THE DYNAMICS OF CROUCH 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

Katherine Muterspaugh Steele

July 2012

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

This dissertation is online at: http://purl.stanford.edu/ph453mr9252

© 2012 by Katherine Muterspaugh Steele. 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.

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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.

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ABSTRACT

Individuals with cerebral palsy commonly have gait pathologies that limit their

mobility and hinder activities of daily living. One of the most common gait

pathologies among individuals with cerebral palsy is crouch gait. Individuals who

walk in a crouch gait have excessive hip and knee flexion which makes walking

difficult and metabolically inefficient. If untreated, crouch gait can lead to joint pain,

bone deformities, and a loss of independent mobility. Current treatments for crouch

gait involve orthopaedic surgery and therapy; however, outcomes are inconsistent.

Clinicians need a better understanding of how the complexities of the neuromuscular

and musculoskeletal systems contribute to this pathologic gait pattern. The goal of this

dissertation was to examine the musculoskeletal dynamics of crouch gait in

individuals with cerebral palsy to better understand its biomechanical causes and

improve treatment of individuals with crouch gait.

There are many proposed causes of crouch gait including excessive muscle

activity from contracture or spasticity, muscle weakness, bone deformities, and

impaired voluntary control. To determine which of these factors contribute to crouch

gait requires an understanding of how individual muscles contribute to motion. We

generated the first three-dimensional musculoskeletal simulations of crouch gait to

evaluate how muscles contribute to joint and mass center acceleration. We found that

individuals with crouch gait use the same muscles to support and propel the body as

unimpaired gait. However, larger and more sustained muscle forces are required

during crouch gait.

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Many individuals with cerebral palsy and crouch gait also develop knee pain

later in life. Since cartilage growth and maintenance is dependent upon the loads

experienced during daily life, we sought to quanitfy how tibiofemoral forces change

during crouch gait. We determined that the compressive tibiofemoral force increases

quadratically with crouch severity and individuals who walk in a severe crouch gait

experience three times the load experienced during unimpaired gait. Elevated

tibiofemoral forces could compromise cartilage health and lead to knee pain.

Muscle weakness is commonly hypothesized as a cause of crouch gait and

many individuals with crouch gait participate in strength training programs. We

performed a meta-analysis of outcomes after strength training in individuals with

cerebral palsy and crouch gait and found that although muscle strength increases after

strength training, changes in gait kinematics are inconsistent. Some individuals with

crouch gait had significantly more knee extension during gait after strength training;

however, other individuals’ gait deteriorated. We determined that hamstring spasticity

may be a contraindication for strength training among individuals with cerebral palsy

and crouch gait; no individuals with hamstring spasticity had improved knee extension

after strength training.

We also used musculoskeletal simulation to evaluate how much muscle

strength is required to walk in a crouch gait compared to an unimpaired gait. We

found that crouch gait requires more quadriceps strength than unimpaired gait but

requires less hip abductor and ankle plantarflexor strength. These results suggest that

weakness of the hip abductors or ankle plantarflexors may contribute to crouch gait

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and strengthening these muscles may lead to more consistent outcomes after strength

training.

This dissertation examines the dynamics of crouch gait among individuals with

cerebral palsy including muscle contributions to motion, changes in joint loads, and

the effects of muscle weakness. This work provides a foundation for using

musculoskeletal modeling and simulation to examine complex gait pathologies and

also suggests exciting future areas of research to improve the care and treatment of

individuals with cerebral palsy and crouch gait.

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ACKNOWLEDGEMENTS Over the past five years I have come to appreciate that earning a PhD is a team

effort that requires incredible collaborators and a tight support network. The

community is the best part of Stanford University and many people have helped to

make this dissertation a reality. The acknowledgements that follow only scratch the

surface and I thank the whole Stanford community for their help and encouragement.

First, I need to thank my advisor, Scott Delp and the Neuromuscular

Biomechanics Laboratory (NMBL). Dr. Delp has provided me with an excellent role

model for how to enjoy research and investigate important questions. The community

provided by NMBL has given me a safe place to explore the field of biomechanics,

take risks, and grow as an engineer and researcher. I especially want to thank Ajay

Seth, Ayman Habib, Jennifer Hicks, Melanie Fox, and Matt DeMers for their

invaluable advice, technical support, and collaboration. My day-to-day work would

also not have been the same without Melinda Cromie sitting across from me to bounce

ideas off of, ask questions, and pursue ideas like creating our own course.

Additionally, the lab would not function as smoothly without the constant attention

and support of Carolyn Mazenko – thank you.

I have also been fortunate enough to have an amazing team of collaborators

outside of NMBL. My reading committee members, Jessica Rose and Tom

Andriacchi, have been a continual source of support, critical evaluation, and clinical

insight. The opportunity to work at Lucille Packard Children’s Hospital with Jessica

Rose has provided me with a weekly reminder of the patients we are trying to help. I

would also like to thank Mike Schwartz from Gillette Children’s Specialty Healthcare

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for not only providing an amazing source of clinical data but, more importantly, for

his insights and lively discussions. I am also thankful to have had the opportunity to

collaborate with Marjolein van der Krogt during her visits to Stanford. Diane Damiano

from the National Institutes of Health has served as a valuable clinical collaborator

and mentor. I hope to continue to work with all of these individuals in the future to

improve the lives of individuals with cerebral palsy.

I must also not forget to acknowledge that research requires money and a

variety of sources have helped to fund this work including an NSF Graduate Research

Fellowship and NIH grants R01-HD33929, R01-HD046814, and U54-GM072970.

Outside of research I have had an incredible community of friends who have

supported me and made the last five years enjoyable. A special thanks to the Barnes

couples, Matt, An, Mai, and our volleyball teams for providing humor and perspective

– the last five years would not have been the same without you. In addition, Sheri

Sheppard, ME Women+, ASEE, and my WISE group have kept me sane and given me

inspiration for the future.

Finally I need to thank my family for their constant love and support. Mom and

Dad, you have always been my anchor and an incredible source of inspiration and

encouragement. Dan, my wonderful husband, I am so happy that we get to share our

journey together as best friends. I also want to thank my extended family including

Kathleen Rand-Burke, the Saponases, the Wilhoits, and the whole Greencrest family

for their support. I love you all and can’t wait to see where our adventures together

lead next.

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CONTENTS Abstract ......................................................................................................................... v 

Acknowledgements ...................................................................................................... ix 

List of Tables .............................................................................................................. xiii 

List of Figures ............................................................................................................. xv 

1. Introduction .............................................................................................................. 1 1.1 Focus of the Dissertation ................................................................................................................ 3 

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

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

2. Background ............................................................................................................... 9 2.1 Gait & Mobility ............................................................................................................................ 10 

2.2 Cerebral Palsy ............................................................................................................................... 14 

2.3 Crouch Gait .................................................................................................................................. 15 

2.4 Musculoskeletal Simulation .......................................................................................................... 40 

3. How do muscles contribute to support and progression during crouch gait? .. 47 Abstract ............................................................................................................................................. 48 

3.1 Introduction .................................................................................................................................. 49 

3.2 Methods ........................................................................................................................................ 51 

3.3 Results .......................................................................................................................................... 55 

3.4 Discussion ..................................................................................................................................... 60 

4. How do muscle contributions to support and progression change with crouch

severity? ....................................................................................................................... 65 Abstract ............................................................................................................................................. 66 

4.1 Introduction .................................................................................................................................. 67 

4.2 Methods ........................................................................................................................................ 69 

4.3 Results .......................................................................................................................................... 76 

4.4 Discussion ..................................................................................................................................... 80 

5. How does tibiofemoral contact force change during crouch gait? ..................... 85 Abstract ............................................................................................................................................. 86 

5.1 Introduction .................................................................................................................................. 87 

5.2 Methods ........................................................................................................................................ 89 

5.3 Results .......................................................................................................................................... 95 

5.4 Discussion ..................................................................................................................................... 98 

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6. How much muscle strength is required to walk in a crouch gait? ................... 103 Abstract ...........................................................................................................................................104 

6.1 Introduction .................................................................................................................................105 

6.2 Methods ......................................................................................................................................107 

6.3 Results .........................................................................................................................................113 

6.4 Discussion ...................................................................................................................................116 

7. What characteristics are associated with positive outcomes after strength

training for crouch gait? .......................................................................................... 123 Abstract ...........................................................................................................................................124 

7.1 Introduction .................................................................................................................................125 

7.2 Methods ......................................................................................................................................127 

7.3 Results .........................................................................................................................................131 

7.4 Discussion ...................................................................................................................................136 

8. Conclusion ............................................................................................................. 141 8.1 Summary .....................................................................................................................................142 

8.2 Future Work ................................................................................................................................143 

References ................................................................................................................. 149 

Appendix A: Chapter 3 Supplementary Material ................................................. 167 A.1 Effects of constraining EMG on muscle contributions ..............................................................167 

A.2 Mass center and joint accelerations from all muscles ................................................................171 

Appendix B: Chapter 5 Supplementary Material ................................................. 175 B.1: Calculating joint forces in OpenSim .........................................................................................175 

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LIST OF TABLES Table 4.1: Subject characteristics (average ± standard deviation) ............................... 70 

Table 5.1: Subject characteristics (average ± standard deviation) ............................... 89 

Table 6.1: Subject characteristics (average ± standard deviation) ............................. 107 

Table 6.2: Description of muscle groups .................................................................... 113 

Table 7.1: Summary of crouch subjects and training programs for all studies .......... 128 

Table 7.2: Results of regression analyses for change in knee flexion angle and knee extensor strength ......................................................................................................... 135 

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LIST OF FIGURES Figure 2.1: Kinematics during unimpaired gait (average ± one standard deviation, in degrees). ........................................................................................................................ 11 

Figure 2.2: Kinetics including joint moments (Nm/kg) and powers (W/kg) during unimpaired gait (average ± one standard deviation). ................................................... 12 

Figure 2.3: Average periods when the muscles are active during unimpaired gait from electromyography data collected at Lucille Packard Children’s Hospital. .................. 13 

Figure 2.4: Average knee flexion during mild, moderate, and severe crouch gait compared to unimpaired gait and a musculoskeletal model illustrating a typical crouch gait pattern. ................................................................................................................... 16 

Figure 2.5: Anatomy of the hamstrings, iliopsoas, and ankle plantarflexors (gastrocnemius and soleus) from the University of Washington Musculoskeletal Atlas. ...................................................................................................................................... 18 

Figure 2.6: Meta-analysis of outcomes after hamstring lengthening including change in popliteal angle, change in knee flexion angle, and change in pelvic tilt. ................. 25 

Figure 2.7: Map of visitors to the website with the simulations and documentation presented in this dissertation from July 1, 2011 to January 1, 2012 (http://www.simtk.org/home/crouchgait/). ................................................................... 41 

Figure 3.1: OpenSim model shown at different phases of single-limb stance during crouch gait. The muscles shown in red are highly activated, while those in blue have a low activation level, as determined using the computed muscle control algorithm. .... 49 

Figure 3.2: Comparison of simulated and experimentally-measured joint angles. Average kinematics for pelvis, hip, knee, and ankle are shown for all 10 subjects. The gray line and shaded regions are the experimentally-measured joint angles (± 1 standard deviation) and the black line and dashed-lines are the kinematics reproduced by the simulation (± 1 standard deviation). The simulated kinematics are not provided during double support as only single-limb stance was simulated. The simulated kinematics were within 1º of experimental kinematics (RMS error) for all trials. ...... 55 

Figure 3.3: Comparison of the simulated and experimentally-measured hip, knee, and ankle moments for all 10 subjects. The gray line and shaded regions are the experimentally-measured joint moments (± 1 standard deviation) and the blue line and dashed-lines are the moments calculated by computed by multiplying the estimated muscle forces and moment arms (± 1 standard deviation). Joint moments are only shown during single-limb stance and swing since force plate data was not available during double support. .................................................................................................. 56 

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Figure 3.4: Comparison of EMG and simulated activation. The EMG signal and activation were normalized to a range of 0 to 1 between the maximum and minimum values for each subject. The gray line and shaded area represents the EMG data (± 1 standard deviation) over a full gait cycle, while the simulated activations during single-limb stance are shown in blue with the dashed lines showing ± 1 standard deviation. Note that estimated muscle activations are not provided during the double support periods of the gait cycle because only single-limb stance was simulated. ...... 57 

Figure 3.5: Average contributions ± 1 standard deviation to hip, knee, and ankle angular accelerations during single-limb stance from the major muscle groups of the stance limb. Positive and negative accelerations correspond to extension and flexion, respectively. Note that the muscles with average values close to zero made small contributions throughout single-limb stance. ............................................................... 58 

Figure 3.6: Contributions to mass center accelerations from the muscles providing the largest magnitude accelerations upward and downward and from gravity. Accelerations are shown for single-limb stance from opposite toe-off (OTO) to opposite heel contact (OHC). The vectors represent the average up/down and forward/backward acceleration of the mass center at each 5% of single-limb stance for all subjects. The magnitude of the accelerations in the forward/backward directions has the same scale as the up/down accelerations shown on the vertical-axis. Skeletal alignment was calculated by subtracting the accelerations due to muscles from the accelerations due to the ground reaction force. ............................................................ 59 

Figure 4.1: Musculoskeletal model of an individual with cerebral palsy and crouch gait. Vertical and fore-aft accelerations of the mass center were calculated by analyzing muscle-driven simulations. .......................................................................... 69 

Figure 4.2: Average hip, knee, and ankle flexion angles and moments during unimpaired gait and mild, moderate, and severe crouch gait. The joint moments are normalized by body mass (kg). .................................................................................... 72 

Figure 4.3: Average ± 1 standard deviation of the EMG signal of each group (gray) and estimated muscle activations for each subject (black lines) from the quadriceps, hamstrings, gastrocnemius, and anterior tibialis during unimpaired gait and mild, moderate, and severe crouch gait. Only one individual with moderate crouch gait had EMG, thus we took the average of multiple gait cycles for comparison to the group. The magnitude of the EMG and activations were normalized from 0 to 1 based upon the minimum and maximum values during the gait cycle. ........................................... 75 

Figure 4.4: The average (A) fore-aft and (B) vertical accelerations of the mass center during stance produced by each muscle and (C) the average muscle force during stance normalized by body weight (BW). Error bars are ± 1 standard error. A ‘*’ indicates a significant difference (p < 0.05) in the student’s t-test comparing unimpaired gait and crouch gait. An arrow indicates a significant change with crouch

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severity (p < 0.05) from a one-way ANOVA comparing mild, moderate, and severe crouch gait. ................................................................................................................... 76 

Figure 4.5: The average (A) fore-aft and (B) vertical accelerations produced per 1 newton of muscle force during stance of each muscle. Error bars are ± 1 standard error. A ‘*’ indicates a significant difference (p < 0.05) in the student’s t-test comparing unimpaired gait and crouch gait. An arrow indicates a significant change with crouch severity (p < 0.05) from a one-way ANOVA comparing mild, moderate, and severe crouch gait. ................................................................................................. 78 

Figure 4.6: The fore-aft accelerations of the mass center produced by the vasti (gray line) and gastrocnemius (black line) during stance. The gray area shows the experimentally measured acceleration of the mass center (fore-aft ground reaction force normalized by body mass). .................................................................................. 79 

Figure 5.1: Tibiofemoral contact forces expressed in multiples of body weight (BW) from experimental forces measured using an instrumented total knee replacement (TKR, gray) and estimated with the computer model (black). The average ± 1 standard deviation is shown from four trials. .............................................................................. 93 

Figure 5.2: Comparison of EMG (gray, average ± one standard deviation over all gait cycles) and muscle activations from static optimization (black line) for the six subjects with crouch gait for whom EMG data was available. EMG and activations were normalized from zero to one for each subject based upon the minimum and maximum values over the gait cycle. Note that subject “Severe 1” did not have EMG data from the gastrocnemius. ........................................................................................................ 94 

Figure 5.3: (A) Average knee flexion angle, (B) average compressive tibiofemoral force, and (C) average quadriceps force expressed as multiples of body weight (BW) during one gait cycle for the subjects who walked with an unimpaired gait and mild, moderate, and severe crouch gait. ................................................................................ 96 

Figure 5.4: Correlation of average knee flexion angle during stance with average compressive tibiofemoral force during stance (black circles), average quadriceps force during stance (dark gray squares), average hamstrings force during stance (light gray triangles), and average gastrocnemius force during stance (black outlined diamonds). Tibiofemoral force and average quadriceps force are expressed as multiples of body weight (BW). A quadratic relationship described the change in both tibiofemoral force and quadriceps force with increasing crouch. .............................................................. 97 

Figure 5.5: Average (A) tibiofemoral contact force, (B) quadriceps force, (C) hamstring force, and (D) gastrocnemius force during stance with the objective function shown in Eqn. 1 and weighting constants, minimizing activation with weighting constants, minimizing activation cubed with weighting constants, and minimizing activation squared with all weighting constants equal to one. ................ 101 

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Figure 6.1: Musculoskeletal models used to create dynamic simulations of gait for individuals that walked in an unimpaired gait pattern (left) and individuals with cerebral palsy who walked in mild (center) and moderate (right) crouch gait. .......... 109 

Figure 6.2: The average hip, knee, and ankle (A) kinematics and (B) kinetics during unimpaired gait (dotted) and mild (light gray) and moderate (dark gray) crouch gait. Joint moments are normalized by body mass (kg). .................................................... 110 

Figure 6.3: Comparison of the required strength for each muscle group of the unimpaired subjects (N=3) when using torso markers for inverse kinematics and without torso markers (average ± 1 standard error).. ................................................. 111 

Figure 6.4: Required strength for each muscle group that was necessary to recreate each subject’s gait pattern expressed as percent of the maximum isometric force (average ± 1 standard deviation, * p < 0.05 from Fisher’s Least Significant Difference test). ............................................................................................................................ 114 

Figure 6.5: Compensatory muscle action when a particular muscle group is weakened, expressed as the average change in muscle force over the gait cycle (times body weight, BW). For each muscle group, the change in force of the weakened muscle group and the change in force of the three muscles with the greatest change in force are shown (average ± 1 standard error). ..................................................................... 115 

Figure 6.6: Average (A) kinematics and (B) kinetics for hip abduction and ankle plantarflexion for unimpaired children (N=82, dotted black) and individuals with cerebral palsy who walked in mild (N = 976, light gray) and moderate (N=209, dark gray) crouch gait who visited Gillette Children’s Specialty Healthcare. The peak hip abductor moment and ankle plantarflexor moment are smaller during mild and moderate crouch gait compared to unimpaired gait (ANOVA, p < 0.001). Joint moments are normalized by body mass (kg). ............................................................. 120 

Figure 7.1: Summary of literature review and study selection. .................................. 128 

Figure 7.2: Histograms of (A) percent change in knee extensor strength and (B) change in minimum knee flexion angle during gait after completing a strength training program. Subjects from each of the three studies are shown separately – Damiano (white), Eek (gray), and Unger (black). ..................................................................... 132 

Figure 7.3: Average hip, knee, and ankle flexion angles for (A) all subjects, (B) the three subjects with the largest increase in knee extension (best outcomes), and (C) the three subjects with the largest increase in knee flexion (worst outcomes) before and after completing strength training program. Note that although there was no significant change in knee flexion for the group as a whole, there were subsets of subjects with significant positive and negative changes. ................................................................. 133 

Figure 7.4: (A) Hamstring spasticity and (B) walking speed were associated with change in minimum knee flexion angle (KFA) during stance. .................................. 135 

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CHAPTER 1

INTRODUCTION

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Walking provides an efficient way to explore and interact with the world;

however, it requires precise coordination of the neuromuscular and musculoskeletal

systems. If this coordination is impaired, an individual’s mobility and quality of life

can be compromised. When problems with movement arise, identifying the cause and

appropriate treatments is challenging.

Individuals with cerebral palsy represent a large population of individuals with

mobility problems. According to the United Cerebral Palsy Foundation, in the United

States alone nearly 800,000 individuals have cerebral palsy. Cerebral palsy is caused

by an injury to the brain that affects coordination and movement. Treatments to

improve mobility typically involve a combination of orthopaedic surgery and physical

therapy; however, outcomes from treatment are inconsistent and often unsatisfactory.

A recent study reported that only 48% of individuals with cerebral palsy had

significant improvements in gait following multi-level orthopaedic surgery (Hicks et

al., 2011).

The complexity of the neuromuscular and musculoskeletal systems hinders our

ability to effectively treat gait pathologies in individuals with cerebral palsy.

Identifying the causes and appropriate treatments for each individual is challenging.

Clinicians need a better understanding of the underlying mechanisms that contribute to

gait pathologies to design optimal treatment strategies. For example, many

orthopaedic surgeries target individual muscles; however, how individual muscles

contribute to motion during pathologic gait is not well understood. Clarifying these

contributions would empower clinicians and researchers to improve treatment.

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Musculoskeletal modeling and simulation provides a powerful tool for

understanding the complexities of human movement and performing studies that

cannot be done experimentally. The Neuromuscular Biomechanics Laboratory at

Stanford University under the guidance of Scott Delp and researchers at other

institutions have helped to develop a freely-available software package, OpenSim, that

allows researchers and clinicians to study the musculoskeletal system. Using a

combination of experimental data and computational methods we can examine the

dynamics of human movement, including pathologic gait patterns in individuals with

cerebral palsy.

This dissertation harnesses musculoskeletal modeling and simulation to

improve our understanding of the dynamics of one of the most common gait

pathologies among individuals with cerebral palsy, crouch gait. Crouch gait,

characterized by excessive hip and knee flexion, is an inefficient gait pattern which, if

left untreated, can lead to joint pain, the formation of bone deformities, and an

inability to walk independently. Using musculoskeletal modeling and simulation, we

can examine the contributions of individual muscles, estimate joint loads, and explore

clinical hypotheses to improve our understanding and ability to treat crouch gait.

1.1 FOCUS OF THE DISSERTATION

The goal of this dissertation was to examine the dynamics of crouch gait in

individuals with cerebral palsy. We created three-dimensional musculoskeletal

simulations of gait that allowed us to probe how individual muscles give rise to

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motion of the musculoskeletal system. We sought to understand important dynamic

factors that occur during crouch gait, including how muscles accelerate the body, how

joint loads change with crouch severity, and how muscle weakness can affect gait. We

found that crouch gait uses similar muscles to accelerate the body as unimpaired gait,

but requires larger and more sustained muscle forces to support the body - which

contributes to the inefficiency of this gait pattern. The larger muscle forces required to

support the body also contribute to increased joint loads. We determined that the

compressive tibiofemoral force increases quadratically with crouch severity (i.e., knee

flexion during stance) and individuals with severe crouch gait experience three-times

the tibiofemoral force compared to those with unimpaired gait. Muscle weakness may

also be an important contributor to crouch gait and we identified that weakness of

some muscle groups, such as the quadriceps, are not likely contributors to crouch gait,

while other muscle groups, such as the hip abductors and ankle plantarflexors, may

contribute to crouch gait. These analyses provide a foundation to understand the

mechanics of pathologic gait patterns and to guide the development of innovative

treatment strategies.

1.2 SIGNIFICANCE

The research questions addressed in this dissertation make important

contributions to both the biomechanics and clinical communities. Understanding the

dynamics of the musculoskeletal system can guide treatment planning and illuminate

the causes of pathological gait patterns; however, this endeavor requires sophisticated

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tools to accurately examine the musculoskeletal system. This dissertation sought to

address important clinical problems while also establishing and sharing the tools

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

• Creating the first three-dimensional musculoskeletal simulations of

individuals with cerebral palsy. We developed the framework and processes

to create and critically analyze simulations of gait for individuals with cerebral

palsy and crouch gait. Previous studies have used musculoskeletal simulations

to examine unimpaired gait and we extended these methods to examine

important research questions for individuals with pathologic gait. These

simulations have also been made available to other researchers and clinicians

at: http://www.simtk.org/home/crouchgait/.

• Identifying the primary muscles that support and propel the body during

crouch gait. Walking requires a complex orchestration of muscle activity to

efficiently move the body from one point to another. We sought to identify

how muscle contributions to mass center acceleration change during crouch

gait. By creating musculoskeletal simulations of gait we were able to identify

that crouch gait uses similar muscle groups to support and propel the body as

unimpaired gait; however, crouch gait requires more sustained contributions

from muscles to support the body. Crouch gait also requires less gluteus

medius force to accelerate the mass center upward and greater ankle

plantarflexor force to accelerate the mass center forward.

• Quantifying the change in tibiofemoral contact force during crouch gait.

Knee pain is common among individuals with cerebral palsy; however, the

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cause of the pain and appropriate treatments are not well understood. Increased

knee loading could compromise cartilage health and lead to knee pain. We

used musculoskeletal modeling to quantify changes in tibiofemoral force

during mild, moderate, and severe crouch gait. The magnitude of the

compressive tibiofemoral force increased quadratically with increasing crouch

severity; individuals with a severe crouch gait experienced peak loads up to six

times body weight as compared to two times body weight during unimpaired

gait.

• Examining how muscle weakness can lead to crouch gait. Muscle weakness

is commonly hypothesized as a contributor to crouch gait and is used to justify

strength training programs. However, an understanding of the mechanisms by

which muscle weakness contributes to crouch gait has not been previously

explored. Therefore, we used musculoskeletal modeling and simulation to

examine the amount of muscle strength required to walk in mild, moderate,

and severe crouch gait compared to unimpaired gait. The results of this

analysis showed that the amount of quadriceps strength required increased

quadratically with increasing crouch severity, suggesting that quadriceps

weakness does not contribute to crouch gait. However, crouch gait required

less hip abductor and ankle plantarflexor strength than unimpaired gait,

suggesting that crouch gait could be a compensatory gait pattern for weakness

of these muscle groups.

• Reviewing outcomes after strength training in individuals with crouch

gait. Over the past two decades strength training has become a popular

7

treatment strategy for individuals with cerebral palsy; however, reported

changes in muscle strength and gait after strength training are inconsistent

(Damiano et al., 2010). Previous studies included individuals with cerebral

palsy with many different gait pathologies which hindered interpretation of

their outcomes. Therefore, to examine the effects of strength training on

individuals with crouch gait, we performed a literature review, requested data

from the authors, and performed a meta-analysis of outcomes after strength

training. The results of this meta-analysis indicated that although individuals

with cerebral palsy and crouch gait were stronger after strength training,

changes in gait were inconsistent. Some subjects’ gait improved to within

normal limits after strength training while other subjects’ gait deteriorated.

• Determining that hamstring spasticity is associated with negative

outcomes after strength training in individuals with crouch gait. To

explore the subject-specific factors that could lead to inconsistent outcomes

after strength training in individuals with crouch gait, we performed regression

analyses with ten physical exam and gait characteristics that we hypothesized

could be associated with outcomes after strength training. The results of these

regression analyses identified that hamstring spasticity was associated with

negative outcomes after strength training; none of the subjects with hamstring

spasticity had improved knee extension during gait after strength training.

8

1.3 THESIS OVERVIEW

This dissertation is focused around five research studies that are presented as

self-contained journal articles. After this general introduction, Chapter 2 outlines the

background material related to gait, cerebral palsy, and musculoskeletal simulation

that is useful for interpreting the following chapters. Chapter 3 examines how muscles

contribute to joint and mass center accelerations during stance in mild crouch gait

(Steele et al., 2010, published in Journal of Biomechanics). Chapter 4 extends this

study to examine how muscle contributions to support and propulsion change with

crouch severity (manuscript in review). Chapter 5 quantifies tibiofemoral contact

forces during crouch gait (Steele et al., 2012, published in Gait & Posture). Chapter 6

explores the mechanisms by which muscle weakness could contribute to crouch gait

(manuscript in review). Chapter 7 examines changes in muscle strength and gait after

strength training in individuals with cerebral palsy and crouch gait (Steele et al., 2012,

published in Journal of Pediatric Rehabilitation Medicine). The final chapter of this

dissertation summarizes the important findings of these studies and outlines areas for

future research. The pronoun “we” is used throughout this dissertation to recognize

that research is a team process that requires input and collaboration from multi-

disciplinary teams. The individuals who contributed to these studies are listed at the

beginning of each chapter.

9

CHAPTER 2

BACKGROUND

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2.1 GAIT & MOBILITY

Walking gives us the freedom to interact with the world and complete the

activities of daily living essential for both work and leisure. The average adult in the

United States takes approximately 6000 to 7000 steps per day (Tudor-Locke et al.,

2004). Beyond enabling mobility, walking has a direct and positive influence on

public health, with demonstrated benefits that include the lowering of rates of chronic

health problems, such as obesity and cardiovascular disease, and reducing medical

expenditures (Lee and Buchner, 2008).

Walking is a cyclic movement that can be accurately and consistently

described by kinematics (joint angles), kinetics (ground reaction forces and moments),

and muscle activity (electromyography). Motion analysis provides a tool to quantify

joint angles and moments during walking and can be used to analyze pathologic gait

patterns. During unimpaired gait, the gait cycle is divided into two primary phases:

stance, when the foot is on the ground (0-60% of the gait cycle), and swing, when the

foot is off the ground (60-100% of the gait cycle). The gait cycle begins with stance at

initial contact or heel strike (see Figure 2.1 for kinematics). At this point in the gait

cycle, the hip is flexed, the knee is near full extension and the ankle is near neutral. In

early stance, the ankle plantarflexes until the foot is in contact with the ground and the

knee flexes slightly. The mass center moves over the stance limb and the hip extends

during stance. The opposite foot contacts the ground at around 40-50% of the gait

cycle. In terminal stance, the ankle plantarflexes to propel the body forward and the

hip and knee flex until the foot is no longer in contact with the ground (at about 60%

of the gait cycle). During swing, the ankle dorsiflexes to clear the ground and the hip

11

flexes to advance the limb for the next step. The knee flexes during the first half of

swing and then extends to near full extension in the second half of swing to prepare

for the next gait cycle.

The magnitude and direction of the force exerted by the foot on the ground,

commonly termed the ground reaction force, can be measured using force plates and is

useful for calculating the moments at each joint. Joint moments describe the net

Figure 2.1: Kinematics during unimpaired gait (average ± one standard deviation, in degrees).

12

moments that are produced by muscles or other passive structures across a joint.

During unimpaired gait, there is a hip extension and hip adduction moment during

stance, a relatively small knee moment that fluctuates between flexion and extension,

and an ankle dorsiflexion moment that increases throughout stance and peaks in

terminal stance (Figure 2.2).

Coordinated muscle activity is required to produce the joint moments shown

above. Muscle activity can be monitored and measured during gait using

electromyography (EMG). During unimpaired gait, EMG has shown that the

quadriceps are active during early stance and gastrocnemius activity increases during

Figure 2.2: Kinetics including joint moments (Nm/kg) and powers (W/kg) during unimpaired gait(average ± one standard deviation).

13

mid and terminal stance (Figure 2.3). In terminal stance and early swing, there is a

burst of rectus femoris activity and the anterior tibialis activates to dorsiflex the ankle.

At the end of swing, the quadriceps and hamstring are active to prepare the limb for

the next gait cycle.

Determining how muscle activity measured from EMG contributes to motion

can be difficult due to the complexities of the musculoskeletal system and the

inconsistencies between EMG magnitude and muscle force. Dynamic coupling

describes the ability of muscles to accelerate joints they do not cross (Zajac and

Gordon, 1989). Since the human body is a system of bodies connected by joints, if a

muscle generates acceleration at one joint it will produce resulting accelerations at

other joints in the system. For example, during stance, activity of the ankle

plantarflexors not only plantarflexes the ankle but also accelerates the knee into

extension; this is commonly referred to as the plantarflexion-knee extension couple

(Gage and Schwartz, 2001; Gage and Schwartz, 2004). Musculoskeletal modeling and

simulation, which will be described in more detail in section 2.4, can be used to

examine how muscles contribute to these complex motions. Previous studies have

Figure 2.3: Average periods when the muscles are active during unimpaired gait from EMG data collected at Lucille Packard Children’s Hospital.

14

demonstrated that during unimpaired gait, the vasti and gluteus maximus support the

body and slow forward progression in early stance, the gluteus medius helps to

support the body during mid stance, and the gastrocnemius and soleus support and

propel the body forward during late stance (Neptune et al., 2001; Anderson and Pandy,

2003; Liu et al., 2006). Understanding how these complicated interactions change

during pathologic gait patterns such as crouch gait is one of the primary objectives of

this dissertation.

2.2 CEREBRAL PALSY

Cerebral palsy is an umbrella term used to describe an injury to the brain at or

near the time of birth that causes problems with movement and coordination. Common

causes of brain injury include hypoxic-ischemia, infections, head injury, and jaundice.

The prevalence of cerebral palsy in the developed world is estimated at between 1.2

and 3.6 cases per 1000 individuals, depending on geographic region and

socioeconomic status (Yeargin-Allsopp et al., 2008; Blair, 2010). The average lifetime

cost for individuals with cerebral palsy was estimated at $921,000 per individual in

2003 (National Institutes of Health).

Cerebral palsy is commonly characterized by the degree of involvement and

movement pattern. Cerebral palsy which affects only one side (right or left) of the

body is referred to as hemiplegia. Diplegia refers to when just the lower limbs are

affected and quadriplegia refers to when the arms and legs are affected. Common

types of altered movement include: spastic, characterized by heightened stretch- or

15

velocity-dependent muscle activation; dystonic, characterized by sustained or

intermittent muscle contractions; ataxic, characterized by decreased muscle tone and

unsteady, shaky movement; and dyskinetic, characterized by involuntary motions (also

referred to as athetoid). Spastic cerebral palsy is the most common type and affects

between 77 and 93% of individuals with cerebral palsy. This dissertation will focus on

individuals with spastic diplegic cerebral palsy.

2.3 CROUCH GAIT

Crouch gait is one of the most common gait pathologies in individuals with

spastic diplegic cerebral palsy. Among pediatric patients who visited one clinical gait

lab, 69% had the increased knee flexion in stance characteristic of crouch gait (Wren

et al., 2005). One of the first descriptions of crouch gait appeared in a manuscript in

1890 by E.H. Bradford who described a gait pattern in which “the heel is not placed

upon the ground, the knee is bent, and the knee is thrown to the inner side.”

Today, crouch gait is an umbrella term for a spectrum of gait patterns that all

share the common feature of excessive knee flexion during stance. Some authors (Lin

et al., 2000; Chambers, 2001; Young et al., 2010) have refined the definition of crouch

gait to differentiate between gait patterns such as jump gait, characterized by excessive

ankle plantarflexion and knee flexion at initial contact which resolves by terminal

stance; apparent equinus, characterized by excessive knee flexion throughout stance

with the heel off the ground; and crouch gait, characterized by calcaneal gait (i.e., flat-

footed, heel contact) and excessive knee flexion throughout stance. This dissertation

16

focuses on individuals with crouch gait who have excessive knee flexion throughout

stance with the heel on the ground (Figure 2.4).

Gait pathologies such as crouch gait negatively affect mobility and are

inefficient due to muscle co-contraction, altered movement patterns, and the use of

assistive devices (see Waters and Mulroy, 1999, for a review). One study reported a

100% increase in the physiological cost of outdoor locomotion (Raja et al., 2007)

among individuals with cerebral palsy and various gait pathologies. Individuals with

cerebral palsy demonstrate slower walking speeds (Campbell and Ball, 1978; Rose et

al., 1990), which makes it difficult for them to keep up with peers. Crouch gait can

also contribute to pain, joint degeneration, and the formation of bone deformities

(Rosenthal and Levine, 1977; Lloyd-Roberts et al., 1985; Murphy, 2009). As

individuals with cerebral palsy and crouch gait enter adulthood, knee pain, hip

subluxation, osteoarthritis, lumbar spondylosis, and cervical stenosis commonly

develop (Murphy, 2009). Furthermore, the gait of individuals with cerebral palsy

deteriorates over time, especially without treatment (Johnson et al., 1997; Bell et al.,

Figure 2.4: Average knee flexion during mild, moderate, and severe crouch gait compared to unimpairedgait and a musculoskeletal model illustrating a typical crouch gait pattern.

17

2002; Rose et al., 2010). In combination, these factors lead to reduced mobility which

limits individuals’ ability to accomplish activities of daily living and negatively affects

quality of life.

There are many proposed causes of crouch gait, including poor neuromuscular

control, impaired balance, altered muscle physiology, and skeletal deformities.

Although cerebral palsy is caused by an injury to the brain, most treatments currently

target the musculoskeletal limitations of individuals with cerebral palsy that result

from the brain injury and limit mobility. The following sections outline

musculoskeletal factors that may contribute to crouch gait and synthesize treatment

options for crouch gait.

2.3.1 CAUSES OF CROUCH: EXCESSIVE FORCE

Excessive force from muscles or passive structures can restrict joint range of

motion and contribute to crouch gait. Muscle contracture, defined as a passive

resistance to stretch, and muscle spasticity, defined as a velocity-dependent resistance

to stretch, are common in individuals with cerebral palsy. Contracture, spasticity, or

over-activity of muscles during movement may contribute to crouch gait by limiting

hip, knee, and ankle motion. Excessive force from the hamstrings, gastrocnemius, and

iliopsoas are the most commonly cited potential contributors to crouch gait and are

common targets for surgical and therapeutic treatments.

18

Hamstrings

Hamstrings contracture, spasticity, or over-activity is thought to contribute to

crouch gait by limiting knee extension during terminal swing or stance. The bi-

articular hamstrings, including the semimembranosus, semitendinousus, and biceps

femoris long head have knee flexion and hip extension moment arms. The biceps

femoris short head is the only uni-articular knee flexor and shares a distal tendon with

the biceps femoris long head. The hamstrings are often grouped into the medial

hamstrings (semimembranosus and semitendinousus) and the lateral hamstrings

(biceps femoris long head and short head), based upon their insertion points distal to

the knee. The hamstrings are hypothesized to contribute to crouch gait because limited

hamstring range of motion and prolonged hamstrings activity during stance have been

reported among individuals with crouch gait (Hoffinger et al., 1993).

Figure 2.5: Anatomy of the hamstrings, iliopsoas, and ankle plantarflexors (gastrocnemius and soleus)from the University of Washington Musculoskeletal Atlas.

19

Determining if the hamstrings cause crouch gait is difficult due to the

complexities of the musculoskeletal system. Due to dynamic coupling, bi-articular

muscles, such as the hamstrings, can accelerate a joint in a direction opposite of the

muscle’s moment arm. Thus, although the bi-articular hamstrings have a knee flexion

moment arm, during activities such as walking, the hamstrings could contribute to

knee extension due to dynamic coupling.

Musculoskeletal modeling and electrical stimulation studies have confirmed

that the bi-articular hamstrings can accelerate the knee into extension through dynamic

coupling if they generate sufficiently large hip extension moments. Electrical

stimulation of the hamstrings in a standing posture has demonstrated that the action of

the hamstrings changes from flexing the knee to extending the knee with increasing

crouch (Stewart et al., 2008). Musculoskeletal simulations have shown that during

unimpaired gait the hamstrings have a knee extension potential (Arnold et al., 2005)

and do not contribute significantly to swing limb knee flexion (Arnold et al., 2007),

although they are active in terminal swing. During crouch gait, the hamstrings have a

small knee extension potential during stance (Hicks et al., 2008, see Chapter 3) and the

hip and knee extension potentials of the hamstrings do not decrease like other muscles

with increasing crouch severity (Hicks et al., 2008) or increasing tibial torsion (Hicks

et al., 2007). These results suggest that excessive force from the hamstrings may not

contribute to the excessive knee flexion characteristic of crouch gait. However, tight

hamstrings due to muscle contracture may still limit knee range of motion. An

experimental study using an exoskeleton built to mimic muscle contracture in

unimpaired individuals found that hamstring contracture did increase knee flexion in

20

terminal swing and early stance (Matjacic and Olensek, 2007) and, therefore,

hamstring contracture may contribute to crouch gait.

There are a variety of clinical exams that are commonly used to determine if

the hamstrings should be treated in an individual with cerebral palsy and crouch gait.

Traditionally, passive physical exams including popliteal angle (maximum extension

of the knee when the patient is supine and the hip is flexed to 90°) and straight leg

raise (maximum hip flexion when the patient is supine and the knee is fully extended)

have been used to measure range of motion of the hamstrings. However, the

association between these measures and gait are not clear. Popliteal angle has been

reported to have a poor correlation with knee flexion during walking (Thompson et al.,

2001; Desloovere et al., 2006) while straight leg raise has been reported to have a

significant correlation to change in knee flexion during gait after surgery (Thometz et

al., 1989). Static physical exam measures may not be ideal for determining the

contribution of the hamstrings to dynamic activities such as gait.

An alternative to static exam measures is calculating musculotendon length

and velocity of the hamstrings during gait using musculoskeletal modeling. Arnold et

al. (2006) examined preoperative and postoperative peak musculotendon length and

velocity of the semimembranosus in 152 subjects with cerebral palsy and observed a

relationship between musclotendon length and velocity and surgical outcome (Delp et

al., 1996; Arnold et al., 2006a; Arnold et al., 2006b). Subjects whose hamstrings peak

lengths or velocities during gait remained short or slow after surgery were unlikely to

have improved knee extension. These results suggest that indicators measured during a

functional activity, such as musculotendon length and velocity, could provide better

21

information for surgical decision making than static exam measures. While measuring

musculotendon lengths and velocities cannot determine whether short musculotendon

lengths are the cause of crouch gait or a result the gait pattern, Van der Krogt et al.

(2007) reported that unimpaired individuals walking in a crouch gait did not have

short or slow hamstrings; this suggests that evidence of short or slow hamstrings in

individuals with cerebral palsy may indicate that the hamstrings are contributing to

crouch gait.

Spasticity of the hamstrings is evaluated using a combination of the Ashworth

Scale, Tardieu Scale, and EMG patterns during gait. Excess hamstring activity during

stance has been suggested to indicate spastic hamstrings (Crenna, 1998); however, the

hamstrings may be active during this time to assist with hip and knee extension. The

spastic velocity threshold, defined as the angular velocity of the joint at which

inappropriate muscle activity is triggered, provides a more quantitative measure for

assessing muscle spasticity. Spastic velocity threshold of the hamstrings has been

shown to be associated with peak knee angular velocity during maximum speed

walking suggesting that hamstrings spasticity could limit knee angular velocity during

gait (Tuzson et al., 2003). More quantitative measures of spasticity are required to

clarify how hamstring spasticity may contribute to crouch gait and to provide

clinically relevant exams.

Surgical treatment for the hamstrings in individuals with crouch gait can

involve lengthening, releasing, or transferring the hamstrings. Release or transfer of a

muscle theoretically eliminates unwanted contributions to motion at a given joint

while musculotendon lengthening reduces passive tension and may diminish the

22

spastic reflex. Little is known however about how these procedures alter muscle

properties or change the force-length or force-velocity properties of muscles. A study

by Granata et al. (2000) noted that although kinematics improved after musculotendon

lengthening, angular velocities and muscle activations did not change significantly.

These findings may indicate that musculotendon lengthening changes the range of

motion of a muscle but does not change the threshold velocity that triggers spasticity.

Hamstring lengthening has been a treatment used by orthopaedic surgeons for

over a century (Bradford, 1890) and is currently the most common surgery for treating

tight or spastic hamstrings. Multiple reviews recommend the use of distal hamstring

lengthening for the treatment of crouch gait (Green and McDermott, 1942; Pollock,

1962; Fixsen, 1979; Gage, 1990). To evaluate the outcomes after hamstring

lengthening we performed a meta-analysis of outcomes after distal hamstring

lengthening. The outcomes included in this analysis were (1) change in popliteal

angle, a clinical exam used to measure the passive range of motion of the hamstrings,

(2) change in knee flexion angle during gait, and (3) change in pelvic tilt during gait

(Figure 2.6). We also compared outcomes for surgeries that lengthened both the

medial and lateral hamstrings versus lengthening only the medial hamstrings.

The results of this meta-analysis indicated that after distal hamstring

lengthening, popliteal angle improved by an average of 19° (Fig. 3, 95% CI: 14-24);

however, the range of improvement in popliteal angle varied from 4° (Gannotti et al.,

2007) to 40° (Baumann et al., 1980). There was no significant difference in the change

in popliteal angle between lengthening the medial and lateral hamstrings versus the

medial hamstrings alone. Knee extension during gait also improved after hamstring

23

lengthening. The average change was 12.8° more knee extension at initial contact

(95% CI: 8.9-16.7) and 10.9° more knee extension during stance (95% CI 6.6-15).

Lengthening the medial and lateral hamstrings increased knee extension at initial

contact and during stance significantly more than lengthening only the medial

hamstring. At initial contact, lengthening the medial and lateral hamstrings increased

knee extension by 13.4° (95% CI 5.5-21.5) versus 9.5° (95% CI, 4-15, p = 0.027) for

lengthening only the medial hamstrings. Knee extension during stance increased by

14.6° (95% CI 3.8-25.5) when lengthening both the medial and lateral hamstrings

versus 6.5° (95% CI, 0.6-12.5, p < 0.001) for lengthening only the medial hamstrings.

Improvements in hip internal rotation (Steinwender et al., 2000; Lovejoy et al., 2007)

and spasticity (Vlachou et al., 2009) have also been reported after hamstring

lengthening but require further study. Despite changes in kinematics, temporal-spatial

parameters have been reported to have minimal changes when normalized by height

(Thometz et al., 1989; van der Linden et al., 2003).

A variety of adverse outcomes have been reported after hamstring lengthening

including increased anterior pelvic tilt, stiff-knee gait, exaggerated lumbar lordosis,

genu recurvatum, and nerve palsy (Hsu and Li, 1990). From the results of the meta-

analysis, the average change in pelvic tilt was 3° increased anterior pelvic tilt (95% CI,

0 – 6). The largest reported change was a 14° increase in anterior pelvic tilt (Rodda et

al., 2006). There was no significant difference in the change in anterior pelvic tilt

(student’s t-test, p=0.17) between lengthening the medial and lateral hamstrings and

lengthening the medial hamstrings. DeLuca et al. (1998) reported an increase in

anterior pelvic tilt when pelvic tilt was within normal limits before surgery and both

24

the medial and lateral hamstrings were lengthened. Multiple studies have also noted

that if anterior pelvic tilt was greater than 16° before surgery, lengthening the

hamstrings did not further increase anterior pelvic tilt (DeLuca et al., 1998; van der

Linden et al., 2003).

Genu recurvatum, hyperextension of the knee during stance, developed in an

average of 11% of subjects after hamstring lengthening in the studies included in the

meta-analysis. Reported risk factors for genu recurvatum included a jump knee gait

pattern and ankle plantarflexor spasticity (Thometz et al., 1989; Adolfsen et al., 2007).

Karol et al. (2008) reported development of nerve palsy, characterized by numbness,

loss of motor function in the foot, or hypersensitivity of the foot in 9.6% of subjects

who underwent hamstring lengthening. Subjects that were at higher risk for nerve

palsy were older, non-ambulatory, or non-communicative. Katz et al. (2004) suggested

that monitoring the evoked potential of the sciatic nerve during surgery may be an

effective way to prevent nerve damage. Muscle weakness is also a common concern

following musculotendon surgery; however, Damiano et al. (1999) reported that

hamstring strength recovered within nine months after lengthening surgery. The

possibility of adverse outcomes after distal hamstring lengthening warrant caution and

judicious lengthening; however, the improvements in knee extension during stance

and passive range of motion support distal hamstring lengthening for the treatment of

crouch gait.

25

Figure 2.6: Meta-analysis of outcomes after hamstring lengthening including change in popliteal angle, change in knee flexion angle, and change in pelvic tilt.

26

Less common surgical treatment options for the hamstrings include proximal

hamstring lengthening, hamstring transfer, and hamstring release. Proximal hamstring

lengthening has been recommended if there is no knee flexion contracture but the

hamstrings are still tight (Fixsen, 1979). Reimers (1974) compared proximal and distal

lengthening and noted that the advantages of the proximal lengthening include a less

visible scar, no plaster casts, shorter periods of immobilization, and access to other

proximal muscles for treatment; however, the author recommended distal lengthening

if more than 5° of knee flexion contracture is present since proximal lengthening does

not affect the short head of the biceps femoris. The effects of proximal lengthening on

gait have not been investigated.

Transferring the hamstrings to the femoral condyles was a popular procedure

in the 1950s and 60s (Eggers, 1952; Eggers and Evans, 1963); however, this procedure

is thought to cause excessive genu recurvatum, a loss of active knee flexion, decreased

pelvic stability, a stiff gait, and accentuated lumbar lordosis (Pollock, 1962; Pollock

and English, 1967; Roosth, 1971; Reimers, 1974; Ray and Ehrlich, 1979; Grujic and

Aparisi, 1982; Young et al., 2010). Keats and Kambin (1962) noted better results

when hamstring transfer was combined with patellar advancement. These early

procedures lacked gait analysis to objectively analyze surgical outcomes. More

recently, Metaxiotis et al. (2004) converted the semitendinousus and gastrocnemius to

monoarticular muscles by transfer to the femur and tibia, respectively, in 20 children

with spastic diplegia and found improved knee extension during stance and

hyperextension in 5 out of 40 limbs. These authors argued that muscle transfer may

prevent muscle weakness that may occur after lengthening procedures.

27

Proximal hamstring release has also been investigated as a treatment for

hamstring contracture. Although this procedure corrected knee flexion deformity and

hamstring range of motion during physical exam (Seymour and Sharrard, 1968;

Drummond et al., 1974; Sharps et al., 1984; Smith and Stevens, 1989), it increased the

risk of lumbar lordosis (Sharps et al., 1984) and genu recurvatum (Drummond et al.,

1974). Drummond et al. (1974) does not recommend proximal hamstring release for

the treatment of crouch gait.

Femoral extension osteotomy and patellar tendon advancement have recently

been proposed as an alternative to distal hamstring lengthening. Femoral extension

osteotomy has been reported to improve knee flexion contractures and increase knee

range of motion during gait (de Morais Filho et al., 2008; Stout et al., 2008). Stout et

al. (2008) reported post-operative knee function that was within normal limits when

femoral extension osteotomy was combined with patellar advancement. Hamstring

length and velocity were also found to increase following femoral extension

osteotomy and patellar tendon advancement without concomitant hamstring surgery

(Healy et al., 2011). Recommended indications for surgery include a persistent crouch

despite treatment, a knee flexion contracture between 10 and 30°, and a quadriceps lag

greater than 10° (Stout et al., 2008). Contraindications include a knee flexion

contracture greater than 30°, femoral malrotation greater than 30°, or patella baja

(Novacheck et al., 2009). Further study of femoral extension osteotomy is warranted

for the treatment of crouch gait.

Non-surgical treatment options for the hamstrings include neruomuscular

toxins such as botulinum toxin type A and baclofen. A limited number of studies have

28

examined the effects of neuromuscular toxins on crouch gait. Thompson et al. (1998)

performed a study of 10 subjects with crouch gait who were treated with isolated

hamstring botulinum toxin type A injections and found a significant increase in medial

hamstring length during gait, an improvement of 15° in knee extension, and increased

walking speed (Thompson et al., 1998). Others have noted improved knee extension in

stance following combination of multi-level botulinum toxin injection, casting, and

orthoses (Corry et al., 1999; Hesse et al., 2000; Papadonikolakis et al., 2003; Scholtes

et al., 2006; Scholtes et al., 2007); however, these improvements in gait may not be

maintained after 12 weeks (Corry et al., 1999; Scholtes et al., 2007). Thompson et al.

(1998) recommended that botulinum toxin is most effective for individuals with

spasticity rather than muscle contracture, since the neuromuscular toxin affects the

neuromuscular junction and not the passive material properties of the muscle. These

recommendations are supported by Sutherland et al. (1996) who found that passive

range of motion of the ankle plantarflexors was not improved after treatment with

botulinum toxin type A. The disadvantages of neuromuscular toxins are that the

effects decrease over a period of three to six months, repeated treatments are less

effective, and the toxins may have negative long-term effects on muscle physiology.

More research on the physiological effects of neuromuscular toxins and long-term

follow-up studies are required to evaluate the efficacy of neuromuscular toxins for the

treatment of crouch gait.

29

Hip flexors

The iliacus and psoas are the primary mono-articular hip flexors and excessive

force due to contracture, spasticity, or over-activity of these muscles could contribute

to excess hip flexion during crouch gait. Excess hip flexion can also contribute to

excess knee flexion through the need to maintain sagittal plane balance (Young et al.,

2010) and through accelerations generated by dynamic coupling. Musculoskeletal

simulations have shown that the psoas has a large knee flexion potential during stance

in both unimpaired (Arnold et al., 2005) and crouch gait (Hicks et al., 2008).

Furthermore, an experimental study using an exoskeleton to mimic muscle contracture

in unimpaired individuals found that hip flexion contracture increased crouch gait

(Matjacic and Olensek, 2007).

The Thomas test, prone hip extension test (Staheli test), and hamstring shift

test are common physical exams used to measure hip flexion contracture and

determine if the hip flexors require treatment in individuals with crouch gait. Similar

to physical exams for the hamstrings, there is no correlation between passive physical

exams and hip motion during gait (Lee et al., 2011). Musculotendon length and

velocity can also be calculated for the hip flexors during gait. Delp et al. (1996)

reported that psoas lengths were more than two standard deviations shorter in

individuals with cerebral palsy and crouch gait than during unimpaired gait. However,

caution needs to be taken when using psoas length to determine if the psoas should be

surgically lengthened since unimpaired individuals walking in a crouch gait also have

short psoas (van der Krogt et al., 2007), suggesting that psoas lengths cannot be used

to differentiate between short psoas that are a cause of crouch gait or a consequence of

30

the crouch posture. Additionally, psoas lengths are sensitive to femoral anteversion

(Schutte et al., 1997) which is commonly not included in musculoskeletal models.

The most common surgical interventions for hip flexors in individuals with

crouch gait are lengthening or releasing the hip flexors. Many methods of lengthening

the hip flexors have been shown to reduce hip flexion contractures, including division

of all hip flexors except the psoas (Roosth, 1971), psoas tenotomy (Nene et al., 1993),

and psoas recession at the pelvic brim (Patrick, 1996; Sutherland et al., 1997;

Novacheck et al., 2002; Zwick et al., 2002). Roosth (1971) reported that relieving hip

flexion contracture resulted in a more erect posture, reduced lumbar lordosis, and

improved balance. A potential adverse outcome of these procedures is reduced active

hip flexion capacity. There is conflicting evidence on the effects of psoas recession at

the pelvic brim on active hip flexion; some studies have reported that subjects

maintain active hip flexion after recession (Sutherland et al., 1997; Novacheck et al.,

2002), but others have reported decreased active hip flexion after surgery (Zwick et

al., 2002). An increased tendency toward genu recurvatum has also been noted when

psoas recession is combined with hamstring lengthening (Zwick et al., 2002; Ma et al.,

2006). DeLuca et al. (1998) recommends lengthening the psoas if hip flexion

contracture is greater than 15°, while Davids et al. (2004) recommends iliopsoas

recession if hip flexion contracture is greater than 30°.

31

Ankle Plantarflexors

The gastrocnemius has a knee flexion moment arm and excess force due to

spasticity, contracture, or over-activity could contribute to excess knee flexion during

crouch gait. The contribution of the gastrocnemius to crouch gait is complicated by the

fact that it shares an insertion through the Achilles tendon with the uni-articular

soleus. Musculoskeletal simulation studies have shown that these two muscles have

significantly different contributions to movement. The gastrocnemius contributes to

knee and hip flexion while the soleus contributes to hip and knee extension during

stance in both unimpaired (Arnold et al., 2005) and crouch gait (Hicks et al., 2008 and

see Chapter 3). Yet, both muscles have been shown to contribute to upward support of

the mass center during crouch gait (see Chapters 3 and 4).

To determine if the gastrocnemius is contributing to crouch gait, clinicians

typically measure ankle range of motion with the knee flexed and the knee extended to

differentiate between soleus and gastrocnemius contracture. Baddar et al. (2002) also

suggested examining the correlation between ankle and knee motion during single-

limb stance; a correlation between knee extension and ankle plantarflexion in

individuals with crouch gait could indicate that the gastrocnemius is restricting knee

motion. Musculotendon lengths and velocities have not been used to examine

gastrocnemius function during crouch gait. Spasticity of the gastrocnemius is often

measured with the Ashworth Scale or by monitoring gastrocnemius EMG activity

during stance (Crenna, 1998).

The most common treatment for the ankle plantarflexors is musculotendon

lengthening of the gastrocnemius, soleus, or both muscles; however, the efficacy of

32

these procedures in individuals with crouch gait is a debated subject. There is

conflicting evidence on the effect of gastrocnemius and soleus lengthening on crouch

gait, likely due to the wide variety of surgical techniques used and the effects of

concomitant surgeries. The gastrocnemius and soleus can be lengthened by a Z-

lengthening, step lengthening, sliding lengthening, tenotomy or subcutaneous

lengthening of the Achilles tendon. The gastrocnemius can be lengthened using the

Strayer, Baker, and Vulpius techniques which leave the soleus intact. Reported

changes in crouch gait after lengthening the gastrocnemius and soleus or the

gastrocnemius alone have been similar; an 8° change in knee extension at initial

contact (Baddar et al., 2002; Galli et al., 2005; Galli et al., 2009), but no significant

change in mid stance knee flexion (Baddar et al., 2002; Orendurff et al., 2002; Galli et

al., 2005). Van der Linden et al. (2003) found that patients who did not have a

gastrocnemius lengthening in conjunction with a hamstring lengthening had 6° more

plantarflexion at initial contact. Musculoskeletal models have shown that tendoachilles

lengthening can significantly reduce the force generating capacity of the plantarflexors

(Delp et al., 1995). Since the gastrocnemius and soleus both contribute to upward

acceleration of the mass center during crouch gait (see Chapters 3 and 4), lengthening

these muscles could compromise individuals’ ability to support themselves. The

appropriate candidates for surgical intervention and the amount of ankle plantarflexor

lengthening are important areas for further investigation.

33

Passive Structures

In addition to excessive force from muscles, excessive force from passive

structures surrounding the hip and knee can also contribute to crouch gait. A fixed hip

or knee flexion contracture is caused by excessive tightness of the passive structures

surrounding the joint. Indicators for fixed contracture include restricted passive range

of motion which persists when an individual is under anesthesia and muscles are not

taut. Treatments for a fixed knee flexion contracture include knee capsulotomy,

anterior femoral hemiepiphysiodesis (also known as “guided growth”), and serial

casting. Knee capsulotomy combined with hamstring lengthening has been reported to

improve popliteal angle by 22° (Woratanarat et al., 2009) while serial casting has been

reported to reduce knee flexion contracture by 12° (Westberry et al., 2006). However,

recurrence of fixed knee flexion contractures is common after both of these

procedures, especially in younger patients. Anterior femoral hemiepiphysiodesis

involves applying staples to the anterior surface of the femur over the growth plate,

resulting in a curvature of the femur during growth. The average reported correction of

knee flexion contracture is 0.9°/month, for a total correction of 12.7° (Kramer and

Stevens, 2001; Klatt and Stevens, 2008). This procedure is minimally invasive and

requires no immobilization, which allows for immediate resumption of bracing and

physical therapy. Klatt et al. (2008) recommended anterior femoral

hemiepiphysiodesis for subjects with greater than 10° knee flexion deformity and

more than 12 months of growth remaining. Changes in gait following these procedures

have not been reported and represent an important area for future research.

34

2.3.1 CAUSES OF CROUCH: INADEQUATE FORCE

The inability of muscles to generate sufficient force to support and propel the

body may also contribute to crouch gait. Weakness may be the result of reduced

physiological cross-sectional area, lack of volitional control, previous surgeries, or

altered muscle physiology. Muscle weakness is well-documented among individuals

with cerebral palsy. Children with cerebral palsy have been shown to have

significantly weaker quadriceps, hamstrings, hip extensors, and ankle muscles

compared to their unimpaired peers (Damiano et al., 1995a; Wiley and Damiano,

1998). During crouch gait, a correlation between knee extensor strength and knee

extension during stance has also been reported (Damiano et al., 1995a; Rethlefsen et

al., 1999) suggesting that muscle weakness may contribute to crouch gait.

From a biomechanics perspective, individuals who walk in a crouch gait may

not be able to generate the required forces and accelerations to achieve an upright gait.

During crouch gait, the hip and knee flexion moments increase dramatically during

stance. Musculoskeletal simulation studies have shown that the hamstrings, gluteus

maximus, vasti, and ankle plantarflexors are the primary contributors to hip and knee

extension during stance in both unimpaired gait (Arnold et al., 2005) and crouch gait

(see Chapter 3). Muscle weakness in any of these muscle groups could contribute to

crouch if individuals are not able to adequately extend their hips and knees or support

their body weight. During swing, the primary contributors to knee extension are the

hip extensors and ankle plantarflexors (Arnold et al., 2007). If these muscles are weak,

knee extension at initial contact could be diminished and the subject may not be able

to reach full knee extension during stance. A crouch posture also diminishes the ability

35

of lower-extremity muscles to extend the hip and knee (Hicks et al., 2007). Therefore,

to create the same angular accelerations of the hip and knee in a crouch posture

requires more muscle force than in an upright posture. These factors magnify the

effects of muscle weakness.

Compensation for weak muscles by other muscle groups could also contribute

to crouch gait. For example, Jonkers et al. (2003) showed that the gluteus maximus,

plantarflexors, and hamstrings play complementary roles to control the stance limb

during unimpaired gait. If one of these muscle groups is impaired, the other muscles

may be recruited to compensate for weakness; however, compensation could have

negative consequences during gait. For example, if gluteus maximus is weak,

increased hamstring and gastrocnemius activity to support the body could increase

knee flexion.

Inadequate muscle force can also be a result of previous surgical interventions,

such as lengthening the Achilles tendon. Musculoskeletal modeling studies have

demonstrated that over-lengthening the Achilles tendon can reduce the amount of

force the ankle plantarflexors can produce (Delp et al., 1995). Adverse outcomes after

Achilles tendon lengthening include excess ankle dorsiflexion and knee flexion

(Sutherland and Cooper, 1978). Wiley et al. (1998) noted that individuals who had

prior Achilles lengthening tended to have weaker plantarflexors, but the difference

was not significant. The prevalence of a crouch gait pattern after lengthening the

Achilles tendon has been reported between 0 and 50% (Bernthal et al.; Craig and van

Vuren, 1976; Segal et al., 1989; Damron et al., 1993; Abel et al., 1999; Borton et al.,

2001; Dietz et al., 2006). De Morais Filho et al. (2010) reported that subjects with a

36

minimum knee flexion angle greater than 30° during stance were more likely to have

had an Achilles lengthening than subjects who did not walk in a crouch gait after

orthopaedic surgery; however, subjects who received an Achilles lengthening surgery

may have been more severely impaired or other factors could have contributed to

crouch gait. These studies indicate that musculotendon lengthening surgery can reduce

the force generating capacity of a muscle and could increase the risk of crouch gait.

Altered musculoskeletal physiology due to impaired development can also

contribute to crouch gait by altering the amount of force a muscle can produce in a

given position. Patella alta refers to an abnormally high patella in relation to the

femur and is thought to be caused by excessive tension in the patellar tendon. This

condition is common in individuals with spastic cerebral palsy. Rosenthal and Levine

(1977) found patella alta in over 50% of patients with spastic cerebral palsy. The

effect of patella alta on the moment generating capacity of the quadriceps is unclear;

Sutherland et al. (1978) reported that patella alta reduces the moment generating

capacity of the quadriceps in all positions except extreme knee flexion, but more

recent studies have indicated that patella alta increases the quadriceps’ moment

generating capacity (Ward et al., 2005; Luyckx et al., 2009). Sheehan et al. (2008)

examined the patellar tendon moment arm in subjects with cerebral palsy, many of

whom had patella alta, and found no significant changes in the patellar tendon moment

arm. If left untreated, patella alta can cause fragmentation of the distal pole of the

patella as a result of excess tension (Rosenthal and Levine, 1977) or patella tendon

rupture (O'Sullivan et al., 2010).

37

Quadriceps lag is another common impairment found in individuals with

cerebral palsy which refers to a lack of full, active knee extension. Individuals with

quadriceps lag may be able to produce sufficient strength when the knee is flexed;

however, the quadriceps are weak when the knee is near full extension. No research is

currently available describing the underlying mechanisms of quadriceps lag and the

influence of quadriceps lag on crouch gait.

The most common treatment option for individuals with cerebral palsy and

muscle weakness is strength training. Studies have shown that strength training can

improve muscle strength in individuals with cerebral palsy to within normal limits

(Damiano et al., 1995b; Dodd et al., 2002; Mockford and Caulton, 2008).

Furthermore, strength training has been shown to improve walking velocity (Damiano

et al., 1995a) and knee extension during gait (Damiano et al., 1995b; Unger et al.,

2006). More recently, inconsistent outcomes among subjects with crouch gait have

been noted. Damiano et al. (2010) reported that after strength training of the hip and

knee extensors some individuals with crouch gait had improved knee extension while

others had more knee flexion during gait. Preliminary results suggest that these

differences in outcome may be related to hamstring spasticity (see Chapter 7); subjects

without hamstring spasticity had better outcomes. Unfortunately, most strength

training studies include subjects with many different gait patterns and do not examine

changes in gait before and after strength training which makes understanding the

efficacy of these programs difficult. Further, more controlled studies are required to

determine which individuals have positive outcomes after strength training programs.

38

Orthoses can also be used to compensate for muscle weakness. For the

treatment of crouch gait, ankle foot orthoses (AFOs) have been shown to have no

effect on knee extension during gait (Abel et al., 1998; Rethlefsen et al., 1999;

Wesdock and Edge, 2003; Brehm et al., 2008). Hassani et al. (2004) reported a

significant improvement in minimum stance knee flexion with both hinged and

dynamic AFOs; however, this study was not specific to individuals with crouch gait.

A more promising AFO for the treatment of crouch gait is the floor reaction AFO.

Several studies have noted a significant improvement in knee extension in stance with

the use of floor reaction AFOs in subjects with greater than 15° of knee flexion during

stance (Lucareli et al., 2007; Rogozinski et al., 2009). Brehm et al. (2008) reported

that improvement in metabolic cost with AFOs was significantly correlated with

minimum knee flexion angle during stance. These results suggest that AFOs that

improve knee flexion could produce a more energy-efficient gait pattern for

individuals with cerebral palsy.

2.3.1 CAUSES OF CROUCH: BONE DEFORMITIES

Rotational deformities of the tibia and/or femur are common in children with

cerebral palsy - a consequence of altered bone loading during development. A tibial

torsion deformity is an excess twisting of the tibia about its long axis and may be an

internal or external rotation. Femoral anteversion deformity is an excess internal twist

of the femoral neck with respect to the shaft of the femur. These deformities may

contribute to crouch gait by altering the moment arms, and hence moment generating

capacity, of muscles. Because the moments generated by muscles at joints can result in

39

motions at other joints due to dynamic coupling, a muscle affected by a bone

deformity may result in movement abnormalities at other joints it does not cross.

Bone deformities may also alter foot ground interaction which can impact

muscle function at joints throughout the body. For example, musculoskeletal modeling

found that although tibial torsion has a minimal effect on the moment arms of muscles

crossing the ankle joint, it has a significant adverse effect on the acceleration produced

by muscles crossing the hip and knee (Hicks et al., 2007). Musculoskeletal modeling

studies have demonstrated that tibial torsion significantly reduces the ability of

muscles to extend the hip and knee (Hicks et al., 2007; Hicks et al., 2008) and support

the mass center (Schwartz and Lakin, 2003). For example, a 30° external tibial torsion

deformity reduces the capacity of major lower-limb extensors including the gluteals

and soleus to extend the knee by over 10%. Hicks et al. (2007) also reported a greater

incidence of crouch gait in subjects with more than 30° of tibial torsion (70% vs.

40%). No studies have been performed on the effects of femoral anteversion on the

dynamic function of muscles during gait.

Distal tibial derotation osteotomies are performed at many clinical centers and

have been shown to be successful in correcting alignment of the tibia with few

complications (Dodgin et al., 1998; Selber et al., 2004; Ryan et al., 2005). Studies that

have reviewed patient outcomes report improved gait function (Stefko et al., 1998;

Selber et al., 2004; Ryan et al., 2005); however, sagittal plane kinematics are not

reported. Analyzing the effects of tibial derotation osteotomies are further complicated

by the fact that the procedure is typically performed as part of multi-level orthopaedic

40

surgery, not a randomized clinical trial, which makes it difficult to isolate the effects

of the tibial derotation osteotomy on gait compared to other concomitant surgeries.

Femoral derotation osteotomies have also been shown to be safe and effective

in correcting femoral alignment; however, there is limited evidence connecting

femoral derotation osteotomies to improvements in crouch gait. Ouunpuu et al. (2002)

et al. performed a prospective analysis with 97 subjects looking at short and long term

outcomes. In addition to improved hip alignment, they also reported improved mean

stance knee flexion, but almost all patients had concomitant treatment, including

hamstrings lengthening.

Foot deformities such as plano pes valgus are also common in individuals with

cerebral palsy and crouch gait. Similar to rotational bone deformities, foot deformities

could also impair the ability of muscles to extend the hip and knee; however, a direct

study of the effects of foot deformities on crouch gait has not been done and is an

important area for future study.

2.4 MUSCULOSKELETAL SIMULATION

The complexities of the human musculoskeletal system make it difficult to

evaluate, diagnose, and treat gait pathologies in individuals with cerebral palsy.

Musculoskeletal modeling and simulation provides a tool for examining this complex

system and evaluating problems with human movement. The benefits of modeling and

simulation include the ability to examine the effect of individual components of

41

complex systems, to perform studies that could not be done experimentally, and to ask

‘what-if’ questions.

OpenSim is a freely-available software that allows researchers and clinicians to

create musculoskeletal models of humans and animals and critically evaluate the

kinematics, kinetics, muscle contributions, and other forces in the system (Delp et al.,

2007). Furthermore, OpenSim allows researchers to share models and simulations,

expand the software, and critically evaluate one another’s work. All of the simulations

created as part of this dissertation are provided for other researchers to download,

evaluate, and use at http://www.simtk.org/home/crouchgait/ (Figure 2.7).

The process to create a musculoskeletal simulation depends upon the specific

question that is being investigated; however, the following paragraphs outline the

basic steps in the process. All investigations start with the selection or creation of a

Figure 2.7: Map of visitors to the website with the simulations and documentation presented in thisdissertation from July 1, 2011 to January 1, 2012 (http://www.simtk.org/home/crouchgait/).

42

musculoskeletal model. For the investigations included in this dissertation, a model of

the lower-limbs and torso which is based upon cadaver and physiological

measurements was used (Delp et al., 1990). This model included 19 degrees of

freedom including three translations and three rotations at the pelvis, a ball-and-socket

joint between the pelvis and torso at approximately the third lumbar vertebrae (i.e.,

L3), a ball-and-socket joint at each hip, a planar joint with coupled translations at each

knee, and revolute joints at each ankle. The muscles were modeled as line segments

with multiple lines of action for muscles with broad attachments. A lumped parameter

Hill-type muscle model generated forces as a function of muscle fiber length and

velocity, tendon length, and activation.

For each subject, the musculoskeletal model is scaled to the subject’s size

based upon anthropometric measurements. This includes scaling segment lengths,

masses, and inertias as well as muscle and tendon lengths. Experimental data from a

motion capture laboratory is used to estimate the subject’s kinematics, or joint angles.

In a motion capture laboratory, subjects perform gait or other movements with

reflective markers on their body that can be tracked by a camera system.

Electromyography and ground reaction forces can also be collected concurrently. In

OpenSim, this data is used to estimate the joint angles, or kinematics, by positioning

the model in a position that minimizes the error between experimental markers and

markers placed on the model using inverse kinematics. These kinematics can then be

coupled with ground reaction forces to calculate joint moments using inverse

dynamics. The kinematics and kinetics calculated from these processes can then be

used to compare a subject’s gait to other individuals.

43

To create a three-dimensional musculoskeletal simulation, the final step is to

determine the muscle excitations needed to produce the subject’s motion. However,

due to modeling and experimental errors, the model’s motion is not dynamically

consistent (Kuo, 1998) with measured ground reaction force (i.e. force ≠ mass x

acceleration). To account for these inaccuracies, non-physiological forces and

moments called residuals are applied to the pelvis. Since these forces are non-

physiological, we minimize the magnitude of these forces using the residual reduction

algorithm which makes small changes in measurements we know have error (such as

joint angles and the location of the torso mass center) to reduce the magnitude of these

residual forces (Delp et al., 2007).

After this step, we can then more confidently estimate muscle excitations. It is

challenging to estimate muscle excitations and forces because each joint in the

musculoskeletal system is crossed by more muscles than its degrees of freedom.

Therefore, we use computed muscle control which combines an optimization problem

with a feedback controller to determine the set of muscle excitations that minimize the

sum of muscle activations squared and tracks the subject’s measured motion (Thelen

et al., 2003; Thelen and Anderson, 2006). If an estimate of the distribution of muscle

forces is the primary outcome of interest in a research study, other less-

computationally expensive methods can be used to estimate muscle activations and

forces, such as static optimization. Static optimization estimates muscle forces by

determining the set of muscle forces required to satisfy the equations of motion at each

time step while minimizing an objective function (e.g., minimizing the sum of

activation squared). The advantages of using computed muscle control over static

44

optimization is that it includes the activation-deactivation timing of muscles, the

effects of musculotendon compliance, and does not allow muscle excitations to change

instantaneously from one time step to the next; however, computed muscle control is

more computationally expensive. The muscle activations or forces estimated with

either of these processes can be compared to experimental electromyography and

muscle excitations can be constrained to electromyography data if there are significant

differences.

Determining the accelerations generated by individual muscles can be useful in

many studies, including Chapters 3 and 4 of this dissertation, to understand how

individual muscles contribute to motion. A perturbation or induced acceleration

analysis can be used to estimate the accelerations produced by individual muscles. A

perturbation analysis estimates these accelerations by applying a unit force to the

muscle of interest, integrating forward a small amount in time (typically 20-30 ms),

and then calculating the accelerations based upon changes in position (Liu et al.,

2006). This analysis uses a spring-damper element applied at the experimentally

measured center of pressure to model foot-floor contact. An induced acceleration

analysis calculates the accelerations produced by a muscle by explicitly solving the

equations of motion and a constraint equation that represents contact between the foot

and the ground (Zajac and Gordon, 1989; Hamner et al., 2010). An advantage of the

induced acceleration analysis is that it is much more computationally efficient than a

perturbation analysis; however, both analyses are dependent upon the foot-ground

contact models used which may not accurately reproduce the interaction between the

45

foot and ground and is an important area for future investigation (Hamner et al., 2010;

Dorn et al., 2011).

There are limitations and challenges to using musculoskeletal modeling and

simulation. Results are based upon inputs and, thus, if the models do not accurately

represent the subject’s physiology or if there are errors in the experimental motion

capture data, the results may not be representative of the subject. The musculoskeletal

models included in this dissertation are scaled from a generic model of an adult which

was created from averaged experimental data. We assume the children with cerebral

palsy included in our study do not have significant bone deformities or altered muscle

physiology compared to typically-developing children; however, the line of action and

properties of muscles may be altered in individuals with cerebral palsy. Creating

subject-specific musculoskeletal models and more quantitative measures of altered

musculoskeletal physiology is an important area for future research. To check if our

simulations recreate experimental data we also compare our kinematics, kinetics, and

muscle activity to experimental measures. These challenges in creating and evaluating

simulations emphasize the importance of maintaining high standards in the analysis of

musculoskeletal simulations and, whenever possible, partnering simulation studies

with experimental measures.

Musculoskeletal modeling and simulation provides a platform for critically

evaluating complex systems and movements. The following chapters document how

this process can be used to examine the dynamics of crouch gait in individuals with

cerebral palsy. This represents a foundation for future researchers and clinicians to

build upon by improving models, creating new computational analyses, and

46

developing experimental tools to couple with simulation. The ultimate goal of this

work is to improve not only our understanding of pathologic gait patterns, but to

improve treatment and quality of life for these individuals.

47

CHAPTER 3

HOW DO MUSCLES CONTRIBUTE TO SUPPORT AND PROGRESSION DURING CROUCH GAIT?

Journal of Biomechanics (2010), vol. 43, pp. 2099-2105

Katherine M. Steele Ajay Seth Jennifer L. Hicks Michael H. Schwartz Scott L. Delp

48

ABSTRACT

Pathological movement patterns like crouch gait are characterized by abnormal

kinematics and muscle activations that alter how muscles support the body weight

during walking. Individual muscles are often the target of interventions to improve

crouch gait, yet the roles of individual muscles during crouch gait remain unknown.

The goal of this study was to examine how muscles contribute to mass center

accelerations and joint angular accelerations during single-limb stance in crouch gait

and compare these contributions to unimpaired gait. Subject-specific dynamic

simulations were created for ten children who walked in a mild crouch gait and had no

previous surgeries. The simulations were analyzed to determine the acceleration of the

mass center and angular accelerations of the hip, knee, and ankle generated by

individual muscles. The results of this analysis indicate that children walking in

crouch gait have less passive skeletal support of body weight and utilize substantially

higher muscle forces to walk than unimpaired individuals. Crouch gait relies on the

same muscles as unimpaired gait to accelerate the mass center upward, including the

soleus, vasti, gastrocnemius, gluteus medius, rectus femoris, and gluteus maximus.

However, during crouch gait these muscles are active throughout single-limb stance,

in contrast to the modulation of muscle forces seen during single-limb stance in

unimpaired gait. Subjects walking in a crouch gait rely more on proximal muscles,

including the gluteus medius and hamstrings, to accelerate the mass center forward

during single-limb stance than subjects with unimpaired gait.

49

3.1 INTRODUCTION

Crouch gait, a common movement pattern among individuals with cerebral

palsy, is characterized by excessive flexion of the hip, knee, and ankle during the

stance phase of gait. This walking pattern is inefficient (Rose et al., 1989; Waters and

Mulroy, 1999) and if left untreated can lead to joint pain (Jahnsen et al., 2004),

formation of boney deformities (Graham and Selber, 2003), and loss of independent

gait (Johnson et al., 1997; Opheim et al., 2009). Clinicians try to identify muscles that

can be strengthened, surgically lengthened, or otherwise treated to enable a more erect

and efficient walking pattern. Little is known, however, about how individual muscles

contribute to joint and mass center motions during crouch gait; thus, it is difficult to

design treatment plans that target muscles most likely to improve gait dynamics.

Figure 3.1: OpenSim model shown at different phases of single-limb stance during crouch gait. The muscles shown in red are highly activated, while those in blue have a low activation level, as determinedusing the computed muscle control algorithm.

50

Humans have developed an efficient walking pattern to achieve forward

progression while supporting body weight. Several studies (Anderson and Pandy,

2003; Neptune et al., 2004; Arnold et al., 2005; Kimmel and Schwartz, 2006; Liu et

al., 2006) have examined how muscles accelerate the joints and mass center during

unimpaired gait. These studies have shown that during early stance the vasti and

gluteus maximus support the body and slow forward progression, while in late stance

the gastrocnemius and soleus support body weight and propel the body forward

(Anderson and Pandy, 2003; Neptune et al., 2004; Liu et al., 2006). Liu et al. (2008)

demonstrated that the roles of these muscles are maintained over a range of walking

speeds.

Changes in joint kinematics and muscle activation patterns during crouch gait

alter how muscles contribute to joint and mass center accelerations. Hicks et al. (2008)

analyzed the potential of individual muscles to accelerate the hip and knee, per unit

force, in crouched walking postures. This analysis revealed that a crouched posture

markedly reduces the potential of several major lower-extremity muscles to generate

extension accelerations of the hip and knee and increases the joint flexion

accelerations from gravity. While this prior study determined the direction (i.e. flexion

or extension) of the accelerations generated by important muscles, the magnitudes of

the accelerations generated by muscles depend on muscle forces, which have not been

estimated for subjects with crouch gait.

Determining how muscles contribute to joint angular accelerations and mass

center accelerations during crouch gait can clarify the role of muscles during this

abnormal walking pattern and elucidate biomechanical consequences of treatments

51

such as surgically lengthening muscles. Thus, the goal of the present study was to

quantify angular accelerations of the hip, knee, and ankle generated by stance-limb

muscles during the single-limb stance phase of crouch gait by creating and analyzing

the first subject-specific dynamic simulations of crouch gait. Additionally, we

characterized how muscles accelerate the mass center, which provides a holistic view

of how muscles contribute to motion of the body during gait. The simulations are

freely available at www.simtk.org, enabling other researchers to reproduce the results

of this study and to perform additional analyses.

3.2 METHODS

3.2.1 SUBJECTS

Ten subjects with spastic diplegic cerebral palsy – age: 8.1 ± 1.7 yrs, height:

1.25 ± 0.09 m, weight: 27.1 ± 9.1 kg, leg length: 0.65 ± 0.06 m (average ± standard

deviation) – were selected from a database of subjects examined at Gillette Children’s

Specialty Healthcare (St. Paul, MN). Each subject included in the study: 1) walked

with a mild crouch gait (minimum knee flexion 15 - 40º during stance), 2) did not

walk in equinus and achieved at least 0º of dorsiflexion during his or her physical

exam, 3) had no previous surgeries, and 4) had no significant torsional skeletal

deformities (less than 30º of tibial torsion and femoral anteversion). All subjects

and/or guardians provided informed written consent for the data collection; analyses of

the data were performed in accordance with the regulations of all participating

institutions.

52

Motion analysis data was collected and kinematics determined using a 12-

camera system (Vicon Motion Systems, Lake Forest, CA) and a standard marker

measurement protocol (Davis et al., 1991). Four force plates (AMTI, Watertown, MA)

were used to record ground reaction forces and moments, which were sampled at 1080

Hz and low-pass filtered at 20 Hz. Our analysis focused on single support because a

lack of consecutive force plate strikes precluded the analysis of double support.

Subjects walked at a self-selected walking speed of 0.92 ± 0.18 m/s. Surface

electromyography (EMG) signals were recorded for nine of the ten subjects from the

medial hamstrings, biceps femoris long head, rectus femoris, gastrocnemius, and

tibialis anterior (Motion Lab Systems, Baton Rouge, LA). EMG was sampled at 1080

Hz, band-pass filtered between 20 and 400 Hz, rectified, and low-pass filtered at 10

Hz. EMG for each muscle was normalized from zero to one based on the minimum

and maximum values of that muscle over all trials for each subject.

3.2.2 DYNAMIC SIMULATION

A generic musculoskeletal model (lower extremities from Delp et al., 1990 and

torso from Anderson and Pandy, 1999) with 19 degrees of freedom and 92

musculotendon actuators was scaled to each subject according to their anthropometric

measurements (Figure 3.1). The degrees of freedom included a ball-and-socket joint

located at approximately the third lumbar vertebra between the pelvis and torso, ball-

and-socket joints at each hip, a planar joint with coupled translations at each knee, and

revolute joints at each ankle. A subject-specific simulation of the single-limb stance

phase of gait was then generated using OpenSim, a freely available biomechanical

53

simulation package (Delp et al., 2007), www.simtk.org. Double support was not

included in this study due to a lack of consecutive force plate strikes in the small set of

subjects who met our inclusion criteria. Kinematic and ground reaction force data

were imported into OpenSim, where the computed muscle control Algorithm

determined the muscle excitations that generated a forward dynamic simulation that

minimized the difference between the experimental and simulated gait kinematics

(Thelen et al., 2003; Thelen and Anderson, 2006). Estimated muscle activations were

scaled in the same manner as the EMG signals, and compared to the experimentally-

measured EMG signals to evaluate the fidelity of the simulation’s muscle activation

timing.

To test the sensitivity of the results to errors in muscle activation timing, we

constrained the simulated activations to match the shape and normalized magnitude of

the EMG for the 10 muscles for which EMG was recorded for one subject (See

Appendix A). When there was a disagreement between the EMG and simulated

activations, the normalized magnitude of the EMG was used to define maximum and

minimum bounds on the magnitude of the simulated activations. Although adding

these constraints changed the magnitude of the contribution of each muscle the

direction (e.g., flexion/extension) did not change. Since these changes in magnitudes

did not alter the conclusions drawn from analyzing this simulation, we chose not to

constrain activations for other subjects.

A perturbation analysis was used to determine the joint angular accelerations

and mass center accelerations generated by each muscle in the model (Liu et al.,

2006). In this analysis, one newton of additional force (the perturbation) was applied

54

to each muscle separately and the model’s equations of motion integrated forward in

time by 20 ms. These parameters for the perturbation analysis were chosen based upon

a sensitivity analysis and experience from previous studies (Neptune et al., 2001;

Goldberg et al., 2004). Evaluating the change in position of each joint and the mass

center after 20 ms, we determined the accelerations generated by each muscle by

assuming constant acceleration over this brief period. This quantity represents the

potential of each muscle to accelerate each joint and the mass center per newton of

force. A muscle’s contribution to joint and mass center accelerations was computed by

multiplying the muscle’s potential by its estimated force from the simulation at each

time step. Upward accelerations of the mass center were considered to contribute to

support of the body and forward accelerations were considered to contribute to

progression of the body. The contributions of each muscle to mass center accelerations

in the subjects with crouch gait were compared to two age, size, and speed matched,

unimpaired subjects (age: 8.6 ± 2.2 yrs; weight: 33.6 ± 10.6 kg; speed: 1.08 ± 0.1 m/s;

leg length: 0.71 ± 0.08 m) for whom motion analysis data were also collected at

Gillette Children’s Specialty Healthcare. The simulation data for these unimpaired

subjects have been previously reported (Liu et al., 2008) and are available at

www.simtk.org.

55

3.3 RESULTS

The muscle-driven simulation of each subject tracked all experimental joint

angles with an RMS error of less than 1° (Figure 3.2). The resultant joint moments

computed by multiplying the estimated muscle forces and moment arms also matched

the joint moments computed by inverse dynamics with an RMS error of less than 1

Nm (Figure 3.3).

Figure 3.2: Comparison of simulated and experimentally-measured joint angles. Average kinematics for pelvis, hip, knee, and ankle are shown for all 10 subjects. The gray line and shaded regions are the experimentally-measured joint angles (± 1 standard deviation) and the black line and dashed-lines are the kinematics reproduced by the simulation (± 1 standard deviation). The simulated kinematics are not provided during double support as only single-limb stance was simulated. The simulated kinematics were within 1º of experimental kinematics (RMS error) for all trials.

56

The normalized simulated activations and EMG showed similar on and off

patterns during single-limb stance (Figure 3.4). Differences between estimated

excitations and EMG included excessive rectus femoris activity during swing and

reduced biceps femoris activity during terminal swing in the simulations.

Figure 3.3: Comparison of the simulated and experimentally-measured hip, knee, and ankle moments for all 10 subjects. The gray line and shaded regions are the experimentally-measured joint moments (± 1 standard deviation) and the blue line and dashed-lines are the moments calculated by computed by multiplying the estimated muscle forces and moment arms (± 1 standard deviation). Joint moments are only shown during single-limb stance and swing since force plate data was not available during double support.

57

Subjects walking in crouch gait utilized higher muscle forces than the

unimpaired subjects. The average total muscle force of all stance-limb muscles during

single-limb stance in crouch gait was 8.6 ± 0.6 times body weight versus 5.3 ± 0.7

times body weight in unimpaired gait. The primary contributors to hip extension were

the gluteus maximus, posterior gluteus medius, and bi-articular hamstrings, while the

primary contributors to knee extension were the vasti, gluteus maximus, and soleus

Figure 3.4: Comparison of EMG and simulated activation. The EMG signal and activation were normalizedto a range of 0 to 1 between the maximum and minimum values for each subject. The gray line and shadedarea represents the EMG data (± 1 standard deviation) over a full gait cycle, while the simulated activationsduring single-limb stance are shown in blue with the dashed lines showing ± 1 standard deviation. Note thatestimated muscle activations are not provided during the double support periods of the gait cycle becauseonly single-limb stance was simulated.

58

(Figure 3.5). The iliacus and psoas muscles generated substantial flexion accelerations

of all three joints. The rectus femoris generated hip flexion acceleration.

The largest upward accelerations of the mass center were from the soleus,

followed by the vasti, then gastrocnemius, gluteus medius, rectus femoris, and gluteus

maximus (Figure 3.6). This subset of muscles provided 90% of the total upward

acceleration of the mass center generated by all muscles of the stance limb during

crouch gait and unimpaired gait. The ankle plantarflexors contributed more to support

during crouch gait, whereas the gluteus medius provided more support during

unimpaired gait. The primary muscles that accelerated the mass center downward

(Figure 3.6) included the anterior tibialis, iliopsoas, biceps femoris short head, hip

adductors (adductor longus, brevis, and magnus), and medial hamstrings

(semimembranosus and semitendinosus). The downward acceleration of the mass

center from gravity was larger in crouch gait as less support was provided by skeletal

alignment than in unimpaired gait (Figure 3.6).

-30000

-20000

-10000

0

10000

20000

30000

Glut Max Glut Med Bi-Art Hams Rectus Vasti Iliopsoas Gastroc Soleus

Hip

Knee

Ankle

Angu

lar A

ccel

erat

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(º/s

2 )ex

tfle

x

Figure 3.5: Average contributions ± 1 standard deviation to hip, knee, and ankle angular accelerationsduring single-limb stance from the major muscle groups of the stance limb. Positive and negativeaccelerations correspond to extension and flexion, respectively. Note that the muscles with average valuesclose to zero made small contributions throughout single-limb stance.

59

Acce

lera

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ccel

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Vasti

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Crouch Gait

Unimpaired Gait

Gastrocnemius

-1

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Gluteus Medius

-1

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Rectus Femoris

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UP

FORWARD

Gluteus Maximus

-10

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Biceps Femoris Short HeadIliopsoas Hip Adductors

Skeletal AlignmentTibialis Anterior Gravity-10

-8

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eler

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n (m

/s2 )

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/s2 )

OTO OHCOTO OHC OTO OHCOTO OHC OTO OHCOTO OHC

OTO OHCOTO OHCOTO OHCOTO OHC

0

1

2

3

4

5

OTO OHCOTO OHC

Figure 3.6: Contributions to mass center accelerations from the muscles providing the largestmagnitude accelerations upward and downward and from gravity. Accelerations are shown for single-limb stance from opposite toe-off (OTO) to opposite heel contact (OHC). The vectors represent theaverage up/down and forward/backward acceleration of the mass center at each 5% of single-limbstance for all subjects. The magnitude of the accelerations in the forward/backward directions has thesame scale as the up/down accelerations shown on the vertical-axis. Skeletal alignment was calculatedby subtracting the accelerations due to muscles from the accelerations due to the ground reaction force.

60

Although the muscles that contributed to the vertical acceleration of the mass

center were similar in crouch gait and unimpaired gait, the profile of the accelerations

differed between the two groups (Figure 3.6). Accelerations of the mass center

generated by muscles during unimpaired gait tended to modulate substantially over the

period of single-limb stance, whereas the stance-limb muscles provided more constant

contributions to mass center accelerations throughout single-limb stance in crouch

gait.

The largest contributors to forward progression during the single-limb stance

phase of crouch gait were the bi-articular hamstrings, gluteus medius, and gluteus

maximus. The gastrocnemius, rectus femoris, vastus, iliopsoas, and hip adductors

slowed forward progression. In contrast, during unimpaired gait, the vasti and soleus

slowed forward progression during early single-limb stance while the gastrocnemius

accelerated the mass center forward in late single-limb stance. The contributions of all

stance-limb muscles to joint and mass center accelerations are provided in Appendix

A.2.

3.4 DISCUSSION

In this study we created the first muscle-actuated simulations of subjects with

crouch gait, which provide insight into how individual muscles contribute to joint

angular accelerations and mass center accelerations during single-limb stance.

Analysis of these simulations indicates that crouch gait is characterized by larger

muscle forces than unimpaired gait to support body weight and propel the body

61

forward throughout single-limb stance. These larger forces were necessary to support

the body in part due to the fact that the skeleton provided less body weight support in

crouch gait, as well as the reduced capacity of muscles to extend the joints (Hicks et

al., 2008) in a crouched posture.

Subjects with crouch gait utilized the same muscle groups to support the body

as unimpaired gait; however, they employed a different support strategy during single-

limb stance. Supporting the body in unimpaired gait requires precise orchestration of

muscle activations, with dramatic modulation of muscle activity throughout single-

limb stance. In contrast, during crouch gait, the support muscles were active

throughout single-limb stance and generated relatively constant accelerations of the

mass center. Subjects with crouch gait also used a different strategy to move the mass

center forward during single-limb stance, relying more on proximal muscles than the

unimpaired subjects.

These different strategies for support and progression during single-limb stance

may underlie why some individuals with cerebral palsy adopt a crouch gait. Given the

excessive muscle activity common in these subjects, they may adopt a support strategy

where muscles are activated consistently throughout single-limb stance. Driving

forward progression with more proximal muscles may also allow subjects to rely less

on controlling distal leg muscles, which are often more severely effected in patients

with cerebral palsy (Carr et al., 1993; Wiley and Damiano, 1998). The use of proximal

muscles for forward progression and walking with slightly flexed knees are also

characteristics of immature gait in unimpaired children (Farmer, 2003). This suggests

62

that some children with cerebral palsy may adopt crouch gait as a feasible gait pattern

given their neurological limitations.

Understanding how individual muscles contribute to joint and mass center

accelerations can help to clarify the effects of treatment. For example, the ankle

plantarflexors are common targets for surgical lengthening in patients with crouch

gait. The gastrocnemius is highly active in stance and has a knee-flexion moment arm,

which might play a role in the excessive knee flexion associated with crouch gait. The

results from our simulations indicate that although the gastrocnemius and soleus both

generate ankle plantarflexion accelerations, they have different effects at the hip and

knee. While the soleus contributes to hip and knee extension throughout single-limb

stance, the gastrocnemius generates flexion accelerations at both joints. Despite these

differences, both muscles accelerate the mass center upward and contribute to support.

The contribution of the gastrocnemius to support indicates that the muscle’s role as an

extensor of the ankle is more significant to the acceleration of the mass center than its

role as a flexor of the hip and knee.

Our subject-specific simulations of crouch gait demonstrate that the soleus is

an important crouch-countering muscle. The soleus not only extends all three joints,

but provides the largest contribution to body weight support, and thus should not be

weakened in this patient population. Furthermore, our results suggest that weakening

the gastrocnemius could compromise a patient’s ability to support his or her body

weight and may lead to excessive dorsiflexion. While lengthening the gastrocnemius

may reduce hip and knee flexion accelerations by reducing the muscle’s force, a

patient may still walk in a crouched posture after a gastrocnemius lengthening if the

63

soleus and other muscles cannot compensate for the decreased contribution to support

from gastrocnemius. These possible negative effects of weakening the gastrocnemius

agree with studies that predicted decreased active moment-generating capacity after

lengthening the gastrocnemius (Delp et al., 1995) and that demonstrated increased

knee flexion after decreasing gastrocnemius activity (Sutherland et al., 1980).

Testing the accuracy of muscle forces estimated from dynamic simulations is

one of the challenges in creating subject-specific simulations. The simulations tracked

the experimental kinematics and joint moments closely, but we observed some

differences between EMG patterns and simulated activations. Given that maximum

voluntary contractions were not available from the study subjects, we could not

directly compare the magnitude of the EMG with the estimated activations. Even if the

magnitude of a muscle’s force changes, the direction of its acceleration (e.g.,

flexion/extension) would be the same since, according to the equations of motion,

direction is determined by the inertial properties of the model, muscle paths, and

posture of the model. We tested the impact of constraining activations to better match

the shape and normalized magnitude of the EMG and found that resulting alterations

in muscle activations did not impact the conclusions of the study.

Previous investigations have tested the induced acceleration analysis technique

used in this study by comparing estimated accelerations to accelerations produced

when individual muscles are electrically stimulated (Stewart et al., 2007; Hernandez et

al., 2008; Stewart et al., 2008; Hunter et al., 2009). These studies have shown that

stimulating a muscle produces accelerations in the same direction as predicted by the

induced acceleration analysis. Future studies that use electrical stimulation to examine

64

the accelerations generated by individual muscles during crouch gait could assist in

further testing the results presented here.

These simulations were generated for individuals who walked flat-footed in a

mild crouch gait. The results of this study may not be extensible to other crouch gait

populations, such as patients with equinus, excessive dorsiflexion, or more severe

knee flexion. Additionally, this study examined single-limb stance and was not able to

explore double support due to a lack of force plate data. However, single-limb stance

is clinically important since an inability to support the mass center during this period

may contribute to crouch gait. Future studies examining double support would provide

valuable information about propulsion and the transition from stance to swing.

The muscle-actuated dynamic simulations generated in this study provide

insights into the support and progression strategies used in crouch gait. The

differences between crouch and unimpaired gait revealed that individuals who walk in

a crouch gait utilize similar muscles to support the mass center but different muscles

to propel the mass center forward during single-limb stance. The results of this study

can be used to identify muscles that are used to support the mass center during crouch

gait for interventions such as strength training, and to inform surgical decision-

making. Although we can measure muscle activity and kinematics during gait,

simulation provides a tool to quantify how the activity of individual muscles

contribute to movement and can lead to a deeper understanding of the biomechanics

underlying crouch gait.

65

CHAPTER 4

HOW DO MUSCLE CONTRIBUTIONS TO SUPPORT AND PROGRESSION CHANGE WITH CROUCH SEVERITY?

Manuscript in review

Katherine M. Steele Ajay Seth Jennifer L. Hicks Michael H. Schwartz Scott L. Delp

66

ABSTRACT

The goals of this study were to determine if the muscle contributions to vertical

and fore-aft acceleration of the mass center differ between crouch gait and unimpaired

gait and if these muscle contributions change with crouch severity. Examining muscle

contributions to mass center acceleration provides insight into the roles of individual

muscles during gait and can provide guidance for treatment planning. We calculated

vertical and fore-aft accelerations using musculoskeletal simulations of typically-

developing children and children with cerebral palsy and crouch gait. Analysis of

these simulations revealed that during unimpaired gait the quadriceps produce large

upward and backward accelerations during early stance, whereas the ankle

plantarflexors produce large upward and forward accelerations later in stance. In

contrast, during crouch gait, the quadriceps and ankle plantarflexors produce large,

opposing fore-aft accelerations throughout stance. The quadriceps force required to

accelerate the mass center upward was significantly larger in crouch gait than in

unimpaired gait and increased with crouch severity. The gluteus medius accelerated

the mass center upward during mid stance in unimpaired gait; however, during crouch

gait the upward acceleration produced by the gluteus medius was significantly

reduced. During unimpaired gait the quadriceps and ankle plantarflexors accelerate the

mass center at different times, efficiently modulating fore-aft accelerations. However,

during crouch gait, the quadriceps and ankle plantarflexors produce fore-aft

accelerations at the same time and the opposing fore-aft accelerations generated by

these muscles contributes to the inefficiency of crouch gait.

67

4.1 INTRODUCTION

Many individuals with cerebral palsy walk in a crouch gait pattern

characterized by excess hip and knee flexion (Wren et al., 2005). Walking in a

crouched posture can lead to joint pain (Jahnsen et al., 2004) and bone deformities

(Graham and Selber, 2003) and is inefficient (Rose et al., 1989; Waters and Mulroy,

1999). Understanding how muscles accelerate the mass center during crouch gait may

provide insight about the underlying mechanics and inefficiencies associated with this

gait pattern.

Previous studies have documented how muscles accelerate the mass center

during unimpaired gait (Neptune et al., 2001; Anderson and Pandy, 2003; Liu et al.,

2008) and have shown that the same muscles that accelerate the mass center upward

also modulate fore-aft acceleration (Liu et al., 2006). Examining muscle contributions

to mass center acceleration can provide insight into the role of individual muscles and

the control strategy used during gait. During unimpaired gait, the vasti and gluteus

maximus accelerate the mass center upward and backward in early stance, the gluteus

medius accelerates the mass center upward in mid stance, and the ankle plantarflexors

accelerate the mass center upward and forward in late stance (Neptune et al., 2001;

Anderson and Pandy, 2003; Liu et al., 2008). This coordinated muscle activity uses

different muscle groups at different periods of stance to efficiently modulate vertical

and fore-aft mass center acceleration.

How muscles modulate vertical and fore-aft accelerations of the mass center

during crouch gait and how these accelerations change with crouch severity is not well

understood. Previous work has shown that similar muscles accelerate the mass center

68

upward during the single-limb stance phase of both mild crouch gait and unimpaired

gait (Steele et al., 2010). However, the role of muscles during the double support

phase, when fore-aft accelerations are largest, is not known for crouch gait. The ability

of muscles such as the gluteus medius and soleus to extend the hip and knee (Hicks et

al., 2008) and accelerate the mass center upward (Correa et al., 2012) has been shown

to decrease in a crouched posture; however, the effect of crouch severity on muscle

contributions to mass center acceleration has not been investigated. Alterations in the

ability of muscles to generate vertical and fore-aft accelerations of the mass center

may change the strategy used to accelerate the mass center during crouch gait and

contribute to the inefficiency of this gait pattern.

The goals of this study were to determine whether: (1) the magnitude and

timing of muscle contributions to vertical and fore-aft accelerations differ between

crouch gait and unimpaired gait, and (2) the muscle contributions to vertical and fore-

aft accelerations change with crouch severity. To calculate muscle contributions to

mass center accelerations we created three-dimensional musculoskeletal simulations

of gait for typically-developing children and children with cerebral palsy and varying

degrees of crouch gait (Figure 4.1). Examining how individual muscles contribute to

vertical and fore-aft accelerations can elucidate the mechanics of crouch gait and

inform treatment strategies.

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4.2 METHODS

Nine children with cerebral palsy were selected from a database of subjects

who had undergone motion analysis at Gillette Children’s Specialty Healthcare. The

selection criteria for the subjects included: (1) a diagnosis of spastic diplegic cerebral

palsy, (2) a minimum knee flexion angle during stance greater than 15°, and (3) a

tibial and femoral torsion deformity less than 30° (Hicks et al., 2007). We also

required that the subjects did not use an assistive device during the motion analysis

and had at least two consecutive force plate strikes. Nine subjects with crouch gait

were divided into three groups based on minimum knee flexion angle during stance:

15 - 30° knee flexion was defined as mild crouch gait, 30 - 50° was defined as

moderate crouch gait, and 50° or larger was defined as severe crouch gait (Table 4.1).

Figure 4.1: Musculoskeletal model of an individual with cerebral palsy and crouch gait. Vertical and fore-aft accelerations of the mass center were calculated by analyzing muscle-driven simulations.

70

Table 4.1: Subject characteristics (average ± standard deviation) Age

(years) Height (cm)

Weight (kg)

KFA* (deg)

Unimpaired 10 ± 3 144 ± 16 36 ± 9 -2 ± 4 Mild Crouch 9 ± 1 124 ± 10 24 ± 4 18 ± 2 Moderate Crouch 11 ± 2 136 ± 6 43 ± 31 34 ± 2 Severe Crouch 14 ± 2 157 ± 12 41 ± 8 64 ± 20 * KFA: Minimum knee flexion angle during stance

The typically-developing children were selected from a group of subjects who

also visited Gillette Children’s Specialty Healthcare for motion analysis and whose

gait has been previously simulated (Liu et al., 2008). Previous studies demonstrated

consistent contributions to vertical and fore-aft accelerations during gait in typically-

developing children; thus, we chose three subjects with an age range similar to the

subjects with crouch gait (Table 4.1).

Motion analysis data was collected using a 12-camera system (Vicon Motion

Systems, Lake Forest, CA) and a standard marker measurement protocol (Davis et al.,

1991). Ground reaction forces were measured with four force plates (AMTI,

Watertown, MA). All subjects walked barefoot at their self-selected speed. Surface

electromyography (EMG) was recorded from the rectus femoris, hamstrings,

gastrocnemius, and anterior tibialis (Motion Laboratory Systems, Baton Rouge, LA)

for nine of the subjects. The nine subjects who had EMG data available included three

typically-developing subjects, three mild crouch gait subjects, one moderate crouch

gait subject, and two severe crouch gait subjects. The EMG signals were sampled at

1080 Hz, band-pass filtered between 20 and 400 Hz, rectified, and low-pass filtered at

10 Hz. The magnitude of the EMG signal was normalized for each muscle group from

zero to one based on the minimum and maximum values observed during the motion

71

analysis. Since EMG was not available for all subjects, we averaged the processed

EMG signals for each group of subjects for comparison to simulated muscle

activations.

To create dynamic musculoskeletal simulations of gait, we used a

musculoskeletal model with 19 degrees of freedom and 92 musculotendon actuators

(lower extremities from Delp et al., 1990 and torso from Anderson and Pandy, 1999).

The degrees of freedom in the model included three translations and three rotations of

the pelvis, a ball-and-socket joint between the pelvis and the torso located at the third

lumbar vertebrae, ball-and-socket joints at each hip, a custom joint with coupled

translations and rotations at each knee, and a revolute joint at each ankle. This model

has previously been used to model typically-developing children (Liu et al., 2006; Liu

et al., 2008) and children with cerebral palsy (Hicks et al., 2008; Reinbolt et al., 2008;

Steele et al., 2010). The model was scaled according to anthropometric measurements

for each subject using OpenSim (Delp et al., 2007). We scaled the maximum isometric

force of all muscles by height-squared (Jaric et al., 2002).

Inverse kinematics, which minimizes the difference between experimental

marker trajectories and markers placed on the model, was used to calculate joint

angles (Figure 4.2). Joint moments were calculated for each subject using inverse

dynamics (Figure 4.2).

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Figure 4.2: Average hip, knee, and ankle flexion angles and moments during unimpaired gait and mild,moderate, and severe crouch gait. The joint moments are normalized by body mass (kg).

73

A dynamic simulation of one gait cycle was generated for each subject. The

residual reduction algorithm (RRA) was used to reduce residuals at the pelvis (Delp et

al., 2007). Residuals are non-physiological forces and moments applied at the pelvis

that balance dynamic inconsistencies resulting from experimental errors and modeling

assumptions. RRA reduced these residuals by making small changes to measurements

that may have experimental error including the position of the torso mass center

(changes were less than 2 cm in magnitude) and the kinematics (changes were less

than 2° for all joint angles). Using the adjusted model and kinematics determined from

RRA, the computed muscle control algorithm (CMC) was used to estimate the muscle

forces required to track each subject’s kinematics (Thelen et al., 2003; Thelen and

Anderson, 2006). At each time step, CMC determines the distribution of muscle

activations, such that model accelerations match the experimental accelerations for all

degrees of freedom. The algorithm accounts for muscle activation and contraction

dynamics, which includes the muscle force-length-velocity relationship. The

distribution of muscle activations was determined by minimizing the sum of muscle

activations squared at each time step. The estimated muscle activations from CMC

were qualitatively compared to the average EMG signal for each gait pattern;

constraints on muscle excitations were used when the simulated muscle activity was

inconsistent with the EMG signals.

An induced acceleration analysis was used to compute the contributions of

individual muscles to vertical and fore-aft mass center accelerations (Zajac, 1989;

Riley and Kerrigan, 1999; Anderson and Pandy, 2003; Hamner et al., 2010) at each

time point of a subject’s gait simulation. This analysis solves the model’s equations of

74

motion, including foot-floor contact constraint equations, to determine the

contributions of gravity, velocity, and each muscle force to the mass center

acceleration. The contact constraint equations used in this analysis enforce a rolling

without slipping constraint to model the foot-floor interaction (Hamner et al., 2010).

The musculoskeletal simulations recreated the dynamics of gait for the

typically-developing children and children with cerebral palsy. The average residual

forces and moments applied at the mass center of the pelvis were 9.7 N and 16.5 Nm,

less than 10% of body weight and body weight*height, respectively, for all subjects.

The on-off timing and magnitude of the simulated activations and electromyography

were qualitatively similar (Figure 4.3); however, there were some deviations, such as

decreased quadriceps activity during early swing of unimpaired gait and increased

gastrocnemius activity during swing of severe crouch gait. These differences had

minimal effects on muscle contributions to vertical and fore-aft accelerations of the

mass center, since these accelerations are generated predominately during stance.

To determine if the muscle contributions to vertical and fore-aft accelerations

differed between unimpaired gait and crouch gait, we performed a student’s t-test with

a significance level of 0.05. To determine if contributions to vertical and fore-aft

accelerations changed with crouch severity we used a one-way ANOVA to compare

mild, moderate, and severe crouch gait with a significance level of 0.05. We used two

methods to examine relative timing of muscle contributions to mass center

accelerations. The first method, a covariance analysis, examined the covariance of the

contributions to fore-aft accelerations of major muscle groups over the gait cycle to

determine if they differed between unimpaired gait and crouch gait (using a student’s

75

t-test) or with crouch severity (using a one-way ANOVA). The second method was to

calculate the area under the fore-aft acceleration versus gait cycle curves for major

muscle groups to determine if they differed between unimpaired gait and crouch gait

(using the student’s t-test) or with crouch severity (using a one-way ANOVA).

Figure 4.3: Average ± 1 standard deviation of the EMG signal of each group (gray) and estimated muscleactivations for each subject (black lines) from the quadriceps, hamstrings, gastrocnemius, and anteriortibialis during unimpaired gait and mild, moderate, and severe crouch gait. Only one individual withmoderate crouch gait had EMG, thus we took the average of multiple gait cycles for comparison to thegroup. The magnitude of the EMG and activations were normalized from 0 to 1 based upon the minimumand maximum values during the gait cycle.

76

4.3 RESULTS

The vasti (p = 0.03) and rectus femoris (p = 0.03) produced greater backward

acceleration of the mass center and the gastrocnemius (p = 0.02) and soleus (p = 0.05)

produced greater forward acceleration of the mass center during crouch gait than

unimpaired gait (Figure 4.4A). The forward acceleration produced by the soleus

increased with crouch severity (p = 0.001). In contrast, the fore-aft accelerations

produced by the gluteus medius (p < 0.001) and iliopsoas (p = 0.02) were significantly

smaller in crouch gait than in unimpaired gait.

The downward acceleration of the mass center from gravity was greater (p =

0.001) during crouch gait than unimpaired gait (Figure 4.4B). In the erect posture of

unimpaired gait, a larger portion of body weight is supported by skeletal alignment

than in a crouched posture and, thus, the acceleration of the mass center due to gravity

Figure 4.4: The average (A) fore-aft and (B) vertical accelerations of the mass center during stanceproduced by each muscle and (C) the average muscle force during stance normalized by body weight(BW). Error bars are ± 1 standard error. A ‘*’ indicates a significant difference (p < 0.05) in the student’st-test comparing unimpaired gait and crouch gait. An arrow indicates a significant change with crouchseverity (p < 0.05) from a one-way ANOVA comparing mild, moderate, and severe crouch gait.

77

is reduced. The contribution of the tibialis anterior to downward acceleration was

greater during crouch gait than unimpaired gait; however, muscle contributions to

downward acceleration of the mass center were small relative to gravity. The vasti,

gastrocnemius, and soleus produced the largest upward accelerations of the mass

center during crouch gait and unimpaired gait. The upward acceleration produced by

the gluteus medius was significantly less during crouch gait than unimpaired gait. The

upward acceleration produced by the gastrocnemius decreased with crouch severity (p

= 0.02).

The forces produced by the vasti (p = 0.04) and rectus femoris (p = 0.01) were

significantly greater in crouch gait than in unimpaired gait, and vasti force increased

(p = 0.005) with crouch severity (Figure 4.4C). The change in vasti force was larger

than the change in upward and backward accelerations produced by the vasti because

of a diminished capacity of the vasti to accelerate the mass center in a crouch posture

(Figure 4.5). For example, vasti force during severe crouch gait increased by 340%

compared to unimpaired gait, but the upward acceleration produced by the vasti only

increased by 184% because the upward acceleration produced per newton of muscle

force of the vasti decreased by 54% in severe crouch gait.

The relative timing and magnitude of the fore-aft accelerations generated by

the vasti and gastrocnemius differed between crouch gait and unimpaired gait, as

indicated by changes in the covariance and area under the fore-aft acceleration curves

(Figure 4.6). In unimpaired gait, the vasti accelerated the mass center upward and

backward during early stance and the ankle plantarflexors accelerated the mass center

upward and forward during late stance. The covariance of the fore-aft accelerations

78

generated by the vasti and gastrocnemius during unimpaired gait was close to zero

(-0.08 ± 0.03), indicating that these muscles were active at different times of the gait

cycle. During crouch gait, the vasti and ankle plantarflexors both contributed to fore-

aft accelerations throughout stance, resulting in large, opposing fore-aft accelerations.

The covariance of the fore-aft accelerations generated by the vasti and gastrocnemius

was -0.71 ± 0.14 during crouch gait, significantly different than unimpaired gait (p =

0.03), indicating that these muscles were active at similar times and accelerated the

mass center in opposite directions. Additionally, the areas under the fore-aft

acceleration curves of the vasti (p = 0.01) and gastrocnemius (p = 0.02) were

significantly greater in crouch gait than in unimpaired gait due to these muscles’

sustained contributions to fore-aft accelerations during crouch gait.

Figure 4.5: The average (A) fore-aft and (B) verticalaccelerations produced per 1 newton of muscle force duringstance of each muscle. Error bars are ± 1 standard error. A ‘*’indicates a significant difference (p < 0.05) in the student’s t-test comparing unimpaired gait and crouch gait. An arrowindicates a significant change with crouch severity (p < 0.05)from a one-way ANOVA comparing mild, moderate, andsevere crouch gait.

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Figure 4.6: The fore-aft accelerations of the mass center produced by the vasti (gray line) andgastrocnemius (black line) during stance. The gray area shows the experimentally measured accelerationof the mass center (fore-aft ground reaction force normalized by body mass).

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4.4 DISCUSSION

As in unimpaired gait, two muscle groups, the quadriceps and ankle

plantarflexors, were largely responsible for accelerating the mass center upward and

modulating fore-aft acceleration during crouch gait. However, unlike unimpaired gait,

these muscles contributed to mass center accelerations throughout stance and

produced large, opposing fore-aft accelerations. During crouch gait, the ankle

plantarflexors accelerated the mass center upward and forward while the vasti

accelerated the mass center upward and backward throughout stance. The coordination

of quadriceps and ankle plantarflexor activity during unimpaired gait provides an

efficient strategy (Liu et al., 2006) which also allows for modulation of speed by

increasing or decreasing quadriceps and plantarflexor muscle force proportionally

across the gait cycle (Liu et al., 2008). This system is compromised during crouch

gait, and muscles are required to make more sustained contributions to vertical and

fore-aft accelerations. These sustained contributions contribute to the inefficiency of

crouch gait and require individuals with crouch gait to adopt a different strategy for

speed modulation.

A crouched posture increases the demand on muscles to accelerate the mass

center upward due to a decrease in skeletal support and an increase in the knee

extensor moment. The quadriceps and ankle plantarflexors produce the greatest

upward acceleration of the mass center during crouch gait, but the gluteus medius’

ability to accelerate the mass center upward is significantly reduced compared to

unimpaired gait (Correa et al., 2012). During unimpaired gait, the gluteus medius

accelerates the mass center upward in mid stance during the transition from quadriceps

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to ankle plantarflexors activity. During crouch gait, the gluteus medius contribution to

upward acceleration is reduced and a different strategy is needed to support the mass

center in mid stance. Furthermore, the upward acceleration produced per newton of

muscle force decreases with crouch severity for both the quadriceps and ankle

plantarflexors (Hicks et al., 2008) and other muscles may need to be recruited to

accelerate the mass center upward. Previous experimental studies have also reported

increased quadriceps demand (Perry et al., 1975; Hsu et al., 1993) and prolonged ankle

plantarflexor activity during crouch gait (Thomas et al., 1996).

Understanding how muscles contribute to vertical and fore-aft accelerations

can assist in evaluating treatment options. Demand on the vasti and rectus femoris was

greater during crouch gait and may contribute to fatigue. Strength training or other

programs that improve the endurance of these muscles may improve the overall

endurance of individuals with crouch gait. The ankle plantarflexors were also critical

muscles for accelerating the mass center upward and forward during crouch gait and

may be targets for strength training programs. Engsberg et al. (2006) reported an

improvement in knee flexion during stance after strengthening the ankle

plantarflexors. Similarly, ankle foot orthoses may assist the ankle plantarflexors and

improve the efficiency of crouch gait (Lucareli et al., 2007; Rogozinski et al., 2009).

From a surgical perspective, weakening or reducing the force-generating capacity of

the gastrocnemius or soleus by musculotendon lengthening, neuromuscular toxins, or

other procedures could reduce an individual’s ability to accelerate their mass center

upward or forward.

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Simulation enables analysis of the accelerations produced by muscles;

however, there are limitations to these methods. The models used in this study were

scaled from adult models and may not reflect bone deformities or altered muscle

physiology of individuals with cerebral palsy. We excluded subjects with significant

bone deformities. However, measurements of how muscle physiology changes in

individuals with cerebral palsy are needed to incorporate the effects of contracture,

spasticity, and other pathologies. These changes in muscle physiology would not

affect the direction of the vertical or fore-aft accelerations produced by each muscle,

but could affect the relative magnitude of force produced by different muscles. To

estimate muscle forces, we minimized activation squared and compared estimated

activations to EMG. EMG data was available from a few muscles in a subset of the

subjects and, although the estimated activations were similar to EMG during stance

when muscles predominately contribute to mass center accelerations, the EMG data

was noisy and varied between subjects. EMG from more muscle groups and analysis

of other minimization criteria could improve simulations of individuals with cerebral

palsy. This study also had a limited number of subjects and may not have had the

power to detect some differences in muscle contributions to vertical and fore-aft

accelerations. We have made the simulations included in this study freely available

on-line for other researchers to evaluate and use for future research

(https://simtk.org/home/crouchgait).

By creating musculoskeletal simulations of individuals with cerebral palsy and

crouch gait, we have determined that a different strategy is used to accelerate the mass

center during crouch gait. The quadriceps and ankle plantarflexors are the primary

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muscle groups that accelerate the mass center upward; however, sustained activity of

these muscles during stance produces large, opposing fore-aft accelerations – like

driving with your parking brake on. Future studies that examine the metabolic costs of

crouch gait and explore why individuals adopt a crouch gait pattern will be critical for

improving treatment and quality of life. Examining how individual muscles contribute

to gait using musculoskeletal simulation provides a foundation for these future studies

and a basis for clinicians and researchers to understand the underlying mechanics of

gait pathologies.

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85

CHAPTER 5

HOW DOES TIBIOFEMORAL CONTACT FORCE CHANGE DURING CROUCH GAIT?

Gait & Posture (2012), vol. 35, pp. 556-60

Katherine M. Steele Matt DeMers Michael H. Schwartz Scott L. Delp

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ABSTRACT

Crouch gait, a common walking pattern in individuals with cerebral palsy, is

characterized by excessive flexion of the hip and knee. Many subjects with crouch gait

experience knee pain, perhaps because of elevated muscle forces and joint loading.

The goal of this study was to examine how muscle forces and compressive

tibiofemoral force change with the increasing knee flexion associated with crouch gait.

Muscle forces and tibiofemoral force were estimated for three unimpaired children and

nine children with cerebral palsy who walked with varying degrees of knee flexion.

We scaled a generic musculoskeletal model to each subject and used the model to

estimate muscle forces and compressive tibiofemoral forces during walking. Mild

crouch gait (minimum knee flexion 20-35°) produced a peak compressive tibiofemoral

force similar to unimpaired walking; however, severe crouch gait (minimum knee

flexion > 50°) increased the peak force to greater than 6 times body weight, more than

double the load during unimpaired gait. This increase in compressive tibiofemoral

force was due primarily to increases in quadriceps force during crouch gait, which

increased quadratically with average stance phase knee flexion (i.e., crouch severity).

Increased quadriceps force contributes to larger tibiofemoral and patellofemoral

loading which may contribute to knee pain in individuals with crouch gait.

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5.1 INTRODUCTION

Crouch gait is a common pathological walking pattern adopted by individuals

with cerebral palsy that is characterized by excessive hip and knee flexion. Walking in

a crouched posture is inefficient (Rose et al., 1989; Waters and Mulroy, 1999) and can

lead to joint pain and compromise an individual’s walking ability (Opheim et al.,

2009). Surgical and therapeutic treatments for crouch gait aim to produce a more

upright posture to improve walking efficiency and prevent joint pain and deterioration.

Altered loads on the knee can have adverse effects on joint health. Cartilage

and bone growth and maintenance depend on the loads experienced during daily life

(Carter and Wong, 1988; Wong and Carter, 2003), and abnormal loading can lead to

joint pain, cartilage degeneration (Eckstein et al., 2002), and the formation of bone

deformities (Graham and Selber, 2003). Joint pain can be a significant contributor to

walking deterioration in adults with cerebral palsy. Jahnsen et al. (2004) found that

41% of adults with diplegic cerebral palsy reported significant knee pain.

To develop successful treatment strategies for crouch gait, surgeons and

therapists need to understand how joint loads change with increasing knee flexion

during crouch gait and how joint loads may change with altered knee flexion.

Treatments are aimed at reducing the excessive knee flexion associated with crouch

gait, but it is unclear if changes in knee flexion will alter joint loads. Quantifying the

relationship between knee flexion, muscle forces, and the compressive force on the

tibia during gait could help clinicians determine if a more upright posture could reduce

the risks caused by altered joint loading.

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Perry et al., (1975) examined knee forces in a static crouched posture using a

cadaver model and reported increasing compressive tibiofemoral force with increasing

knee flexion. In dynamic activities, such as walking, we expect larger joint forces than

in a static posture due to the additional muscle forces required to support the body

weight during movement and propel the body forward (Liu et al., 2008). Compressive

tibiofemoral forces during unimpaired walking have been reported in the range of 2-3

times body weight (Shelburne et al., 2005; D'Lima et al., 2006; Mundermann et al.,

2008; Kutzner et al., 2010). During crouch gait, muscle forces in the stance-limb are

higher than during unimpaired walking (Steele et al., 2010). Since muscle forces are

the primary contributors to joint loading (Inman, 1947; Sasaki and Neptune, 2010), we

expect that compressive tibiofemoral forces are higher during crouch gait, yet the

relationship between crouch gait severity and the compressive tibiofemoral force

remains unknown.

The purpose of this study was to estimate the magnitude of the compressive

tibiofemoral force during crouch gait and examine how this force changes with crouch

severity. To achieve this goal we estimated the muscles forces and the compressive

force on the tibia in unimpaired children and children with cerebral palsy who walked

in varying degrees of crouch severity. We used a freely-available biomechanics

software package, OpenSim (Delp et al., 2007), to scale a musculoskeletal model to

each individual and estimate muscle joint loads based upon each individual’s gait

dynamics.

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5.2 METHODS

5.2.1 SUBJECTS

The subjects for this study were selected from a database of patients treated at

Gillette Children’s Specialty Healthcare (St. Paul, MN; Table 5.1). Nine subjects with

spastic diplegic cerebral palsy were selected to cover a broad range of crouch severity

and were divided evenly into three groups: mild crouch gait (minimum knee flexion

angle of 20-35º), moderate crouch gait (minimum knee flexion angle of 35-50º), and

severe crouch gait (minimum knee flexion angle greater than 50º). All subjects walked

with excess knee and hip flexion and had at least 5º of ankle dorsiflexion during

stance. We excluded subjects that had greater than 30º of femoral or tibial torsion,

which can affect muscle moment arms and the ability of muscles to generate

accelerations (Hicks et al., 2007).

Table 5.1: Subject characteristics (average ± standard deviation) N Age

(yrs) Height (cm)

Weight (kg)

Speed/Height (s-1)

Minimum KFA* (deg)

Unimpaired 3 10.3 ± 3.4 145 ± 16 36.3 ± 8.8 0.79 ± 0.1 1.7 ± 5.5 Mild Crouch 3 8.8 ± 0.8 123 ± 7 24.2 ± 3.6 0.67 ± 0.1 19.1 ± 3.8 Moderate Crouch 3 9.2 ± 2.9 123 ± 15 43.1 ± 37 0.63 ± 0.1 36.1 ± 4.0 Severe Crouch 3 14.0 ±2.3 158 ± 12 40.1 ± 6.8 0.61 ± 0.1 58.6 ± 5.6 *KFA: knee flexion angle during walking

Three unimpaired subjects were chosen who were representative of the age and

stature of the subjects with cerebral palsy. Additionally, a subject with an

instrumented total knee replacement (TKR, age: 80 yrs, weight: 64 kg, walking

speed/height: 0.74 s-1) was included to provide experimental measurements of the

compressive tibiofemoral force for comparison with forces estimated from the

musculoskeletal model. This subject was not included in subsequent comparisons

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between unimpaired gait and crouch gait due to differences in age and stature in

relation to the other subjects.

5.2.2 MOTION ANALYSIS

Motion analysis data was collected at Gillette Children’s Specialty Healthcare

(St. Paul, MN) using a 12-camera system (Vicon Motion Systems, Lake Forest, CA),

four force plates (AMTI, Watertown, MA), and a standard marker protocol (Davis et

al., 1991). Ground reaction forces and moments were sampled at 1080 Hz and low-

pass filtered at 20 Hz. Electromyography (EMG) was collected for six of the crouch

gait subjects from the quadriceps, hamstrings, and gastrocnemius (Motion Laboratory

Systems, Baton Rouge, LA). The EMG data was sampled at 1080 Hz, band-pass

filtered between 20 and 400 Hz, rectified, and low-pass filtered at 10 Hz. All subjects

walked at their self-selected speed and achieved two consecutive force plate strikes

during which only one foot contacted each force plate. The motion analysis data for

the subject with the instrumented TKR was obtained from www.simtk.org where it is

freely available for researchers (Zhao et al., 2007).

5.2.3 MUSCULOSKELETAL MODELING

A generic musculoskeletal model based upon adult cadaver data (Delp et al.,

1990) with 19 degrees of freedom and 92 musculotendon actuators was scaled to each

subject according to anthropometric measurements. This musculoskeletal model has

been used for studies involving unimpaired children and children with cerebral palsy

(Hicks et al., 2008; Liu et al., 2008; Reinbolt et al., 2008). The degrees of freedom in

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the musculoskeletal model included six degrees of freedom at the pelvis, a ball-and-

socket joint at the third lumbar vertebra between the pelvis and torso, a ball-and-

socket joint at each hip, a planar joint with coupled translations at each knee

(Yamaguchi and Zajac, 1989), and a revolute joint at each ankle. Joint angles during

walking were calculated by minimizing the error between experimental marker

trajectories and markers placed on the model at locations corresponding to the

experimental markers.

Static optimization was used to calculate the muscle forces required to

reproduce the joint moments of each subject throughout the gait cycle. To distribute

muscle forces, static optimization was used to minimize the objective function:

1

where N is the number of muscles in the model, a is the activation level (between zero

and one) of each muscle, and c is an integer weighting constant for each muscle with a

default value of one. The weighting constants were determined by comparing

calculated compressive tibiofemoral force to the experimentally measured force for

the subject with the instrumented TKR, as described below.

The compressive tibiofemoral force was calculated using the joint reaction

analysis in OpenSim. A detailed description of this analysis is provided in Appendix

B.1. Briefly, the tibiofemoral force was calculated as a point load acting on the tibial

plateau using the Newton-Euler equation:

∑ (2)

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In Equation 2, is the force from the femur on the tibia, [M]tibia is the matrix of

inertial properties of the tibia, is the six dimensional angular and linear

acceleration of the tibia, is the force from the foot on the tibia, and and

are the muscle forces and gravitational forces acting on the tibia. The

compressive tibiofemoral force was calculated as the component of parallel to

the longitudinal axis of the tibia and used for all subsequent analyses.

For the subject with the instrumented TKR, we varied the static optimization

weighting constants for the major muscle groups that cross the knee: the hamstrings,

gastrocnemius, and quadriceps. The hamstrings included independent muscle models

for the semimembranosus, semitendinousus, biceps femoris long head, and biceps

femoris short head. The quadriceps included independent muscle models for the rectus

femoris, the vastus medialis, the vastus intermedius, and the vastus lateralis. The same

weighting constant was applied to all muscles in each group and the results for the

muscles within each group were compared and, if found to be similar, were combined

to facilitate analysis. The weighting constants were given integer values between one

and ten. We performed static optimization for all combinations of integer weighting

constants and calculated the resulting compressive tibiofemoral force. The peak

compressive force was compared to the experimentally measured force, and we

selected the combination of weighting constants that had the minimum average value

and resulted in a difference between the estimated and experimental peak compressive

force of less than 20% body weight. The set of weighting constants that met this

criterion was a weight of three for the hamstrings, seven for the gastrocnemius, and

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one for the quadriceps. This combination of weighting constants resulted in a root

mean square error of 0.28 times body weight and an average error of 0.02 times body

weight over the gait cycle between the estimated force and the experimental

measurements (Figure 5.1). These weighting constants were then used to perform

static optimization for all other subjects. OpenSim’s joint reaction analysis algorithm

was used to calculate the compressive tibiofemoral force for one representative gait

cycle for each subject.

To evaluate whether muscle activations calculated from static optimization

reflected the subjects’ muscle activity we qualitatively compared the estimated muscle

activations to EMG recordings during stance for the six subjects for whom EMG data

was available (Figure 5.2). EMG and estimated muscle activations indicated that the

quadriceps were active during stance. Hamstring activity decreased during stance in

both the EMG and estimated muscle activations; however, estimated muscle

activations decreased earlier in stance than indicated by EMG for some of the subjects.

For these subjects, increased hamstring activity during stance would have increased

estimates of the compressive tibiofemoral contact force. The gastrocnemius muscle

Figure 5.1: Tibiofemoral contact forces expressed in multiples of body weight (BW) from experimental forces measured using an instrumented total knee replacement (TKR, gray) and estimated with the computermodel (black). The average ± 1 standard deviation is shown from four trials.

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was active during the majority of stance in both the EMG and estimated muscle

activations.

Figure 5.2: Comparison of EMG(gray, average ± one standarddeviation over all gait cycles) andmuscle activations from staticoptimization (black line) for thesix subjects with crouch gait forwhom EMG data was available.EMG and activations werenormalized from zero to one foreach subject based upon theminimum and maximum valuesover the gait cycle. Note thatsubject “Severe 1” did not haveEMG data from thegastrocnemius.

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5.3 RESULTS

Compressive tibiofemoral force was higher during moderate and severe crouch

gait than during unimpaired gait (Figure 5.3). Subjects with a mild crouch gait had

similar compressive tibiofemoral forces to subjects with unimpaired gait. The

maximum force during mild crouch gait was 3.2 ± 0.4 times body weight compared to

3.0 ± 0.5 times body weight during unimpaired gait. Maximum force during a

moderate crouch gait was 4.2 ± 1.2 times body weight. During a severe crouch gait

maximum force was 6.5 ± 0.7 times body weight.

Compressive tibiofemoral force during stance exhibited two peaks in

unimpaired and crouch gait. These two peaks in the tibiofemoral force coincided with

the two characteristic peaks of the ground reaction force. The largest tibiofemoral

forces occurred during early and late stance with smaller forces in mid stance and

swing. During unimpaired gait, the primary contributors to compressive tibiofemoral

force were the quadriceps in early stance and the gastrocnemius during late stance.

During crouch gait, the quadriceps were the primary contributors to tibiofemoral force

throughout stance.

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There was a quadratic relationship between the average knee flexion angle

during stance and the average compressive tibiofemoral force during stance (r2 = 0.97,

Figure 5.4). The relationship is described by:

0.0013 0.06 2.54 (3)

Figure 5.3: (A) Average knee flexion angle,(B) average compressive tibiofemoral force,and (C) average quadriceps force expressed asmultiples of body weight (BW) during onegait cycle for the subjects who walked with anunimpaired gait and mild, moderate, andsevere crouch gait.

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where Fknee is the average compressive tibiofemoral force during stance, and Ө is the

average knee flexion angle during stance with values from 15 to 70° of flexion.

The increase in average compressive tibiofemoral force during stance with

increasing crouch severity was primarily due to an increase in quadriceps force. The

average quadriceps force during stance also increased quadratically with knee flexion

angle (r2=0.99, Figure 5.4) with the relationship:

0.0011 0.03 0.7 (4)

The average force produced by the hamstrings during stance did not change

with knee flexion; however, the average force of gastrocnemius decreased with crouch

severity. Individuals with crouch gait had smaller ankle plantarflexor moments during

terminal stance.

Figure 5.4: Correlation of average knee flexion angle during stance with average compressive tibiofemoralforce during stance (black circles), average quadriceps force during stance (dark gray squares), averagehamstrings force during stance (light gray triangles), and average gastrocnemius force during stance (blackoutlined diamonds). Tibiofemoral force and average quadriceps force are expressed as multiples of bodyweight (BW). A quadratic relationship described the change in both tibiofemoral force and quadricepsforce with increasing crouch.

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5.4 DISCUSSION

Individuals who walk in a moderate or severe crouch gait experience

substantially greater compressive tibiofemoral forces than individuals with an

unimpaired gait; however, individuals who walk in a mild crouch gait have similar

compressive tibiofemoral forces to unimpaired gait. The increase in tibiofemoral force

was primarily due to the increase in quadriceps force required to support the body

during crouch gait. There was a quadratic increase in quadriceps force with increasing

knee flexion which is similar to a reported quadratic increase in EMG magnitude in

static, crouch postures (Hsu et al., 1993). The increase in quadriceps force with crouch

severity not only contributes to increased tibiofemoral load but would also increase

patellofemoral load (Dhaher and Kahn, 2002) and may give rise to knee pain in

individuals with cerebral palsy and crouch gait. To reduce the average compressive

tibiofemoral force and quadriceps force during stance to within one standard deviation

of the average during unimpaired gait, individuals with crouch gait need to achieve an

average knee flexion angle less than 25° during stance.

Compressive tibiofemoral force during crouch gait reported here are slightly

higher than those estimated by Perry et al. (1975), who used statically loaded cadavers

in a crouch posture. Perry determined the compressive tibiofemoral force at 30 and

45° of knee flexion to be 2.9 and 3.8 times body weight, respectively, whereas we

found the maximum force during a crouch gait with an average knee flexion angle of

30 and 45° to be 3.3 and 4.1 times body weight. The static cadaver testing

implemented by Perry did not include contributions from the gastrocnemius or

hamstring muscles to compressive tibiofemoral force. The small difference in

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compressive tibiofemoral force between standing and walking demonstrates that,

although walking requires additional muscle force to propel the body forward (Steele

et al., 2010), the increased quadriceps demand arising from a static crouched posture

accounts for the majority of the increased tibiofemoral force. The tibiofemoral contact

force of the unimpaired children included in this analysis were also similar to

previously reported results (Shelburne et al., 2005; D'Lima et al., 2006; Mundermann

et al., 2008; Kutzner et al., 2010).

Our calculation of compressive tibiofemoral force depends on the accuracy of

estimated muscle activations. The estimated muscle activations showed patterns

similar to EMG such as increased activity of the quadriceps; however, EMG activity

was available for a limited number of muscles in six of the subjects. When muscle

activations differed from the EMG signals the optimization tended to underestimate

muscle activity compared to EMG signals. This suggests that the optimization

functions commonly used for unimpaired walking may not be appropriate for

individuals with cerebral palsy who have altered motor control and muscle

physiology. Muscle over-activity and excess co-contraction are common in individuals

with cerebral palsy. Greater muscle forces due to co-contraction would increase the

estimated tibiofemoral contact forces, suggesting that our calculations of compressive

tibiofemoral force may be low estimates.

We compared our calculated tibiofemoral forces to experimental forces from

an instrumented total knee replacement, but this did not provide a robust evaluation of

knee forces during crouch gait. The total knee replacement data was used to select the

static optimization weighting constants that reduced the error between the estimated

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and measured compressive tibiofemoral force. Different weighting constants may be

appropriate for younger patients or patients with gait pathology. In this study, the

weighting constants penalized recruitment of the hamstrings and gastrocnemius, which

resulted in the recruitment of other muscles to actuate the hip and ankle without

increasing the compressive load on the tibia. Although the quadriceps are the major

contributors to compressive tibiofemoral force, increasing the quadriceps’ weighting

constant did not reduce the estimated tibiofemoral force since no other muscles could

replace the quadriceps’ function at the knee.

To test the sensitivity of our results to the objective function we evaluated how

estimated tibiofemoral contact force changed with altering the weighting constants and

the power of activation. The quadratic relationship between knee flexion angle and

tibiofemoral contact force and quadriceps force was similar in all tested objective

functions (Figure 5.5). Using a linear objective function resulted in an average

reduction in tibiofemoral contact force during stance of 7% while an objective

function that minimized activation cubed increased tibiofemoral contact force during

stance by 11%. Using weighting constants of one for all muscles also increased the

estimated tibiofemoral contact force during stance by an average of 15% due primarily

to a 10% average increase in gastrocnemius force during stance. Future studies that

measure compressive tibiofemoral force from individuals with instrumented total knee

replacements walking in pathologic gait patterns, such as crouch gait, could provide

further points of comparison for model-based estimates of compressive tibiofemoral

force and help to determine the optimal objective functions.

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Figure 5.5: Average (A) tibiofemoral contact force, (B) quadriceps force, (C) hamstring force, and (D)gastrocnemius force during stance with the objective function shown in Eqn. 1 and weighting constants,minimizing activation with weighting constants, minimizing activation cubed with weighting constants,and minimizing activation squared with all weighting constants equal to one.

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This study has demonstrated that walking in a moderate or severe crouch gait

increases the compressive tibiofemoral force, which could be contributing to joint pain

and cartilage degeneration. Surgeries and therapies that produce a more upright

walking posture will reduce forces at the knee and may help moderate the adverse

effects of excessive joint loading.

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CHAPTER 6

HOW MUCH MUSCLE STRENGTH IS REQUIRED TO WALK IN A CROUCH GAIT?

Publication in review

Katherine M. Steele Marjolein M. van der Krogt Michael H. Schwartz Scott L. Delp

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ABSTRACT

Muscle weakness is commonly cited as a cause of crouch gait in individuals

with cerebral palsy; however, outcomes after strength training are variable and

mechanisms by which muscle weakness may contribute to crouch gait are unclear.

Understanding how much muscle strength is required to walk in a crouch gait

compared to an unimpaired gait may provide insight into how muscle weakness

contributes to crouch gait and assist in the design of strength training programs. The

goal of this study was to examine how much muscle groups could be weakened before

crouch gait becomes impossible. To investigate this question, we first created muscle-

driven simulations of gait for three typically-developing children and six children with

cerebral palsy who walked with varying degrees of crouch severity. We then simulated

muscle weakness by systematically reducing the maximum isometric force of each

muscle group until the simulation could no longer reproduce each subject’s gait. This

analysis indicated that moderate crouch gait required significantly more knee extensor

strength than unimpaired gait. In contrast, moderate crouch gait required significantly

less hip abductor strength than unimpaired gait, and mild crouch gait required

significantly less ankle plantarflexor strength than unimpaired gait. The reduced

strength required from the hip abductors and ankle plantarflexors during crouch gait

suggests that weakness of these muscle groups may contribute to crouch gait and that

these muscle groups are potential targets for strength training.

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6.1 INTRODUCTION

Cerebral palsy is caused by a lesion to the brain that occurs at or near the time

of birth and results in impaired movement. It is the most common childhood

movement disorder and affects approximately 3.6 of every 1000 children born in the

United States (Yeargin-Allsopp et al., 2008). Many individuals with cerebral palsy

walk in a crouch gait pattern characterized by excessive flexion of the hip, knee, and

ankle during the stance phase of gait. Walking in a crouch is inefficient and can lead to

joint pain (Jahnsen et al., 2004) and bone deformities (Graham and Selber, 2003).

There are many suggested causes of crouch gait, including contracted

hamstrings, contracted hip flexors, impaired balance, foot deformities, impaired

proprioception, and muscle weakness (Gage, 1990). Muscle weakness can be caused

by various mechanisms such as impaired motor control and reduced physiological

cross-sectional area of muscles. Muscle weakness is common in individuals with

cerebral palsy (Damiano et al., 1995b; Wiley and Damiano, 1998), and strength

training is often incorporated into therapy (Dodd et al., 2002; Pippenger and Scalzitti,

2004; Mockford and Caulton, 2008). Although individuals with cerebral palsy can

increase their muscle strength after completing a strength training program (Damiano

et al., 1995b; Dodd et al., 2002; Mockford and Caulton, 2008), the improvements in

gait after strength training are variable. Previous studies have reported improvements

in knee extension (Damiano et al., 1995a) and functional walking tests after strength

training (Blundell et al., 2003; Dodd et al., 2003); however, other studies have found

no significant change in walking tests (Kerr et al., 2006; Liao et al., 2007) or

deterioration in gait for some subjects (Damiano et al., 2010).

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A rationale for strength training is that individuals with crouch gait may not

have adequate strength to walk in an upright posture. However, previous studies have

shown that walking in a crouch gait requires a greater knee extensor moment (Hsu et

al., 1993; Lin et al., 2000) and greater total muscle force (Steele et al., 2010) than

walking in an upright gait. Although crouch gait requires larger forces in some

muscles, there may be other muscles that are too weak to achieve an upright gait

pattern. Unimpaired gait has been shown to be most sensitive to weakness of the ankle

plantarflexors, hip abductors, and hip flexors (van der Krogt et al., 2012). Comparing

the amount of muscle strength required during crouch gait to unimpaired gait can

provide insight into how muscle weakness contributes to crouch gait and how strength

training could improve gait.

The aim of this study was to examine how much muscle groups could be

weakened before walking in a crouch gait becomes impossible. We used a

musculoskeletal model in which it was possible to reduce the force-generating

capacity of particular muscle groups to simulate weakness. We created muscle-driven

simulations of unimpaired subjects and subjects with cerebral palsy who walked in

varying degrees of crouch gait. For each subject, we examined how much particular

muscle groups could be weakened before the simulation could no longer reproduce the

subject’s gait pattern. Identifying muscle groups that require less strength to walk in a

crouch gait than unimpaired gait may suggest which muscles may be too weak to walk

in an upright posture and may be targets for strength training programs.

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6.2 METHODS

Three typically-developing children and six children with spastic diplegic

cerebral palsy (Table 6.1) were selected from a database of subjects who had visited

Gillette Children’s Specialty Healthcare for motion analysis. Three-dimensional

motion analysis data was collected using a 12-camera system (Vicon Motion Systems,

Lake Forest, CA) and a standard marker measurement protocol (Davis et al., 1991).

Ground reaction forces were measured with four force plates (AMTI, Watertown,

MA), sampled at 1080 Hz, and low-pass filtered at 20 Hz. All subjects walked

barefoot at their self-selected speed without walking aids.

Table 6.1: Subject characteristics (average ± standard deviation) N Age

(years) Height (cm)

Weight (kg)

Unimpaired 3 10 ± 3 144 ± 16 36 ± 9 Mild Crouch 3 9 ± 1 124 ± 10 24 ± 4 Moderate Crouch 3 11 ± 2 136 ± 6 43 ± 31

The subjects with cerebral palsy all walked in a crouch gait and had a

minimum knee flexion angle during stance greater than 15° and a maximum ankle

dorsiflexion angle during stance greater than 5°. The crouch subjects were divided

evenly into two groups based upon crouch severity: mild crouch gait (N=3, minimum

knee flexion angle of 15-30°) and moderate crouch gait (N=3, minimum knee flexion

angle of 30-50°).

Muscle-driven simulations were created that represent the gait dynamics of

each subject using OpenSim, a freely available biomechanical simulation package

(Delp et al. (2007), http://opensim.stanford.edu). Using simulation allowed us to

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selectively weaken particular muscle groups, account for some of the complexities of

the musculoskeletal system, such as the force-length-velocity relationship of muscle,

and examine the compensatory actions from other muscles in response to simulated

muscle weakness. A generic musculoskeletal model (lower extremities from Delp et

al., 1990, and torso from Anderson and Pandy, 1999) with 19 degrees of freedom and

92 musculotendon actuators was scaled to each subject using anthropometric

measurements (Figure 6.1). The degrees of freedom in this model included three

rotations and translations of the pelvis, a ball-and-socket joint between the pelvis and

torso at the third lumbar vertebra, a ball-and-socket joint at each hip, a planar joint

with coupled translations at each knee, and a revolute joint at each ankle. The

maximum isometric forces of the muscles in the model were geometrically scaled by

height-squared of each subject. We scaled muscle strength by height-squared because

muscle strength is proportional to a muscle’s physiological cross-sectional area, which

is correlated with height-squared in adults and children (Schantz et al., 1983; Parker et

al., 1990; Jaric et al., 2002).

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Joint angles were calculated for one walking trial for each subject by

computing the joint angles that minimize the difference between experimental marker

positions and virtual markers placed on the model (Figure 6.2A). Joint moments were

calculated using inverse dynamics (Figure 6.2B). To determine the motion of the

torso, experimental marker data was available for all of the unimpaired subjects and

three of the six subjects with crouch gait. For the individuals without torso markers,

torso position was set to 20° lumbar flexion, 0° lumbar bending, and 0° lumbar

rotation. To test the effects of torso position, we completed the analysis for the

Figure 6.1: Musculoskeletal models used to create dynamic simulations of gait for individuals that walkedin an unimpaired gait pattern (left) and individuals with cerebral palsy who walked in mild (center) andmoderate (right) crouch gait.

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unimpaired subjects with and without torso markers and found no significant

differences in the results (Figure 6.3).

Figure 6.2: The average hip, knee, and ankle (A) kinematics and (B) kinetics during unimpaired gait(dotted) and mild (light gray) and moderate (dark gray) crouch gait. Joint moments are normalized by bodymass (kg).

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The residual reduction algorithm was used to improve the dynamic consistency

of the simulation (Delp et al., 2007). This algorithm makes small changes to

kinematics (< 2°) and the torso mass center location (< 2 cm) to reduce the residual

forces applied to the pelvis. After running the residual reduction algorithm, the

residual forces were less than 10% of body weight and the residual moments were less

than 10% of body weight times height for all subjects. Muscle excitations were

estimated using the computed muscle control (CMC) algorithm, which determines a

set of muscle excitations that recreates the subject’s kinematics (Thelen et al., 2003;

Thelen and Anderson, 2006). At each time step, CMC determines the set of muscle

excitations that produce the forces that generate measured accelerations for all degrees

of freedom taking into account muscle activation dynamics and force-length-velocity

properties. The distribution of muscle excitations among redundant actuators was

determined by minimizing the sum of activations-squared at each time step. Idealized

torque actuators, known as reserve actuators, were included for each degree of

freedom in the model to provide extra torque if the muscles could not generate the

Figure 6.3: Comparison of the required strength for each muscle group of the unimpaired subjects (N=3)when using torso markers for inverse kinematics and without torso markers (average ± 1 standard error).There was no significant difference in the results with or without torso markers.

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measured accelerations. Reserve actuator torques were used to determine when the

muscles could no longer produce the subject’s motion.

To assess the accuracy of the simulation we compared the simulated

kinematics and kinetics to experimental data. The simulated joint angles reproduced

the joint angles calculated by inverse kinematics with a maximum difference of less

than 2°. Additionally, the sum of the moments generated by the muscle forces at each

degree of freedom reproduced the joint moments computed using the residual

reduction algorithm with an average root mean square error of 1.7 ± 0.9 Nm across all

subjects.

To determine how much particular muscle groups could be weakened, each of

seven muscle groups were sequentially weakened by systematically reducing the

maximum isometric force of each muscle in the group. Table 6.2 lists the muscles in

each group. Each muscle group was weakened in isolation. We reduced the maximum

isometric force until the CMC algorithm could no longer determine a set of muscle

excitations that would recreate the subject’s dynamics with an error less than 2° for all

degrees of freedom and torques from the reserve actuators that were less than 10% of

the maximum joint moment at each degree of freedom. We used the bisection method

(Burden and Faires, 1985) to determine how much the maximum isometric force of

each muscle group could be reduced. This method searches through the space of all

possible values for the maximum isometric force by iteratively taking the middle of an

interval representing the maximum and minimum possible values from previous

iterations until it converges upon the minimum value that could recreate the subject’s

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dynamics. This point was termed the required muscle strength for each muscle group

and was expressed as a percent of the muscle group’s maximum isometric force.

Table 6.2: Description of muscle groups Name Description Gluteus Maximus Three musculotendon actuators representing the medial, intermediate, and

lateral components of the muscle Hip Abductors Gluteus medius and gluteus minimus each modeled as three musculotendon

actuators representing the anterior, intermediate, and posterior components of the muscle

Iliopsoas Iliacus and psoas each modeled by a single musculotendon actuator Hamstrings Three musculotendon actuators representing the bi-articular hamstrings

including the biceps femoris long head, semimembranosus, and semitendinousus

Quadriceps Four musculotendon actuators representing the rectus femoris, vastus medials, vastus intermedius, and vastus lateralis

Ankle Plantarflexors Three musculotendon actuators representing the soleus and the medial and lateral heads of the gastrocnemius

Ankle Dorsiflexors Musculotendon actuators representing the anterior tibialis, extensor digitorum, extensor hallus longus, and peroneus tertius

Because of the limited number of subjects, we used a protected Fisher’s Least

Significant Difference test to determine if the required muscle strength was different

between unimpaired gait and mild and moderate crouch gait. We first performed a

one-way ANOVA for each muscle group; if the p-value of the one-way ANOVA was

less than 0.1 we then performed a Fisher’s Least Significant Difference test to

determine differences between gait patterns with a significance level of 0.05. We also

performed regression analyses to determine if required muscle strength changed with

crouch severity.

6.3 RESULTS

The strength, or force-generating capacity, required from each muscle group

could be reduced substantially while the model could still produce the dynamics of

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unimpaired gait and crouch gait (Figure 6.4). This occurs in the simulations because

neither unimpaired gait nor crouch gait requires maximum strength, and other muscles

can compensate for the diminished strength of a particular muscle group. When we

reduced the maximum isometric force of one muscle group, the activation level of that

muscle group increased and other compensatory actions arose from muscles with

similar function (Figure 6.5). For example, the strength required from the gluteus

maximus could be reduced to near zero in the simulations and the dynamics of

unimpaired gait and crouch gait could be maintained. The gluteus maximus represents

about 35% of the hip extension moment generating capacity; thus, when its strength is

reduced, other muscles, such as the gluteus medius and bi-articular hamstrings

increase their activity level.

Figure 6.4: Required strength for each muscle group that was necessary to recreate each subject’s gaitpattern expressed as percent of the maximum isometric force (average ± 1 standard deviation, * p < 0.05from Fisher’s Least Significant Difference test). Crouch gait required more quadriceps strength and lesship abductor and ankle plantarflexor strength than unimpaired gait.

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Moderate crouch gait required significantly more quadriceps strength than

unimpaired gait and mild crouch gait (Figure 6.4). Furthermore, the quadriceps

strength required increased quadratically with crouch severity (r2=0.75). This trend is

largely due to the greater knee extensor moment required from inverse dynamics

during stance in crouch gait compared to unimpaired gait (see knee extensor moment

in Figure 6.2B).

The hip abductor strength required was significantly less during moderate

crouch gait than unimpaired gait (Figure 6.4) and decreased linearly with crouch

severity (r2= 0.58). The hip abductor moment required from inverse dynamics was

Figure 6.5: Compensatory muscle action when a particular muscle group is weakened, expressed as theaverage change in muscle force over the gait cycle (times body weight, BW). For each muscle group, thechange in force of the weakened muscle group and the change in force of the three muscles with thegreatest change in force are shown (average ± 1 standard error).

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also reduced in crouch gait compared to unimpaired gait, especially during terminal

stance (see hip abductor moment in Figure 6.2B). The muscles that were weakened in

the simulation included the gluteus medius and the gluteus minumus, which represent

about 70% of the hip abductor moment generating capacity, and few other muscles

can compensate for weakness of these muscles.

The ankle plantarflexor strength required was significantly less during mild

crouch gait than during unimpaired gait (Figure 6.4). The ankle plantarflexor moment

required from inverse dynamics during early and mid stance was larger during crouch

gait; however, the peak plantarflexor moment required in terminal stance was reduced

during crouch gait (see ankle plantarflexor moment in Figure 6.2B).

The ankle dorsiflexor strength required was similar across all gait patterns

(Figure 6.4). No consistent differences in the amount of hamstring or iliopsoas

strength required were identified between unimpaired gait and crouch gait.

6.4 DISCUSSION

Our results indicate that the required knee extensor strength increased with

crouch severity, required hip abductor strength was reduced in moderate crouch gait,

and required ankle plantarflexor strength was reduced in mild crouch. Identifying

which muscle groups require more or less strength during crouch gait than unimpaired

gait can provide insight into how muscle weakness, or a reduced force-generating

capacity, could contribute to crouch gait and provide guidance for strength training

programs. Weakness of muscle groups that require more strength during crouch gait

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than unimpaired gait, such as the quadriceps, are not likely contributors to crouch gait;

however, weakness of muscle groups that require less strength during crouch gait than

unimpaired gait could contribute to crouch gait. Weakness of the hip abductors and

ankle plantarflexors may preclude individuals with crouch gait from achieving an

upright gait pattern, and these muscle groups may be important targets for strength

training programs.

The focus of this study was to isolate the effects of reduced force-generating

capacity on the dynamics of crouch gait; however, multiple mechanisms including

reduced physiological cross-sectional area, impaired neural drive, altered selective

motor control, and reduced voluntary force capacity can contribute to muscle

weakness. Neural mechanisms such as reduced voluntary force capacity (Elder et al.,

2003; Rose and McGill, 2005) and muscle properties such as reduced physiological

cross-sectional area (Moreau et al., 2009) have been documented in individuals with

cerebral palsy. Future investigations are required to differentiate between these

mechanisms.

The small number of subjects available for simulation and analysis is a

limitation of this study. Some of the muscle groups, such as the hamstrings and

iliopsoas, had variable results which may require a larger number of subjects to

understand the relationship between required strength and crouch gait.

Our analysis demonstrated that moderate crouch gait places a greater demand

on the quadriceps than unimpaired gait. This suggests that if subjects are able to walk

in a crouch gait that they have sufficient force-generating capacity to walk in an

upright gait. Previous studies have reported an increase in quadriceps activity with

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crouch severity measured using electromyography taken during a static crouch posture

(Hsu et al., 1993) or estimated from cadavers positioned in a crouch posture (Perry et

al., 1975). Strength training programs designed for individuals with cerebral palsy and

crouch gait have targeted the hip and knee extensors (Damiano et al., 1995a; Damiano

et al., 2010) and reported inconsistent improvements in knee extension. The results of

our study may help to explain the inconsistent outcomes after these strength training

programs because crouch gait requires greater quadriceps force than unimpaired gait

and may not contribute to crouch gait in some individuals. However, case studies have

documented a lack of force-generating capacity when the knee is near full extension in

some individuals with cerebral palsy (Gage and Novacheck, 2001). Thus, although

crouch gait required more quadriceps strength than unimpaired gait, if individuals with

crouch gait cannot generate sufficient force when the knee is in full extension,

quadriceps weakness may still contribute to crouch gait. Examining the relationship

between quadriceps strength and knee flexion angle is an important area for further

investigation in individuals with cerebral palsy.

Moderate crouch gait required less hip abductor strength than unimpaired gait

and mild crouch gait required less ankle plantarflexor strength than unimpaired gait. In

the subjects included in this study, we also observed from inverse dynamics reduced

hip abductor moments and ankle plantarflexor moments during stance. To investigate

if reduced joint moments were present in a larger population, we examined the

kinematic and kinetic data for all crouch gait subjects who visited Gillette Children’s

Specialty Healthcare from February 1994 to January 2010. This analysis included 82

typically-developing children, 976 mild crouch gait subjects and 209 moderate crouch

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gait subjects using the same criteria described in the methods. A comparison of the hip

abductor moment in this larger population indicated that the hip abductor moment

during crouch gait was significantly reduced compared to unimpaired gait (Figure

6.6), as determined by a one-way ANOVA (p < 0.001). Additionally, the ankle

plantarflexor moment during terminal stance was significantly reduced during crouch

gait (p < 0.001) and the ankle dorsiflexion angle during stance increased with crouch

severity (p < 0.001). Our simulations revealed a significant decrease in the ankle

plantarflexor strength required during mild crouch gait compared to unimpaired gait,

but not during moderate crouch gait. As the ankle dorsiflexion angle increases with

crouch severity, the ankle plantarflexion moment arms of the gastrocnemius and

soleus decrease, which would require greater ankle plantarflexor force to produce the

required ankle plantarflexor moment.

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Ankle plantarflexor weakness has previously been noted as a potential cause of

crouch gait (Gage, 1990). Previous studies have reported that ankle plantarflexor

strength in individuals with diplegic cerebral palsy is reduced to 40-60% of age-

matched typically-developing peers (Wiley and Damiano, 1998; Elder et al., 2003).

Potential causes of ankle plantarflexor weakness include impaired control, over-

lengthening of the Achilles tendon, or effects from injections of neural toxins.

Outcome studies after surgical lengthening of the Achilles tendon have noted an

Figure 6.6: Average (A) kinematics and (B) kinetics for hip abduction and ankle plantarflexion forunimpaired children (N=82, dotted black) and individuals with cerebral palsy who walked in mild (N =976, light gray) and moderate (N=209, dark gray) crouch gait who visited Gillette Children’s SpecialtyHealthcare. The peak hip abductor moment and ankle plantarflexor moment are smaller during mild andmoderate crouch gait compared to unimpaired gait (ANOVA, p < 0.001). Joint moments are normalized bybody mass (kg).

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increased risk of crouch gait (Damron et al., 1994; Dietz et al., 2006). These results

support the theory that some individuals may adopt crouch gait as a result of weak

ankle plantarflexors. Engsberg et al. (2006) found that strengthening the ankle

plantarflexors improved knee extension during stance in individuals with cerebral

palsy.

Limited information is available regarding hip abductor strength in individuals

with cerebral palsy. Wiley et al. (1998) reported that average hip abductor strength in

individuals with diplegic cerebral palsy was 55% of age-matched typically-developing

children. Hip abductor weakness has previously been associated with a Trendelenburg

gait pattern, characterized by exaggerated torso bending in the coronal plane (Perry,

1992). To examine if torso motion contributed to the reduced hip abductor moment

during crouch gait, we compared the torso motion of the subjects with crouch gait who

had torso markers and crouch gait subjects from Gillette Children’s Specialty

Healthcare who had torso markers (mild crouch gait N=31, moderate crouch gait

N=10) to unimpaired gait (N=82). We found no significant difference in torso bending

during mild and moderate crouch gait compared to unimpaired gait, suggesting that

crouch posture rather than torso motion contributed to the reduced hip abductor

strength required during crouch gait. Further study is required to determine the extent

of hip abductor weakness in individuals with crouch gait and if strengthening the hip

abductors improves crouch gait.

This study used muscle-driven simulations to examine how much the

maximum isometric force of particular muscle groups could be reduced and maintain

the dynamics of crouch gait compared to unimpaired gait. The simulations allowed us

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to examine the effects of individual muscle group weakness that could not be

elucidated with other methods. The results of this study suggest that crouch gait

requires greater quadriceps strength than unimpaired gait; however, moderate crouch

gait requires less hip abductor strength and mild crouch gait requires less ankle

plantarflexor strength than unimpaired gait. Future studies that investigate the effects

of strengthening the hip abductors or ankle plantarflexors on crouch gait can further

improve our understanding of how weakness of these muscles contributes to crouch

gait and assist in the design of strength training programs that improve walking ability.

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CHAPTER 7

WHAT CHARACTERISTICS ARE ASSOCIATED WITH POSITIVE OUTCOMES AFTER STRENGTH TRAINING FOR CROUCH GAIT?

Journal of Pediatric Rehabilitation Medicine, (2012), vol. 5, pp. 99-106

Katherine M. Steele Diane L. Damiano Meta Nyström Eek Marianne Unger Scott L. Delp

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ABSTRACT

Muscle weakness may contribute to crouch gait in individuals with cerebral

palsy, and some individuals participate in strength training programs to improve

crouch gait. Unfortunately, improvements in muscle strength and gait are inconsistent

after completing strength training programs. The purpose of this study was to examine

changes in knee extensor strength and knee extension angle during walking after

strength training in individuals with cerebral palsy who walk in crouch gait and to

determine subject characteristics associated with these changes. A literature review

was performed of studies published since January 2000 that included strength training,

three-dimensional motion analysis, and knee extensor strength measurements for

individuals with cerebral palsy. Three studies met these criteria and individual subject

data was obtained from the authors for thirty crouch gait subjects. Univariate

regression analyses were performed to determine which of ten physical examination

and motor performance variables were associated with changes in strength and knee

extension during gait. Change in knee extensor strength ranged from a 25% decrease

to a 215% increase, and change in minimum knee flexion angle during gait ranged

from an improvement of 9º more knee extension to 15º more knee flexion. Individuals

without hamstring spasticity had greater improvement in knee extension after strength

training. Hamstring spasticity was associated with an undesired increase in knee

flexion during walking. Subject-specific factors such as hamstring spasticity may be

useful for predicting which subjects will benefit from strength training to improve

crouch gait.

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7.1 INTRODUCTION

Crouch gait, a common movement pattern in individuals with cerebral palsy, is

characterized by excessive knee flexion during the stance-phase of gait. There are

several proposed causes of crouch gait, including contracted hamstrings, weak ankle

plantarflexors, contracted hip flexors, impaired balance, general muscle weakness, and

foot malalignment (Gage, 1990). If left untreated, crouch gait can lead to joint pain

(Jahnsen et al., 2004), bone deformities (Graham and Selber, 2003), and walking

limitations (Johnson et al., 1997; Opheim et al., 2009). Treatment of crouch gait

frequently involves orthopaedic surgery. Surgery can be effective in reducing

excessive knee flexion, correcting bony deformities, and improving walking ability

(Rodda et al., 2006). However, surgery does not correct underlying muscle weakness.

Weakness of the extensor muscles in the lower extremity is present in many

individuals with cerebral palsy (Damiano et al., 1995b; Wiley and Damiano, 1998).

Weakness in individuals with a crouch gait could compromise their ability to generate

the muscle forces required to produce an upright gait pattern. Muscles such as the

gluteus maximus, vasti, gastrocnemius, and soleus are major contributors to

supporting body weight during crouch gait (Steele et al., 2010); therefore,

strengthening these muscles could potentially improve an individual’s ability to walk

in a more upright posture.

There is conflicting evidence on the efficacy of strength training in cerebral

palsy. Individuals with cerebral palsy can gain muscle strength after participation in

strength training programs (Healy, 1958; McCubbin and Shasby, 1985), but the

functional changes after a strength training program are variable. Damiano et al.

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(1995a) observed improvement in knee extension at initial contact during walking and

increased stride length after strength training, and Blundell et al. (2003) and Dodd et

al. (2003) demonstrated an improvement in functional tests after strength training.

Other studies have not found significant changes in functional tests (Kerr et al., 2006;

Liao et al., 2007), or observed increased knee flexion during gait in some subjects

after strength training (Damiano et al., 2010). There is a lack of consensus regarding

the efficacy of strength training in individuals with cerebral palsy (Dodd et al., 2002;

Mockford and Caulton, 2008; Scholtes et al., 2008; Scianni et al., 2009), and it is

unclear which muscles should be strengthened to improve crouch gait.

It is challenging to characterize the efficacy of strength training programs in

individuals with cerebral palsy because most studies include individuals with different

gait patterns and levels of impairment. Furthermore, most studies only report average

changes and do not document individual outcomes. This makes it difficult to

understand the variability in outcomes between subjects and confounds efforts to

determine which subjects benefit from strength training. Individuals with cerebral

palsy represent a heterogeneous population. Strengthening may not be effective in all

individuals with crouch gait, and a better understanding of the characteristics

associated with improved strength and function following strength training is needed.

The goals of this study were to: (1) examine the variability in outcomes after

progressive resistance strength training for individuals with cerebral palsy who walk in

a crouch gait, and (2) identify the subject characteristics associated with gains in

strength and improved knee extension during gait after strength training. To achieve

this goal we performed a literature search for studies that combined three-dimensional

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motion analysis and a progressive resistance strength training program for subjects

with crouch gait. Data from studies that met these criteria (Unger et al., 2006; Eek et

al., 2008; Damiano et al., 2010) were used to create a database of strength

measurements and walking kinematics before and after strength training. We

performed regression analyses to identify characteristics associated with gains in

strength and improvement in knee extension.

7.2 METHODS

7.2.1 LITERATURE REVIEW

To investigate the effects of strength training in individuals with cerebral palsy

who walk with a crouch gait, we performed a literature search for studies published

since January 2000 that included (1) a progressive resistance strength training

program, (2) a three-dimensional motion analysis before and after strength training,

and (3) a goal of improved knee extension for individuals who walked in a crouch

gait. The time period was chosen to increase the likelihood that individual data not

included in the manuscript would be retrievable. PubMED was used as the search

database in addition to scanning reference lists. A combination of the following search

terms was used: cerebral palsy AND strength AND (training OR program). 58 articles

were identified in the initial literature search that had been published since January

2000 (Figure 7.1). Of these articles, 32 were review articles, post-operative

rehabilitation programs, or not strength training programs for individuals with cerebral

palsy. Additionally, 23 articles were excluded that did not include three-dimensional

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motion analysis, knee extensor strength measurements, or a progressive resistance

strength training protocol.

Three studies (Unger et al., 2006; Eek et al., 2008; Damiano et al., 2010) were

identified that met all criteria (Table 7.1). The first authors were contacted and agreed

to collaborate in this study. Subject information, physical exam measures, muscle

strength data, and gait kinematics were collected for all subjects in each study. All

studies were performed according to the human subject research requirement at their

respective institutions. All data shared as part of this analysis was de-identified.

Table 7.1: Summary of crouch subjects and training programs for all studies

Study N Age (yrs)

Height (cm)

Weight (kg) Training Program

Damiano (2010)

7 8.1 ± 2.6 118 ± 13 20.5 ± 4.8 8 weeks (3 times/week) Progressive resistance with weight machines & cuffs Targeted hip and knee extensors

Unger (2006)

17 16.2 ± 1.4 158 ± 12 51.5 ± 9.5 8 weeks (1-3 times/week) Progressive resistance with weights & resistance bandsFull body

Eek (2008)

6 12.4 ± 1.6 145 ± 9 40.5 ± 9.2 8 weeks (3 times/week) Progressive resistance with weights & resistance bandsTargeted 4 muscle groups per child

Total 30 13.7 ± 3.8 147 ± 20 42.4 ± 15.2

Literature SearchDatabase: PubMedN = 72

Published since January 2000N = 58

Screened titles and abstracts

Excluded (N = 32)Post‐op rehabilitation: 4Not strength training program: 14Review articles: 14Included (N = 26)

Evaluated inclusion criteria

Excluded (N = 23)Not progressive resistance training: 10No 3D motion analysis: 11Did not measure knee extensor strength:  2Included (N = 3)

Figure 7.1: Summary of literature review and study selection.

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7.2.2 Subject Selection

Individuals who walked in a crouch gait pattern were selected from each study.

Crouch gait was defined as a minimum knee flexion angle greater than 10º during

stance. Thirty subjects met this criterion and were included in the study (Table 7.1).

The subjects included 14 who had a mild crouch with a minimum knee flexion angle

less than 20°, 12 who had a moderate crouch gait with a minimum knee flexion angle

between 20° and 30°, and 3 who had a minimum knee flexion angle greater than 30°.

The average minimum knee flexion angle during stance was 20°. GMFCS levels were

available for two of the studies (Eek et al., 2008; Damiano et al., 2010) and the crouch

gait subjects included 3 GMFCS Level I, 6 GMFCS Level II, and 4 GMFCS Level III.

All studies excluded subjects who had surgery within the past 12 months.

7.2.3 STRENGTH TRAINING PROGRAMS

The studies consisted of 8-week progressive resistance strength training

programs including both home and therapist-supervised training sessions and targeted

a range of muscle groups. The subjects in the program reported by Damiano et al.

(2010) were younger than the other two studies and participated in a program targeting

the hip and knee extensors in therapist-supervised sessions three times per week.

Unger et al. (2006) organized a school-based circuit strength training program that

subjects completed one to three times per week. Eek et al. (2008) designed

individualized strength training programs that targeted four lower-extremity muscle

groups that subjects completed three times per week (twice at home and once at a

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physiotherapy clinic). Detailed information on each study is provided in the original

publications.

7.2.4 OUTCOMES MEASURES

Since the focus of this study is on individuals with a crouch gait, we examined

change in knee extensor strength and change in minimum knee flexion angle during

stance after strength training. Knee extensor strength was measured using an isokinetic

strength assessment at 30°/s (Damiano et al., 2010) or an isometric strength

assessment using a dynamometer (Unger et al., 2006; Eek et al., 2008). Change in

knee extensor strength was calculated as the percent change in maximum knee

extensor torque after strength training. Change in minimum knee flexion angle was

calculated from kinematics obtained from three-dimensional motion analysis.

7.2.5 SUBJECT-SPECIFIC CHARACTERISTICS

Ten subject characteristics were selected based upon literature and clinical

experience that could be associated with changes in knee extensor strength and knee

extension during gait. These included: (1) hamstring spasticity, (2) popliteal angle, (3)

knee flexion at initial contact, (4) minimum knee flexion angle during stance, (5)

quadriceps strength, (6) age, (7) height, (8) weight, (9) walking speed, and (10) Gross

Motor Function Classification System (GMFCS) level. All characteristics were

measured before the strength training program.

Hamstring spasticity, popliteal angle, and GMFCS level were only available

for the subjects in studies by Damiano et al. (2010) and Eek et al. (2008). Hamstring

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spasticity was included as a binary variable with an Ashworth score ≥ 2 indicating

hamstring spasticity.

7.2.6 REGRESSION ANALYSES

Univariate linear regression analyses were performed between each of the 10

subject-specific characteristics and the two outcome measures, (1) change in knee

extensor strength and (2) change in minimum knee flexion angle during stance, to

determine which characteristics had the strongest association with each outcome

measure. A random effect term for “study” was also included in each model to account

for between-study variation (Pinheiro and Bates, 2009). No corrections were made for

multiple comparisons (Rothman, 1990). To compare the relative effects of the

characteristics, we performed a multivariate linear regression analysis that included all

the characteristics with a significant association for each outcome measure (p < 0.05).

Significant associations were also checked for confounding effects of age, height, and

weight. All statistics were performed using R, a statistical analysis package (www.r-

project.org/index.html).

7.3 RESULTS

The 30 crouch gait subjects had variable changes in knee extensor strength and

minimum knee flexion angle during gait after completing a strength training program.

The average change in knee extensor strength was a 23% increase; however, the range

varied from a 25% decrease to a 215% increase (Figure 7.2). The average change in

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minimum knee flexion angle after strength training for the group was 0º; however, the

range varied from an improvement of 9º more knee extension to a deterioration of 15º

more knee flexion (Figure 7.2).

Although the average knee kinematics of the group suggest that the strength

training program had no effect on knee kinematics (Figure 7.3), examining the

changes in knee flexion for the subjects with the best and worst outcomes

demonstrates that some subjects had substantial improvements while others had

deterioration after completing the strength training program. For example, the top ten

Figure 7.2: Histograms of (A) percent change in knee extensor strength and (B) change in minimum knee flexion angle during gait after completing a strength training program. Subjects from each of the three studies are shown separately – Damiano (white), Eek (gray), and Unger (black). A negative change in minimum knee flexion angle indicates a more upright posture, or a positive outcome, after strength training. Note that in all three studies the outcomes were variable between subjects.

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percent of subjects had an average improvement of 9° more knee extension during

stance, whereas the bottom ten percent of subjects, with the greatest increase in

minimum knee flexion, had an average change of 10° more knee flexion. After the

strength training program, the subjects with the best outcomes achieved knee

extension within normal limits in late stance.

Figure 7.3: Average hip, knee, and ankle flexion angles for (A) all subjects, (B) the three subjects with the largest increase in knee extension (best outcomes), and (C) the three subjects with the largest increase in knee flexion (worst outcomes) before and after completing strength training program. Note that although there was no significant change in knee flexion for the group as a whole, there were subsets of subjects with significant positive and negative changes.

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There was a significant association between change in minimum knee flexion

angle and change in minimum hip flexion angle (slope = 0.59, p = 0.001) suggesting

that individuals with improved knee extension also had improved hip extension after

strength training. There was no association between change in knee flexion angle and

change in maximum dorsiflexion angle during stance. Average hip flexion angle and

ankle dorsiflexion angle did not change significantly after strength training for the

group, but the inter-subject variability was similar to the variability in change in knee

flexion angle.

Hamstring spasticity was associated with change in minimum knee flexion

angle after strength training (Table 7.2). No subject with an Ashworth Score ≥ 2 had

an improvement in knee flexion angle after strength training (Figure 7.4). Individuals

with a hamstring Ashworth score equal to one had an average improvement of 3° more

knee extension, and 4 out of 6 of these subjects showed improved knee extension after

the strength training program. The association between hamstring spasticity and

change in knee flexion angle was maintained after controlling for age, height, and

weight. Walking speed recorded before the strength training program was also

associated with change in minimum knee flexion angle (p = 0.03); individuals who

walked faster were more likely to have improved knee extension after the strength

training program (Figure 7.4). However, when included in a multi-regression analysis

with hamstring spasticity, walking speed did not add additional information to the

model and was no longer significant. Walking speed was correlated with hamstring

spasticity (r2 = -0.55), indicating that individuals with hamstring spasticity tended to

walk slower.

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Table 7.2: Results of regression analyses for change in knee flexion angle and knee extensor strength Kinematics: Strength:

Minimum knee flexion angle Knee extensor strength Coeff S.E. p-value p-adj** Coeff S.E. p-value

Hamstring spasticity* 8.51 3.06 0.02 0.006 0.13 0.1 0.21 Popliteal angle* (deg) -0.14 0.15 0.36 -0.01 0.005 0.11 KFA at initial contact (deg) 0.12 0.08 0.12 0.005 0.006 0.43 Min KFA (deg) -0.05 0.12 0.66 -0.002 0.01 0.77 Knee extensor strength (Nm/kg) 6.43 21.2 0.76 -2.83 0.79 0.11 Age (yr) -0.35 0.28 0.22 -0.02 0.03 0.45 Height (cm) -0.08 0.05 0.13 < 0.001 < 0.001 0.99 Weight (kg) -0.07 0.07 0.35 < 0.002 0.01 0.52 Walking speed/height (s-1) -16.7 6.95 0.02 0.02 0.01 0.57 0.99 GMFCS level* 2.51 2.62 0.36 0.03 0.13 0.79 p < 0.05 Each regression analysis included a random effects term, “study,” as a covariate. Coeff, Regression coefficient; S.E., Standard Error; GMFCS, Gross Motor Function Classification System * Data available for subjects from studies by Damiano and Eek ** Adjusted for age, height, and weight

There were no significant associations between the subject characteristics and

percent change in knee extensor strength (Table 7.2). There was also no relationship

between the change in minimum knee flexion angle and change in knee extensor

strength (R2 = 0.0).

Figure 7.4: (A) Hamstring spasticity and (B) walking speed were associated with change in minimum knee flexion angle (KFA) during stance with a p-value < 0.05.

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7.4 DISCUSSION

Individuals with cerebral palsy who walk in a crouch gait have inconsistent

outcomes after strength training. Although the majority of subjects had an increase in

knee extensor strength, the change in knee extension during gait was variable. Some

individuals had an improvement in knee extension during gait that was comparable to

outcomes after orthopaedic surgery (Adolfsen et al., 2007); however, other subjects

with crouch gait walked with greater knee flexion after strength training. Determining

which subjects will improve knee extension after strength training is necessary to

determine who should participate in these programs.

Hamstring spasticity was associated with more knee flexion after strength

training. Strength training in subjects with hamstring spasticity to improve crouch gait

is not supported by our analysis. However, from the small sample included in this

study, it does not appear that strength training exacerbated spasticity. The Ashworth

score for the hamstrings changed for only two subjects after strength training; one

subject had a lower Ashworth score and another had a higher Ashworth score. The

association between hamstring spasticity and increased knee flexion after strength

training may be a result of increased muscle strength amplifying the effects of

excessive muscle activity during gait. Future studies should incorporate more

quantitative spasticity measurements and evaluate spasticity of multiple muscle groups

before and after strength training.

No significant associations were found between the subject characteristics and

change in quadriceps strength. The lack of associations may be confounded by the

different methods used for measuring knee extensor strength between studies. Not all

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subjects included in this analysis increased quadriceps strength after completing a

strength training program; therefore, future studies to explain the variability in

changes in strength between subjects would be valuable. Other factors such as

selective motor control, hip range of motion, or rotational deformities may contribute

to variability in change in knee extensor strength.

The change in knee flexion angle after strength training was significantly

correlated with change in hip flexion angle but not with change in ankle dorsiflexion

angle. The individuals included in this study walked with varying degrees of ankle

dorsiflexion during stance which likely contributed to the lack of correlation between

change in knee and ankle angle. Eight of the thirty individuals included in this study

had a maximum dorsiflexion angle during stance of less than 5°. We tested to see if

the outcomes or regression models were different for those individuals who walked

with reduced dorsiflexion during stance; however, there were no significant

differences. Future studies that examine differences between subgroups of crouch gait

could further improve our ability to determine the optimal treatment for each subject.

Strength training programs designed for individuals who walk in a crouch gait,

including those in this analysis, have focused on strengthening the hip and knee

extensors. However, weakness of these muscle groups may not be a primary cause of

crouch gait. During normal gait, the vasti and gluteus maximus support the body

weight in early stance and the ankle plantarflexors support the body weight in terminal

stance (Liu et al., 2008). In crouch gait, the knee extensor moment during stance is

larger, which requires higher forces to be generated by the knee extensors. These

larger loads may lead to patellar fracture or patella alta (Rosenthal and Levine, 1977;

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Murphy, 2009; O'Sullivan et al.). Since walking in an erect gait requires less strength

than walking in crouch gait, strengthening of the knee extensors may not correct

crouch gait in some subjects.

In contrast, ankle plantarflexor weakness is commonly cited as a potential

cause of crouch gait (Gage, 1990). A previous study examined the effects of ankle

plantarflexor strengthening and reported an improvement in knee flexion during

stance, although the study was not specific to individuals with crouch gait (Engsberg

et al., 2006). If we could identify the primary cause of crouch gait in each individual

this would improve our ability to target the correct muscles for strength training

programs or other treatment strategies.

The limited number of subjects and combination of outcomes from three

centers limits the power of this analysis. No corrections were made for multiple

comparisons, which increases the probability of Type I errors in our statistical

analysis. This analysis also combined data from three independent studies performed

according to different protocols at different institutions. The change in knee flexion

angle and percent change in knee extensor strength were similar in magnitude at all

three institutions and all three studies had variable outcomes between subjects. The

limited number of subjects also limited the number of subject characteristics that could

be included in the analysis. Additionally, other factors that were not included in the

original studies such as selective motor control, range of motion, and spasticity in

other muscle groups could be important predictors of outcomes after strength training.

There may also be benefits of strength training programs that are not captured by the

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outcome measures included in this analysis such as increased physical activity,

improved cardiovascular health, and enhanced self-image (Faigenbaum et al., 2009).

The Ashworth score was used by the studies included in this analysis to measure

hamstring spasticity; however, more quantitative measures of spasticity would be

desirable. Due to these limitations, future studies are required to test the

generalizability of the results.

The goal of strength training studies in individuals with cerebral palsy should

be to identify those subjects with the greatest likelihood for a positive outcome. Some

subjects benefit from progressive resistance strength training, but it is unlikely that

strengthening is the ideal therapy for all subjects. Methods that determine which

subjects are unlikely to respond well can save resources of patients, clinicians, and

care-givers. Understanding how characteristics such as spasticity and changes in

muscle strength affect functional outcomes are important areas for future research to

inform the design of optimal, subject-specific treatments.

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CHAPTER 8

CONCLUSION

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8.1 SUMMARY

This dissertation presents the first three-dimensional musculoskeletal

simulations of individuals with cerebral palsy and has contributed to our

understanding of how muscle contributions, joint loads, and the effects of muscle

weakness change in individuals with cerebral palsy and crouch gait. The simulations

created for these analyses have been made freely-available for researchers and

clinicians to download, use, and evaluate at http://www.simtk.org/home/crouchgait/.

This work has provided insight into the underlying dynamics of crouch gait and

created pathways to improve treatment.

The first objective of this dissertation was to examine how individual muscles

contribute to motion during crouch gait. Chapters 3 and 4 evaluated how muscles

contribute to joint and mass center accelerations to support and propel the body during

crouch gait and how these contributions change with crouch severity. The results of

these analyses indicated that crouch gait uses similar muscles to support and propel the

body as unimpaired gait; however, larger and more sustained muscle activity is

required during crouch gait, which contributes to the inefficiencies of this gait pattern.

The second objective of this dissertation was to examine how the compressive

tibiofemoral force changes in individuals with cerebral palsy and crouch gait (Chapter

5). Knee pain is common among individuals with crouch gait and the results of this

study demonstrated that tibiofemoral load increases quadratically with crouch severity.

Individuals who walk in a severe crouch gait experience three-times the tibiofemoral

load than during unimpaired gait. The elevated tibiofemoral forces during crouch gait

could contribute to cartilage degeneration and knee pain.

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The final objective of this dissertation was to examine one of the common

suggested causes of crouch gait: muscle weakness. We used musculoskeletal

simulations to determine how much muscle groups can be weakened and still

reproduce mild and moderate crouch gait (Chapter 6). The results of this analysis

demonstrated that crouch gait requires greater quadriceps strength but less hip

abductor and ankle plantarflexor strength than unimpaired gait; suggesting that these

latter muscles may be better targets for strength training programs. We also performed

a meta-analysis of individuals with crouch gait who had participated in strength

training programs (Chapter 7). This analysis demonstrated that outcomes after strength

training are inconsistent, even among individuals with cerebral palsy and crouch gait.

Hamstring spasticity was associated with poor outcomes after strength training and

may be a contraindication for strength training.

8.2 FUTURE WORK

The work presented in this dissertation has created a foundation of knowledge

about the dynamics of crouch gait in individuals with cerebral palsy. The simulations

created as part of this dissertation are available on-line for other researchers to use,

evaluate, and extend (http://www.simtk.org/home/crouchgait/). For example, the

results of these simulations provide a foundation to investigate important questions to

improve the evaluation and treatment of individuals with cerebral palsy such as:

• What are the actions of the hamstrings during crouch gait and how does

musculotendon lengthening of the hamstrings improve knee extension in some

individuals?

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• How sensitive are musculoskeletal simulations of individuals with cerebral

palsy to (1) altered muscle properties such as contracture, (2) kinematics and

structure of the foot, and (3) alignment and orientation of the knee?

• What are the effects of femoral extension osteotomy and other skeletal

procedures on the kinematics, muscle activity, joint loading, and

musculotendon lengths during gait?

• Does crouch gait provide a more stable posture than upright gait?

• How does the simulated muscle activity during crouch gait in individuals with

cerebral palsy differ from unimpaired individuals voluntarily walking in a

crouch gait?

The results of the studies included in this dissertation also suggest exciting

avenues for future work using both simulation and experimentation. The following

sections outline important areas of future work that can further expand our

understanding of gait pathologies and lead to innovative treatment strategies:

• How is muscle physiology different in individuals with cerebral palsy?

Altered muscle physiology including contracture and spasticity are common

among individuals with cerebral palsy; however, the mechanics of how muscle

physiology changes and the effects these changes have on gait are not well

understood. Future studies should quantify changes in muscle physiology in

individuals with cerebral palsy. Quantifying these changes will allow

researchers and clinicians to generate improved muscle models, develop more

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physiologically representative simulations, and improve our understanding of

how altered muscle physiology affects the dynamics of gait pathologies.

• How do the dynamics of gait change after surgical intervention?

Multi-level orthopaedic surgery is a common treatment for individuals with

cerebral palsy and consists of multiple surgeries including musculotendon

lengthenings, rotational osteotomies, and various other procedures.

Musculoskeletal modeling and simulation can be used to evaluate the

dynamics of gait before and after surgery to provide a more quantitative

understanding of the effects of these procedures on each subject’s ability to

produce an efficient gait pattern.

• How can predictive modeling be used to examine pathologic gait patterns?

The simulations created as part of this dissertation are based upon experimental

motion capture data that is used to estimate the muscle excitations required to

reproduce each subject’s motion. An alternative method is to use predictive

computational methods to evaluate what gait pattern a model will adopt with a

given objective function. These methods allow researchers to investigate

‘what-if’ questions and could provide a new platform for evaluating the

mechanisms that cause crouch gait and predicting surgical outcomes.

• How does increased tibiofemoral loading affect cartilage health?

Knee pain is common among individuals with cerebral palsy and crouch gait

and this dissertation demonstrated that tibiofemoral force increases with crouch

severity. Future studies should investigate if these increased loads affect

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cartilage growth, maintenance, or development in individuals with cerebral

palsy.

• How does spasticity affect outcomes after strength training?

The meta-analysis of strength training outcomes included in this dissertation

found an association between hamstring spasticity and poor outcomes after

strength training in individuals with cerebral palsy and crouch gait.

Investigations are required to determine if these results extend to a larger

population and if spasticity in other muscle groups could also be predictive of

outcomes after strength training.

• How does strengthening the hip abductors and ankle plantarflexors affect

crouch gait?

Crouch gait requires less hip abductor and ankle plantarflexor force than

unimpaired gait, suggesting that crouch gait may be a compensation for

weakness of these muscle groups. Future studies should investigate if strength

training programs that target the hip abductors and/or the ankle plantarflexors

have more consistent, positive outcomes than current strength training

programs.

• How can modeling and simulation be integrated into the clinic?

Modeling and simulation provides a wide variety of information that clinicians

can use in surgical and therapeutic decision-making. The framework,

methodology, and tools for integrating this information into the clinic will need

to be developed to accelerate the translation from research to clinical

outcomes.

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The long term goal of the work presented in this dissertation and the proposed

studies outlined above is to improve quality of life for individuals with cerebral palsy.

The freedom to walk, explore, and interact with the world is a skill that many of us

take for granted every day. Through the combination of musculoskeletal modeling and

simulation, experimental studies, and clinical outcomes we can help individuals with

gait pathologies achieve this freedom throughout their life.

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Zwick, E.B., Saraph, V., Zwick, G., Steinwender, C., Linhart, W.E. and Steinwender, G., 2002. Medial hamstring lengthening in the presence of hip flexor tightness in spastic diplegia. Gait Posture 16, 288-96.

167

APPENDIX A: CHAPTER 3 SUPPLEMENTARY MATERIAL A.1 EFFECTS OF CONSTRAINING EMG ON MUSCLE CONTRIBUTIONS

A comparison of estimated activations to normalized EMG (gray area) before (dashed line) and after (solid line) constraints were applied to improve agreement between the timing, normalized magnitude, and shape for one subject.

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

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0.6

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1

0

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0.4

0.6

0.8

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0

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0.4

0.6

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1

Rectus Femoris

Stance Limb

Medial Hamstrings

20 30 40 50 70 80 90 100

20 30 40 50 70 80 90 100

20 30 40 50 70 80 90 100

20 30 40 50 70 80 90 100

20 30 40 50 70 80 90 100

Lateral Hamstrings

Anterior Tibialis

Gastrocnemius

EMGUnconstrained ActivationConstrained Activation

Swing Limb

Nor

mal

ized

Act

ivat

ion

Nor

mal

ized

Act

ivat

ion

Nor

mal

ized

Act

ivat

ion

Nor

mal

ized

Act

ivat

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Nor

mal

ized

Act

ivat

ion

% Gait Cycle % Gait Cycle

168

Hip, knee, and ankle accelerations with and without constraining activations to EMG as shown above. Positive and negative accelerations correspond to extension and flexion, respectively. The average change in the magnitude of each muscle’s contribution to acceleration was 16, 16, and 15% at the hip, knee, and ankle, respectively.

169

A comparison of mass center contributions before (solid gray lines) and after (dotted red lines) constraining activations to EMG as shown above. Each line represents the direction of the horizontal and vertical acceleration generated at 5% increments through single-limb stance. The scale of the horizontal accelerations are equivalent to the vertical scale. The magnitude of vertical and horizontal mass center accelerations generated by each muscle changed by 10 and 3%, on average. Note that there are small changes in magnitude; however, the direction of the acceleration does not change after constraining the activations.

170

171

A.2 MASS CENTER AND JOINT ACCELERATIONS FROM ALL MUSCLES

Average acceleration generated at the mass center by all muscle compartments of the stance limb. Each line represents the direction of the horizontal and vertical accelerations generated by a muscle at 5% increments through single-limb stance. The scale of the horizontal accelerations are equivalent to the vertical scale.

Gluteus mediusGluteus medius 1 Gluteus medius 2 Gluteus medius 3

Acce

lera

tion

(m/s

2 )

0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

Gluteus mediusGluteus medius 1 Gluteus medius 2 Gluteus medius 3

Acce

lera

tion

(m/s

2 )

0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

UP

FORWARD

Crouch GaitUnimpaired Gait

Gluteus minimusGluteus minimus 1 Gluteus minimus 2 Gluteus minimus 3

Acce

lera

tion

(m/s

2 )

0

0.2

0.4

0

0.2

0.4

0

0.2

0.4

Gluteus minimusGluteus minimus 1 Gluteus minimus 2 Gluteus minimus 3

Acce

lera

tion

(m/s

2 )

0

0.2

0.4

0

0.2

0.4

0

0.2

0.4

0

0.2

0.4

0

0.2

0.4

0

0.2

0.4

Hamstrings

Acce

lera

tion

(m/s

2 )

Semimembranosus Semitendinosus Biceps femoris long head Biceps femoris short head

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

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0.2

0.4

-0.4

-0.2

0

0.2

0.4

Hamstrings

Acce

lera

tion

(m/s

2 )

Semimembranosus Semitendinosus Biceps femoris long head Biceps femoris short head

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

0

0.2

0.4

Hip flexorsIliacus Psoas Sartorius

Acce

lera

tion

(m/s

2 )

-0.6

-0.4

-0.2

0

-0.6

-0.4

-0.2

0

-0.6

-0.4

-0.2

0

Hip flexorsIliacus Psoas Sartorius

Acce

lera

tion

(m/s

2 )

-0.6

-0.4

-0.2

0

-0.6

-0.4

-0.2

0

-0.6

-0.4

-0.2

0

-0.6

-0.4

-0.2

0

-0.6

-0.4

-0.2

0

-0.6

-0.4

-0.2

0

OtherTensor fascia lata Quadratus Femoris Gemmelus Piriformus

Acce

lera

tion

(m/s

2 )

-0.2

0

0.2

0.4

0.6

-0.2

0

0.2

0.4

0.6

-0.2

0

0.2

0.4

0.6

-0.2

0

0.2

0.4

0.6

-0.2

0

0.2

0.4

0.6

-0.2

0

0.2

0.4

0.6

-0.2

0

0.2

0.4

0.6

-0.2

0

0.2

0.4

0.6

Gluteus maximusGluteus maximus 1 Gluteus maximus 2 Gluteus maximus 3

Acce

lera

tion

(m/s

2 )

0

0.2

0.4

0.6

0.8

1

1.2

0

0.2

0.4

0.6

0.8

1

1.2

0

0.2

0.4

0.6

0.8

1

1.2

Gluteus maximusGluteus maximus 1 Gluteus maximus 2 Gluteus maximus 3

Acce

lera

tion

(m/s

2 )

0

0.2

0.4

0.6

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1

1.2

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1.2

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0.2

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1

1.2

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0.6

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1

1.2

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1

1.2

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172

UP

FORWARD

Crouch GaitUnimpaired Gait

Hip adductorsAdductor magnus 1 Adductor magnus 2 Adductor magnus 3 Adductor Longus

Adductor brevis Pectineus Gracilis

Acce

lera

tion

(m/s

2 )A

ccel

erat

ion

(m/s

2 )

-0.4

-0.2

0

-0.4

-0.2

0

-0.4

-0.2

0

-0.4

-0.2

0

-0.4

-0.2

0

-0.4

-0.2

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0

Hip adductorsAdductor magnus 1 Adductor magnus 2 Adductor magnus 3 Adductor Longus

Adductor brevis Pectineus Gracilis

Acce

lera

tion

(m/s

2 )A

ccel

erat

ion

(m/s

2 )

-0.4

-0.2

0

-0.4

-0.2

0

-0.4

-0.2

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-0.4

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QuadricepsRectus femoris Vastus medialis Vastus intermedius Vastus lateralis

Acc

eler

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n (m

/s2 )

0

1

2

3

0

1

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3

0

1

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QuadricepsRectus femoris Vastus medialis Vastus intermedius Vastus lateralis

Acc

eler

atio

n (m

/s2 )

0

1

2

3

0

1

2

3

0

1

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3

0

1

2

3

0

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3

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0

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3

0

1

2

3

Ankle plantarflexorsMedial gastrocnemius Lateral gastrocnemius Soleus Tibialis posterior

Acc

eler

atio

n (m

/s2 )

0

1

2

3

4

5

6

0

1

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3

4

5

6

0

1

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4

5

6

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3

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5

6

Ankle plantarflexorsMedial gastrocnemius Lateral gastrocnemius Soleus Tibialis posterior

Acc

eler

atio

n (m

/s2 )

0

1

2

3

4

5

6

0

1

2

3

4

5

6

0

1

2

3

4

5

6

0

1

2

3

4

5

6

0

1

2

3

4

5

6

0

1

2

3

4

5

6

0

1

2

3

4

5

6

0

1

2

3

4

5

6

OtherTibialis anterior Peroneus brevis Peroneus longus Peroneus tertius

Flexor digitorum longus Flexor hallicus longus Extensor digitorum longus Extensor hallicus longus

Acce

lera

tion

(m/s

2 )A

ccel

erat

ion

(m/s

2 )

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

-1

-0.8

-0.6

-0.4

-0.2

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0.2

-0.4

-0.2

0

-0.4

-0.2

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-0.4

-0.2

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-0.4

-0.2

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OtherTibialis anterior Peroneus brevis Peroneus longus Peroneus tertius

Flexor digitorum longus Flexor hallicus longus Extensor digitorum longus Extensor hallicus longus

Acce

lera

tion

(m/s

2 )A

ccel

erat

ion

(m/s

2 )

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

-0.4

-0.2

0

-0.4

-0.2

0

-0.4

-0.2

0

-0.4

-0.2

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-0.4

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173

Average angular acceleration (± 1 standard deviation) generated at the hip, knee, and ankle by all muscle compartments of the stance limb during single-limb stance in crouch gait.

Gluteus maximus

Gluteus mediusGluteus medius 1 Gluteus medius 2 Gluteus medius 3

Acce

lera

tion

(deg

/s2 )

Gluteus minimusGluteus minimus 1 Gluteus minimus 2 Gluteus minimus 3

Acce

lera

tion

(deg

/s2 )

Hamstrings

Acce

lera

tion

(deg

/s2 )

Semimembranosus Semitendinosus Biceps femoris long head Biceps femoris short head

Hip flexorsIliacus Psoas Sartorius

Gluteus maximus 1 Gluteus maximus 2 Gluteus maximus 3Ac

cele

ratio

n (d

eg/s

2 )Ac

cele

ratio

n (d

eg/s

2 )

OtherTensor fascia lata Quadratus Femoris Gemmelus Piriformus

Acce

lera

tion

(deg

/s2 )

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

HipKneeAnkle

174

Hip adductorsAdductor magnus 1 Adductor magnus 2 Adductor magnus 3 Adductor Longus

Adductor brevis Pectineus Gracilis

Acce

lera

tion

(deg

/s2 )

Acc

eler

atio

n (d

eg/s

2 )

QuadricepsRectus femoris Vastus medialis Vastus intermedius Vastus lateralis

Ankle plantarflexorsMedial gastrocnemius Lateral gastrocnemius Soleus Tibialis posterior

OtherTibialis anterior Peroneus brevis Peroneus longus Peroneus tertius

Flexor digitorum longus Flexor hallicus longus Extensor digitorum longus Extensor hallicus longus

Acce

lera

tion

(deg

/s2 )

Acce

lera

tion

(deg

/s2 )

Acc

eler

atio

n (d

eg/s

2 )Ac

cele

ratio

n (d

eg/s

2 )

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

-5000

0

5000

HipKneeAnkle

175

APPENDIX B: CHAPTER 5 SUPPLEMENTARY MATERIAL B.1: CALCULATING JOINT FORCES IN OPENSIM

The joint reaction analysis in OpenSim applies a general method to calculate

joint loads transferred between two contacting bodies. This method computes the

resultant forces and moments that represent the internal loads carried by the joint

structure. For example, this study reports joint forces representing the sum of contact

forces between the tibial and femoral cartilage and all ligament forces crossing the

tibiofemoral joint.

OpenSim uses multibody dynamics and simulation methods from Simbody, a

free and open source library for representing rigid body dynamics

(https://simtk.org/home/simbody). Simbody constructs models as tree structures in

which rigid bodies connect in kinematic chains that can branch with joints or

reconnect with constraints. The equations of motion of the system are represented in

terms of the generalized coordinates and generalized forces of the model. Solving

these generalized equations of motion does not require calculating internal forces,

such as the joint contact forces. Therefore, the joint reaction analysis in OpenSim

incorporates a post-processing procedure that uses the muscle forces and joint

kinematics to calculate resultant joint loads.

Figure B.1 shows an example model consisting of segments linked in a

kinematic chain. Joints between these segments do not need to have classical

engineering definitions, such as a revolute joint or spherical joint, but instead can have

more physiologic descriptions. For example, the motion between body segments

176

and may be described by splines that couple the rotations and translations of the

knee. For each time point in an analysis, a recursive operation begins with the most

distal bodies and progresses proximally to calculate the joint loads. The force at each

joint is calculated by performing a force balance on the body distal to the joint.

A single step in this recursive procedure is analogous to constructing a free

body diagram for each rigid body and resolving the point load that must be applied to

Figure B.1: (A) Example kinematic chain of body segments that can be represented in OpenSim. The joint between body segments Si and Si-1 is described by splines that represent an elliptical surface (Seth et al., 2010) and thus need not be an idealized pin joint. (B) Single-body system used to calculate , the reaction load at the proximal joint of Si. The calculation is in terms of Si’s inertial forces, muscle forces (black arrows), other external forces, and the previously calculated reaction force at the distal joint.

177

the joint to balance the forces and motions of the body. To calculate , the resultant

forces and moments at joint i, the body distal to joint i, , is treated as an independent

body with known kinematics in a global reference frame. In the example system

(Figure B.1), represents the six dimensional vector of known angular and linear

accelerations of . Since these accelerations are reconstructed from Simbody’s

generalized equations of motion, they capture any kinematic complexity in the joint

description. and represent the previously calculated forces and

moments applied by external loads and musculotendon actuators respectively.

represents the joint reaction load applied at the distal joint. is known since it

was calculated in the previous recursive step. Using the known generalized

coordinates ( ) and generalized speeds ( ) of the body segment and all other applied

forces, the desired resultant force is calculated as the vector sum:

∑ ∑

The sum requires that all terms be described in a common reference frame located at

the body origin, thus is the joint force and moment expressed at the body origin.

is the six-by-six mass matrix for body segment i. represents

constraint forces applied to the body, if applicable. Since the all terms other than

result from generalized coordinates and forces previously solved by Simbody, we can

calculate the moment and force at the body origin, and , that are required to

balance the equation. Finally, expressed at the body origin is shifted to an

equivalent moment and force, and , at the joint center:

178

0

where is the vector pointing from the body origin to the joint location.

The joint reaction analysis algorithm is available in OpenSim versions 1.9 and

later. The value of this algorithm is that it leverages the generalized coordinate

representation and rich set of joint definitions provided by Simbody and OpenSim and

provides a free tool for researchers to use to calculate joint loads for any

musculoskeletal structure.