongradi et al., 1979; Sutherland et al., 1990;

DeLuca et al., 1997; Chambers et al., 1998). However, over-activity of the vasti could

increase the knee extensor moment and decrease toe-off velocity at toe-off, similar to

over-activity of the rectus femoris. Musculoskeletal simulation of unimpaired gait has

identified the vasti as having a large potential to decrease knee flexion velocity during

double support (Goldberg et al., 2004).

Experimental evidence suggesting vasti over-activity as a cause of stiff-knee

gait is sparse. Gage et al. (1987) stated that reflex activity in vastus medialis may

31

contribute to stiff-knee gait, but provided no surgical results. In the stroke population,

Kerrigan et al. (1991) observed prevalent inappropriate vasti activity in preswing and

early swing and concluded that this prevalence implied a relationship with stiff-knee

gait; however neither a correlation nor causal relationship was examined. Also in the

stroke population, Waters et al. (1979) performed tenotomy of one or 2 heads of the

quadriceps, based on inappropriate muscle activity during swing. They found that

improvement in swing phase peak knee flexion was larger when all heads of the quads

with inappropriate activity were released, suggesting that vasti may contribute to stiff-

knee gait. However, it should be noted that the group with inappropriate muscle

activity in fewer heads of the quadriceps may have been less involved, which may

have contributed to the difference in outcomes between the groups. In opposition to

this evidence, Chambers et al. (1998) found no difference in outcome of subjects with

cerebral palsy after rectus femoris surgery (transfer in most, release in others) between

a group with only abnormal rectus femoris activity alone and a group with abnormal

activity in both rectus femoris and vastus lateralis.

The vasti are not a common target of treatment for stiff-knee gait in cerebral

palsy, and there is no quantitative report of outcomes following vasti treatment in

cerebral palsy. It has been suggested that surgical treatment of the vasti may

compromise knee stability in stance (Sutherland et al., 1975; Waters et al., 1979).

Namdari et al. (2010) performed rectus femoris transfer with vastus lengthening in 37

subjects with stiff-knee gait due to stroke or traumatic brain injury and reported an

average increase of 25 degrees in peak knee flexion in 21 subjects. Hebela and Keenan

(2004) described fractional lengthening of over-active vasti in subjects with upper

32

motor neuron syndromes, but did not report quantitative outcomes. Waters et al.

(1979) performed tenotomy of one or two heads of the quadriceps in unilateral stiff-

knee stroke subjects, based on inappropriate muscle activity during swing. They

reported variable changes in swing phase peak knee flexion with an average of 10

degrees and a range of -21 to 30 degrees.

2.2.3 ANKLE MECHANICS

Another proposed cause of stiff-knee gait is abnormal ankle mechanics. Two

mechanisms have been proposed describing how abnormal ankle mechanics may limit

knee flexion in swing. The first is walking in equinus, or excessive ankle

plantarflexion. Kerrigan et al. (2001a) reported that normal subjects performing toe-

walking experienced a significant reduction in peak knee flexion (from 59 to 42

degrees), suggesting that toe-walking may contribute to stiff-knee gait. They also

acknowledged that not all patients who toe-walk have stiff-knee gait.

The second mechanism proposed in the literature is that insufficient ankle

plantarflexion moment before toe-off may limit swing phase knee flexion through

dynamic coupling. Many stiff-knee subjects have diminished ankle plantarflexion

moments (Kerrigan et al., 2001b; Goldberg et al., 2006; Robertson et al., 2009).

However, Goldberg et al. (2006) noted that ankle plantarflexion moments during

double support did not correlate with knee flexion velocity at toe-off in 23 subjects

with stiff-knee gait and cerebral palsy. It is unclear whether low plantarflexion

moments might be due to weak gastrocnemius or weak soleus which have potentially

contradictory effects on knee motion.

33

The effect of preswing plantarflexion moment on swing phase knee flexion is

unclear. Though simulation studies of normal gait agree that soleus activity in

preswing accelerates the knee into extension (Yamaguchi and Zajac, 1990; Neptune et

al., 2001; Fox and Delp, 2010, chapter 5 of this dissertation), simulation evidence for

gastrocnemius function has been more variable. Fox and Delp (2010, chapter 5 of this

dissertation) found that gastrocnemius induced a small knee flexion acceleration,

though its effect on the knee was variable, while Yamaguchi and Zajac (1990)

reported a large knee flexion effect. Neptune et al. (2001) found that gastrocnemius

contributed to knee extension acceleration in preswing. Since the bi-articular

gastrocnemius generates both a plantarflexion moment that induces knee extension

acceleration and a knee flexion moment that induces knee flexion acceleration, its

action is sensitive to the muscle’s ankle and knee moment arms, body position, and

foot contact model, which varied among the studies.

Experimental study using surface electrodes to stimulate muscle during gait

(Stewart et al., 2007) found that soleus caused ankle plantarflexion and knee extension

while gastrocnemius caused ankle dorsiflexion and knee flexion during preswing in

five adult subjects. Riley and Kerrigan (1999) used simulation to investigate the effect

of plantarflexion moment on the knee in stiff-knee stroke subjects, but did not account

for the effect of the portion of the ground reaction force that was induced by the ankle

moment on the knee.

Although the net effect of the plantarflexors may be to extend the knee, studies

have suggested that they play a role in swing initiation. It has been observed that hip

flexors compensate during preswing when plantarflexors are weak due to stroke

34

(Nadeau et al., 1999) or absent due to amputation (Zmitrewicz, 2007). Neptune et al.

(2008) suggested that gastrocnemius contributes to swing initiation by delivering

energy to the preswing leg. Van der Krogt et al. (2010) created forward dynamic

simulations of stable cyclic walking and found that magnitude of the push off impulse

increased swing phase knee flexion. Evidence for ankle plantarflexion moment deficiency as a cause of stiff-knee

gait has been presented in the stroke population. Kerrigan and Glenn (1994) conducted

an interventional study in a spinal cord injury patient who walked with a stiff-knee

gait. The patient was treated with an ankle-foot orthosis to resist dorsiflexion and an

exercise program to strengthen gastrocnemius and soleus. After two weeks, the patient

showed improved peak knee flexion (from 22 to 35 degrees) though still diminished

from normal, while walking speed remained unchanged. Plantarflexion strength was

not shown to be increased by manual muscle test, but ankle plantarflexion moment in

preswing was increased. It is unclear whether the follow-up gait analysis was

conducted with or without the prescribed ankle-foot orthosis. In another study,

Kerrigan et al. (1991) also observed delayed heel rise in 21 of 23 subjects with stiff-

knee gait due to stroke or head injury. The authors proposed that delayed heel rise may

be indicative of plantarflexor weakness and proposed a relationship between delayed

heel rise and peak knee flexion in swing, though no quantitative correlation was

performed. Since no intervention was performed, it is unclear whether delayed heel

rise was a cause of stiff-knee gait, a compensation, or an unrelated abnormality. More

research is needed to understand the functions of soleus and gastrocnemius in swing

35

initiation and to determine whether dysfunction of either muscle can contribute to

stiff-knee gait.

2.2.4 INSUFFICIENT HIP FLEXION MOMENT

Insufficient hip flexion moment has been proposed as a cause of stiff-knee gait

in stroke patients (Kerrigan et al., 1999). Through dynamic coupling, a hip flexion

moment induces a knee flexion acceleration. Simulation studies agree that adequate

preswing hip flexion moment is important for knee flexion in swing in normal gait

(Yamaguchi and Zajac, 1990; Piazza and Delp, 1996; Neptune et al., 2008; Fox and

Delp, 2010, chapter 5 of this dissertation). The preswing hip flexion moment is not

generally diminished among stiff-knee subjects, but there is variability among

subjects. All 23 subjects with stiff-knee gait and cerebral palsy in a study by Goldberg

(2006) had both preswing and swing phase hip flexion moments that were within two

standard deviations of normal. In fact, many subjects had excessive hip flexion

moments in double support, which the authors suggested could be due to a delay in

peak hip flexion moment which normally occurs before double support. In populations

of subjects with stiff knee gait due to stroke (n = 10, Robertson et al., 2009) and TBI

(n = 20, Kerrigan et al., 2001b) preswing hip moments were within normal limits.

If insufficient hip flexion moment is a contributor to stiff-knee gait, possible

interventions may include hip flexor strengthening exercises, biofeedback focused on

hip flexion, and strategies to electrically stimulate the hip flexors (Kerrigan and Riley,

1998). Kerrigan and Riley (1998) reported that in a single stiff-knee stroke subject

who underwent daily hip flexor strengthening, knee flexion during swing improved

36

nine degrees after two months; however, the authors did not provide quantitative

evidence that hip flexor strength increased.

2.2.5 HAMSTRINGS OVER-ACTIVITY

Two other mechanisms have been proposed by which hamstrings over-activity

may contribute to stiff-knee gait including 1) hamstrings over-activity could generate

an excessive hip extension moment and 2) hamstrings over-activity could limit knee

velocity during swing.

Kerrigan et al. (1999) postulated that inappropriate hamstrings activity during

preswing or early swing could contribute to stiff-knee gait in stroke subjects by

generating an excessive hip extension moment. Musculoskeletal simulation suggests

that the effect of hamstrings activity on knee motion may vary throughout the gait

cycle. Simulation studies have shown that the hamstrings contribute to knee extension

during single limb support (Arnold et al., 2005; Hicks et al., 2008) and early swing

(Arnold et al., 2007b) in unimpaired gait and crouch gait (Hicks et al., 2008) and,

therefore, may limit knee extension in swing during these periods. In contrast, during

double support, hamstring activity contributes to knee flexion velocity at toe-off in

normal gait (Goldberg et al., 2004). More work is required to investigate the

contributions of hamstrings to knee flexion in impaired gait. It should be recognized

that interpretation of bi-articular muscle activity in simulations is dependent on the

modeled ratio of moment arms of the muscle at each joint and the foot floor contact

model used during the analysis.

37

It has also been proposed that hamstrings spasticity may limit knee flexion in

swing indirectly. Tuzson et al. (2003) showed that maximum knee flexion velocity

(occurring in preswing) was correlated with maximum knee extension velocity

(occurring in terminal swing) in 18 children with cerebral palsy (r = .94, p < .001). It

has been suggested that stable walking requires this symmetry (Mcgeer, 1990). If so, it

is possible that a limitation of knee extension velocity, due to hamstrings over-activity

in terminal swing, may cause a patient to walk with reduced knee flexion velocity at

toe-off to maintain symmetry, resulting in a stiff-knee gait. Tuzson et al. (2003)

measured the minimum knee angular velocities at which a spastic response was

elicited or spastic threshold velocity, in the quadriceps and hamstrings muscle groups

of subjects with cerebral palsy. In subjects with spastic responses in both the

quadriceps and hamstrings muscle groups, the lower spastic threshold velocity of the

two muscle groups was correlated with knee angular velocity during walking (Cheung

et al., 2003; Tuzson et al., 2003). These results suggest that stiff-knee subjects may

reduce their knee flexion velocity at toe-off to match the spastic threshold of their

hamstrings in terminal swing.

Whether either mechanism enables the hamstrings to contribute to stiff-knee

gait, there has been a lack of clinical evidence of hamstrings involvement in stiff-knee

gait. Kerrigan et al. (1991) compared kinematics between two groups of stroke

subjects (one with preswing hamstring activity and one without) with stiff-knee gait,

most of whom had inappropriate rectus femoris activity, and did not find a difference

in preswing or peak knee flexion between the groups. The only clinical evidence

supporting hamstrings as a cause of stiff-knee gait is in the stroke population. Kerrigan

38

and Riley (1998) performed a temporary intramuscular neurolysis of the hamstrings in

one stiff-knee stroke subject with inappropriate hamstrings activity which resulted in a

five degree increase in peak knee flexion in swing.

Although there is a lack of understanding of how hamstrings may contribute to

stiff-knee gait, it has been repeatedly reported clinically that hamstrings lengthening

can induce stiff-knee gait. There have been many reports of stiff-knee induced by

hamstrings lengthening without rectus femoris surgery (Gage et al., 1987; Thometz et

al., 1989; Damron et al., 1993; Nicholson, 2000). Van der Linden et al. (2003)

reported peak knee flexion was decreased on average in 32 limbs of 18 subjects with

hamstrings lengthening without rectus femoris surgery, but when walking speed was

accounted for, the postoperative peak knee flexion was at least 100% of normal peak

knee flexion for slower speeds, suggesting the importance of accounting for walking

speed when reporting outcomes. Hsu et al. (1990) reported 10 out of 49 hamstrings

lengthening patients developed stiff-knee gait postoperatively, but also reported that

all cases of stiff-knee gait resolved with physical therapy. Goldberg et al. (2004)

proposed that hamstrings lengthening could lead to stiff-knee gait by reducing the

force output of the hamstrings which they showed contributed to knee flexion velocity

at toe off.

Though there are no commonly employed treatments for hamstrings as a cause

of stiff-knee gait in cerebral palsy, Kerrigan et al. (1999) suggested if reduced hip

flexion and power generation are observed in concert with inappropriate hamstrings

activity, a temporary motor point block may be used in the hamstrings to determine

their involvement in stiff-knee gait. If the motor point block improves swing phase

39

knee flexion, they recommend stretching exercises for the hamstrings. They

recommend against permanent block to the hamstrings due to concern for stance phase

stability.

2.2.6 CROUCH GAIT

Although the precise nature of the interaction between crouch gait and stiff-

knee gait is not well-defined, there is much evidence that the two conditions may be

related. Many authors have observed quadriceps and hamstrings spasticity frequently

occur together (Csongradi et al., 1979; Gage et al., 1984; Gage, 1990). Outcomes

following treatment for crouch and stiff-knee gait also appear to be related. Csongradi

et al. (1979) observed both the development of crouch following rectus femoris release

and the development of hyperextended knee gait following hams transfer or

lengthening. Many studies confirm the finding of stiff-knee gait resulting from

hamstrings lengthening without concomitant rectus femoris transfer (Gage et al., 1987;

Thometz et al., 1989; Hsu and Li, 1990; Damron et al., 1993; Nicholson, 2000).

Studies of hamstrings lengthening with rectus femoris transfer report improved knee

range of motion and knee extension in stance (Hadley et al., 1992; Nene et al., 1993;

Rethlefsen et al., 1999; Yngve et al., 2002; Carney and Oeffinger, 2003; Park et al.,

2009).

It has been suggested that crouch gait may play a role in contributing to stiff

knee gait. Three mechanisms have been proposed by which crouch gait may contribute

to stiff-knee gait. The first mechanism proposes hamstrings spasticity, a commonly

40

cited cause of crouch gait, may contribute directly to stiff knee gait. The evidence for

this mechanism has been presented previously in this article.

The second mechanism proposes that excessive quadriceps activity in

preswing, either of the vasti or rectus femoris, necessary to achieve the high knee

extension moments required to hold the body upright in a crouched posture, may limit

the knee flexion acceleration necessary in preswing to achieve normal knee flexion in

swing. Lin et al. (2000) observed an increase in both preswing knee extension moment

and rectus femoris activity in subjects with cerebral palsy walking in a crouch gait,

defined as increased knee flexion throughout stance phase, as compared to subjects

with cerebral palsy not walking with a crouch gait pattern. Goldberg et al. (2006) also

noted excessive knee extension moments in double support in 17 of 23 subjects with

stiff knee gait. They reported that some subjects walked with excessive stance phase

knee flexion, though they did not report the incidence of preoperative crouch gait.

They also noted that decreases in the average knee extension moment in double

support were associated with improvements in stiff-knee gait.

One argument against this proposed mechanism is that unimpaired subjects

walking in a voluntary crouch gait (van der Krogt et al., 2007) or a crouch gait

induced by exoskeleton (Matjacic and Olensek, 2007) do not exhibit reduced or

delayed peak knee flexion during swing. One counter argument to this is that it is not

known whether unimpaired individuals may be able to compensate in ways that

individuals with cerebral palsy may not, therefore achieving adequate swing phase

knee flexion despite decreased knee flexion acceleration in preswing. Another counter

argument is that muscle relaxation rates in individuals with cerebral palsy may be

41

delayed compared to typically developing individuals, which may prolong the

excessive knee extension moment and interfere with the transition to knee flexion

acceleration. Tammik et al. (2008) reported significantly longer relaxation times in

quadriceps of children with spastic diplegia compared to age-matched controls.

Downing et al. (2009) also found a decreased rate of net knee extension moment

relaxation in subjects with cerebral palsy compared to able-bodied controls.

Clinical evidence of the relationship between excessive knee extension

moments in crouch and stiff knee gait is inconclusive. Both Gage et al. (1987) and

Goldberg et al. (2006) observed residual stance phase knee flexion in subjects with

poor outcomes following rectus femoris transfer, but it is not clear from either study

whether the residual crouch posture was causing the stiff-knee gait or rather was

coexisting with the stiff-knee gait.

The final mechanism proposes that the passive dynamics of crouch gait can

result in diminished knee flexion in swing. This mechanism was proposed by van der

Krogt et al. (2010) who created a simulation of cyclic walking using a two-

dimensional simple model with a passive swing knee. They initially set both knees at a

certain degree of knee flexion, locked the stance knee, and applied an external “push-

off” impulse to the swing limb. They also employed methods to prevent swing limb

hyperextension and represent foot contact. Some limitations of this approach included

non physiological kinematics such as a rigid ankle, no knee flexion velocity at toe-off,

and zero degrees of knee flexion throughout stance in the normal simulation. They

noticed that with increasing degrees of initial knee flexion angle, or crouch severity,

the simulated peak knee flexion in swing was increasingly diminished. They explained

42

that this was due to a decrease in the contribution of gravitational force to knee flexion

during swing with more crouched postures.

Earlier simulation studies investigated gravitational contribution to swing

phase knee flexion (Anderson et al., 2004) and knee flexion acceleration (Arnold et

al., 2007b) in normal gait using a three-dimensional model. These studies found that

gravity did not contribute substantially to peak knee flexion during swing because it

accelerated all of the segments of the swing limb, including the swing-limb side of the

pelvis, downward nearly uniformly. They recognized that using a model in which the

trajectory of the hip was prescribed, would have resulted in a substantial contribution

from gravity knee extension. The model created by van der Krogt et al. (2010) could

be considered a fixed hip flexion trajectory, since the stance leg was locked and two-

dimensional motion did not allow for pelvic list, however their results describe gravity

inducing knee flexion during swing rather than knee extension as proposed by

Anderson et al. (2004) and Arnold et al. (2007b). It is hard to generalize the results of

the simple model study to human walking in the presence of many non-physiologic

assumptions and simplifications.

2.2.7 OTHER POTENTIAL CAUSES

It is possible that other biomechanical abnormalities may contribute to stiff-

knee gait. The effects of patella alta on the moment arm of the quadriceps has been

studied (Ward et al., 2005; Sheehan et al., 2008; Luyckx et al., 2009) but it remains

unclear whether patella alta affects the moment arm of the knee extensors and could

contribute to stiff-knee gait. Others have suggested that femoral anteversion could lead

43

to increased rectus femoris stretch and cause stiff-knee gait (Piccinini et al., 2009;

Cimolin et al., 2010), but the effect has not been adequately investigated.

2.3 METHODOLOGY: USING SIMULATION TO UNDERSTAND MUSCLE

FUNCTION

Modeling and simulation are valuable tools for understanding muscle function

in gait. Dynamic simulation allows us to quantify the contribution of muscle forces to

joint motion, which can be unintuitive since muscles contribute to motion of joints that

they do not span and bi-articular muscles can accelerate joints in a direction opposite

of that assumed by anatomy (Zajac and Gordon, 1989). Simulation is also a valuable

tool in representing the extremely complex interactions that are necessary to generate

motion. Neural excitations from the brain or spinal cord activate muscles by causing a

diffusion of calcium ions in muscle fiber cells. Activated muscle fibers then generate

force which is dependent upon the level of activation, the length of muscle fibers, the

velocity at which the muscle fibers contract or lengthen, and other factors. Fiber forces

are transmitted across tendons to the bones. Muscle forces are applied across joints

creating joint moments. Joint moments affect the motion of all the joints in the body,

resulting in motion. In addition, reaction forces occur when the body contacts objects

in the environment. Simulation allows representation and investigation of these

complex interactions.

44

2.3.1 SIMULATION OF GAIT

In this dissertation, we used a model with 12 rigid segments, 21 degrees of

freedom and 92 muscle-tendon actuators to represent the human musculoskeletal

system (Delp et al., 1990). The position and orientation of the pelvis segment with

respect to ground were defined by six degrees of freedom. The head, arms and torso

were represented by a single rigid segment articulating with the pelvis by a ball-and-

socket joint. Each hip was modeled as a ball-and-socket joint, each knee as a planar

joint with tibiofemoral and patellofemoral kinematics defined by knee flexion angle

(Delp et al., 1990), and each ankle and subtalar joint as revolute joints (Inman, 1976).

Muscle paths were represented by line segments, with multiple lines of action for

muscles with broad attachments. Wrapping surfaces and via points represented

interaction of the muscle path with bone surfaces and soft tissue. Muscle force-

generating properties were represented with a lumped parameter model that accounted

for muscle force as a function of the muscle fiber length, muscle fiber velocity, tendon

length, and activation.

Simulations were generated using a four-step process. First, the

musculoskeletal model is scaled to match the subject’s anthropometry. This includes

scaling the segment lengths, masses, and inertias. Muscle and tendon lengths are also

scaled such that the ratio of muscle length to tendon length is maintained. Next,

inverse kinematics is applied to determine the set of joint angle trajectories over time

that minimize the least-squares distance between model markers and experimental

markers over the duration of the motion. Forces generated by the feet contacting the

ground, known as ground reaction forces, are measured during experimental data

45

collection. Due to inaccuracies in the model and errors in experimental measurement

of body motion and ground reaction forces, the model’s motion is not dynamically

consistent with the measured ground reaction force, i.e., maF ≠ . To make the

simulation dynamically consistent, a residual elimination algorithm is implemented,

which solves for the joint moments required to track the model’s motion while

measured ground reaction forces are applied, allowing small deviations in kinematics

to eliminate dynamic inconsistencies (Thelen and Anderson, 2006). An alteration on

this algorithm is residual reduction algorithm, which reduces rather than eliminates the

non-physical residual forces and moments resulting from dynamic inconsistency (Delp

et al., 2007). This modified algorithm, which was used in Chapter 5, prevents

excessive flexion and rotation of the torso segment that can be induced by the residual

elimination algorithm. The next step is to determine the individual muscle excitations

that generate the net joint moments that drive the model’s motion. This is

accomplished using the computed muscle control algorithm (Thelen et al., 2003). This

algorithm applies a feedback controller and an optimizer to choose the set of muscle

excitations that minimizes the sum of squared muscle activations that sufficiently

tracks the motion. The end result is a set of muscle excitation trajectories over time

that accurately reproduces the measured motion when applied to the musculoskeletal

model in concert with the ground reaction forces. The simulated muscle excitations are

compared to experimentally collected muscle electromyographic data to determine

how well the simulated muscle activity represents the measured muscle activity. If

inconsistencies are observed, simulated muscle excitations are constrained and

46

computed muscle control is reapplied. This step is repeated until the resulting

kinematics, kinetics, and muscle activity satisfactorily represent the experimental data.

2.3.2 ANALYSIS OF SIMULATIONS

In all three of the studies presented in this dissertation, forward dynamic

simulation was used to create altered simulations after making changes to muscles in

the unaltered simulation in order to analyze muscle function. This was done in

different contexts, with different simulations, to answer specific clinical questions. In

all cases, altering muscle force in a simulation requires a foot-floor contact model to

account for the resulting change in the ground reaction force. In all of these studies,

linear and rotational spring-damper elements were used to model the change in the

ground reaction force. The spring-damper elements were attached to the center of

pressure of the foot, or the point at which the resultant of the ground reaction force is

applied. As the change in the muscle force alters the path of the foot in the altered

simulation, the spring-damper elements apply a force and torque, proportional to

deviations in foot position and velocity, to the foot in the perturbed simulation that

pull it toward the position of the foot in the unaltered simulation. A scaling function is

used to apply these spring-damper forces smoothly as the foot transitions in and out of

contact with the ground and as the foot rotates in and out of foot-flat position.

The studies outlined in chapters 3 and 4 perform large changes to muscles in the

altered simulation and compare the resulting kinematics to the unaltered simulation to

determine the effect on knee motion. In contrast, the study presented in chapter 5

employs very small perturbations to muscle force in order to more precisely quantify

47

contributions of muscles to knee motion at specific time points throughout the gait

cycle. This technique is known as perturbation analysis (Liu et al., 2006b). Although

we used this method, other analysis methods have been employed to investigate

muscle function in gait (Anderson and Pandy, 2003; Hamner et al., 2010; Lin et al.,

2011). Using perturbation analysis, the contribution of the force of a muscle m to the

acceleration of a joint at time it , )( im tx&& , is determined by calculating the sensitivity,

m

m

Fx

∂∂ && , of the joint acceleration to force generated by muscle m and then scaling it by

the force produced by the muscle in the unaltered simulation, mF :

mm

im FFx

tx∂

∂=

&&&& )(

The sensitivity of the joint acceleration to force generated by the muscle of interest is

defined by:

m

imimm

m FtFxtFFx

Fx

Δ−Δ+

=∂

∂ ),(),( &&&&&&

where it is the current time in the unaltered simulation, x&& is the joint acceleration, mF

is the force generated by muscle m, and mFΔ is the perturbation applied to the muscle

force. This forward difference method is an exact expression for the sensitivity since

acceleration and force are linearly related. The component of the ground reaction force

generated in response to the muscle’s perturbation is accounted for by the foot-floor

contact model described previously. This sensitivity is calculated by incrementing the

force of a single muscle m in the simulation by a constant force perturbation, chosen to

48

be mFΔ = 1.0 N, integrating the simulation forward in time over a short interval, and

quantifying the resulting change in knee motion.

The change in joint angular acceleration induced by the muscle perturbation is

estimated assuming a constant acceleration over the short interval, picked to be 20ms,

of the forward integration. The acceleration is estimated using equations of constant

acceleration that are based on changes in position. This process was repeated for each

muscle in the model. A similar approach was utilized to quantify the contribution of

gravitational acceleration to the knee angular acceleration.

A unique contribution of this dissertation was the development of an algorithm to

quantify the contributions of Coriolis and centrifugal accelerations to knee angular

acceleration. This procedure involved setting all forces in the simulation to zero, such

that the motion resulting after forward integration was due only to the initial velocities

of the coordinates in the model and the resulting Coriolis and centrifugal accelerations.

The contribution, )( iv tx&& , of Coriolis and centrifugal accelerations to knee angular

acceleration at time ti was then defined by:

[ ]m

imimimmiv F

ttFxtFxttFFxtx

ΔΔ−−Δ+Δ+

=),(),(),(2

)(&

&&

With the development of the algorithm to calculate contributions of Coriolis and

centrifugal accelerations to joint acceleration, all contributions in the system to joint

acceleration can be quantified. Summing all contributions to joint acceleration in the

system and comparing to the actual acceleration of the joint of interest allows one

check of the appropriateness of the algorithm implementation and the foot-floor

contact model.

49

3 IMPORTANCE OF PRESWING RECTUS FEMORIS

ACTIVITY IN STIFF-KNEE GAIT 3.1 ABSTRACT

Stiff-knee gait is characterized by diminished and delayed knee flexion during

swing. Rectus femoris transfer surgery, a common treatment for stiff-knee gait, is

often recommended when a patient exhibits prolonged activity of the rectus femoris

muscle during swing. Treatment outcomes are inconsistent, in part, due to limited

understanding of the biomechanical factors contributing to stiff-knee gait. This study

used a combination of gait analysis and dynamic simulation to examine how activity

of the rectus femoris during swing, and prior to swing, contribute to knee flexion. A

group of muscle-actuated dynamic simulations was created that accurately reproduced

the gait dynamics of ten subjects with stiff-knee gait. These simulations were used to

examine the effects of rectus femoris activity on knee motion by eliminating rectus

femoris activity during preswing and separately during early swing. The increase in

peak knee flexion by eliminating rectus femoris activity during preswing (7.5 ± 3.1°)

was significantly greater on average (paired t-test, p = 0.035) than during early swing

(4.7 ± 3.6°). These results suggest that preswing rectus femoris activity is at least as

influential as early swing activity in limiting the knee flexion of persons with stiff-

knee gait. In evaluating rectus femoris activity for treatment of stiff-knee gait,

preswing as well as early swing activity should be examined.

50

3.2 INTRODUCTION

Stiff-knee gait is a debilitating consequence of cerebral palsy characterized by

diminished knee motion and delayed peak knee flexion during swing. Each year, three

out of every 1000 children manifest one or more of the symptoms of cerebral

palsy(CDC, 2004). Approximately 48–79% of all individuals with cerebral palsy are

ambulatory (Stanley, 2000). Stiff-knee gait is one of the most common gait

abnormalities in ambulatory children with spastic cerebral palsy (Wren et al., 2005b).

Many individuals with stiff-knee gait frequently trip or perform inefficient

compensatory movements due to inadequate toe clearance (Sutherland and Davids,

1993).

Distal transfer of the rectus femoris is a common surgical treatment for stiff-

knee gait (Gage et al., 1987; Perry, 1987). Though increased vasti and decreased

iliopsoas activity have been identified as potential causes of stiff-knee gait (Goldberg

et al., 2004), the limited knee flexion is usually attributed to abnormal prolongation of

rectus femoris activity into early swing phase (Sutherland et al., 1975; Waters et al.,

1979; Gage et al., 1987; Perry, 1987; Sutherland et al., 1990; Sutherland and Davids,

1993). Rectus femoris transfer surgery is intended to decrease the muscle’s ability to

extend the knee while preserving its ability to generate hip flexion moment (Gage et

al., 1987; Perry, 1987; Asakawa et al., 2002), which promotes knee flexion (Piazza

and Delp, 1996; Kerrigan and Riley, 1998; Asakawa et al., 2002). Several studies have

reported that rectus femoris transfer typically improves knee flexion (Gage et al.,

1987; Sutherland et al., 1990; Ounpuu et al., 1993a; Ounpuu et al., 1993b; Rethlefsen

51

et al., 1999). However, less positive outcomes related to swing phase peak knee

flexion have more recently been reported in some patients (Yngve et al., 2002).

Outcomes of surgical treatments for stiff-knee gait are inconsistent, in part, due to

insufficient understanding of the biomechanical factors contributing to stiff-knee gait.

Although rectus femoris transfer is thought to improve knee flexion by decreasing

knee extension moment, Goldberg et al. (2003) found that many subjects with stiff-

knee gait did not walk with abnormally large knee extension moments during early

swing, but they walked with abnormally low knee flexion velocity at toe-off. Goldberg

et al. (2006) subsequently reported that many subjects with stiff-knee gait walked with

abnormally large knee extension moments during double support, which were

correlated with low knee flexion velocity at toe-off. Moreover, most subjects with

favorable outcomes following surgery walked with decreased knee extension moments

during double support and corresponding increased knee flexion velocities at toe-off

(Goldberg et al., 2006). These results suggest that knee extension moment, which is

influenced by rectus femoris activity, prior to toe-off, rather than after toe-off, may be

a more prevalent contributor to stiff-knee gait than previously thought. A better

understanding of when rectus femoris activity contributes to stiff-knee gait is

necessary to refine clinical indications for rectus femoris transfer surgery.

This study used dynamic simulation, in combination with gait analysis, to

evaluate the relative importance of preswing (i.e., the period immediately prior to toe-

off) rectus femoris activity as a biomechanical factor contributing to diminished knee

flexion in subjects with stiff-knee gait. We hypothesized that rectus femoris activity

during preswing has a greater impact on peak knee flexion than rectus femoris activity

52

during early swing (i.e., the period from toe-off to peak knee flexion) in subjects with

stiff-knee gait. We tested this hypothesis by simulating the elimination of rectus

femoris activity during preswing and separately during early swing for a group of ten

subjects with cerebral palsy walking with stiff-knee gait and computing the resulting

changes in knee flexion. Identifying the function of rectus femoris activity during

preswing and early swing in subjects with stiff-knee gait contributes to our

understanding of this gait abnormality and provides insights needed to improve

treatment planning.

3.3 METHODS

The subjects in this study underwent gait analysis at Connecticut Children’s

Medical Center in Hartford, CT. Gait analysis data, including three-dimensional joint

angles, ground reaction forces and moments, and surface electromyographic (EMG)

recordings from preamplifier electrodes, were collected as a routine part of treatment

planning. Our inclusion criteria (Goldberg et al., 2006) required that each subject (i)

subsequently underwent rectus femoris transfer surgery as a correctional treatment for

stiff-knee gait, (ii) was between 6 and 17 years of age prior to surgery, (iii) had not

undergone a selective dorsal rhizotomy, and (iv) walked without orthoses or other

assistance. Ten subjects were identified and categorized as exhibiting stiff-knee gait in

at least one limb preoperatively (Table 3.1).

53

Table 3.1 Descriptive values for 10 subjects with stiff-knee gait and 15 able-bodied subjects

54

Four gait parameters (Goldberg et al., 2006) were used to determine whether a

subject walked with stiff-knee gait: peak knee flexion in swing phase (Gage et al.,

1987; Sutherland et al., 1990), knee range of motion in early swing (Goldberg et al.,

2003), total knee range of motion (Gage et al., 1987; Ounpuu et al., 1993b; Ounpuu et

al., 1993a), and timing of peak knee flexion during swing phase (Sutherland et al.,

1990; Ounpuu et al., 1993b; Ounpuu et al., 1993a). A limb was classified as ‘‘stiff’’ if

three or more of these measures were more than two standard deviations below (or

above in the case of the timing measure) the average control value. Control data were

collected from 15 able-bodied subjects of approximately the same average age, height,

and weight as the subjects with cerebral palsy (Table 3.1). Surface EMG data were not

used to include or exclude subjects from this study. However, all of the subjects with

stiff-knee gait did exhibit abnormal rectus femoris activity (Table 3.2). All subjects

gave informed consent for the collection of their gait data. Mutual institutional

approval was obtained for retrospective analysis of these data. The data analysis

included the creation of subject-specific dynamic simulations.

55

Table 3. 2 Description of abnormal rectus femoris activity in subjects

A three-dimensional, full-body musculoskeletal model with 21 degrees of

freedom and 92 muscle–tendon actuators formed the foundation of each simulation

(Fig. 3.1). The position and orientation of the pelvis relative to ground was defined

with 6 degrees of freedom. The head, arms, and torso were represented as a rigid

segment connected with the pelvis by a ball-and-socket joint (Anderson and Pandy,

1999). The remaining lower extremity joints were modeled as follows: each hip as a

ball-and-socket joint, each knee as a planar joint with tibiofemoral and patellofemoral

translational constraints as a function of knee flexion (Delp et al., 1990), and each

ankle and subtalar joints as revolute joints (Inman, 1976). Each muscle–tendon

actuator was modeled as a Hill-type muscle in series with tendon based on

musculotendon parameters from Delp et al. (1990). The musculoskeletal model and

corresponding dynamic simulation code were produced using SIMM and the

Dynamics Pipeline (Delp and Loan, 2000) along with SD/FAST (Parametric

56

Technology Corporation, Waltham, MA). The musculoskeletal model was used in

conjunction with gait analysis data to create subject-specific dynamic simulations.

Figure 3.1 Muscle-actuated dynamic simulation of a subject’s gait during the period of preswing through early swing. A three-dimensional, full-body musculoskeletal model with 21 degrees of freedom and 92 muscle-tendon actuators was used in conjunction with the subject’s gait analysis data to create each subject-specific simulation. The dynamic simulation is shown at the initiation of preswing (left), just following toe-off (center), and at the termination of early swing (right). Each subject-specific simulation was used to conduct simulation experiments to evaluate the relative importance of preswing rectus femoris activity as a biomechanical factor contributing to the subject’s diminished knee flexion.

A muscle-actuated dynamic simulation of each subject was created using a

four-step process. First, the musculoskeletal model was scaled to represent the

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experimentally measured size of each subject. Second, inverse kinematics analysis

was utilized to obtain values of generalized coordinates for the model that closely

matched the experimentally measured kinematics of each subject. Third, a residual

elimination algorithm (Thelen and Anderson, 2006) was applied to achieve dynamic

consistency between the model’s motions and the experimentally measured ground

reactions of each subject, by adjusting pelvis translations and back rotations. Fourth,

computed muscle control (Thelen et al., 2003) was implemented to determine an

optimal set of muscle activities that produced forward simulations and that were

generally consistent with the experimentally measured kinematics and EMG patterns

of each subject. Constraints were placed on the muscle activity of each simulation

based on the recorded EMG. For example, when activity was recorded for rectus

femoris during early swing, the simulated rectus femoris was required to have activity

during this time as well. This four-step process was used to create simulations for each

subject’s preoperative gait during the period of preswing through peak knee flexion in

swing. The simulated joint angles reproduced the subjects’ measured hip, knee, and

ankle angles within 31. The subject-specific dynamic simulations were used to

conduct subsequent simulation experiments.

The simulation of each subject was altered to examine the effects of rectus

femoris activity on knee motion. In particular, the activity of rectus femoris was

eliminated during preswing and separately during early swing, creating two new

simulations per subject, to determine the muscle’s relative importance to peak knee

flexion for each case (Fig. 3.2). By observing the changes in peak knee flexion

between the new and unperturbed simulations, the muscle’s contribution to knee

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motion was inferred for that period of time in which its activity was eliminated. For

these simulation experiments, preswing was defined to be the period of the gait cycle

before toe-off equal in length of time to early swing. Early swing was defined to be the

period of the gait cycle from toe-off to peak knee flexion. Equal lengths of time were

chosen for preswing and early swing to remove any intrasubject variability which

would weight the effects of each period by a percentage of simulation time. On

average, the duration of preswing was 20 ms longer than double support.

Figure 3.2 Example (subject 7) of methods used to determine increase in peak knee flexion when rectus femoris activity was eliminated during preswing and separately during early swing. (a) Rectus femoris surface EMG of a subject with stiff-knee gait was recorded over an entire gait cycle. Normal rectus femoris EMG timing is indicated by horizontal white bars (Bleck, 1987). Toe-off is indicated by a vertical dashed line at 61% of the gait cycle. Two time periods were selected for analysis: early swing (i.e., period from toe-off to peak knee flexion) and preswing (i.e., period before toe-off equal in duration to early swing). (b) Two simulation experiments were conducted by eliminating rectus femoris activity during preswing (dashed line) and separately during early swing (dotted line) to determine the muscle’s effect on peak knee flexion. (c) Simulated changes in knee flexion angles were different when rectus femoris activity was eliminated during preswing (dashed line) or early swing (dotted line). The unperturbed simulation (thick solid line) and experimentally measured (thin solid line) knee angles are shown for comparison. Normal knee flexion (shaded line) and two standard deviations of the normal curve (shaded region) are shown as well.

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We evaluated our hypothesis regarding the relative importance of preswing

and early swing rectus femoris activity by conducting a paired t-test at the 0.05

significance level. A one-tailed test was used due to a priori expectation about

directionality (i.e., rectus femoris activity during preswing has a greater impact on

peak knee flexion than rectus femoris activity during early swing in subjects with stiff-

knee gait). The null hypothesis was that the difference in peak knee flexion change

between the preswing and the early swing simulations was zero. The test was

performed against the right-tailed alternative hypothesis that peak knee flexion

increased more, on average, in the simulations when rectus femoris activity was

eliminated during preswing than during early swing.

3.4 RESULTS

Peak knee flexion increased more (p = 0.035), on average, when rectus femoris

activity was eliminated during preswing than during early swing in our simulations

(Fig. 3.3). Peak knee flexion increased 7.5±3.1° when activity was eliminated during

preswing and 4.7±3.6° when eliminated during early swing. Peak knee flexion

increased more for the preswing case than for the early swing case in the majority of

subject simulations. For six subjects (1, 4, 5, 7, 9, and 10), the increase in peak knee

flexion was 90% higher or more for the preswing case than for the early swing case.

For three subjects (2, 6, and 8), the increase in peak knee flexion was similar (within

10%) for the preswing case and the early swing case. For the remaining subject (3),

the increase in peak knee flexion was substantially lower (37%) for the preswing case

than for the early swing case.

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Figure 3.3 Increase in peak knee flexion caused by eliminating rectus femoris activity during preswing and separately during early swing in simulations of ten subjects with stiff-knee gait (ordered by increasing unperturbed peak knee flexion). The increase was determined by eliminating rectus femoris activity in a forward dynamic simulation and computing the change in peak knee flexion compared with the unperturbed value (Fig. 3.2). The changes in simulated knee motion give insight into the biomechanical contribution of rectus femoris for that period of time in which its activity was eliminated. 3.5 DISCUSSION

Rectus femoris transfer surgery is often performed to treat stiff-knee gait when

a patient exhibits prolonged activity of the rectus femoris into early swing. However,

Goldberg et al. (2006) suggested that rectus femoris activity prior to toe-off may also

contribute to stiff-knee gait by causing abnormally large knee extension moments and

corresponding low knee flexion velocity at toe-off. Our results confirm that preswing

rectus femoris activity is at least as important as early swing activity and, for some

subjects with stiff-knee gait, may limit knee flexion more than activity in early swing.

The subject population in this study was diverse, and findings may not generalize to

all subjects with stiff-knee gait. In evaluating rectus femoris activity for treatment of

stiff-knee gait, preswing and early swing EMG should be examined. It should be

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noted, however, that surface EMG may be subject to cross-talk from the vasti (Barr et

al., 2010).

There are several possible biomechanical explanations why preswing rectus

femoris activity may limit knee flexion more than early swing activity. First, impaired

motor control may cause varying levels of preswing and early swing rectus femoris

activity (Fig. 3.4). In fact, preswing and early swing EMG activity of the rectus

femoris varies considerably in children with stiff-knee gait (Miller et al., 1997).

Excessive preswing activity (Fig. 3.4a) may result in above normal muscle force that

limits knee flexion. Second, the delay between muscle excitation and muscle force

generation suggests that preswing rectus femoris activity may cause forces that persist

into early swing phase and limit knee flexion. This delay in electromechanical

coupling has been reported to be between 30 and 100 ms (Cavanagh and Komi, 1979),

which is roughly 25–75% of the duration of preswing or early swing for the subjects in

this study. Third, musculoskeletal geometry and multibody dynamics may cause

varying magnitudes of preswing and early swing muscle forces that produce joint

motion. The transmission of muscle force to joint motion depends on the muscle’s

moment arm, which varies during movement. In fact, rectus femoris has large

potential during double support to decrease peak knee flexion velocity (Goldberg et

al., 2004). Preswing activity may result in a potentially large knee extension moment

that limits knee flexion.

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Figure 3.4 Two subjects with varying levels of preswing and early swing rectus femoris activity. (a) Subject 8 had more rectus femoris activity in preswing compared to early swing. (b) Subject 3 had less rectus femoris activity in preswing compared to early swing.

There are several possible reasons why simulated increases in peak knee

flexion varied across subjects. First, EMG patterns and simulated muscle activity

varied across subjects. Constraints were placed on the muscle activity of each

simulation based on the recorded EMG. As a result, elimination of high rectus femoris

activity led to large simulated increases in peak knee flexion. For example, subject 3

had more activity in early swing compared to preswing (Fig. 3.4b); consequently, peak

knee flexion increased more when rectus femoris activity was eliminated during early

swing than during preswing (Fig. 3.3). The presence of high vasti activity in lieu of

rectus femoris activity may have attenuated the simulated increases in peak knee

flexion. Second, joint motion and body mass properties varied across subjects and

these can affect the change in knee motion caused by rectus femoris activity. For

example, improper positioning of the foot before toeoff may dramatically decrease the

ankle power required for proper knee flexion. Third, the duration of the simulation

times varied across subjects and long simulations may have produced large changes in

knee flexion. Given two simulations differing only in length of time, a longer

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simulation eliminating rectus femoris activity increases peak knee flexion more than a

shorter simulation because the inhibitory knee extension moment, in part due to rectus

femoris muscle force, is reduced for a longer period of time.

By carefully defining the duration of preswing to equal the duration of early

swing, the intra-subject results were not contaminated by the effects of a long

perturbation being compared with those of a short perturbation. The period of double

support is defined by vertical ground reaction force measurements. Knee flexion

motion along with ground reactions defines early swing. There was significant

variation between double support and early swing durations for each subject (Table

3.1). For example, double support was roughly 54 ms shorter than early swing for

subject 2. If we had not controlled the duration over which we perturbed RF activity in

the simulations, then this difference would have allowed the early swing perturbations

to affect the model motion for 60% more time than double support perturbations. For

this reason, preswing was defined to be the period before toe-off equal in length of

time to early swing.

The simulated elimination of rectus femoris activity was not intended to

represent the activity of able-bodied control subjects. Although rectus femoris activity

for an individual subject is repeatable, there are significant differences across subjects

(Arsenault et al., 1986). In some cases using surface electrodes, a bi-phasic pattern

(i.e., one main burst during swing-to-stance transition and the second main burst

during stance-to-swing transition) can be observed (Murray et al., 1984; Shiavi, 1985;

Arsenault et al., 1986). In other cases using fine wire electrodes, no muscle activity or

a brief, weak burst is observed during stance-to-swing transition (Perry, 1987). In a

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study with both types of electrodes, cross-talk from the underlying vasti contaminated

the EMG of rectus femoris recorded with surface electrodes (Nene et al., 2004).

Rather than simulating rectus femoris activity of able-bodied control subjects, the

simulations in this study allowed the muscle’s contribution (i.e., importance) to knee

flexion to be determined for that period of time in which its activity was eliminated.

The muscle-actuated simulations of stiff-knee gait developed in this study had

several limitations. First, the model used in this study was scaled to represent the size

and mass properties of each subject, but not individual impairments (e.g., skeletal

deformities, muscle contractures, and spasticity). Second, the simulations did not

explicitly model arm motions, which may have minimally affected the motions of

other body segments. Third, the model utilized muscle parameters representative of an

able-bodied adult, whereas the subjects in this study were children with neuromuscular

abnormalities. Fourth, the forces produced by muscles in our simulations may not

have accurately represented the forces generated by individual subjects even though

the net joint moments were representative of each subject. Although the increases in

peak knee flexion reported may change if we made different modeling assumptions,

our conclusions regarding the relative importance of preswing and early swing activity

would be unlikely to change significantly because the same assumptions would be

simulated across both time periods.

Our finding that preswing rectus femoris activity is an important

biomechanical factor contributing to diminished knee flexion in subjects with stiff-

knee gait is consistent with the findings of others. Several studies have shown that

swing-phase initial conditions are important in generating knee flexion during normal

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gait with (Piazza and Delp, 1996) and without (Mochon and McMahon, 1980; Mena et

al., 1981) muscle activity. More recently, (Goldberg et al., 2003) demonstrated the

importance of swing-phase initial conditions, particularly knee flexion velocity at toe-

off, in stiff-knee gait. Our finding supports these studies because preswing muscle

forces generate initial conditions for swing phase (e.g., knee flexion velocity at toe-

off). In particular, excessive rectus femoris force during double support has the

potential to decrease knee flexion velocity at toe-off in normal gait (Goldberg et al.,

2004). Some studies have reported subjects with stiff-knee gait exhibit a below normal

knee flexion velocity at toe-off (Granata et al., 2000; Goldberg et al., 2003), and others

have simulated the proportional relationship between knee flexion velocity at toe-off

and swing-phase knee flexion for normal gait (Piazza and Delp, 1996) and stiff-knee

gait (Goldberg et al., 2003). Our finding of the cause–effect relationship between

preswing rectus femoris activity and swing-phase knee flexion is consistent with these

studies as well. The current work demonstrates the impact of rectus femoris activity on

swing-phase knee flexion and provides a direct comparison of preswing and early

swing importance for a number of subjects with stiff-knee gait.

Many subjects with stiff-knee gait walked with excessive knee flexion in

stance phase (e.g., crouch gait). This results in larger than normal knee extension

moments during double support. Large knee moments generated by the knee extensors

are necessary to support the body (McNee et al., 2004), but diminish knee flexion

velocity at toe-off and reduce peak knee flexion (Goldberg et al., 2006). Recent

analyses (Goldberg et al., 2006) suggest that the improvements in stiff-knee gait are

associated with sufficient decreases in excessive knee extension moments during

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double support and corresponding increases in knee flexion velocity at toe-off. Further

analyses are necessary to determine if the correction of excessive knee flexion in

stance may diminish the excessive knee extension moments in double support. If so,

excessive rectus femoris excitation may no longer be necessary for body support.

Correcting excessive knee flexion in stance may increase knee flexion in swing.

The combination of gait analysis and dynamic simulation in this study identified the

importance of preswing rectus femoris activity in stiff-knee gait. This result indicates

that excessive preswing rectus femoris activity is a biomechanical factor contributing

to diminished knee flexion in subjects with stiff-knee gait. While gait analysis tools

alone are useful for characterizing stiff-knee gait, dynamic simulation provides an

additional, valuable tool for investigating its underlying biomechanical causes and the

mechanisms leading to improvement following treatment.

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4 MECHANISMS OF IMPROVED KNEE FLEXION AFTER

RECTUS FEMORIS TRANSFER SURGERY 4.1 ABSTRACT

Rectus femoris transfer is frequently performed to treat stiff-knee gait in

subjects with cerebral palsy. In this surgery, the distal tendon is released from the

patella and re-attached to one of several sites, such as the sartorius or the iliotibial

band. Surgical outcomes vary, and the mechanisms by which the surgery improves

knee motion are unclear. The purpose of this study was to clarify the mechanism by

which the transferred muscle improves knee flexion by examining three types of

transfers. Muscle-actuated dynamic simulations were created of ten children

diagnosed with cerebral palsy and stiff-knee gait. These simulations were altered to

represent surgical transfers of the rectus femoris to the sartorius and the iliotibial band.

Rectus femoris transfers in which the muscle remained attached to the underlying vasti

through scar tissue were also simulated by reducing but not eliminating the muscle’s

knee extension moment. Simulated transfer to the sartorius, which converted the

rectus femoris’ knee extension moment to a flexion moment, produced 32° ± 8°

improvement in peak knee flexion on average. Simulated transfer to the iliotibial band,

which completely eliminated the muscle’s knee extension moment, predicted only

slightly less improvement in peak knee flexion (28° ± 8°). Scarred transfer

simulations, which reduced the muscle’s knee extension moment, predicted

significantly less (p < 0.001) improvement in peak knee flexion (14° ± 5°).

Simulations revealed that improved knee flexion following rectus femoris transfer is

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achieved primarily by reduction of the muscle’s knee extension moment. Reduction

of scarring of the rectus femoris to underlying muscles has the potential to enhance

knee flexion.

4.2 INTRODUCTION

Stiff-knee gait, characterized by diminished and delayed peak knee flexion in

swing (Sutherland and Davids, 1993), is one of the most common gait problems in

children with cerebral palsy (Wren et al., 2005b). Insufficient knee flexion during

swing can lead to tripping and falling, and energy-inefficient compensatory

movements. Despite the prevalence of stiff-knee gait, its causes are not well

understood. Several factors may contribute to stiff-knee gait (Kerrigan and Glenn,

1994; Piazza and Delp, 1996; Riley and Kerrigan, 1998; Kerrigan et al., 1999;

Goldberg et al., 2003), but over-activity of the rectus femoris muscle is considered a

primary cause (Waters et al., 1979; Perry, 1987; Sutherland et al., 1990). Treatments

including rectus femoris transfer surgery and botulinum toxin injection aim to alter the

function of this muscle. A rectus femoris transfer relocates the insertion of the rectus

femoris from the patella to a more posterior site to augment knee flexion (Gage et al.,

1987; Perry, 1987).

Average improvement in knee flexion after rectus femoris transfer is positive

but variable. Most studies report an average increase in peak knee flexion after

transfer between 7-10° (Gage et al., 1987; Ounpuu et al., 1993b; Chambers et al.,

1998; Saw et al., 2003; Moreau et al., 2005). Some studies report increases in peak

knee flexion between 12-26° (Sutherland et al., 1990; Miller et al., 1997; Hemo et al.,

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2007). Even studies that report no significant improvement (Hadley et al., 1992;

Ounpuu et al., 1993a; Rethlefsen et al., 1999) or an average decrease (Yngve et al.,

2002; Carney and Oeffinger, 2003) in peak knee flexion in swing find that patients

exhibit an average increase in knee range of motion, typically when rectus femoris

transfers are performed in conjunction with hamstrings lengthenings. There is limited

understanding of how the transferred rectus femoris affects knee motion and a lack of

consensus regarding the effects of transfer site. Several studies have reported no

difference among transfer sites on peak knee flexion improvement (Ounpuu et al.,

1993a; Muthusamy, 2006), whereas others have suggested that outcome is dependent

on transfer site (Chung et al., 1997; Hemo et al., 2007).

The mechanism by which rectus femoris transfer may increase knee flexion is

unclear. The transfer was originally intended to convert the muscle from a knee

extensor to a knee flexor (Perry, 1987), and a study on cadavers showed that the rectus

femoris has a knee flexion moment arm after transfer to the sartorius or

semitendinosus (Delp et al., 1994). However, examination of postoperative patients

revealed that the transferred muscle generates a knee extension moment upon

electrical stimulation (Riewald and Delp, 1997). In vivo dynamic imaging confirmed

that the muscle is not converted to a knee flexor but that the knee extension capacity

of the rectus femoris is diminished after surgery (Asakawa et al., 2002). In these same

subjects, magnetic resonance imaging also revealed the formation of scar tissue

between the rectus femoris and the vasti postoperatively. This connective tissue may

allow force to be transmitted from the rectus femoris to the vasti, resulting in the

rectus femoris producing a net knee extension moment despite transfer of its distal

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tendon to the sartorius or semitendinosus (Asakawa et al., 2004). A proposed

mechanism of improvement in knee flexion after rectus femoris transfer is reduction

of the muscle’s knee extension moment with preservation of its hip flexion moment

(Delp et al., 1994; Riewald and Delp, 1997; Asakawa et al., 2002), which promotes

knee flexion through dynamic coupling (Piazza and Delp, 1996; Kerrigan and Riley,

1998). However, there is little evidence indicating whether this mechanism is likely to

increase knee flexion in patients with stiff-knee gait following rectus femoris surgery.

The purpose of this study was to investigate the mechanisms of improved knee flexion

after rectus femoris transfer by comparing the changes in knee flexion predicted by

simulating transfers to sartorius, transfers to iliotibial band, scarred rectus femoris

transfers, and botulinum toxin injection of the rectus femoris. This study evaluated the

relative importance of the transferred muscle’s hip and knee moments by analyzing

subject-specific simulations of children with stiff-knee gait.

4.3 METHODS

Muscle-actuated simulations were created to investigate the mechanism by

which rectus femoris transfer alters muscle function. We created simulations that

reproduced the gait dynamics of ten subjects with stiff-knee gait prior to treatment.

The rectus femoris was then altered to simulate the effects of different treatments.

Resulting changes in peak knee flexion were compared.

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Subjects

All ten subjects in this study were diagnosed with spastic cerebral palsy and

classified as exhibiting stiff-knee gait (Fig. 4.1). To be classified as “stiff” the

subject’s knee motion was outside a normal range by more than two standard

deviations for at least three of four gait parameters: (1) peak knee flexion angle, (2)

range of knee flexion in early swing (from toe-off to peak knee flexion), (3) total

range of knee motion, and (4) timing of peak knee flexion in swing (Goldberg et al.,

2006). Control data was collected from 15 typical children of approximately the same

average age, height, and weight as the subjects with stiff-knee gait. Each stiff-knee

subject underwent a physical exam and gait analysis at Connecticut Children’s

Medical Center in Hartford, CT. All subjects met the following selection criteria: (i)

underwent rectus femoris transfer surgery to treat stiff-knee gait, (ii) were 6 - 17 years

of age at surgery, (iii) had not undergone a selective dorsal rhizotomy, and (iv) walked

without orthoses or other assistance. The group of subjects had an average age of 10.6

years. Rectus femoris was transferred distally to sartorius in all subjects.

Retrospective analysis of these data was performed with approval of participating

institutions.

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Figure 4.1 Average experimental knee flexion (in more stiff limb) of ten subjects with stiff-knee gait (thick line) ± one standard deviation (dark shaded region), compared to average knee flexion of typical subjects (thin line) ± one standard deviation (light shaded region).

Creating subject-specific simulations

The musculoskeletal system was represented by a three-dimensional model

with 21 degrees of freedom and 92 muscle-tendon actuators. The position and

orientation of the pelvis segment with respect to ground was defined with six degrees

of freedom. A single rigid segment articulating with the pelvis by a ball and socket

joint represented the head, arms, and torso. Each hip was modeled as a ball and socket

joint, each knee as a planar joint with tibiofemoral and patellofemoral kinematics

defined by knee flexion angle (Delp et al., 1990), and each ankle and subtalar joint as

revolute joints (Inman, 1976). The musculoskeletal model and corresponding

dynamic simulation code were produced using SIMM (Delp and Loan, 2000) and

SD/FAST (Parametric Technology Corporation, Waltham, MA).

The musculoskeletal model was scaled to match the size and weight of each

subject. Next, we solved for the joint angles that minimized the distances between

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virtual markers on the model and experimentally measured marker positions. Then, a

residual elimination algorithm (Thelen and Anderson, 2006) was applied to make

model kinematics consistent with measured ground reaction forces by adjusting pelvis

translations and back angles. Finally, computed muscle control (Thelen et al., 2003)

was utilized to determine a set of muscle excitations that produced a forward

simulation of the subject’s preoperative kinematics. The muscle excitations were

constrained to be consistent with measured EMG patterns. Sagittal knee, hip, and

ankle angles were within 3° of measured preoperative angles. Simulations represented

a portion of the gait cycle from preswing to peak knee flexion, centered around toe-

off.

Comparing effects of simulated treatments on knee flexion

Three types of rectus femoris transfers and a botulinum toxin injection into the

rectus femoris were simulated for each subject. The three different types of rectus

femoris transfer investigated included transfer to the sartorius, transfer to the iliotibial

band, and a transfer in which rectus femoris was scarred to the underlying vasti. The

preoperative musculoskeletal model for each subject (Fig. 4.2a) was altered to

represent each transfer scenario. The tendon slack length of the transferred muscle

was adjusted to keep muscle fibers operating near preoperative length ranges. The set

of muscle excitations from each subject’s preoperative simulation was applied to each

transfer model to simulate the effects of the surgery.

To simulate a transfer of the rectus femoris to the sartorius the rectus femoris

insertion was relocated to the effective insertion of the sartorius in the model (Fig.

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4.2b). Even though the effective insertion of the sartorius is more proximal and

posterior than the anatomical insertion, the simulated rectus femoris transfer closely

approximates moment arms of transferred muscles measured experimentally by Delp

et al. ((1994); compare model to experiment in Fig. 4.2b). To simulate the negligible

knee extension moment arm (0-5 mm) measured by Delp et al. (1994) after transfer to

the iliotibial band, the muscle’s insertion was fixed on the femur, transforming it into a

uniarticular hip flexor. To simulate the effects of a transfer surgery in which the

rectus femoris becomes scarred to the underlying vasti we reduced the knee extension

moment arm of rectus femoris by half (Fig. 4.2d). Although the model for the scarred

transfer does not resemble a typical transfer surgery, it represents the net effect of a

scarred rectus femoris transfer on the muscle’s knee extension capacity based on the

subject who showed the least reduction in rectus femoris knee extension capacity in

the study of Asakawa et al. (2002). To simulate the effects of injection of botulinum

toxin into the rectus femoris, which decreases active muscle force by inhibiting the

release of acetylcholine from the neuromuscular junction (Burgen et al., 1949), we

applied the set of muscle excitations in the preoperative simulation to the preoperative

model but eliminated rectus femoris excitation.

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Figure 4.2 Illustrations of the rectus femoris muscle (top panels) and its moment arm at the knee averaged over 20-60 degrees of knee flexion (bottom panels). The moment arms of the models (black bars) are compared with moment arms measured experimentally (grey bars) by Delp et al. (1994) in cadaver specimens in the (a) preoperative condition, after (b) transfer to the sartorius, and after (c) transfer to the iliotibial band. The muscle insertions shown in models (b) and (c) are effective insertions used to calculate moment arms (see Methods). The muscle’s knee extension moment arm in the (d) scarred transfer model is compared to its moment arm calculated from in vivo measurements of the muscle’s displacement in the patient from Asakawa et al. (2002) with the minimum reduction in knee extension moment arm after rectus femoris transfer.

After creating simulations of each treatment for each subject, the

improvements in peak knee flexion, measured at the point of preoperative peak knee

flexion, were quantified (Fig. 4.3). The average amounts of peak knee flexion

improvement for all subjects were compared among treatments, using a two-tailed,

paired t-test (p < 0.05) with Bonferroni correction for multiple comparisons.

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Figure 4.3 Peak knee flexion resulting from simulation of (a) preoperative gait, (b) RF transfer to sartorius, (c) RF transfer to iliotibial band, (d) scarred RF transfer, and (e) botulinum toxin injection for a single subject.

Comparing influence of hip and knee moments of rectus femoris on knee flexion

To investigate the relative importance of the hip and knee moments of

transferred rectus femoris on peak knee flexion in swing, we analyzed four additional

simulations for each subject to represent conditions under which the hip and knee

moments of the muscle were separately eliminated or preserved. The simulations of

each subject’s preoperative gait served as the first condition that preserved both hip

and knee moments of the muscle. A second model was created for each subject in

which the muscle’s knee extension moment was eliminated, while its hip flexion

capacity after transfer was preserved. We preserved the transferred muscle’s hip

flexion capacity by maintaining its hip flexion moment arm and adjusting tendon slack

length to approximate the range of fiber operating lengths in the preoperative

simulation. A third model was created for each subject in which the muscle’s hip

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flexion moment was eliminated while its knee extension moment was preserved. A

fourth model was created for each subject in which rectus femoris was removed from

the model, eliminating both hip and knee moments.

The set of muscle excitations found for each subject’s preoperative simulation was

applied to each model to simulate the effects of each condition on knee flexion. We

compared the changes in peak knee flexion from the preoperative condition using a

two-tailed, paired t-test (p < 0.05) with Bonferroni correction.

4.4 RESULTS

The largest improvement in peak knee flexion (32° ± 8°) occurred after

simulated transfer of the rectus femoris to sartorius (Fig. 4.4). Transfer of the muscle

to the iliotibial band predicted a smaller (p < 0.001) improvement in peak knee flexion

(28° ± 8°). Simulated scarred rectus femoris transfer resulted in an average

improvement in peak knee flexion of 14° ± 5°, which was significantly less (p <

0.001) than the average improvement from unscarred transfer to either the sartorius or

the iliotibial band. Simulated botulinum toxin injection to the rectus femoris, which

eliminated the muscle’s active hip flexion and knee extension moments, resulted in an

average improvement of 12° ± 5° in knee flexion.

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Figure 4.4 Average increases (and one standard deviation) in peak knee flexion of the subject group for each of the simulated treatments.

The knee extension moment of rectus femoris was more influential than its hip

flexion moment on peak knee flexion (Fig. 4.5). All subjects showed larger (p <

0.001) increase in peak knee flexion (28° on average) when knee extension moment

was eliminated compared to decrease in peak knee flexion (-8° on average) when hip

flexion moment was eliminated. In the absence of the muscle’s knee extension

moment, average improvement in peak knee flexion was 3° greater (p < 0.001) with

hip flexion moment than without hip flexion moment.

Figure 4.5 Average increases (and one standard deviation) in peak knee flexion of the subject group for simulations in which knee extension or hip flexion moments of rectus femoris were independently eliminated.

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4.5 DISCUSSION

Our results suggest that the primary mechanism by which rectus femoris

transfer improves knee flexion is the reduction of the rectus femoris’ knee extension

moment. Previous observations that the surgery diminishes knee extension moment

but generally does not convert the rectus femoris to a knee flexor (Riewald and Delp,

1997; Asakawa et al., 2002) support this finding.

A secondary mechanism of improvement is preservation of some of the

muscle’s hip flexion moment, which induces knee flexion (Piazza and Delp, 1996;

Riley and Kerrigan, 1998). However, it is likely the hip flexion moment generated by

the rectus femoris is diminished after transfer. The hip flexion moment generated by

the rectus femoris could not be preserved in simulations in which the muscle’s

insertion was relocated. In the preoperative simulation, the rectus femoris lengthened

due to the patella translating distally on the femur with knee flexion. In the transfer

simulations in which the rectus femoris was relocated from the patella the muscle

shortened. Concentric muscle contraction in the transfer simulations produced less

force than the eccentric muscle contraction in the preoperative simulations; this

reduced the hip flexion moment generated by the rectus femoris in transfer

simulations. This suggests that when the rectus femoris is transferred from its

insertion on the patella the muscle’s hip flexion moment may not be preserved,

reducing the contribution of the muscle’s hip flexion moment to knee flexion and

increasing the importance of reducing, or eliminating, the muscle’s knee extension

moment.

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Our results show that rectus femoris transfers to either the sartorius or the

iliotibial band predicted greater improvements in peak knee flexion than a scarred

transfer, suggesting that methods to reduce postoperative scarring of the muscle to

underlying vasti may be beneficial. Transfer to the sartorius predicted only slightly

greater peak knee flexion in swing (approximately 4°) than transfer to the iliotibial

band, even though the simulated transfer to the sartorius converted the muscle to a

knee flexor. Although the rectus femoris had a knee flexion moment arm in the model

of transfer to the sartorius, the amount of force the rectus femoris produced was

diminished after transfer since the change in muscle path caused the muscle to shorten

rather than lengthen while contracting. Transfer to semitendinosus or gracilis, which

have larger knee flexion moment arms than sartorius, may result in larger changes in

knee flexion. Transfer to sartorius was investigated in this study because of its

prevalence as a surgical option (Gage et al., 1987; Ounpuu et al., 1993a; Saw et al.,

2003; Moreau et al., 2005; Hemo et al., 2007).

Simulated botulinum toxin injection to the rectus femoris predicted less peak

knee flexion improvement than transfer of the muscle. This is likely due to the

preservation of detrimental passive knee extension moments (i.e., the knee extension

moment generated by stretch of the rectus femoris even when it is inactive) and

elimination of helpful active hip flexion moments. The simulated result may

overestimate anticipated clinical improvement since injection of botulinum toxin is

unlikely to achieve complete elimination of active muscle force. Stoquart et al. (2008)

reported a 5° average increase in peak knee flexion after botulinum toxin injection into

rectus femoris in adults with stiff-knee gait due to stroke. Other studies have reported

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no significant change (Chantraine et al., 2005) and 9° average improvement (Sung and

Bang, 2000) in peak knee flexion after motor branch block of the rectus femoris in

patients with stiff-knee gait.

Simulations of rectus femoris transfers to the sartorius and the iliotibial band

resulted in larger peak knee flexion improvements than those reported clinically or

observed in the postoperative kinematics of our subjects (2° ± 13°) measured

approximately one year postoperatively. This is likely to occur because the rectus

femoris may not produce the intended knee flexion moment due to scarring of the

transferred muscle to underlying soft tissues (Asakawa et al., 2004). Also, the subjects

in this study were treated with other surgeries that may affect knee flexion. All ten

subjects received hamstrings lengthenings and many received additional bony or soft-

tissue surgeries. We have not attempted to model the effects of concomitant surgeries

in our subject group because our goal was to isolate the effects of rectus femoris

transfer surgery. Our simulations of scarred rectus femoris transfers predict

improvements in knee flexion of 14° on average, which is similar to a clinical report

of 12° of increase after isolated rectus femoris transfer (Hemo et al., 2007).

Several assumptions were made in implementing the gait simulations. First,

the muscle excitations used to drive the treatment simulations were assumed to remain

unchanged from preoperative simulations. While some muscle excitations are likely

to change, Patikas et al. (2007) found no significant changes in rectus femoris activity

after multilevel surgery, including rectus femoris transfer. Secondly, muscle

parameters prescribed in these models were based on data for typical adults, which are

unlikely to be accurate representations of muscles in children with cerebral palsy.

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Additionally, our subject-specific models were scaled to the sizes of each subject and

accurately represented the kinematics and kinetics measured preoperatively for each

subject, but did not replicate skeletal deformities or contractures which may have been

present. Also, we cannot be certain that the muscle forces produced in our simulations

accurately represented the forces generated by individual subjects in vivo, although the

net joint moments and muscle excitations in the preoperative simulations were

consistent with those measured in the gait lab. Finally, we modeled the net effect of a

scarred transfer by reducing the average moment arm of rectus femoris at the knee by

half. This is an approximation of the function of a scarred transfer, and may not

represent secondary effects of scarring or variations in the actual moment arm of the

transferred muscle throughout a range of knee flexion. Although different modeling

assumptions may have resulted in different peak knee flexion improvements, the

relationships of improvement in peak knee flexion among treatments would not be

likely to change since the same assumptions were used in each treatment simulation.

Our dynamic simulations of individual subjects with stiff-knee gait revealed

that substantial improvement in peak knee flexion in swing after rectus femoris

transfer may be obtained by reducing the muscle’s knee extension moment.

Preserving the muscle’s hip flexion moment may provide some additional

improvement, but was less influential than decreasing the muscle’s knee extension

moment. Surgeries that intend to convert the rectus femoris to a knee flexor may

instead only reduce its knee extension moment, possibly due to scarring (Asakawa et

al., 2002). Reducing postoperative scarring of the rectus femoris to underlying tissues

may improve postoperative peak knee flexion in swing.

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5 CONTRIBUTIONS OF MUSCLES AND PASSIVE

DYNAMICS TO SWING INITIATION OVER A RANGE OF WALKING SPEEDS 5.1 ABSTRACT

Stiff-knee gait is a common walking problem in cerebral palsy characterized

by insufficient knee flexion during swing. To identify factors that may limit knee

flexion in swing, it is necessary to understand how unimpaired subjects successfully

coordinate muscles and passive dynamics (gravity and velocity-related forces) to

accelerate the knee into flexion during double support, a critical phase just prior to

swing that establishes the conditions for achieving sufficient knee flexion during

swing. It is also necessary to understand how contributions to swing initiation change

with walking speed, since patients with stiff-knee gait often walk slowly. We

analyzed muscle-driven dynamic simulations of eight unimpaired subjects walking at

four speeds to quantify the contributions of muscles, gravity, and velocity-related

forces (i.e. Coriolis and centrifugal forces) to preswing knee flexion acceleration

during double support at each speed. Analysis of the simulations revealed

contributions from muscles and passive dynamics varied systematically with walking

speed. Preswing knee flexion acceleration was achieved primarily by hip flexor

muscles on the preswing leg with assistance from biceps femoris short head. Hip

flexors on the preswing leg were primarily responsible for the increase in preswing

knee flexion acceleration during double support with faster walking speed. The hip

extensors and abductors on the contralateral leg and velocity-related forces opposed

preswing knee flexion acceleration during double support.

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5.2 INTRODUCTION

The biomechanical causes of diminished and delayed swing-phase knee

flexion, or stiff-knee gait, in children with cerebral palsy are unclear, making it

difficult to determine appropriate treatment. Over-activity of the rectus femoris is

commonly thought to be the primary cause of stiff-knee gait (Perry, 1987; Sutherland

et al., 1990), yet many patients do not improve after rectus femoris transfer (Hadley et

al., 1992; Ounpuu et al., 1993a; Rethlefsen et al., 1999; Yngve et al., 2002; Carney

and Oeffinger, 2003), a surgery aimed at reducing the muscle’s knee extension

moment, suggesting that there may be other causes in some cases. Other proposed

causes of stiff-knee gait include over-activity of the vasti (Waters et al., 1979;

Kerrigan et al., 1991), weakness of the hip flexors (Kerrigan and Riley, 1998), and

weakness of the ankle plantarflexors (Kerrigan and Glenn, 1994). A better

understanding of the factors that contribute to stiff-knee gait will allow clinicians to

employ treatment strategies that address underlying causes.

To determine the cause of an individual’s stiff-knee gait, it is necessary to

understand how muscles and passive dynamics (gravity and velocity-related forces)

contribute to swing initiation in normal gait. Preswing has been identified as a key

portion of the gait cycle affecting swing-phase peak knee flexion because the muscle

forces produced during preswing determine the knee flexion velocity at toe-off, which

is highly correlated to swing-phase peak knee flexion (Mochon and McMahon, 1980;

Piazza and Delp, 1996; Goldberg et al., 2003; Reinbolt et al., 2008). However, a

thorough understanding of the biomechanical factors that accelerate the knee during

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this period does not exist. Understanding these factors can be challenging because

muscles that do not cross the knee can still accelerate the knee due to dynamic

coupling (Zajac and Gordon, 1989). Modeling and simulation tools are valuable in

analyzing gait dynamics because they enable quantification of the effects of muscles,

gravity, and velocity-related forces on knee flexion acceleration.

It is necessary to understand how contributions to swing initiation change with

walking speed, since patients with stiff-knee gait often walk more slowly than

typically developing children. Walking speed affects kinematics, kinetics, and muscle

activity during gait (Andriacchi et al., 1977; Murray et al., 1984; Kirtley et al., 1985;

Shiavi et al., 1987; Stansfield et al., 2001b; Stansfield et al., 2001a; Hof et al., 2002;

van der Linden et al., 2002; den Otter et al., 2004; Nymark et al., 2005; Cappellini et

al., 2006; Stansfield et al., 2006; Schwartz et al., 2008). The contributions of muscles

and passive dynamics to support and progression of the body’s mass center (Liu et al.,

2008; Neptune et al., 2008) and knee flexion in swing (Arnold et al., 2007a) change

with walking speed. Thus, it is essential to understand how contributions of muscles

and passive dynamics to swing initiation may change with walking speed.

Comparison of contributors to swing initiation between a child with stiff-knee gait and

a typically developing child walking at a similar speed will enable discrimination

between differences due to pathology or walking speed.

The objectives of this study were to identify the major contributors to preswing

knee flexion acceleration during double support and to determine how these

contributions change with walking speed.

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5.3 METHODS

We analyzed simulations created and tested by Liu et al. (2008) using

OpenSim software (Delp et al., 2007). The software and simulations are freely

available at http://simtk.org. Liu et al. (2008) created these simulations to quantify

muscle contributions to support and progression during walking. In this study, we

have analyzed the simulations to determine muscular and passive contributions to knee

flexion acceleration during double support. The double support period of simulations

of eight unimpaired subjects walking at four speeds was analyzed. The subjects’ ages

ranged from 7 to 18 years with a mean of 12.9 years. Protocols for collection and

processing of gait data, including ground reaction forces, kinematics, and

electromyographic (EMG) recordings, were reported by Schwartz et al. (2008).

Walking trials for each subject were assigned post-hoc to categories of very slow,

slow, free, and fast speeds as described by Liu et al. (2008) using a non-

dimensionalized walking speed leggLvv /*= , where v is absolute walking velocity,

Lleg is leg length, and g is gravitational acceleration (Hof, 1996). Average walking

speeds were 0.54 m/s for very slow, 0.75 m/s for slow, 1.15 m/s for free, and 1.56 m/s

for fast.

The musculoskeletal model and procedures for creating and testing the

simulations is described in detail elsewhere (Liu et al., 2008). Briefly, a generic

musculoskeletal model (Delp et al., 1990; Thelen and Anderson, 2006) with 23

degrees of freedom and 92 muscle-tendon actuators was scaled to match each

subject’s anthropometry. Subtalar and metatarsophalangeal joints were locked at

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neutral anatomical angles. Dynamic inconsistency between the measured ground

reaction forces and the model kinematics was resolved by applying small external

forces and torques (i.e. residuals) to the pelvis and making small adjustments to the

model’s mass properties and kinematics (Delp et al., 2007). Computed muscle control

(Thelen et al., 2003), with constraints on muscle excitations applied as necessary, was

used to find a set of actuator excitations that when applied to the model in concert with

external ground reaction forces would both track the experimental kinematics and be

generally consistent with experimental and literature-reported EMG patterns. We

verified that the excitation patterns from the simulations at the different walking

speeds generally scaled with speed as reported in the literature (Hof et al., 2002; den

Otter et al., 2004; Cappellini et al., 2006; Schwartz et al., 2008).

In each simulation, we quantified the contributions of individual muscles,

gravity, and velocity-related forces to preswing knee flexion acceleration using a

perturbation analysis (Liu et al., 2006a). This analysis independently calculated the

contribution from each force (individual muscles, gravity, or velocity-related) and was

repeated for all contributors in the simulation at 10 ms intervals throughout double

support. For each muscle, we added 1 N to the force produced by an individual

muscle in the simulation, integrated forward the equations of motion for a 10 ms

period, and observed the resulting change in preswing knee flexion angle. The

resulting change in preswing knee flexion angle was used to calculate the preswing

knee flexion acceleration generated by 1 N of muscle force, assuming that the

acceleration generated by the muscle over the short 10 ms integration period was

constant. The preswing knee flexion acceleration generated by 1 N of muscle force

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was multiplied by the muscle’s force in the unperturbed simulation to quantify the

muscle’s contribution to preswing knee flexion acceleration at the beginning of the 10

ms period. Translational and rotational spring-dampers applied to the center of

pressure of each foot accounted for changes in the ground reaction force induced by

the muscle perturbation. A similar technique was applied to determine the

contribution of gravity to preswing knee flexion acceleration. To quantify

contributions from velocity-related forces, the model was set in its original

configuration and given its original velocities at the start of every 10 ms period. No

muscle, gravity, or ground reaction forces were applied; only reaction forces from the

spring-dampers representing foot-floor contact were applied. We integrated forward

the equations of motion for a 10 ms period and observed the resulting change in

preswing knee flexion angle. The contribution of velocity-related forces to preswing

knee flexion acceleration was calculated from this change in preswing knee flexion

angle, assuming that the acceleration generated by the velocity-related forces over the

short 10 ms integration period was constant. All contributions (muscle, gravity, and

velocity-related) were averaged over the period of double support in each simulation.

To test the validity of our method, we verified that the sum of all calculated

contributions to preswing knee flexion acceleration was in agreement with the

unperturbed preswing knee flexion acceleration at each time point of analysis

throughout double support (Fig. 5.1). This suggests that our model of foot-floor

contact is a reasonable representation of the constraints on the foot during double

support.

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Figure 5.6 Knee flexion angle and acceleration of subject 5, a representative subject, for the simulation (thick gray line) compared to experimentally measured values (thin black line) during the free speed trial. The simulation closely tracked experimental knee flexion. Shaded region represents ± one standard deviation from the mean of the free speed trials of all eight subjects. Black dots represent the sum of all calculated contributions from the perturbation analysis at each step. Overlap of the black dots with the thick gray line indicates that the sum of contributors to preswing knee flexion acceleration calculated by the perturbation analysis closely approximated the knee flexion acceleration of the simulation.

We performed a one-way repeated measures analysis of variance (SPSS Inc.,

Chicago, IL) to determine if walking speed had a significant effect on the average

contributions of muscles, gravity, and velocity to preswing knee flexion acceleration.

For data that violated sphericity assumptions, a Huynh-Feldt epsilon correction was

applied. When speed was determined to significantly affect a contributor, we

analyzed the within-subject repeated contrasts to determine if there was a significant

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difference between successive speed pairs (i.e., very slow to slow, slow to free, free to

fast). The significance level for all tests was α ≤ 0.05.

5.4 RESULTS

In preparation for swing, the preswing knee is strongly accelerated into flexion

during double support. Most of the flexion acceleration occurs before the toe leaves

the ground, resulting in a peak knee flexion velocity around toe-off (Fig. 5.2A).

Achieving a sufficient knee flexion velocity at toe-off is crucial to achieving sufficient

peak knee flexion in swing. Knee flexion velocity at toe-off increased with walking

speed (p < 0.05; Fig. 5.2B). This was achieved by an increase in average knee flexion

acceleration during double support with increased walking speed (p < 0.01; Fig. 5.2C).

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Figure 5.7 (A) Knee flexion angle over the gait cycle averaged over all eight subjects for each speed with the period of double support highlighted by the thick regions. The slope of this curve represents knee flexion velocity, which peaks near toe-off. (B) Knee flexion velocity at toe-off averaged over all eight subjects increased with walking speed. (C) Knee flexion acceleration averaged over double support and across all eight subjects increased with walking speed. * denotes significant (p < 0.05) difference between successive speeds.

Muscles on both legs contributed to acceleration of the preswing knee (Fig.

5.3). The net effect of muscles on the preswing leg was to accelerate the knee into

flexion during double support. This was accomplished primarily by the hip flexors

(mainly iliacus and psoas) with assistance from biceps femoris short head (BFSH)

(Fig. 5.4). With faster walking speed, the hip flexors contributed more to knee flexion

acceleration (slow to free, p < 0.01; free to fast, p < 0.01). Other preswing leg

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muscles, including gastrocnemius and the ankle dorsiflexors (DF), also contributed to

preswing knee flexion acceleration, but made small contributions relative to the

preswing hip flexors. Some muscles on the preswing leg decelerated knee flexion,

including the uniarticular plantarflexors (UPF) (mainly soleus), vasti, rectus femoris,

and the hip extensors and abductors. The net effect of muscles on the contralateral leg

at all speeds was to decelerate preswing knee flexion. This was primarily due to hip

extensors and abductors on the contralateral leg. Hip flexors on the contralateral leg

opposed the extension effect, but to a lesser extent. Contributions from back muscles

and residual forces and torques varied across subjects, but were small on average.

Average residual contributions to knee flexion acceleration across subjects at each

speed were -417 °/s2 for very slow, -170 °/s2 for slow, -1646 °/s2 for free, and -939 °/s2

for fast.

The contributions of passive dynamics during double support varied

systematically with walking speed (Fig. 5.3). Gravity accelerated the knee into flexion

(Movie 1) with a relatively constant magnitude across speeds, though slightly greater

at free and fast speeds (p < 0.01). Velocity-related (Coriolis and centrifugal) forces

mildly decelerated preswing knee flexion with an increasing effect with faster walking

speed (very slow to slow, p < 0.001; slow to free, p < 0.001; free to fast, p = 0.012).

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Figure 5.8 Net contributions of preswing leg muscles, contralateral leg muscles, velocity-related forces, and gravity to preswing knee flexion acceleration averaged over double support at four walking speeds. Bars represent mean contributions during double support across all eight subjects. Error bars represent ± one standard deviation. * denotes significant (p < 0.05) difference between successive speeds.

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Figure 5.9 Contributions from muscle groups, grouped by functional action, on the preswing leg to preswing knee flexion acceleration during double support averaged across all subjects at each speed. Error bars represent ± one standard deviation. * denotes p < 0.05 for within-subjects repeated contrasts analyses. Model depicts major contributors to flexion as blue line muscles and major contributors to extension as red line muscles. Green arrows represent the ground reaction forces. HipFlx, the hip flexors, includes iliacus, psoas, tensor fasciae latae, and sartorius. BFSH is the biceps femoris short head. DF, the ankle dorsiflexors, includes tibialis anterior, extensor digitorum longus, extensor hallucis longus, and peroneus tertius. Gas includes medial and lateral gastrocnemius. HipExt, the hip extensors, includes gluteus maximus, adductor magnus, biceps femoris long head, semimembranosus, and semitendinosus. HipAbd, the hip abductors, includes gluteus medius and gluteus minimus. RF is the rectus femoris. VAS includes vastus medialis, vastus intermedius, and vastus lateralis. UPF, the uniarticular plantarflexors, includes soleus, tibialis posterior, flexor digitorum longus, flexor hallucis longus, peroneus longus, and peroneus brevis. Other includes all of the other muscles of the preswing leg in the model.

5.5 DISCUSSION

Our simulations showed that the hip flexors, iliacus and psoas, on the preswing

limb were primarily responsible for accelerating the knee into flexion during double

support. This is consistent with previous simulation studies (Yamaguchi and Zajac,

1990; Goldberg et al., 2004). The increase in knee flexion acceleration during double

support with faster walking speed was primarily due to increased force generated by

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the hip flexors. Neptune et al. (2008) also found a dramatic increase in iliopsoas

muscle work to accelerate the preswing leg at faster walking speeds. In our subjects,

peak hip flexion moment during double support increased three-fold between very

slow and fast speeds, a larger increase than either the knee or ankle moments. Large

increases in hip moment during double support with increasing speed were also

observed in other studies (Stansfield et al., 2001b; van der Linden et al., 2002;

Schwartz et al., 2008). Additionally, we found the vasti, rectus femoris, and hip

abductors and extensors decelerate knee flexion during double support, consistent with

other studies (Neptune et al., 2001, Fig. 8; Goldberg et al., 2004).

Our results showed the two major plantarflexors, soleus and gastrocnemius,

had opposite effects on preswing knee acceleration. The knee extension acceleration

of soleus is consistent with other studies (Goldberg et al., 2004; Neptune et al., 2001,

Fig. 8). The mild knee flexion acceleration of gastrocnemius that we found contrasts

with reports that the gastrocnemius has a large flexion effect (Yamaguchi and Zajac,

1990; Goldberg et al., 2004) or an extension effect (Neptune et al., 2001, Fig. 8) on the

preswing knee. The gastrocnemius generates a plantarflexion moment that induces

knee extension acceleration and a knee flexion moment that induces knee flexion

acceleration; thus, its action is sensitive to the muscle’s ankle and knee moment arms,

body position, and foot contact model, which varied among the studies. Although the

net effect of the plantarflexors may be to extend the knee, studies have suggested they

play a role in swing initiation since it has been observed that hip flexors compensate

during preswing when plantarflexors are weak (Nadeau et al., 1999) or absent

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(Zmitrewicz, 2007). Neptune et al. (2008) suggested that gastrocnemius contributes to

swing initiation by delivering energy to the preswing leg.

The roles of hip flexion and ankle plantarflexion moments in swing initiation

have been demonstrated in dynamic walking models. Kuo et al (2002) reported that

an increased hip torque produces increased step frequency, while an increased toe-off

impulse produces longer steps at an approximately constant step frequency; they

suggested that a combination of hip work and toe-off impulse may improve walking

energetics. Other studies have demonstrated a torque applied at the hip and/or a push-

off impulse applied to the foot can produce stable gait on level ground (Collins et al.,

2005).

In our simulations, the contralateral leg muscles contributed an extension

acceleration to the preswing knee at all speeds through their action on the pelvis.

Muscles on the contralateral leg including hip extensors, posterior hip abductors

(which have hip extension moment arms), and vasti extended the knee and hip of the

contralateral leg. In the body configuration of double support, this caused the pelvis to

tilt posteriorly, list upward on the side of preswing leg, and rise slightly. As a result,

the hip joint on the preswing leg was pushed upward (superiorly) and forward

(anteriorly). Reaction forces at the preswing hip joint extended the preswing knee

since the foot of the preswing leg remained on the ground during double support

(Movie 2). At faster walking speeds, the contralateral leg muscles had a stronger

deceleration effect on preswing knee flexion (Fig. 5.3).

Classic texts and studies of passive dynamic walkers have suggested that

muscle activity during preswing sets the initial conditions for passive knee motion

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during swing (Mochon and McMahon, 1980; Mcgeer, 1990; Perry and Newsam, 1992;

Gage and Schwartz, 2004; Boakes, 2006). However, muscles are active during swing,

and studies muscle-actuated models have found that this muscle activity contributes

during both preswing and early swing to achieve appropriate knee motion before and

during swing. Although this study focused on double support, muscular or passive

forces during early swing phase (the period of swing before peak knee flexion) may

also affect peak knee flexion during swing. The knee undergoes a large flexion

acceleration during double support to prepare for toe-off (Fig. 5.2C). After toe-off the

knee undergoes an extension acceleration throughout early swing (Arnold et al.,

2007b). During double support or early swing, forces causing inadequate knee flexion

acceleration or excessive knee extension acceleration may limit peak knee flexion

during swing, resulting in stiff-knee gait. In this study we found that during double

support the preswing knee is accelerated into flexion mainly by swing leg muscles

(primarily the hip flexors and biceps femoris) and gravity at all speeds. Arnold et al.

(2007a; 2007b) found that during early swing the swing knee is extended by stance leg

muscles (mainly vasti and uniarticular plantarflexors) and velocity-related forces at all

speeds. It is necessary to analyze muscle contributions during both preswing and early

swing to investigate possible causes of stiff-knee gait.

Our results should be interpreted in light of several limitations of this study.

First, our estimates of muscle contributions to knee flexion acceleration were

dependent on the force produced by each muscle during the simulation. Although

experimental joint moments and EMG were generally consistent with simulated

values, it was not feasible to compare simulated muscle forces to experimentally

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measured forces. Secondly, residual actuators in the model, which applied external

forces and torques to the pelvis, contributed to knee flexion acceleration with a

magnitude comparable to net muscle contribution in some trials. These residual

actuators do not represent real physical forces, but instead characterize errors in

kinematic and kinetic measurements and deficiencies in the model, such as the lack of

arms and joint simplifications. We chose a method to reduce rather than eliminate

these residual forces, as the latter can result in implausible motions of the back. In

these trials, net muscle contributions were affected, but the relative magnitude of

individual muscle contributions was consistent with trials in which residuals did not

contribute substantially to knee flexion acceleration. Thirdly, although care was taken

to validate simulated muscle activations with experimental EMG, rectus femoris and

gastrocnemius activations for some subjects during double support did not increase

with speed as expected (Hof et al., 2002; den Otter et al., 2004; Cappellini et al., 2006;

Schwartz et al., 2008). If activations and forces in the gastrocnemius and rectus

femoris were greater, we would have observed slightly larger contributions to knee

acceleration.

This study identifies the factors that contribute to knee flexion acceleration

during double support and provides a framework for future studies to investigate the

muscular and passive contributions to knee flexion acceleration in subjects with stiff-

knee gait. Further studies may further elucidate the role of the ankle plantarflexors in

other aspects of swing initiation, such as forward propulsion of the swing leg.

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6 PRELIMINARY WORK: RECTUS FEMORIS VELOCITIES

BEFORE AND AFTER RECTUS FEMORIS LENGTHENING SURGERY

6.1 INTRODUCTION

There is a need for evidence-based clinical indicators for rectus femoris

lengthening surgery. Rectus femoris intramuscular lengthening surgery intends to

increase or maintain peak knee flexion in swing when simultaneous hamstrings

lengthening is performed. A proposed mechanism by which this surgery affects knee

motion is a reduction of rectus femoris spasticity that limits rectus femoris lengthening

velocity and knee flexion prior to surgery. However, it is unclear whether rectus

femoris lengthening velocity increases after surgery or whether greater rectus femoris

velocity leads to improved knee range of motion during gait. We have conducted some

preliminary investigation to determine whether peak rectus femoris lengthening

velocity increases after rectus femoris lengthening surgery and whether preoperative

peak rectus femoris lengthening velocity is predictive of increase in knee range of

motion following surgery.

6.2 METHODS

We analyzed 42 subjects (68 limbs), with cerebral palsy who received rectus

femoris intramuscular lengthening. These patients were treated at Connecticut

Children’s Medical Center between 1991 and 2008, and many of them received other

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surgeries in addition to rectus femoris intramuscular lengthening (e.g., 53 limbs also

received medial hamstring lengthenings). Subjects underwent both preoperative and

postoperative kinematic and kinetic data collection as part of the standard of care (Fig.

6.1). The average time of postoperative gait analysis after surgery was 18.7 months.

The average age at surgery was 9 ± 3 years.

Figure 6. 1 Average and standard deviation of knee flexion angle over gait cycle for rectus femoris lengthening limbs (red) and unimpaired control limbs (grey).

We positioned a three-dimensional musculoskeletal model (Delp et al., 1990)

with subjects’ hip and knee kinematics to estimate rectus femoris musculotendon

lengths (i.e., the origin-to-insertion lengths) over the gait cycle (Fig. 6.2). The

trajectory of musculotendon lengths over the gait cycle were low-pass filtered using a

second-order Butterworth filter with a cut-off frequency of 3 Hz. Rectus femoris

musculotendon velocities were then calculated by differentiating rectus femoris

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lengths with respect to time (Fig. 6.3). For each limb, the peak rectus femoris

lengthening velocity, which occurs before toe-off, was identified. Peak rectus femoris

velocities were also calculated for 14 typically developing subjects. Musculotendon

velocities were normalized by peak velocity of the typical subjects during gait. Rectus

femoris peak velocities were considered “slow” if they were slower than two standard

deviations below the average of the typical group.

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Figure 6. 2 Average and standard deviation of rectus femoris musculotendon lengths (upper) and velocities (lower) for unimpaired limbs (grey) normalized by peak length and velocity of the unimpaired group. Preoperative rectus femoris musculotendon length and velocity for a representative subject (red).

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Univariate linear regression was used to test whether a significant correlation

existed between (1) preoperative peak rectus femoris lengthening velocity and change

in velocity after surgery and (2) preoperative peak rectus femoris velocity and

improvement in knee range of motion (defined as maximum minus minimum knee

flexion during gait) after surgery. Multivariate linear regression was used to determine

whether preoperative peak rectus femoris lengthening velocity was predictive of

change in knee range of motion during gait when accounting for confounding

variables (e.g. concomitant surgeries, walking speed, and age) which may influence

both the outcome variable and the predictor of interest. A subset of the limbs (n = 57)

were included in the multivariate model whose preoperative knee range of motion

during gait was less than two standard deviations below the average for the group of

typical subjects.

6.3 RESULTS

We found that 34 out of 68 limbs had faster peak RF lengthening velocities

after surgery. Rectus femoris muscles that were slower preoperatively tended to have

greater increases in lengthening velocity after rectus femoris intramuscular

lengthening (Fig. 6.4; p < 0.0001). Only 3 of the 21 rectus femoris muscles that were

not slow preoperatively lengthened faster after surgery.

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Figure 6. 3 Normalized preoperative peak rectus femoris musculotendon lengthening velocities for each rectus femoris lengthening subject limb plotted against his or her change in normalized rectus femoris peak musculotendon lengthening velocity after surgery.

Preoperative rectus femoris peak velocity had a significant (p < 0.01;

determined by t-test) but weak (r2 = 0.10) correlation with improvement in knee range

of motion following surgery that included rectus femoris lengthening (Fig. 6.5).

Subjects with slower preoperative rectus femoris velocities showed a greater increase

in knee range of motion during gait.

Figure 6. 4 Normalized preoperative peak rectus femoris musculotendon lengthening velocities for each rectus femoris lengthening subject limb plotted against his or her change in knee range of motion during gait after surgery.

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Multivariate linear regression showed that when confounding variables

(walking speed in particular) were accounted for, preoperative rectus femoris peak

lengthening velocity was not a significant predictor (p > 0.05) of change in knee range

of motion during gait following surgery (Table 6.1). Concomitant femoral derotation

osteotomy, however, was strongly (p < 0.001) predictive of a decrease in knee range

of motion during gait.

Table 6. 1 p-values and coefficients for variables in the multivariate model predicting change in knee range of motion after surgery.

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6.4 DISCUSSION

Our results showed that subjects with slower rectus femoris lengthening

velocities preoperatively tended to show greater increases in rectus femoris

lengthening velocity after surgery. However, it is unclear whether increase in peak

rectus lengthening velocity is due to rectus femoris lengthening or other concomitant

surgeries, such as hamstrings lengthening. Most of the limbs analyzed received

concomitant hamstrings lengthening which may increases rectus femoris velocity by

increasing knee flexion velocity with improvement in knee range of motion during

gait. Despite the surgical cause, we observed that rectus femoris muscles that were not

slow preoperatively did not tend to get faster after surgery.

Preoperative rectus femoris lengthening velocity was not significantly

predictive of improvement in knee range of motion after surgery when accounting for

confounding variables. There may be several explanations for this finding. One

possibility is that rectus femoris lengthening may reduce rectus femoris spasticity, but

other factors, such as concomitant surgeries may have a greater effect on knee range of

motion. This finding seems to be suggested by the large impact other surgeries, such

as femoral derotation osteotomy and gastrocnemius lengthening, had on range of

motion in the multivariate model. Another possibility is that slow rectus femoris

lengthening velocity may not be caused by rectus femoris spasticity. For example,

hamstrings spasticity may directly limit knee extension velocity in swing while

indirectly limiting knee flexion velocity, and therefore rectus femoris velocity, to

maintain balance. A final possible explanation is that rectus femoris musculotendon

lengthening velocity was not sufficiently representative of rectus femoris sapsaticity.

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There are several potential criticisms and limitations of this study. It is unclear

to what extent overall musculotendon velocity is representative of muscle fiber

velocity in the rectus femoris. Although muscles with more compliant tendons are

more susceptible to inconsistencies between musculotendon length changes and fiber

length changes, it is unclear whether the assumption is valid for rectus femoris.

Additionally, we have not modeled the effects of bony deformities which may be

present in the limbs of our subjects. In particular, we have not accounted for the

effects of patella alta in estimating change in musculotendon lengths. If patella alta

affects the moment arm of the rectus femoris, this could impact the velocity of the

muscle over the gait cycle. However, it is difficult to account for the effect of patella

alta since there is currently no consensus in the literature on whether patella alta

increases or does not affect the moment arm of the knee extensors (Ward et al., 2005;

Luyckx 2009; Sheehan 2008). Additionally, it is possible that femoral anteversion may

affect rectus femoris lengths and velocities. We have addressed this possibility by

performing a sensitivity analysis of calculated rectus femoris musculotendon lengths

to varying degrees of femoral anteversion over the range of -80 to 90 degrees of

femoral anteversion. We found that peak rectus femoris musculotendon length over

the gait cycle varied by less than 2 % over this large range of femoral anteversion

angles, meaning that degree of femoral anteversion has an insignificant effect on

estimated muscultotendon lengths and velocities.

We used a multivariate model to assess the significance of one variable,

preoperative peak rectus femoris lengthening velocity, in predicting change in knee

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range of motion while accounting for confounding factors such as age, involvement,

and concomitant surgeries. However, this data set and limited number of subjects is

not ideally suited for determining the best multivariate model, with the most powerful

combination of preoperative variables, for predicting change in knee range of motion

following surgery. An important next step would be to create a multivariate model,

with more subjects and a larger selection of preoperative predictive variables, to

determine whether some combination of preoperative data can improve predictions of

postoperative outcome.

Our multivariate model showed that concomitant femoral derotation osteotomy

had a negative effect on knee range of motion during gait after surgery. Another

important step would be to determine the cause of this effect. One would expect a

derotational osteotomy, as we observe for the tibial derotation osteotomy, to have a

restorative effect on muscle function and limb alignment, thereby resulting in

improved knee range of motion. It is possible that a non-included factor correlated

with the incidence of femoral derotation osteotomy is contributing to this effect.

Though our multivariate model accounted for overall involvement, the addition of a

preoperative severity of crouch variable may help shed some light on this

unanticipated result.

One final follow-up step would be to improve the accuracy of both the

musculoskeletal model and the statistical model. It is recommended to test the

accuracy of the rectus femoris musculotendon length and velocity measurements in the

presence of patella alta. If patella alta greatly affects these measurements it would be

necessary to obtain some clinical measure of patella height in order to accurately

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represent it in the musculoskeletal model. Regarding the statistical model, much of the

data was taken from two limbs of a single subject, making these non-independent data.

A statistical correction is recommended to account for this effect since it breaks the

assumption of independent data in the multivariate model.

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7 CONCLUSION 7.1 SUMMARY

The goal of this work was to clarify biomechanical causes of stiff-knee gait

and the functional mechanism of surgical treatment. The motivation for this work was

to contribute to the understanding of stiff-knee gait as a step towards improving

indications for treatment and reducing the variability of surgical outcomes. We used

computer simulation of gait to quantify muscle function during inappropriate timing,

after surgical transfer, and in unimpaired gait. We also implemented an addition to

perturbation analysis to allow comprehensive quantification of contributions to knee

flexion acceleration.

The findings of this work clarify the indications for rectus femoris transfer and

illuminate muscle coordination of normal gait. The main conclusions of this research

are:

• Preswing rectus femoris activity can contribute to stiff-knee gait

In our comparison of the simulated effects of preswing to early swing phase

activity of rectus femoris in stiff-knee gait, we identified preswing rectus femoris

activity as a potential contributor to stiff-knee gait. In many subjects, preswing

rectus femoris activity had a greater limiting effect on peak knee flexion in swing

than early swing activity. Our results suggest that preswing rectus femoris EMG

may be a useful indicator for surgical treatment. Additionally, comparison of

patient EMG to speed-matched unimpaired EMG may help to diagnose improper

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preswing rectus femoris activity, since unimpaired subjects exhibit preswing rectus

femoris activity at free and fast speeds while many patients with stiff-knee gait

walk at slower speeds. Care should be taken in interpreting surface EMG of the

rectus femoris, as it may be subject to cross-talk from the vasti (Barr et al., 2010).

• Rectus femoris transfer improves knee flexion primarily by reduction of the

muscle’s knee extension moment

By comparing the simulated knee flexion resulting from models of rectus femoris

transfer surgery, we determined that reduction of the muscle’s knee extension

moment to values comparable to experimental measures (Asakawa et al., 2002)

was sufficient to achieve improved peak knee flexion. Simulated peak knee flexion

improvement using the scarred transfer model was most similar to average

clinically reported improvement in peak knee flexion following isolated transfer

(Hemo et al., 2007).

• Hip flexor muscles are the largest contributors to knee flexion acceleration

during double support in unimpaired gait

Comparing contributions averaged over double support to knee flexion

acceleration from muscles and passive dynamics, we determined hip flexors to be

the primary contributors at all speeds. Hip flexor muscles were also primarily

responsible for increasing knee flexion acceleration in double support with

increasing walking speed.

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• Muscles other than rectus femoris may contribute to stiff-knee gait in

children with cerebral palsy

Our study of muscle contributions in chapter 5, revealed that several muscles

contribute to double support knee flexion acceleration. Diminished force in the

contributors, such as hip flexors and biceps femoris short head, may contribute to

stiff-knee gait. Additionally, over-activity in the muscles that contribute to knee

extension acceleration, such as vasti and soleus, may cause stiff-knee gait.

7.2 FUTURE WORK

Though this dissertation work has important implications for the diagnosis and

treatment of stiff-knee gait, much additional work is needed to improve treatment

outcomes. In order to correctly diagnosis the cause of stiff-knee gait, more research is

required to identify contributors to stiff-knee gait, aside from rectus femoris over-

activity, in children with cerebral palsy. Though our study in chapter 5 investigated

potential muscle contributors to stiff-knee gait, it is necessary to evaluate the

prevalence of these contributors in a clinical population and to establish protocols for

diagnosing these causes. Additionally, clinical studies evaluating the efficacy of

interventions targeting these additional muscle contributors would be a valuable step

in improving treatment planning. There may be additional contributors to stiff-knee

gait that are not muscular in origin. For example, it is unknown how bony deformities,

such as femoral anteversion or patella alta, may affect the ability of muscles to effect

knee motion. Another potential cause of stiff-knee gait that deserves more research

effort is the relationship between stiff-knee and crouch gait. Although some

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preliminary work has investigated the relationship (van der Krogt et al., 2010), it

remains unclear whether crouch gait can lead to stiff-knee gait, or what the appropriate

treatment to address this cause should be.

More thorough investigation into the biomechanical effects of surgical

treatment could also lead to improved surgical technique and patient selection. In

chapter 4, we modeled the effects of scarring of the rectus femoris by altering the

muscle’s capacity to generate a knee moment, but more detailed models representing

force transmission between muscles through connective tissue could provide

additional insight into the transferred muscle’s postoperative function. Furthermore,

muscle remodeling and neural adaptation following musculoskeletal surgery is not

well understood, and could have important implications for surgical technique and

postoperative rehabilitation procedures.

A related area of future research that has the potential for immediate clinical

impact is identifying better indications for rectus femoris surgeries. To reduce

variability in outcomes, and prevent subjects who would have poor outcomes from

having the surgery, it is necessary to refine the current indications for rectus femoris

transfer and lengthening surgeries. Some preliminary work has identified outcome-

based quantitative metrics for recommending rectus femoris transfer surgery (Reinbolt

et al., 2009). Additional work may identify a model with stronger, more clinically

relevant predictors and may test the model across multiple institutions.

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