The Effects of Simulated Muscle Weakness on Lower Extremity Muscle Function During

The Effects of Simulated Muscle Weakness on Lower Extremity Muscle Function during

Gait in Healthy, Older Subjects

Thesis

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in

the Graduate School of The Ohio State University

Amanda Nicole Strube, B.S.

Graduate Program in Mechanical Engineering

The Ohio State University

2012

Thesis Committee:

Robert A. Siston, Advisor

Laura C. Schmitt

Amanda Nicole Strube

2012

Abstract

As the human body ages, key physiological changes take place that affect a person’s ability to perform daily functional tasks such as walking. Some of these changes associated with aging are loss of muscle mass (sarcopenia), muscle atrophy, and generalized muscle weakness. Studies have shown that muscle weakness in the lower extremity due to aging make it more difficult for older individuals to walk. Additionally, it is known that elderly adults have altered gait kinematics and kinetics, which is related to losses in lower extremity strength. However, no studies have looked at how lower extremity muscles contribute to gait in elderly adults and the effects of specific muscle group weakness on gait in elderly adults.

Another contributor to increased difficulty walking is knee osteoarthritis.

Osteoarthritis is a degenerative joint disease that most often affects the cartilage in joints.

Some of the major side effects associated with knee osteoarthritis include pain, swelling, and loss of motion in the affected joint. One of the most disabling limitations associated with knee osteoarthritis is weakness in the quadriceps femoris muscle, which can in turn affect how an individual walks. Together, all of these side effects can contribute to decreased walking speed or increased difficulty walking. The quadriceps muscles are known to contribute to vertical support and slowing of the body in the early part of the stance phase during gait in healthy, young adults. However, it is unknown how lower

ii extremity muscles in healthy, elderly adults contribute to a normal gait pattern. While weakened quadriceps have been strongly correlated with functional limitations in patients with knee osteoarthritis, the important cause-effect relationships between abnormal lower extremity muscle function and patient function remain unknown. This study has three purposes: to 1) characterize the gait kinematics and kinetics of healthy, older adults, 2) determine how individual lower extremity muscles produce force during gait in healthy, older subjects, and 3) determine how individual lower extremity muscles compensate for simulated lower extremity weakness in the stance phase of gait in healthy, older subjects.

I have used OpenSim, an open source software package that can be used to generate inverse dynamic simulations, to simulate weakened quadriceps, plantarflexors, and gluteus muscles in gait trials from healthy, older subjects. As I systematically weakened the quadriceps to 70% and 40% of their original strength, the gluteus maximus increased its peak force by 2.3% and 10.9%, respectively. As I systematically weakened the plantarflexors to 70% and 40% of their original strength, the soleus, iliopsoas, knee flexors, hamstrings, and minor ankle plantarflexors increased their peak force in late stance and the gastrocnemius, rectus femoris, tibialis anterior, and minor ankle dorsiflexors decreased their peak force in late stance. Additionally, as the gluteus muscles were systematically weakened, the gluteus muscles, iliopsoas, and the hip adductors produced less force and the hip external rotators, sartorius, knee extensors, tensor fasciae latae, hamstrings, and minor ankle plantarflexors and dorsiflexors produced more force.

iii The results from these simulations have determined which other lower extremity muscles naturally increase their contributions to force production during gait in response to weakened lower extremity muscles, which are characteristic of knee osteoarthritis and aging. This information can then be used to inform physical therapy programs to specifically target certain muscles to compensate for weak quadriceps muscles.

iv Acknowledgements

I would like to thank my advisor, Dr. Rob Siston. My first contact with Dr. Siston was two years ago in my senior capstone design class. During my time with Dr. Siston, I have learned what being an engineer means and I greatly appreciate that he continues to challenge me to achieve more each day. I am extremely grateful for his guidance, support, and confidence in me.

I would also like to thank the other member of my Masters committee, Dr. Laura

Schmitt. She has provided me much insight and guidance on this project. She has been an excellent resource and I know this project would have been much more difficult without her. She has also graciously provided me with data to analyze. Dr. Schmitt collected this data at the University of Delaware as part of her PhD dissertation and has always made herself available to me as I analyzed this data.

Next, I would like to thank Julie Thompson and the rest of my NMBL labmates.

Julie has shared all of her knowledge of OpenSim and Matlab coding with me and I am extremely grateful for all the help and guidance she has given me. Julie has been a great mentor to me during this project and has always been willing to sit down with me and work through any problems I may have had. I would also like to thank the rest of my

NMBL labmates for all of the encouragement, advice, and laughs they have offered the past year.

v I would like to thank my fiancé, Zachary Hinger, and my loving family and friends. Zack has been there with me every step of the way, always providing me with unconditional love and encouragement. Your words of wisdom have gotten me through many tough times. I would also like to thank my parents, Ronald and Patricia Strube, for all of their love and support. They have helped me grow into the person that I am today.

Thank you for being there for me always and being the best role models I have. And to all of my family and friends, thank you for all of your love, support, and prayers.

Finally, I would like to thank the First-Year Engineering Program at Ohio State.

Not only has this program provided me with funding, but they have also helped me develop as an engineer and as a person the past six years.

vi Vita

June 2007………………………Mount Notre Dame High School

2011………………...... B.S. Mechanical Engineering, The Ohio State University

2011 to present……..………….First Year Engineering Graduate Teaching Associate

Fields of Study

Major Field: Mechanical Engineering

vii Table of Contents

Abstract ...... ii Acknowledgements ...... v Vita ...... vii Table of Contents ...... viii List of Tables ...... x List of Figures ...... xii Chapter 1: Introduction ...... 1 1.1. Focus of Thesis...... 8 1.2. Significance of Research ...... 9 1.3. Overview of Thesis ...... 10 Chapter 2: Methods ...... 11 2.1. Data Collection ...... 12 2.2. Data Analysis ...... 15 2.3. Subject Specific Simulations ...... 15 2.4. Lower Extremity Muscle Weakness ...... 18 Chapter 3: Results ...... 21 3.1. Full Strength Model ...... 21 3.2. Simulated Atrophy of Quadriceps Femoris ...... 32 3.3. Simulated Atrophy of Plantarflexors ...... 38 3.4. Simulated Atrophy of Gluteus Maximus, Medius, and Minimus ...... 51 Chapter 4: Discussion ...... 65 4.1. Full Strength Model ...... 65 4.2. Simulated Atrophy of Quadriceps Femoris ...... 76 4.3. Simulated Atrophy of Plantarflexors ...... 78 4.4. Simulated Atrophy of Gluteus Maximus, Medius, and Minimus ...... 81 Chapter 5: Conclusions ...... 84 5.1. Major Findings ...... 84 5.2. Contributions ...... 88 viii 5.3. Future Work ...... 88 5.4. Summary ...... 90 References ...... 91 Appendix A: Supplemental Information ...... 94 Simulated Atrophy of Plantarflexors ...... 94 Simulated Atrophy of Gluteus Muscles ...... 106

ix List of Tables

Table 1: Subject anthropometric data ...... 12

Table 2: Quadriceps femoris muscle atrophy ...... 19

Table 3: Plantarflexor muscle atrophy ...... 19

Table 4: Gluteus muscle atrophy ...... 20

Table 5: Peak average forces from the seven major muscle groups obtained during Static

Optimization ...... 30

Table 6: Muscle force changes in response to quadriceps femoris atrophy ...... 32

Table 7: Muscle group force changes in response to plantarflexor atrophy ...... 40

Table 8: Muscle group force changes in response to gluteus atrophy in early stance ...... 52

Table 9: Muscle group force changes in response to gluteus atrophy in late stance ...... 53

Table 10: Muscle group force changes in response to gluteus atrophy in swing ...... 53

Table 11: Comparison of gait kinematics across various subject populations ...... 67

Table 12: Comparison of peak flexion-extension moments at the hip, knee, and ankle between the healthy, elderly patient population and the normal patient population from

Thompson et al. [28] (from Figure 40) ...... 70

Table 13: Comparison of peak flexion-extension moments at the hip, knee, and ankle between the healthy, elderly patient population and the normal patient population from van der Krogt et al. [27] ...... 71

x Table 14: Comparison of peak flexion-extension moments at the hip, knee, and ankle between the healthy, elderly patient population and the healthy, elderly patient population walking fast and the healthy, young population from Kerrigan et al. [10] ...... 72

Table 15: Comparison of muscle force timing during stance in various subject populations ...... 73

Table 16: Approximate peak forces of major muscle groups in lower extremity during stance for various populations ...... 75

Table 17: Summary of muscular compensations that occur with weakness of different muscle groups ...... 87

Table 18: Individual muscle force changes in response to plantarflexor atrophy ...... 94

Table 19: Individual muscle force changes in response to gluteus atrophy ...... 106

xi List of Figures

Figure 1: A complex relationship exists between knee osteoarthritis and quadriceps muscle weakness. Adapted from Hurley, 1999 [23]...... 6

Figure 2: Retroreflective marker placement for motion analysis ...... 13

Figure 3: EMG data (black) normalized to the peak value of the simulated muscle activation and compared to static optimization muscle activation patterns (blue). The solid line is the average activation across all subjects and the shading is the standard deviation...... 22

Figure 4: Average gait kinematics of the healthy, elderly subjects determined form

Inverse Kinematics of the hip (black), knee (red) and ankle (blue); Positive: Flexion

(Dorsiflexion), Negative: Extension (Plantarflexion) ...... 24

Figure 5: Inverse dynamics joint moments averaged across all eight subjects and normalized to body weight and height; Positive: Extension (Plantarflexion), Negative:

Flexion (Dorsiflexion) ...... 26

Figure 6: Static optimization muscle forces for full strength model averaged across all eight subjects ...... 28

Figure 7: Individual muscle forces from seven major muscle groups in the lower extremity from the full strength model, averaged across all eight subjects ...... 29

xii Figure 8: Plot of individual muscle forces normalized to body weight from seven major muscle groups in the lower extremity from the full strength model, averaged across all eight subjects ...... 31

Figure 9: Rectus femoris force as a function of quadriceps femoris atrophy, which decreased during swing as the quadriceps were weakened ...... 33

Figure 10: Rectus femoris activation as a function of quadriceps femoris atrophy, which increased during stance and swing as the quadriceps were weakened ...... 34

Figure 11: Vasti group force as a function of quadriceps weakness, which decreased during stance and increased during swing as the quadriceps were weakened ...... 35

Figure 12: Vastus lateralis activation as a function of quadriceps femoris atrophy, which increased as the quadriceps were weakened ...... 36

Figure 13: Gluteus maximus force as a function of quadriceps femoris atrophy, which increased as the quadriceps were weakened ...... 37

Figure 14: Gluteus maximus activation as a function of quadriceps femoris atrophy, which increased as the quadriceps were weakened ...... 38

Figure 15: Gastrocnemius (lateral and medial) force as a function of plantarflexor weakness, which decreased as the plantarflexors were weakened ...... 41

Figure 16: Lateral gastrocnemius activation as a function of plantarflexor weakness, which increased as the plantarflexors were weakened ...... 41

xiii Figure 17: Soleus force as a function of plantarflexor atrophy, which increased as the plantarflexors were weakened...... 42

Figure 18: Soleus activation as a function of plantarflexor weakness, which increased slightly as the plantarflexors were weakened ...... 43

Figure 19: Iliopsoas (Iliacus and psoas) force as a function of plantarflexor weakness, which increased slightly in late stance as the plantarflexors were weakened ...... 44

Figure 20: Minor hip and knee flexors (gracilis and sartorius) force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened...... 45

Figure 21: Rectus femoris force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened ...... 46

Figure 22: Vasti (vastus lateralis, medialis, and intermedius) force as a function of plantarflexor weakness, which remained constant as the plantarflexors were weakened 46

Figure 23: Hamstrings force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened ...... 47

Figure 24: Tibialis anterior force as a function of plantarflexor weakness, which decreased in late stance and swing as the plantarflexors were weakened ...... 48

Figure 25: Minor ankle plantarflexor force as a function of primary plantarflexor

(gastrocnemius and soleus) weakness, which increased in late stance as the plantarflexors were weakened ...... 49

xiv Figure 26: Minor ankle dorsiflexors force as a function of plantarflexor weakness, which decreased in late stance and swing as the plantarflexors were weakened ...... 50

Figure 27: Gluteus muscle force (maximus, medius, minimus) as a function of gluteus weakness, decreased in both stance and swing as the gluteus muscles were weakened .. 54

Figure 28: Gluteus maximus activation as a function of gluteus muscle weakness, which increased in both stance and swing as the gluteus muscles were weakened ...... 55

Figure 29: Gluteus medius activation as a function of gluteus muscle weakness, which increased in both stance and swing as the gluteus muscles were weakened ...... 56

Figure 30: Gluteus minimus activation as a function of gluteus muscle weakness, which increased in both stance and swing as the gluteus muscles were weakened ...... 56

Figure 31: Iliopsoas force as a function of gluteus muscle weakness, which decreased in late stance and swing as the gluteus muscles were weakened ...... 57

Figure 32: Hip external rotators force as a function of gluteus muscle weakness, which increased in early stance and swing as the gluteus muscles were weakened ...... 58

Figure 33: Hip adductors muscle force as a function of gluteus muscle weakness, which decreased in early and late stance as the gluteus muscles were weakened ...... 59

Figure 34: Sartorius force as a function of gluteus weakness, which increased in both stance and swing as the gluteus muscles were weakened ...... 60

Figure 35: Knee extensors force as a function of gluteus muscle weakness, which increased in both early and late stance as the gluteus muscles were weakened ...... 61

xv Figure 36: Tensor fasciae latae force as a function of gluteus muscle weakness, which increased throughout all of stance and swing as the gluteus muscles were weakened ..... 62

Figure 37: Hamstrings force as a function of gluteus muscle weakness, which increased in early stance and slightly in late stance as the gluteus muscles were weakened ...... 63

Figure 38: Ankle plantarflexors force as a function of gluteus muscle weakness, which increased slightly in late stance and swing as the gluteus muscles were weakened ...... 64

Figure 39: Ankle dorsiflexors force as a function of gluteus muscle weakness, which increased in late stance and swing as the gluteus muscles were weakened ...... 64

Figure 40: Flexion-extension joint moments during walking for a healthy, young population [28], with an average age of 21.9 ± 2.3 yrs, average free speed of 1.32 ± 0.13 m/s, and N = 7 ...... 69

Figure 41: Lateral head of the gastrocnemius force as a function of plantarflexor weakness, which decreased as the plantarflexors were weakened ...... 95

Figure 42: Medial head of the gastrocnemius as a function of plantarflexor weakness, which decreased as the plantarflexors were weakened ...... 95

Figure 43: Soleus force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened...... 96

Figure 44: Iliacus force as a function of plantarflexor weakness, which increased slightly during stance as the plantarflexors were weakened ...... 96

xvi Figure 45: Psoas force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened...... 97

Figure 46: Gracilis force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened...... 97

Figure 47: Sartorius force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened...... 98

Figure 48: Rectus femoris force as a function of plantarflexor weakness, which decreased during stance as the plantarflexors were weakened ...... 98

Figure 49: Tensor fasciae latae force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened ...... 99

Figure 50: Biceps femoris long head force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened ...... 99

Figure 51: Biceps femoris short head force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened ...... 100

Figure 52: Semimembranosus force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened ...... 100

Figure 53: Semitendinosus force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened ...... 101

Figure 54: Tibialis anterior force as a function of plantarflexor weakness, which decreased as the plantarflexors were weakened ...... 101

xvii Figure 55: Flexor digitorum force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened ...... 102

Figure 56: Flexor hallucis force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened ...... 102

Figure 57: Peroneus brevis force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened ...... 103

Figure 58: Peroneus longus force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened ...... 103

Figure 59: Tibialis posterior force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened ...... 104

Figure 60: Peroneus tertius force as a function of plantarflexor weakness, which decreased in late stance as the plantarflexors were weakened ...... 104

Figure 61: Extensor digitorum force as a function of plantarflexor weakness, which decreased in late stance as the plantarflexors were weakened ...... 105

Figure 62: Extensor hallucis force as a function of plantarflexor weakness, which decreased in late stance as the plantarflexors were weakened ...... 105

xviii

Chapter 1: Introduction

Human gait is a cyclic repetition of muscle contractions that cause movement of the lower extremities. Normal, forward gait can be divided into two phases: stance and swing.

The stance phase comprises approximately 60% of the gait cycle, whereas swing phase makes up the remaining 40%. One complete cycle begins with the stance phase on one leg and ends as the ipsilateral leg completes the swing phase. The stance phase begins with heelstrike and is characterized by at least one foot remaining in contact with the ground.

During the stance phase, the body mass center is accelerated over the foot in contact with the ground and can be modeled as an inverted pendulum. The swing phase begins with toe-off and ends with heel strike of the ipsilateral leg.

Muscles in the lower extremity that are active during gait can contribute to either vertical support or forward progression [1]. In the early part of stance phase, the body mass center decelerates in the fore-aft direction until approximately midstance. Once midstance is reached in the gait cycle, the body mass center is accelerated in the forward direction over the stance leg. Throughout the stance phase, the musculoskeletal system provides vertical support to resist gravity. During swing phase, the contralateral limb undergoing stance provides vertical support and modulates forward progression.

Numerous studies have been done to determine the individual contributions of lower extremity muscles to support and progression during stance phase in human gait [1-4]. Liu et al. [1] found that during normal forward gait, the muscles that provide vertical support in early stance also decelerate the body mass center and during late stance, the group of muscles that provide vertical support work to accelerate the body mass center forward. Liu et al. [1] found that the hip and knee extensors, primarily the vasti group and the gluteus maximus, are the largest contributors to vertical support and forward deceleration to the body mass center in the early part of stance. Similarly, during the latter part of stance, the gastrocnemius and soleus muscles are the primary contributors to vertical support and forward acceleration of the body mass center. The gluteus medius muscle contributes to vertical support throughout the majority of the stance phase and follows the same pattern where in early stance the gluteus medius decelerates the body mass center and accelerates the body mass center forward in the late part of stance.

In a similar study in 2008, Liu et al. [2] determined the individual muscle contributions in the lower extremity to support and forward progression at a range of walking speeds. The results in this second study agreed with what was found two years prior.

Additionally, it was found that as walking speed increased, the contributions of the gluteus maximus, vasti, hamstrings, gastrocnemius, and soleus muscles to vertical support and forward progression increased. The gluteus maximus, hamstrings, and vasti all increased their contributions to vertical support in early stance as walking speed increased, while soleus increased its contribution to vertical support in late stance as walking speed increased from very slow to fast. With regards to forward progression, as walking speed increased from very

slow to fast, the vasti and gluteus maximus increased their contributions to slow forward progression in early stance while the plantarflexors increased their contributions to forward propulsion in late stance. The vasti provided more horizontal deceleration than the gluteus maximus and the soleus contributed more to forward acceleration than the gastrocnemius.

Muscle Function and Gait of Elderly Subjects

Previous studies that have used forward dynamic simulations to investigate individual muscle contributions to support and forward progression during gait analyzed the muscle contributions of young, healthy subjects. The average ages of the subjects in those studies were 12.9±3.3 years, 26±3 years, and 22.2±2.1 years, conducted by Liu et al. [2], Anderson et al. [3], and Neptune et al. [4], respectively. However, major physiological changes occur that can decrease muscle strength after the age of 60 [5-7]. These physiological changes include a decrease in muscle volume due to a reduced number of muscle fibers [7] and a decrease in contractile speed of muscle fibers [8]. A study by Frontera et al. [9] looked at the effects of age on skeletal muscle and found that the reduction in cross-sectional area of muscle, primarily the quadriceps femoris muscle, was due to a decrease in the number of muscle fibers present in the muscle. These changes in the properties of skeletal muscle as age increases can lead to strength deficits in elderly patients [5-9]. Therefore, because major differences in muscle properties exist between young and elderly populations, it is important to analyze the individual contributions of lower extremity muscles in elderly patients for comparison with the results of younger patients from previous simulations [1, 2].

Additionally, differences in gait kinematics and kinetics between young adults and elderly adults have been documented [10-12]. Winter et al. [12] found that the elderly subjects’ free walking speed was significantly slower than that of young subjects and the elderly subjects exhibited a less powerful toe-off and a more plantarflexed heel-strike.

Kerrigan et al. [10] found that elderly subjects exhibited reduced peak hip extension, increased anterior pelvic tilt, and reduced ankle plantarflexion when compared to younger subjects. DeVita et al. [11] found that elderly subjects exhibited less knee flexion in early stance and less ankle plantarflexion in late stance than the speed-matched, young adult control group. DeVita et al. also found that the elderly subjects produced more power in the hip extensors and less power in the knee extensors and ankle plantarflexors when compared to the young adults. These results support the relationship between aging, lower extremity muscle weakness, and changes in gait patterns.

Osteoarthritis

In addition to age, another major contributor to muscle weakness, particularly in the quadriceps femoris muscles, is osteoarthritis (OA). According to the Centers for Disease

Control and Prevention (CDC), the incidence of osteoarthritis increases dramatically after the age of 45 [13]. It is important to study osteoarthritis because it is the most common form of arthritis [14] and in the year 2008, OA affected approximately 27 million Americans over the age of 25 [15]. It is predicted that by 2030, over 67 million will be affected by osteoarthritis

[16]. OA most frequently affects the knee joint and a number of side effects of osteoarthritis can contribute to decreased walking speed or increased difficulty walking, including joint

pain and muscle weakness [17-19]. Walking has long been an important functional skill for individuals who lead independent lives.

Evidence from recent studies suggests that one of the most disabling physical limitations associated with knee osteoarthritis is weakness in the quadriceps femoris muscle

[20, 21]. In a study by Stevens et al. [22], it was found that the quadriceps muscles were weaker in the OA affected knee than in the unaffected, contralateral limb. Additionally, some research exists that suggests that quadriceps weakness may precede osteoarthritis [21, 23]. In a study by McAlindon et al. [20], it was found that some patients with severe radiographic joint damage experienced only limited knee pain while other patients who experienced severe knee pain did not show signs of severe radiographic joint damage. Instead, quadriceps weakness was found to be the underlying association between pain and disability and functional limitations. Hurley [23] depicted this complex relationship between muscle weakness, aging, disability, and osteoarthritis (Figure 1). As can be seen in Figure 1, a cycle exists between disability, muscle weakness, and osteoarthritis (red arrows). These three factors affect each other and it is still unknown which symptom occurs first, although research suggests that quadriceps weakness may predate osteoarthritis and functional limitations.

Figure 1: A complex relationship exists between knee osteoarthritis and quadriceps muscle weakness. Adapted from Hurley, 1999 [23].

Regardless of the cause-effect relationship that exists between weakened quadriceps and osteoarthritis, there are numerous studies that have shown that patients with osteoarthritis have weaker quadriceps than those without osteoarthritis [22-24]. Additionally, quadriceps weakness has been positively correlated with disability as determined by WOMAC function scores [21]. In order to reduce the disabling effects of quadriceps weakness and osteoarthritis, research has looked at the possibility of strengthening lower extremity muscles in order to improve functionality of patients with weak quadriceps [17, 25, 26]. In a study by

Chandler et al. [17], improvements in physical performance and disability were found to be positively correlated with lower extremity strength gains. Patients with high levels of

functional limitations completed a strength training regime that targeted the bilateral knee extensors and flexors, plantarflexors, and dorsiflexors. Gains in lower extremity strength were found to increase gait speed, chair rise performance, and mobility tasks. In a study by

Hurley et al. [25], the quadriceps muscles in patients with OA were specifically targeted. The subjects in the study completed an exercise regime that included MVICs with visual feedback of force output, resistance biking, knee flexion and extension resistance exercises, and functional exercises. In all of the subjects, the gains in quadriceps strength were maintained after the exercise regime; however, the exercise regime was labor intensive and costly to implement for the subjects. While these studies did show increases in lower extremity strength, one study [17] did not focus specifically on the quadriceps muscles and the other study [25] found that the increases in quadriceps strength came at the expense of labor intensive and costly exercise regimes. At this point, no gold standard training program has been developed that can help reverse the effects of weak quadriceps.

Gaps in Current Research

There are gaps of knowledge in current research surrounding the relationship between weak quadriceps and other lower extremity muscles and functional limitations in everyday tasks such as walking in elderly subjects. It is known that muscle properties change with increasing age but it is unknown how muscles in elderly patients contribute to support and vertical progression during gait. van der Krogt [27] has demonstrated which lower extremity muscles compensate for generalized lower extremity muscle weakness during gait for healthy, young individuals, but the relationship remains unknown in the elderly population.

Additionally, it is unknown what the individual muscular contributions are in the lower extremities of elderly subjects affected by weak muscles. It is important to understand the effects of weak muscle groups on functional tasks such as walking because muscle weakness and functional impairments have been strongly linked to aging [5, 9, 17, 25]. Therefore, it is imperative to determine the relationship between weak muscle groups and lower extremity muscle function during gait in elderly subjects.

Current research is analyzing the contributions of individual lower extremity muscles to support and forward progression during gait in elderly subjects who have osteoarthritis.

This data is being compared to the contributions of individual lower extremity muscles in young, healthy subjects who have simulated quadriceps weakness [28]. However, current gaps in this research exist, also, because there are known physiological differences between muscle in young people and muscle in elderly people. Therefore, the question remains how individual lower extremity muscles during gait in healthy, older subjects will react to simulated weakened muscles.

1.1. Focus of Thesis

The purpose of this thesis was to investigate the contributions of individual lower extremity muscles to force production during gait in healthy, older subjects. Additionally, the response of the lower extremity muscles to simulated quadriceps, plantarflexors, and gluteus weakness and during gait was analyzed. The response of lower extremity muscles to simulated quadriceps, plantarflexors, and gluteus weakness in elderly subjects is an important step in understanding the mechanisms of knee osteoarthritis.

1.2. Significance of Research

Data from the 2010 United States Census [29] reveals that 40.3 million Americans are over the age of 65, which amounts to 13.0% of the total population. By the year 2030, the number of Americans over the age of 65 is expected to increase to 72.1 million [30].

Additionally, loss of muscle mass (sarcopenia) and muscle weakness is associated with aging

[31]. The Department of Health of Human Services [30] released data regarding elderly adults’ functional limitations performing activities of daily living (ADLs). Approximately

17% of people aged 65-74 reported difficulty walking, approximately 27% of people aged

75-84 reported difficulty walking, and 47% of people over the age of 85 reported difficulty walking. Muscle weakness and sarcopenia have been associated with difficulty walking.

It is predicted that by the year 2030, approximately 67 million people will have osteoarthritis [16]. Osteoarthritis is a major cause of functional limitations including walking, stair climbing, and rising from a chair [19]. Recent studies that have been conducted have shown that quadriceps weakness is associated with osteoarthritis [19-21] and quadriceps weakness often predates radiographic evidence of osteoarthritis [23].

If it can be determined through simulation what other lower extremity muscles naturally increase their contributions to support and forward progression in response to weak muscles from either the natural aging process or disease, physical therapy programs can be created to target these lower extremity muscles. If these other lower extremity muscles are strengthened to compensate for weakened quadriceps in patients who have OA or at risk for

OA, these patients can potentially increase their functional capabilities and return to a higher quality of life. This thesis is the first study to look at the contributions of individual lower

extremity muscles in response to simulated weakened quadriceps in healthy, elderly subjects.

This work will have a positive influence not only on the osteoarthritis community, but on the growing population at risk for osteoarthritis.

1.3. Overview of Thesis

This thesis has four subsequent chapters. Chapter 2 presents the data collection methods utilized in this study. Chapter 3 presents the results from the OpenSim inverse dynamic simulations. Chapter 4 will discuss the lower extremity muscle function of healthy, elderly subjects during gait and the compensatory strategies of lower extremity muscles in response to simulated quadriceps, plantarflexors, and gluteus weakness. Chapter 5 summarizes the key findings and contributions of this study and presents future extensions of this research.

Chapter 2: Methods

Eight healthy older subjects were recruited from the community to participate in this study (Table 1). All subjects gave their informed consent that was approved by the Human

Subjects Review Board of the University of Delaware. Subjects were considered healthy if they reported no history of knee OA, which was confirmed by radiograph, or lower extremity injury. Subjects were considered older if they were above the age of 60. These subjects were a control group as part of a larger study on the relationship between strength, joint laxity, and walking patterns and knee OA [32]. Gait data and electromyography (EMG) data were collected as the subjects walked at a self-selected speed over level ground.

Table 1: Subject anthropometric data

Lower Leg Free Non- Stride Extremity Age Mass Length Speed dimensional Length Tested Subject Gender [years] [kg] [m] [m/s] Free Speed* [m] (EMG) A141 F 68 68.4 0.83 1.60 0.56 1.57 Right AS46 F 67 74.4 0.92 1.48 0.49 1.48 Right BP40 M 68 127.4 0.88 1.57 0.54 1.63 Left C139 F 67 69.3 0.90 1.49 0.50 1.46 Right FA46 F 74 53.4 0.77 1.54 0.56 1.31 Left J145 M 72 74.0 0.95 1.59 0.52 1.69 Left J332 M 69 72.2 0.93 1.53 0.51 1.63 Right KA32 F 60 62.4 0.92 1.31 0.44 1.37 Right Average 68.1 75.2 0.89 1.51 0.51 1.52

Standard 4.1 22.2 0.06 0.09 0.04 0.13 Deviation

*Free speed normalized by √

2.1. Data Collection

Gait Data

These data were collected as part of a larger study [32] at the University of Delaware.

The subjects walked at a self-selected speed over a 9-m level walkway for 10 separate trials.

To ensure that the walking speed did not vary more than 5% from their self-selected speed,

two photo-electric beams measured and recorded walking speed. Lower extremity motion

during gait was captured with a 6-camera, passive, 3-dimensional motion analysis system

(Vicon 512 M-Series Cameras, Workstation 512 with software version 3.17 build 074, Vicon

Park, Oxford) sampled at 120Hz. The cameras were calibrated to a 1.5-m x 2.4-m x 1.5-m

volume. The maximum accepted calibration residual was 0.6-mm. The six-camera motion

analysis system detected 33 retroreflective markers (2.5-cm in diameter) placed on both

lower extremities. The markers were placed on the bilateral iliac crests, bilateral greater 12

trochanters, bilateral lateral knee joint line, bilateral lateral malleoli, and bilateral lateral aspect of the fifth metatarsal head. To track lower extremity motion during walking trials, two markers were placed on the heel of the shoe, and clusters of markers rigidly secured to thermoplastic shells were secured to the posterior-lateral aspects of the bilateral thigh and shank. Additionally, a cluster of three markers rigidly mounted in a triangular pattern to a thermoplastic shell was secured to the posterior aspect of the sacrum (Figure 2).

Figure 2: Retroreflective marker placement for motion analysis 13

Vertical, anterior-posterior, and medial-lateral ground reaction forces were measured using a 6-component force platform (Bertec, Worthington, OH) sampled at 1920Hz. Ground reaction data was used to calculate net joint moments about the hip, knee, and ankle to determine heel-strike and toe-off during gait.

Electromyographic (EMG) Data

A 16-channel EMG system (MA-300-16, Motion Lab Systems, Baton Rouge, LA) was used to sample (1920Hz) muscle activation simultaneously with the Vicon motion capture system. Double differential EMG surface electrodes with pre-amplification (MA-317

EMG pre-amplifiers, Motion Lab Systems, Baton Rouge, LA) and with parallel sensor contacts (12 mm disks) set 18 mm apart were used to measure the muscle activation of six muscle groups. The EMG surface electrodes were secured over the mid-muscle bellies of the lateral and medial quadriceps (L/MQ), lateral and medial hamstrings (L/MH), and lateral and medial heads of the gastrocnemius (L/MG). EMG data were collected for the six muscle groups simultaneously as subjects walked at a self-selected speed over level ground.

Additionally, subjects performed a maximal volitional isometric contraction (MVIC) for the six muscle groups while EMG data were recorded.

2.2. Data Analysis

Raw Data Processing

Motion capture and ground reaction force data were collected for ten gait trials for each subject that captured an entire gait cycle for one limb, from heel strike to toe-off.

Ground reaction forces and marker trajectories were filtered with a second-order, phase corrected Butterworth filter with a cutoff frequency of 40Hz for the ground reaction forces and 6Hz for the motion capture data. The raw motion capture and ground reaction force data were processed at the University of Delaware.

All EMG data were band pass filtered with a fourth order filter from 20Hz to 350Hz and corrected for a DC offset. A linear envelope was created with full-wave rectification and the data were filtered with a 20Hz low-pass, eighth-order, phase-corrected Butterworth filter.

The linear envelope data were normalized to the maximum activation signal obtained during static optimization.

2.3. Subject Specific Simulations

OpenSim was used to create 3D subject specific simulations of one gait trial per subject [33]. Muscle-driven, inverse dynamic simulations were performed to analyze the gait kinematics, kinetics, and individual muscle forces during one complete gait cycle, from heel strike to toe off. The lower extremity that was analyzed during the stance and swing phases of the gait cycle will be referred to as the “stance leg.” A 3D generic musculoskeletal model was created that consisted of 20 degrees of freedom and 86 individual muscles [34-36]. The model consisted of a pelvis and two lower extremities where each lower extremity consisted

of 5 rigid body segments: a femur, tibia/fibula, talus, calcaneus, and toes. The hip joint was modeled as a ball-and-socket joint and the knee, ankle, subtalar, and metatarsophalangeal

(mtp) joints were modeled as one degree-of-freedom hinge joints. Additionally, the pelvis contained six degrees of freedom with respect to ground (rotation and translation). The mass of the head, arms, and torso (HAT) and pelvis were centered at the pelvis. The moment of inertia of the pelvis segment was scaled appropriately to account for the added mass of the

HAT segment. This generic musculoskeletal model was then scaled to match the length and mass properties of each subjects (see Section 2.3).

Gait Data Conversion

Only one self-selected speed gait trial per subject was analyzed per subject. Using

VBC3DEditor (VBC3DEditor version 1.0.69, Baton Rouge, LA: Motion Lab Systems, Inc.,

2011), the individual gait trials for each subject were inspected. Based on the absence of noise present in the horizontal and vertical ground reaction forces, a single gait trial was chosen for analysis for that particular subject. Gait events, such as heel strike and toe off, were also identified using the VBC3DEditor for each gait trial.

The Gait Extraction Toolbox [37] was used in conjunction with MATLAB

(MATLAB version 7.13.0, Natick, MA: The MathWorks Inc., 2011) to convert the raw .c3d files into the required file formats for use with OpenSim. In addition to converting data into the appropriate formats, the Gait Extraction Toolbox calculated the leg length, stride length, and average trial speed for each subject’s gait trial that was analyzed (Table 1). Leg length

was calculated as the distance between the retroreflective markers placed on the iliac crest and the ipsilateral lateral malleolus.

OpenSim Workflow

OpenSim was used to create inverse dynamics simulations of one self-selected speed gait trial per subject for eight subjects. The following OpenSim workflow was utilized:

 Scaling: weighted least squares problem to scale each segment (length and mass

properties) in the generic musculoskeletal model so that the distances between the

model markers match the distances between the experimental markers

 Inverse Kinematics (IK): weighted least squares problem to obtain the generalized

coordinates that positions the musculoskeletal model in a pose that best matches the

experimental marker positions throughout the entire gait trial

 Inverse Dynamics (ID): inverse dynamics problem to obtain the net joint moments

and residual forces and moments at the pelvis so that the model is dynamically

consistent with the kinematics

 Static Optimization (SO) [38]: static optimization at each time step in the gait trial to

determine the individual muscle activation patterns to produce the net joint torques

found in inverse dynamics that minimized the objective function, where am is the

activation for muscle m:

∑ (1)

To determine individual muscle forces and activation patterns, static optimization was chosen over other analysis methods. The gait data did not contain one full gait cycle from the same leg while the ipsilateral leg was on a force plate, and, in order to analyze an entire gait cycle, static optimization was chosen over computed muscle control (CMC) [39]. Studies have found that static optimization solutions produce nearly equivalent results as those produced by dynamic optimization solutions, such as computed muscle control [40, 41].

2.4. Lower Extremity Muscle Weakness

Static optimization simulations were run on each subject at the full strength of the model; muscle strength values were determined from the work of Delp et al. [34]. In order to determine the effects of muscle weakness on lower extremity muscle function during gait, further static optimization simulations were performed on each subject. Muscle atrophy was prescribed by lowering the peak isometric force of the desired muscles to some percentage of the full strength.

Quadriceps Femoris

Quadriceps femoris muscle atrophy was prescribed by lowering the peak isometric force of the rectus femoris, vastus lateralis, vastus medialis, and vastus intermedius muscles on the stance leg. Three atrophy cases were analyzed: normal (100%) quadriceps muscle strength, 70% quadriceps muscle strength, and 40% quadriceps muscle strength (Table 2).

Table 2: Quadriceps femoris muscle atrophy

Peak Isometric Force (N) Quadriceps 100% Strength 70% Strength 40% Strength Muscle (Normal) Rectus Femoris 1169 818.3 467.6 Vastus Lateralis 1871 1309.7 748.4 Vastus Medialis 1294 905.8 517.6 Vastus Intermedius 1365 955.5 546

Plantarflexors

Weakness of the plantarflexors was studied as a group. Plantarflexor atrophy was prescribed by lowering the peak isometric force of the gastrocnemius and soleus muscles together. Three atrophy cases were analyzed: normal (100%) strength, 70% strength, and

40% strength (Table 3).

Table 3: Plantarflexor muscle atrophy

Peak Isometric Force (N) Plantarflexor 100% Strength 70% Strength 40% Strength Muscle (Normal) Lateral Head of 683 478.1 273.2 Gastrocnemius Medial Head of 1558 1090.6 623.2 Gastrocnemius Soleus 3549 2484.3 1419.6

Gluteus Maximus, Medius, and Minimus

Weakness of the gluteus muscles was studied as a group. Gluteus atrophy was prescribed by lowering the peak isometric force of the gluteus maximus, medius, and 19

minimus muscles together. In OpenSim, each gluteus muscle was modeled as three separate muscle fibers, each with their own peak isometric force. The peak isometric force of each fiber for each gluteus muscle was lowered. Three atrophy cases were studied: normal (100%) strength, 70% strength, and 40% strength (Table 4).

Table 4: Gluteus muscle atrophy

Peak Isometric Force (N) Plantarflexor 100% Strength 70% Strength 40% Strength Muscle (Normal) Gluteus Maximus 1 573 401.1 229.2 Gluteus Maximus 2 819 573.3 327.6 Gluteus Maximus 3 552 386.4 220.8 Gluteus Medius 1 819 573.3 327.6 Gluteus Medius 2 573 401.1 229.2 Gluteus Medius 3 653 457.1 261.2 Gluteus Minimus 1 270 189 108 Gluteus Minimus 2 285 199.5 114 Gluteus Minimus 3 323 226.1 129.2

Chapter 3: Results

3.1. Full Strength Model

EMG Data

EMG data were compared to the muscle activation patterns from the static optimization simulation results for full lower extremity muscle strength for each subject

(Figure 3). For each subject, the processed EMG data (see Section 2.2) were discretized to

2% bins and averaged across all eight subjects. The averaged EMG signals were then normalized to the maximum signal obtained during the static optimization trials [27].

Similarly, the static optimization activation data for all eight subjects were discretized to 2% bins and averaged across all eight subjects. The lateral hamstrings (LH) comprised of an average between the biceps femoris short head and biceps femoris long head muscle activations. The medial hamstrings (MH) comprised of an average between the semitendinosus and semimembranosus muscle activations.

Both the experimental EMG data and the static optimization results show that the lateral (VL) and medial (VM) vasti are active during the first part of stance and that the lateral quadriceps are more active than the medial quadriceps. Similarly, both experimental

and simulation results show that the lateral (LG) and medial (LG) heads of the gastrocnemius are nearly fully activated in mid-late stance.

Both the experimental EMG data and the static optimization results show that the lateral (LH) and medial (MH) hamstrings are active during the early part of stance and decrease in activation toward late stance.

Gait Kinematics

In the static optimization simulations, the subjects were forced to track “normal” gait, or the natural, three dimensional gait kinematics exhibited by each subject. Table 1 contains the average gait characteristics for the healthy, elderly patient population from this study.

The eight healthy, elderly subjects walked 1.51 ± 0.09m/s when instructed to walk at a self- selected speed. Each subject’s free speed was then normalized by dividing the free speed by√ . The average nondimensional free speed for the healthy, elderly subjects was 0.51

± 0.04. The average stride length was 1.52 ± 0.13m.

In Inverse Kinematics (see Section 2.3), the subject-specific models were forced to track the gait kinematics from the motion capture data. Figure 4 shows the average hip, knee, and ankle flexion-extension angles from the identified stance leg (Table 1) for each subject along with the standard deviation (shaded region). The flexion-extension angles are shown as a percentage of the entire gait cycle; however, only the stance phase (0 – 60% gait) is shown in Figure 4. At heel-strike, the hip began at approximately 25° of flexion and reached the maximum extension of approximately -30° around 50% of the gait cycle. The knee began at

0° at heel-strike and became hyperextended by approximately 10° around 40% of the gait

cycle. The ankle began at 15° of plantarflexion at heel-strike and on average, did not move into dorsiflexion throughout all of stance.

Figure 4: Average gait kinematics of the healthy, elderly subjects determined form Inverse Kinematics of the hip (black), knee (red) and ankle (blue); Positive: Flexion (Dorsiflexion), Negative: Extension (Plantarflexion)

Gait Kinetics

Inverse Dynamics (see Section 2.3) was used to calculate the net joint moments at all lower extremity joints during the gait cycle. The hip, knee, and ankle joint moments from the selected stance leg for each subject (Table 1) were normalized to the subjects’ body weight and height. The joint moments were then discretized to 2% bins and averaged across all subjects. Figure 5 shows the average hip, knee, and ankle flexion-extension moments for all eight subjects along with the standard deviation for each moment as a percent of the gait cycle.

Figure 5: Inverse dynamics joint moments averaged across all eight subjects and normalized to body weight and height; Positive: Extension (Plantarflexion), Negative: Flexion (Dorsiflexion)

At heel-strike, the external moment tends to flex the hip with a magnitude of approximately 5 times greater than the body weight time height. The hip joint reached a maximum flexion moment of 7.5 times greater than the body weight times height and a 26

maximum extension moment of 5.5 times greater than the body weight times height during stance. At heel-strike, the external moment tends to flex the knee joint, reaching a peak magnitude approximately 4 times greater than the body weight times height. The knee reached a maximum extension moment 1.75 times greater than the body weight times height and a maximum flexion moment of 5.25 times greater than the body weight times height during stance. Just after heel-strike, the external moment plantarflexed the ankle and peaked at 1.75 times greater than the body weight times height. Around 11% of the gait cycle, the external moment dorsiflexed the ankle joint and peaked at 9.5 times greater than the body weight times height during stance.

Muscle Forces during Gait

Static Optimization was used to determine the individual muscle forces in the lower extremity that would produce the measured gait kinematics and kinetics (see Section 2.3).

When the model was at full strength for all lower extremity muscles [34], including the quadriceps muscles, seven major muscle groups in the lower extremity produced the majority of the force throughout the gait cycle, as seen below in Figure 6. The following muscles make up the seven major muscle groups in the lower extremity:

 GlutMax: all fibers of the gluteus maximus muscle

 Hams: lateral (biceps femoris long head and biceps femoris short head) and medial

(semitendinosus and semimembranosus) hamstrings

 RF: rectus femoris

 Vasti: vastus lateralis, medialis, and intermedius

 Gastroc: lateral and medial heads of the gastrocnemius

 Sol: soleus

 TA: tibialis anterior

Figure 6: Static optimization muscle forces for full strength model averaged across all eight subjects

During stance, the 43 muscles that make up one lower extremity of the generic musculoskeletal model that was used to simulate the gait of healthy, elderly subjects produced as much as 8800N of force, with the seven major muscles in one lower extremity

producing as much as 5500N. These maximum points occurred at 42% of the gait cycle, just before toe-off. During swing, the maximum force produced by one lower extremity was only

2950N, with the seven major muscle groups contributing 2100N of that force.

To examine the contributions of the individual major muscle groups throughout the gait cycle, Figure 7 shows how the muscle forces from the seven major muscle groups in the lower extremity sum to produce the total muscular force during one complete gait cycle.

Figure 7: Individual muscle forces from seven major muscle groups in the lower extremity from the full strength model, averaged across all eight subjects

Peak forces for each of the seven major muscle groups from Figure 7 were tabulated and can be found in Table 5. It can be seen that the gluteus maximus, hamstrings, vasti, gastrocnemius, soleus, and tibialis anterior all peaked during the stance phase of gait and the rectus femoris peaked during the swing phase of gait for the healthy, elderly subjects. The lateral and medial heads of the gastrocnemius produced the highest force during gait, reaching 2104N. Additionally, the vasti group (lateral, medial, and intermediate) produced more force together (676N) than the rectus femoris alone (371.3N). Of the vasti, the vastus lateralis produced the most force and the vastus medialis produced the least amount of force.

Table 5: Peak average forces from the seven major muscle groups obtained during Static Optimization

Muscle Peak Force [N] % Gait Cycle Phase GlutMax 562.5 11.5 Stance Hams 1838.2 1 Stance RF 356.4 63.5 Swing Vasti 670.4 13 Stance Gastroc 2103.0 44.5 Stance Sol 882.1 52 Stance TA 401.3 40 Stance

Upon comparison of the parfait plot in Figure 7 and the muscle activation plots from

Figure 3, it can be seen that the hamstrings, quadriceps, and gastrocnemius produce force at the same points in the gait cycle that the muscles are activated. The sum of the lateral and medial hamstrings (HAMS) produce a large amount of force in the early part of stance, just after heel strike, and again in mid-late stance prior to toe-off. The gastrocnemius produces a large amount of force in the later part of stance and the vasti produce force in the first part of stance.

For comparisons with other patient populations and gait pathologies, the muscle forces determined from Static Optimization were normalized to each subject’s bodyweight, discretized to 2% bins, and averaged across all eight subjects (Figure 8).

Figure 8: Plot of individual muscle forces normalized to body weight from seven major muscle groups in the lower extremity from the full strength model, averaged across all eight subjects

From Figure 8, it can be seen that at 42% of the gait cycle, the muscles in one lower extremity produce on average up to 14 times the bodyweight of a particular subject, with the seven major muscle groups contributing 62.7% of this peak force. The peak force production 31

in one lower extremity during the swing phase is considerably lower at four times bodyweight, which occurs at 90.5% of the gait cycle, with the seven major muscle groups contributing 70.9% of this peak force.

3.2. Simulated Atrophy of Quadriceps Femoris

As the quadriceps were atrophied to 70% and 40% of their normal strength level during Static Optimization (see Section 2.4), changes in the force production of other lower extremity muscles were observed. Table 6 contains the peak force from the full strength model, the change in peak force from the original, and the percent change for both atrophy cases for the seven major muscle groups in the lower extremity.

Table 6: Muscle force changes in response to quadriceps femoris atrophy

Full Strength 70% Quads Strength 40% Quads Strength Change from Change from Muscle Peak Force [N] % change % change Normal [N] Normal [N] RF 356.4 -34.6 -9.7% -123.3 -34.6% Vasti 670.4 -14.4 -2.1% -70.3 -10.5% GlutMax 562.5 13.1 2.3% 61.1 10.9% Hams 1838.2 0 0% 0 0% Gastroc 2103.0 0.1 0% 0 0% Sol 882.1 0.1 0% 0.4 0% TA 401.3 0.1 0% 0.1 0%

As the quadriceps were atrophied, the resulting peak forces exerted by the rectus femoris and vasti decreased. The rectus femoris exhibited greater changes in peak force production than the vasti group. Additionally, the decrease in force in the quadriceps was not linearly related to the amount of atrophy prescribed.

The rectus femoris only increased its peak force production during swing phase

(Figure 9). However, in order to produce the same amount of force during the stance phase, the activation of the rectus femoris increased during the stance phase (Figure 10).

Figure 9: Rectus femoris force as a function of quadriceps femoris atrophy, which decreased during swing as the quadriceps were weakened

Figure 10: Rectus femoris activation as a function of quadriceps femoris atrophy, which increased during stance and swing as the quadriceps were weakened

The summed contributions of the vasti group (vastus lateralis, vastus medialis, vastus intermedius) increased in early stance as the peak isometric force of the vasti was reduced (Figure 11). Similar to the rectus femoris, the vasti (lateralis, medialis, and intermedius) showed increases in activation during the stance phase. Figure 12 shows the increase in activation of the vastus lateralis in response to quadriceps femoris atrophy. The vastus medialis and intermedius exhibited similar trends and therefore, are not shown.

Figure 11: Vasti group force as a function of quadriceps weakness, which decreased during stance and increased during swing as the quadriceps were weakened

Figure 12: Vastus lateralis activation as a function of quadriceps femoris atrophy, which increased as the quadriceps were weakened

The only other lower extremity muscle that experienced changes in force production in response to the weakened quadriceps was the gluteus maximus. As the quadriceps were atrophied, the gluteus maximus increased force production to compensate for the weak quadriceps. When the quadriceps were atrophied by 30%, the gluteus maximus increased its peak force production by only 2.3%. However, when the quadriceps were atrophied by 60%, the gluteus maximus increased its peak force production by 10.9%. The gluteus maximus force as a function of quadriceps weakness is shown below in Figure 13.

Figure 13: Gluteus maximus force as a function of quadriceps femoris atrophy, which increased as the quadriceps were weakened

In order to produce more force, the gluteus maximus increased its muscular activation during early stance in response to the weakened quadriceps (Figure 14). The gluteus maximus exhibited the greatest increase in both force and activation when the quadriceps were weakened to 40% of their original strength.

Figure 14: Gluteus maximus activation as a function of quadriceps femoris atrophy, which increased as the quadriceps were weakened

3.3. Simulated Atrophy of Plantarflexors

As the plantarflexors were atrophied to 70% and 40% of their normal strength level during Static Optimization (see Section 2.4), changes in the force production of other lower extremity muscles were observed. The soleus and lateral and medial heads of the gastrocnemius were atrophied. Table 7 contains the peak force during mid-late stance from the full strength model, the change in peak force from the original, and the percent change for both atrophy cases for the major muscle groups in the lower extremity that exhibited changes in force. Only the peak force during mid-late stance was tabulated because the gastrocnemius

and soleus are only active during mid-late stance; therefore, compensation strategies were only observed during mid-late stance. Table 18 in the Appendix contains the changes in muscle force in response to plantarflexor weakness for individual muscles, rather than functional groups. The individual muscles that make up the functional muscle groups are as follows:

 Gastroc: lateral and medial heads of the gastrocnemius

 Sol: soleus muscle

 Iliopsoas: iliacus and psoas major muscles

 Minor knee flexors: gracilis and sartorius muscles

 RF: rectus femoris muscle

 Hams: biceps femoris long head and short head, semimembranosus, and

semitendinosus muscles

 TA: tibialis anterior

 Minor ankle plantarflexors: flexor digitorum, flexor hallucis, peroneus brevis,

peroneus longus, and tibialis posterior muscles

 Minor ankle dorsiflexors: extensor digitorum, extensor hallucis, and peroneus tertius

muscles

Table 7: Muscle group force changes in response to plantarflexor atrophy

70% Plantarflexor 40% Plantarflexor Full Strength Strength Strength Functional Peak Force Change from Change from Muscle % change % change [N] Normal [N] Normal [N] Group Gastroc 2104 -501 -23.8% -1164.1 -55.3% Sol 882.1 64 7.3% 96.4 10.9% Iliopsoas 2262 20 0.9% 91 4.0% Minor Knee 152.5 9.8 6.4% 56.6 37.1% Flexors RF 133.3 -35.72 -26.8% -53.35 -40.0% Hams 1465 83 5.7% 281 19.2% TA 401.3 -120.2 -30.3% -368.53 -91.8% Minor Ankle 882.2 413.8 46.9% 1113.8 126.3% Plantarflexors Minor Ankle 437.6 -247.5 -56.6% -425.73 -97.3% Dorsiflexors

As the peak isometric strength for the lateral and medial gastrocnemius was lowered

to 70% and 40% of the original strength, the amount of force produced by the sum of the

contributions of the lateral and medial heads of the gastrocnemius decreased. However, the

decrease in force production was not linearly related to the reduction in peak isometric

strength. Figure 15 below shows the gastrocnemius force as a function of plantarflexor

weakness.

In order for the gastrocnemius to produce more force with a reduced peak isometric

force, the lateral and medial heads were activated more as the peak isometric force was

lowered. Figure 16 below shows the lateral gastrocnemius activation as a function of

plantarflexor weakness. The medial gastrocnemius showed similar activation trends and a

plot can be found in the appendix.

Figure 15: Gastrocnemius (lateral and medial) force as a function of plantarflexor weakness, which decreased as the plantarflexors were weakened

Figure 16: Lateral gastrocnemius activation as a function of plantarflexor weakness, which increased as the plantarflexors were weakened 41

Contrary to the trends exhibited by the gastrocnemius, the soleus muscle produced slightly more force during mid-late stance as the peak isometric force was reduced. When the soleus and gastrocnemius were atrophied to 70% of their original strength, the soleus muscle produced 7.3% more force and when the soleus and gastrocnemius were atrophied to 40% of their original strength, the soleus produced 10.9% more force (Figure 17). In order to produce more force despite its reduced peak isometric force, the soleus muscle activated more during mid-late stance (Figure 18).

Figure 17: Soleus force as a function of plantarflexor atrophy, which increased as the plantarflexors were weakened

Figure 18: Soleus activation as a function of plantarflexor weakness, which increased slightly as the plantarflexors were weakened

As the gastrocnemius and soleus muscles were atrophied to 70% and 40% of their peak isometric strength, the iliopsoas muscle, which is the summed contributions of the iliacus and psoas muscles, increased its force production by 0.9% and 4.0% respectively

(Figure 19). The iliopsoas is the primary hip flexor in the lower extremity.

Figure 19: Iliopsoas (Iliacus and psoas) force as a function of plantarflexor weakness, which increased slightly in late stance as the plantarflexors were weakened

The minor hip and knee flexors, the gracilis and sartorius, produced 6.4% and 37.1% more force as the plantarflexors were atrophied to 70% and 40% of their original strength, respectively. The minor hip and knee flexors produced their peak force at 50% of the gait cycle. However, the minor hip and knee flexors do not produce much force during the gait cycle; the minor hip and knee flexors only produce 150-200N of peak force.

Figure 20: Minor hip and knee flexors (gracilis and sartorius) force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened

The rectus femoris exhibited a reduction in force production during late stance as the plantarflexors were atrophied. The peak force of the rectus femoris during late stance decreased 26.8% and 40.0% as the plantarflexors were atrophied to 70% and 40% of their peak isometric strength, respectively (Figure 21). The peak force produced by the rectus femoris in late stance was only 133.3N; however, the rectus femoris is primarily active during the swing phase. The rectus femoris produced 356.4N of force during swing (Table 6).

Even though the rectus femoris exhibited a reduction in force production, the remaining quadriceps muscles, the vasti, did not exhibit any compensatory strategy in response to plantarflexor atrophy (Figure 22). 45

Figure 21: Rectus femoris force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened

Figure 22: Vasti (vastus lateralis, medialis, and intermedius) force as a function of plantarflexor weakness, which remained constant as the plantarflexors were weakened 46

The hamstrings, comprised of the summed contributions from the biceps femoris long and short heads, semimembranosus, and semitendinosus, function as knee flexors and hip extensors. In response to gastrocnemius and soleus atrophy, the hamstrings increased their force production by 5.7% and 19.2% in mid-late stance (Figure 23). Even though the hamstrings are active at other portions of the stance phase, the hamstrings did not exhibit compensatory strategies outside of mid-late stance.

Figure 23: Hamstrings force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened

The tibialis anterior, one of the primary ankle dorsiflexors, exhibited a decrease in force production during mid-late stance in response to the atrophy of the primary plantarflexors. As the plantarflexors were atrophied to 70% and 40% of their original strength, the tibialis anterior decreased its force production during mid-late stance by 30.0% and 91.8%, respectively (Figure 24). Additionally, the tibialis anterior exhibited decreased force production in late swing. The tibialis anterior is one of the primary muscles that exhibited a compensation strategy for the plantarflexor weakness.

Figure 24: Tibialis anterior force as a function of plantarflexor weakness, which decreased in late stance and swing as the plantarflexors were weakened

The minor ankle plantarflexors increased the amount of force they produced as a group in response to the weakness of the gastrocnemius and soleus. The minor plantarflexors consist of the summed contributions from the flexor digitorum, flexor hallucis, peroneus brevis, peroneus longus, and the tibialis posterior. The minor ankle plantarflexors saw increases in force production during mid-late stance of 46.9% and 126.3% as the major plantarflexors were atrophied to 70% and 40% of their original strength (Figure 25). The minor ankle plantarflexors are one of the primary compensators for gastrocnemius and soleus atrophy.

Figure 25: Minor ankle plantarflexor force as a function of primary plantarflexor (gastrocnemius and soleus) weakness, which increased in late stance as the plantarflexors were weakened

The minor ankle dorsiflexors decreased the amount of force they produced during mid-late stance in response to major plantarflexor weakness. The minor ankle dorsiflexors consists of the summed contributions of the extensor digitorum, extensor hallucis, and the peroneus tertius. The minor ankle dorsiflexors saw decreases in force production of 56.6% and 97.3% as the plantarflexors were atrophied to 70% and 40% of their original strength, respectively (Figure 26). The minor ankle dorsiflexors are one of the primary compensators for plantarflexor weakness.

Figure 26: Minor ankle dorsiflexors force as a function of plantarflexor weakness, which decreased in late stance and swing as the plantarflexors were weakened

3.4. Simulated Atrophy of Gluteus Maximus, Medius, and Minimus

As the gluteus muscles were systematically atrophied to 70% and 40% of their original, peak isometric strength (Table 4) during Static Optimization (see Section 2.4), changes in the force production of other lower extremity muscles were observed. Because the gluteus muscles are active throughout the majority of the gait cycle, different compensatory strategies in lower extremity muscle groups were exhibited at different portions of the gait cycle. Therefore, the changes in muscle forces have been tabulated for early stance (Table 8), late stance (Table 9), and swing phase (Table 10). Table 19 contains the peak force changes for individual muscles in response to gluteus muscle atrophy. The individual muscles that make up the functional muscle groups are as follows:

 Gluts: gluteus maximus, gluteus medius, and gluteus minimus muscles

 Iliopsoas: iliacus and psoas muscles

 Hip External Rotators: quadratus femoris, gemellus, and piriformis muscles

 Hip Adductors: adductor longus, adductor brevis, adductor magnus, pectineus, and

gracilis muscles

 Sartorius: sartorius muscle

 Knee Extensors: rectus femoris, vastus lateralis, vastus intermedius, and vastus

medialis muscles

 TFL: tensor fasciae latae muscle

 Hams: biceps femoris long head, biceps femoris short head, semimembranosus, and

semitendinosus muscles

 Ankle PF: lateral and medial heads of the gastrocnemius, soleus, flexor digitorum,

flexor hallucis, peroneus brevis, peroneus longus, and tibialis posterior muscles

 Ankle DF: tibialis anterior, extensor digitorum, extensor hallucis, and peroneus tertius

muscles

Table 8: Muscle group force changes in response to gluteus atrophy in early stance

Early Stance Local Maxima Changes Full Strength 70% Gluteus Strength 40% Gluteus Strength Functional Change from Change from Peak Force [N] % change % change Muscle Group Normal [N] Normal [N] GLUTS 2526 -314 -12.4% -933 -36.9% Iliopsoas - - - - - Hip External Rotators 127.7 119.6 93.7% 309.8 242.6% Hip Adductors 83.57 -0.25 -0.3% -5.72 -6.8% Sartorius 54.47 11.96 22.0% 97.93 179.8% Knee Extensors 675.7 120.2 17.8% 251.7 37.3% TFL 138.1 75.9 55.0% 161.7 117.1% Hams 502.1 190.6 38.0% 412.5 82.2% Ankle PF - - - - - Ankle DF 558.4 - - - -

Table 9: Muscle group force changes in response to gluteus atrophy in late stance

Late Stance Local Maxima Changes Full Strength 70% Gluteus Strength 40% Gluteus Strength Functional Change from Change from Peak Force [N] % change % change Muscle Group Normal [N] Normal [N] GLUTS 1642 -250 -15.2% -639 -38.9% Iliopsoas 2261 -26 -1.1% -83 -3.7% Hip External Rotators 104.1 -33.95 -32.6% 7.1 6.8% Hip Adductors 157.9 -52.7 -33.4% -143.47 -90.9% Sartorius 106.8 24.7 23.1% 37.9 35.5% Knee Extensors 133.3 6.4 4.8% 39.6 29.7% TFL 191.9 29.3 15.3% 58.3 30.4% Hams 1464 -25 -1.7% -27 -1.8% Ankle PF 2462 51 2.1% 166 6.7% Ankle DF 837.6 25.7 3.1% 245.4 29.3%

Table 10: Muscle group force changes in response to gluteus atrophy in swing

Swing Local Maxima Changes Full Strength 70% Gluteus Strength 40% Gluteus Strength Functional Change from Change from Peak Force [N] % change % change Muscle Group Normal [N] Normal [N] GLUTS 566.5 -52.7 -9.3% -192.7 -34.0% Iliopsoas 475.9 -54.5 -11.5% -200.6 -42.2% Hip External Rotators 118.8 46.3 39.0% 130.7 110.0% Hip Adductors 323.1 - - - - Sartorius 15.78 4.19 26.6% 12.51 79.3% Knee Extensors 371.9 - - - - TFL 12.15 10.62 87.4% 40.79 335.7% Hams 1140 - - - - Ankle PF 353.2 22.5 6.4% 64.9 18.4% Ankle DF 323.2 26 8.0% 75.2 23.3%

As the gluteus muscles were weakened to 70% and 40% of their initial peak isometric strength, the summed force contributions of the gluteus muscles decreased in early stance, late stance, and swing phase (Figure 27). The gluteus muscles exhibited the greatest decrease in force production in late stance, decreasing by 15.2% and 38.9% as the gluteus muscles were weakened to 70% and 40% of their initial strength, respectively.

Figure 27: Gluteus muscle force (maximus, medius, minimus) as a function of gluteus weakness, decreased in both stance and swing as the gluteus muscles were weakened

In order to produce the amount of force that the gluteus muscles produced in their weakened states, the activations increased. Gluteus maximus (Figure 28) increased its activation primarily in early stance. Gluteus medius (Figure 29) increased its activation throughout stance and swing. Gluteus minimus (Figure 30) increased its activation primarily during stance.

Figure 28: Gluteus maximus activation as a function of gluteus muscle weakness, which increased in both stance and swing as the gluteus muscles were weakened

Figure 29: Gluteus medius activation as a function of gluteus muscle weakness, which increased in both stance and swing as the gluteus muscles were weakened

Figure 30: Gluteus minimus activation as a function of gluteus muscle weakness, which increased in both stance and swing as the gluteus muscles were weakened 56

In response to gluteus muscle weakness, the iliopsoas (iliacus and psoas) produced slightly less force in late stance and significantly less force during the swing phase (Figure

31). The iliopsoas is the primary hip flexor and produced 42.2% less force in swing phase when the gluteus muscles were atrophied to 40% of their initial strength.

Figure 31: Iliopsoas force as a function of gluteus muscle weakness, which decreased in late stance and swing as the gluteus muscles were weakened

The hip external rotators, the quadratus femoris, gemellus, and piriformis, produced significantly more force in early stance and swing as the gluteus muscles were atrophied

(Figure 32). The hip external rotators compensated for gluteus weakness more in early stance than in the swing phase. However, during late stance, there is no clear relationship between the force produced by the hip external rotators and the degree of weakness in the gluteus muscles.

Figure 32: Hip external rotators force as a function of gluteus muscle weakness, which increased in early stance and swing as the gluteus muscles were weakened

The hip adductors exhibited slight changes in force production in response to gluteus muscle weakness during early stance and significant changes during late stance (Figure 33).

As the gluteus muscles were weakened to 40% of their initial strength, the hip adductors produced 6.8% less force in early stance and 90.9% less force in late stance. The hip adductors did not exhibit any compensatory strategies during the swing phase of gait.

Figure 33: Hip adductors muscle force as a function of gluteus muscle weakness, which decreased in early and late stance as the gluteus muscles were weakened

In response to gluteus muscle weakness, the sartorius muscle produced more force during both the stance and swing phases to compensate (Figure 34). The sartorius muscle can

perform several functions at both the hip and the knee, including flexion, abduction, and external rotation of the hip and knee flexion. Along with the hip external rotators, the sartorius was one of the largest compensators for gluteus weakness in early stance. This is likely due to the fact that the sartorius can act as an external rotator at the hip. When the gluteus muscles were weakened to 40% of their initial strength, the sartorius produced

179.8% more force in early stance, 35.5% more force in late stance, and 79.3% more force in the swing phase.

Figure 34: Sartorius force as a function of gluteus weakness, which increased in both stance and swing as the gluteus muscles were weakened

As the gluteus muscles were atrophied, the knee extensors, the quadriceps, produced more force in early stance and slightly more force in late stance (Figure 35). The knee extensors produced 37.3% more force in early stance when the gluteus muscles were weakened to 40% of their initial strength. The knee extensors did not exhibit a compensatory strategy for gluteus muscle weakness during swing phase.

Figure 35: Knee extensors force as a function of gluteus muscle weakness, which increased in both early and late stance as the gluteus muscles were weakened

The tensor fasciae latae, which assists the gluteus maximus and stabilizes the knee joint during extension, increased the amount of force it produced in both stance and swing to compensate for gluteus muscle weakness (Figure 36). The tensor fasciae latae produced

117.1% more force in early stance, 30.4% more force in late stance, and 335.7% more force in swing when the gluteus muscles were weakened to 40% of their initial strength.

Figure 36: Tensor fasciae latae force as a function of gluteus muscle weakness, which increased throughout all of stance and swing as the gluteus muscles were weakened

The hamstrings exhibited a complex compensatory strategy for gluteus muscle weakness. The hamstrings, which act to flex the knee and extend the hip, produced 82.2% more force in early stance when the gluteus muscles were weakened to 40% of their initial strength (Figure 37). However, during late stance, the hamstrings produced slightly less force as the gluteus muscles were weakened and did not alter their force production during swing.

Figure 37: Hamstrings force as a function of gluteus muscle weakness, which increased in early stance and slightly in late stance as the gluteus muscles were weakened

The ankle plantarflexors (Figure 38) and ankle dorsiflexors (Figure 39) exhibited similar compensatory strategies in response to gluteus muscle weakness. The ankle

plantarflexors and dorsiflexors produced more force in late stance and swing phase as the gluteus muscles were weakened.

Figure 38: Ankle plantarflexors force as a function of gluteus muscle weakness, which increased slightly in late stance and swing as the gluteus muscles were weakened

Figure 39: Ankle dorsiflexors force as a function of gluteus muscle weakness, which increased in late stance and swing as the gluteus muscles were weakened

Chapter 4: Discussion

4.1. Full Strength Model

EMG Data

From Figure 3, both the experimental EMG and simulated activation patterns for the vastus lateralis (VL) and vastus medialis (VM) suggest that the lateral and medial quadriceps are active during the early portion of the stance phase. The timing of the quadriceps activation patterns agree with a study by Liu et al. [2] that studied normal gait in teenagers; however, the quadriceps activation patterns of the healthy, elderly subjects are lower in magnitude than those found by Liu et al. for the fast walking speed trials. The fast walking speed trial was selected from the Liu et al. study because the walking speed of the healthy elderly subjects (1.51 ± 0.09m/s) most closely matches the fast walking speed of the healthy teenagers (1.56 ± 0.21m/s).

Additionally, it can be seen that the experimental and simulated lateral (LG) and medial (MG) gastrocnemius muscle activations match very well. Both the experimental EMG and simulation results suggest that the gastrocnemius is nearly fully activated during the mid- late portion of the stance phase in healthy, elderly subjects. The gastrocnemius activation timing patterns agree with other studies that have analyzed gait in other patient populations

[2, 27]. However, the magnitude of the plantarflexors’ activation from the healthy, elderly

subjects (0.8 – 1.0) most closely matches the plantarflexors’ activation from the Liu et al. study in the speed-matched case (fast walking, 0.70).

There is some disagreement in the hamstrings activation patterns between the experimental EMG results and the static optimization simulation results. Both experimental and simulation results suggest that the lateral (LH) and medial (MH) hamstrings are 50% activated at heel-strike and become active towards the end of the swing phase. One of the main differences between the experimental and simulation results is that the static optimization results show that both the lateral and medial hamstrings are active around 40% of the gait cycle. Despite this difference, the experimental and simulation results for the hamstrings match very well. The magnitude of the hamstrings’ activation from the healthy, elderly subjects (0.5 – 0.7) most closely matches the hamstrings’ activation from the Liu et al. [2] study in the speed-matched case (fast walking, 0.6 – 0.8).

Gait Kinematics

In order to begin comparing gait kinematics of the healthy, elderly population from this study with other subject populations, certain gait characteristics from various studies were tabulated (Table 11). The healthy, elderly subjects’ free speed from this study was faster than that of healthy adolescents [27], healthy pre-teenagers [2], healthy young adults [28], and another healthy, elderly population [10]. However, the fast speed in the Kerrigan et al. [10] study

(1.55 ± 0.20m/s) closely matches the free speed of the healthy, elderly subjects in this study.

Therefore, when not looking at the very fast case from the Kerrigan et al. [10] study, walking speed is a confounding variable in addition to age.

Table 11: Comparison of gait kinematics across various subject populations

Leg Free Non- Fast Patient # of Age Height Mass Length Speed dimensional Speed Population Subjects [yrs] [m] [kg] [m] [m/s] Free Speed* [m/s] Healthy, 68.1 ± 1.65 ± 75.2 ± 0.89 ± 1.51 ± 8 0.51 ± 0.04 Elderly 4.1 0.11 22.2 0.06 0.09 Healthy, 1.75 ± 1.08 ± Adolescents 6 16 ± 1 68 ± 5 0.09 0.16 [27] Healthy, Pre- 12.9 ± 51.8 ± 0.81 ± 1.15 ± 1.56 ± 8 0.41 ± 0.03 teenagers [2] 3.3 19.2 0.09 0.08 0.21 Healthy, 21.9 ± 1.74 ± 72.8 ± 0.90 ± 1.32 ± Young Adult 7 0.44 ± 0.04 2.3 0.08 11.4 0.06 0.13 [28] Healthy, 72.7 ± 1.62 ± 68.3 ± 1.19 ± 1.55 ± 31 Elderly [10] 5.5 0.09 12.9 0.13 0.20

When comparing the hip, knee, and ankle flexion-extension angles during swing

(Figure 4) to the joint kinematics of the healthy, elderly population walking very fast (1.55 ±

0.20m/s) from the Kerrigan et al. [10] study, the hip joint was more extended in late stance than the population from this study. We found that our subjects experienced more hip extension, knee extension, and ankle plantarflexion during stance than Kerrigan et al. The subjects from the Kerrigan et al. study only reached 14.5° of hip extension whereas the subjects from this study reached 29.8° of hip extension. In the Kerrigan et al. study, the knee reached a peak of 2.2° of flexion at mid-stance (40% gait) and the subjects from this study reached 10.55° of extension at mid-stance (40% gait). Additionally, this study found that the subjects’ ankles were plantarflexed throughout stance whereas Kerrigan et al. found that the ankle joint moved into dorsiflexion.

When comparing to the gait results of the healthy pre-teenagers from the Liu et al. [2] study, we found that the hip joint of the elderly subjects in the present study were much less flexed during early stance and much more extended during late stance. Similarly, the knee joint of the

elderly subjects were less flexed during early stance and more extended during late stance than the young subjects from the Liu et al. study. We also found that the ankle joint in the elderly subjects remained plantarflexed for the duration of stance and reached a peak of -33° (plantarflexion) in early stance while Liu et al. found that the young subjects remained dorsiflexed for the majority of stance and only reached a peak of approximately -10° (plantarflexion) in early stance.

From comparison with two different patient populations [2, 10] walking at approximately the same speed as the healthy, elderly subjects, we have found that the hip, knee, and ankle joints of the healthy, elderly subjects have been more extended than healthy pre-teenagers and another healthy, elderly population. The largest differences were found between the healthy, elderly subjects in our study and the healthy, pre-teenagers in the Liu et al. [2] study. As the joint kinematics were compared to the speed-matched case in the Liu et al. study, it is likely that the age difference is the leading cause for the different gait kinematics.

Gait Kinetics

Flexion-extension moments for the hip, knee, and ankle joints for a young, healthy patient population are shown below in Figure 40 [28]. The average age of the adult population from this study (N = 7) was 21.9 ± 2.3 years old and all subjects were screened for musculoskeletal and neurological abnormalities. The average free walking speed of this population was 1.32 ± 0.13 m/s.

Figure 40: Flexion-extension joint moments during walking for a healthy, young population [28], with an average age of 21.9 ± 2.3 yrs, average free speed of 1.32 ± 0.13 m/s, and N = 7

Peak values from Figure 40 were found and tabulated in Table 12. Peak normalized joint moments from the healthy, elderly population (Figure 5) from our study were also found and tabulated in Table 12.

Table 12: Comparison of peak flexion-extension moments at the hip, knee, and ankle between the healthy, elderly patient population and the normal patient population from Thompson et al. [28] (from Figure 40)

Normalized Lower Extremity Flexion-Extension Moments [to % BW*height] Peak Joint Hip 1 Hip 2 Knee 1 Knee 2 Knee 3 Knee 4 Ankle 1 Ankle 2 Moments* Healthy, -7.5 5.4 -4.0 1.8 -5.3 -0.1 1.8 -9.4 Elderly Healthy, Young -4.4 4.7 -2.7 2.8 -2.5 0.8 1.2 -8.7 [28] *Positive: extension (plantar-flexion), Negative: flexion (dorsi-flexion)

Upon comparison of the peak, normalized flexion-extension moments at the hip, knee, and ankle from Table 12, it can be seen that the hip joint of the healthy, elderly population experienced more extreme flexion-extension moments than the healthy, young population from the Thompson et al. [28] study (21.9 ± 2.3 yrs, 1.32 ± 0.13 m/s). The same phenomenon was seen at the knee and ankle joints in the healthy, elderly population.

Additionally, in the healthy, young population, the knee experienced an extension moment at the end of stance whereas the healthy, elderly patient population experienced a flexion moment. When comparing the joint kinetics from these two populations, it is important to note that the two populations differ in age and walking speed.

Our peak flexion-extension moments at the hip, knee, and ankle are also expressed as

N-m below in Table 13 so that our joint moments can be compared with those from van der

Krogt et al. [27]. Upon comparison of our flexion-extension moments with those of the healthy, young subjects (16 ± 1 yrs, 1.08 ± 0.16 m/s) from the van der Krogt et al. study, we found that our hip, knee, and ankle joints were more flexed or extended at each peak.

However, when comparing the joint kinetics from these two young populations, it is

important to note that the two populations differ in both age and walking speed. This is the same trend that was observed when comparing the flexion-extension moments at the hip, knee, and ankle joints of the healthy, elderly subjects to the healthy, young population from the Thompson et al. [28] study.

Table 13: Comparison of peak flexion-extension moments at the hip, knee, and ankle between the healthy, elderly patient population and the normal patient population from van der Krogt et al. [27]

Lower Extremity Flexion-Extension Moments [Nm] Peak Joint Hip 1 Hip 2 Knee 1 Knee 2 Knee 3 Knee 4 Ankle 1 Ankle 2 Moments* Healthy, -82.4 59.5 -44.9 19.9 -56.4 19.6 18.9 -103.6 Elderly Healthy, Young -55 57 -28 14 -14 22 7 -90 [27] *Positive: extension (plantar-flexion), Negative: flexion (dorsi-flexion)

Our peak flexion-extension moments at the hip, knee, and ankle are also expressed as

N-m/kg-m below in Table 14Table 13 so that our joint moments can be compared with those from Kerrigan et al. [10]. When comparing the joint kinetics from our study with those of the healthy, elderly population walking very fast (72.7 ± 5.5 yrs, 1.55 ± 0.20 m/s) from the

Kerrigan et al. [10] study, there is some disagreement between our results. However, the elderly subjects walking very fast in the Kerrigan et al. [10] study (elderly, fast) exhibited greater peak flexion-extension moments than the young control group (28.5 ± 4.9yrs, 1.37 ±

0.17 m/s). The hip, knee, and ankle moments were more flexed or extended in the elderly, fast walking speed case at the local peaks than those for the young control group [10]. This is the same trend that was found when our results were compared to those of the healthy,

younger populations from the Thompson et al. [28] study and the van der Krogt et al. [27] study.

Table 14: Comparison of peak flexion-extension moments at the hip, knee, and ankle between the healthy, elderly patient population and the healthy, elderly patient population walking fast and the healthy, young population from Kerrigan et al. [10]

Normalized Lower Extremity Flexion-Extension Moments [to N-m/kg-m] Peak Joint Hip 1 Hip 2 Knee 1 Knee 2 Knee 3 Knee 4 Ankle 1 Ankle 2 Moments* Healthy, -0.76 0.55 -0.41 0.18 -0.54 -0.01 0.18 -0.96 Elderly Healthy, Elderly -0.50 0.71 -0.09 0.46 -0.15 0.33 0.11 -0.74 (Very Fast) [10] Healthy, Young -0.46 0.57 -0.10 0.41 -0.12 0.29 0.09 -0.77 [10] *Positive: extension (plantar-flexion), Negative: flexion (dorsi-flexion)

These changes in joint kinetics between the healthy, elderly subjects and the healthy, young populations [27, 42] are due to the variations in joint kinematics between the two patient populations. Our results agree with the finding that the gait of healthy, elderly subjects is fundamentally different than the gait of healthy, young subjects. Therefore, it would follow that the joint kinetics in the healthy, elderly population would differ from the joint kinetics in a healthy, young population.

Muscle Forces during Gait

We can compare the muscle forces found from Static Optimization (Figure 7) for the healthy, elderly population to muscle forces from various other subject populations that have

studied muscle forces in the lower extremity during gait. Table 15 contains a summary of when major muscle groups produce their peak force during stance for several different patient populations.

Table 15: Comparison of muscle force timing during stance in various subject populations

Healthy, Healthy, Healthy, Pre- Adolescents Healthy, Young Muscle Elderly Teenagers [2] [27] Adults [28] Average Age [yrs] 68.1 ± 4.1 12.9 ± 3.3 16 ± 1 21.9 ± 2.3 Free Speed [m/s] 1.51 ± 0.09 1.15 ± 0.08 1.08 ± 0.16 1.32 ± 0.13 Gluteus Maximus early stance early stance early stance early stance early stance & early stance & Hamstrings early stance early stance mid-late stance mid-late stance late stance & early & mid-late early & mid-late Rectus Femoris all of stance early swing stance stance early & late Vasti Group early stance early stance early stance stance Gastrocnemius mid-late stance mid-late stance mid-late stance mid-late stance Soleus late stance mid-late stance mid-late stance mid-late stance early stance & early stance & early stance & early stance & Tibialis Anterior mid-late stance mid-late stance mid-late stance early swing

From Table 15, it can be seen the gluteus maximus muscle produces force at the same time during stance for healthy pre-teenagers, adolescents, young adults, and elderly adults.

Similarly, the gastrocnemius muscle produces its peak force in mid-late stance for all subject populations in Table 15. One muscle that may change function with age is the soleus muscle.

In the younger subject populations, the soleus muscle produces force starting in the middle part of stance continuing through to the end of stance, whereas in the elderly subject population, the soleus muscle only produces force in the late part of stance. Similarly, the rectus femoris muscle produces force in the early and mid-late parts of stance in the younger

patient populations while only producing force in the late part of stance in the elderly population. All other major muscle groups (hamstrings, vasti, and tibialis anterior) produce force in approximately the same time periods during stance in all subject populations.

In addition to when the major muscles in the lower extremity produce force, the amount of force that the major muscle groups in the lower extremity produce during gait can be compared. Comparing the Static Optimization muscle force results from Figure 7 and the

Computed Muscle Control (CMC) muscle force results from the healthy, young adult population [28], the total force production of the lower extremity muscles in the two populations follow similar trends. There is a peak in force production in early stance and a higher peak in mid-late stance. The healthy, young adults produced a higher peak force in early stance but approximately the same amount of force in mid-late stance. The healthy, elderly adults also produced less force during swing than the healthy, young adults.

Table 16 contains the peak Static Optimization forces for the seven major muscle groups in the lower extremity for the healthy, elderly adults and the approximate peak

Computed Muscle Control forces for the healthy, adolescent population [27] and the healthy, young adult population [28]. The gluteus maximus in the healthy, elderly population produced more force in early stance than the two younger populations. A similar trend was seen in the gastrocnemius and the hamstrings, which was composed of the biceps femoris long head and short head, semimembranosus, and semitendinosus. The rectus femoris, vasti, and tibialis anterior all produced nearly the same amount of force at their peak in all three populations; however, as stated earlier, the rectus femoris in the healthy, elderly subjects peaked in the swing phase rather than the stance phase like the two younger populations.

Table 16: Approximate peak forces of major muscle groups in lower extremity during stance for various populations

Approximate Peak Force [N] Healthy, Healthy, Healthy, Muscle Adolescents Young Adults Elderly Adults [27] [28] Average Age [yrs] 68.1 ± 4.1 16 ± 1 21.9 ± 2.3 Free Speed [m/s] 1.51 ± 0.09 1.08 ± 0.16 1.32 ± 0.13 GlutMax 562.5 220 380 Hams 1838.2 900 1350 RF 356.4 315 315 Vasti 670.4 305 760 Gastroc 2103.0 900 1500 Sol 882.1 1500 1700 TA 401.3 375 505

One notable difference in the healthy, elderly population is the soleus muscle. The soleus muscle in the two younger populations produced approximately the same amount of peak force in mid-late stance; whereas the soleus muscle in the healthy, elderly population produced roughly half of the soleus force in the younger populations in late stance. The soleus and gastrocnemius are responsible for plantarflexion at the ankle joint. In the healthy, elderly population, we found an increase in the gastrocnemius force but a decrease in the soleus force when compared to younger populations. Additionally, we found that the ankle joint in the elderly population was more plantarflexed than other populations (Figure 4).

These changes in lower extremity force production during stance likely come from an increase in subject age and changes in gait kinematics associated with gait speed.

Unfortunately, there are no studies to date that have looked at muscle forces in either an age- matched population or gait speed-matched population so that direct relationships may be discussed between gait kinematics, kinetics, and muscle forces and subject age and walking speed.

It becomes difficult to make direct comparisons between muscle force results from the subject populations presented in Table 15 and Table 16 due to the different models and simulations that were used. Liu et al. [2], van der Krogt et al. [27], and Thompson et al. [28], used a generic musculoskeletal model within OpenSim with 23 degrees of freedom and 92 musculotendon actuators whereas we used a model with 20 degrees of freedom and 86 musculotendon actuators to study the elderly patient population. Additionally, Liu et al. [2], van der Krogt et al. [27], and Thompson et al. [28], used Computed Muscle Control (CMC) to determine muscle forces and we used Static Optimization. While Lin et al. [40] found that

CMC and Static Optimization produce nearly equivalent results for gait, the differences in generic musculoskeletal model, simulation type, and gait speed make direct comparisons difficult. However, we have found definitive differences in gait kinematics, kinetics, and muscle forces in our healthy, elderly population.

4.2. Simulated Atrophy of Quadriceps Femoris

When the quadriceps femoris muscle, including the rectus femoris and vastus lateralis, medialis, and intermedius, were atrophied to 70% and 40% of its initial strength, several different compensatory strategies arose. As expected, the quadriceps muscles decreased in force output in response to the lowered peak isometric strength. However, in order to produce force, the quadriceps were activated more. Of the four quadriceps muscles, the rectus femoris saw the largest deficits in force production. The rectus femoris is the only bi-articular muscle in the quadriceps and acts as a knee extensor and hip flexor.

The other lower extremity muscle that exhibited a compensatory strategy for weakened quadriceps was the gluteus maximus. The gluteus maximus increased its peak force in early stance by 10.1% when the quadriceps were atrophied to 40% of their original strength. The gluteus maximus is a powerful extensor of the hip and also works synergistically with the quadriceps to maintain an upright body position. Therefore, if the quadriceps are weakened and cannot produce as much force in early stance, it would follow that the gluteus maximus would compensate and help the body maintain its upright position.

Two other studies have looked at simulated muscle weakness in the lower extremities during gait, one by van der Krogt et al. [27] and one by Thompson et al. [28]. Van der Krogt et al. looked at compensatory strategies of lower extremity muscles during gait in response to generalized muscle weakness and weakness in particular muscle groups in healthy, adolescents (16 ± 1yrs, 1.08 ± 0.16m/s). Thompson et al. [28] looked at compensatory strategies of lower extremity muscles during gait in response to quadriceps weakness in healthy, young adults (21.9 ± 2.3yrs, 1.32 ± 0.13m/s).

Similar to our findings, van der Krogt et al. found that as the vasti were atrophied, the activation of each of the vasti increased and gluteus maximus force increased in early stance while the force from the vasti decreased in early stance. Additionally, biceps femoris short head and semitendinosus saw decreases in force during late stance and early swing and the gastrocnemius, tibialis anterior, and adductor magnus all exhibited slight decreases in force output.

Additionally, when the rectus femoris was weakened in the van der Krogt et al. study, biceps femoris short head and semitendinosus saw decreases in force during late stance and early swing and the gastrocnemius and soleus all exhibited slight decreases in force output. 77

Thompson et al. [28] found that as the quadriceps were atrophied to 40% of the initial strength, the gluteus maximus increased its force production in early stance by 17.1% and the soleus increased its force by 7.7%. Our findings differ from those of Thompson et al. because we did not find that the soleus muscle produced more force in response to quadriceps weakness in elderly gait.

An important thing to note when comparing our findings to the findings of the van der Krogt et al. study and the Thompson et al. study is the difference between the subject populations. However, despite these differences, both studies agree with our finding that the gluteus maximus is a compensatory muscle for quadriceps weakness.

4.3. Simulated Atrophy of Plantarflexors

As the primary plantarflexors, both heads of the gastrocnemius and the soleus, were progressively atrophied, a complicated chain reaction of compensatory strategies was started in the lower extremity. When the peak isometric strength of both heads of the gastrocnemius and the soleus were reduced, the gastrocnemius produced less force, as expected, and the soleus muscle produced more force. This compensation strategy by the soleus was not expected. However, it is reasonable that the soleus would increase its force to produce more plantarflexion in late stance to prepare for toe-off because the gastrocnemius cannot produce as high of a plantarflexion moment at full strength.

When the gastrocnemius and soleus were atrophied, the primary sources of plantarflexion in mid-late stance were weakened. In response, the minor ankle plantarflexors increased their force production to provide sufficient torque to plantarflex the ankle in

preparation of toe-off. The minor ankle plantarflexors were one of the primary compensators for gastrocnemius and soleus atrophy as expected. However, the tibialis anterior and other minor ankle dorsiflexors exhibited decreased force production in response to plantarflexor atrophy. Therefore, it is reasonable to assume that the soleus and minor plantarflexors could not produce a plantarflexion moment in mid-late stance equivalent to that of the gastrocnemius at full strength. In order to offset the reduced plantarflexion moment, the dorsiflexion moment would have to be decreased so that the model would track the same kinematics and kinetics as the full strength model.

The effects of the plantarflexor weakness did not end at the ankle joint. Because the gastrocnemius is a bi-articular muscle and acts to flex the knee in mid-late stance, compensatory strategies were found in several thigh and hip muscle groups. To compensate for the lack of force produced by the gastrocnemius, the hamstrings and minor knee flexors

(sartorius and gracilis) increased their force production to contribute to knee flexion and the rectus femoris decreased its force production that opposed knee flexion. Similar to the ankle joint, the amount that the gastrocnemius contributed to the knee flexion moment in mid-late stance could not be entirely compensated for by the hamstrings and minor knee flexors.

Therefore, the rectus femoris decreased its force production in mid-late stance. Of the quadriceps, the rectus femoris was the only muscle that exhibited any compensatory strategy.

The vasti muscles did not experience decreased force production in mid-late stance because the vasti are not active in mid-late stance.

Because the rectus femoris is not only a knee extensor but also a hip flexor, as the force produced by the rectus femoris decreased, another group of muscles needed to increase their force production to supply the needed hip flexion in mid-late stance. For this reason, the 79

major hip flexors, the iliacus and psoas, increased their force production to compensate for the decrease in rectus femoris force.

In summary, the minor ankle plantarflexors, minor ankle dorsiflexors, and tibialis anterior were the primary compensators for the weakened gastrocnemius and soleus muscles.

The minor ankle plantarflexors produced more force to compensate for the weakened gastrocnemius and soleus and, in turn, the minor ankle dorsiflexors and tibialis anterior produced less force opposing the plantarflexors. Because the gastrocnemius is a bi-articular muscle, muscles that span the knee and hip joints were also affected by the weakened gastrocnemius. Muscles exhibited compensatory strategies only during mid-late stance, when the gastrocnemius and soleus are active. The weakness in the major plantarflexors did not affect muscles that are active in early stance.

Our results can be compared to those from van der Krogt et al. [27] that looked at compensatory strategies in healthy, adolescents. Van der Krogt et al. weakened the gastrocnemius and soleus separately; therefore, some of the compensatory strategies of muscles that span the knee and hip in response to weakened plantarflexors differ from our results. Despite these slight differences, our results are very similar to those of van der Krogt et al. In both populations, the minor ankle plantarflexors produced more force and the minor ankle dorsiflexors produced less force. When van der Krogt et al. weakened the gastrocnemius, they found that the hamstrings and sartorius produced more force, the rectus femoris and the vasti produced less force, and the iliopsoas produced more force. Our findings agree with van der Krogt et al. that lower extremity muscle function is very sensitive to plantarflexor weakness.

One of the major differences between the two populations is that van der Krogt et al. found that the gluteus medius and minimus produced more force. Additionally, the vasti exhibited compensatory strategies. This is in line with our simulated quadriceps femoris results. We have found that the quadriceps are active at different times in the gait cycle than the younger subjects from van der Krogt et al., Liu et al. [2], and Thompson et al. [28].

Therefore it follows that we would see slightly different behavior from the vasti in response to muscle weakness.

4.4. Simulated Atrophy of Gluteus Maximus, Medius, and Minimus

Similar to the simulated plantarflexor weakness results, weakness in the gluteus maximus, medius, and minimus muscles produced complex compensatory strategies in lower extremity functional muscle groups that span the hip, knee, and ankle joints.

The gluteus muscles function as external rotators and abductors of the hip joint.

Therefore, as the gluteus muscles produced less force due to atrophy, it follows that the hip external rotators would produce more force to compensate for the weakness. Our results support this because the hip external rotators as a group produced more force. Similarly, as the primary hip abductors, the gluteus muscles, produced less force, we saw that the hip adductors produced less force to maintain a balanced moment about the hip joint.

The primary function of the gluteus muscles is hip extension. Therefore, as the force produced by the gluteus muscles decreased, the other hip extensors, the hamstrings, produced more force to compensate. We also saw that the iliopsoas, the chief hip flexors, produced less force in response to gluteus weakness. This is likely because it was cheaper for the optimizer

to reduce the flexors force than activate the hamstrings more to maintain the original flexion moment about the hip. As the hamstrings produced more force, which also function to flex the knee, the knee extensors, the quadriceps, produced more force to maintain the original flexion moment about the knee.

We also saw that both the ankle plantarflexors and dorsiflexors produced more force as the gluteus muscles were atrophied. The plantarflexors and dorsiflexors are antagonists and if one muscle group produced more force, the other muscle group would have to produce more force to maintain a balanced flexion moment about the ankle.

Our compensation results agree with what should physiologically happen when the gluteus muscles are weakened. Our results have also shown that gluteus muscle weakness elicits a complex chain of compensation strategies in the lower extremity. Not only did gluteus atrophy affect the hip, knee, and ankle joints, but it also elicited compensation strategies throughout the entire gait cycle. This is because the gluteus muscles are active throughout stance and swing. Additionally, certain muscles were required to produce more force in certain portions of the gait cycle and less in others, namely the hamstrings.

Therefore, a higher level of neural control would be required to implement these compensation strategies in order to produce a normal gait pattern.

Our gluteus atrophy results can be compared to those from the van der Krogt et al.

[27] study; however, van der Krogt et al. weakened the gluteus maximus and the gluteus medius individually and did not weaken the gluteus minimus. Therefore, a direct comparison of our results with theirs cannot be made. Van der Krogt et al. found that gait was very robust to gluteus maximus weakness and very sensitive to gluteus medius weakness. We have found

that weakness in all gluteus muscles elicits complex compensation strategies from all functional muscle groups throughout the entire gait cycle.

When van der Krogt et al. weakened the gluteus maximus, they found that the gluteus medius was the primary compensator. In addition, gluteus minimus, the hamstrings, hip adductors, vasti, quadratus femori, and piriformis were minor compensators for gluteus maximus weakness and all produced more force. Although we cannot make a direct comparison, we found that the hamstrings, vasti, and piriformis produced more force in response to gluteus muscle weakness.

When van der Krogt et al. weakened the gluteus medius, the hamstrings, tensor fasciae latae, sartorius, gastrocnemius, and rectus femoris all produced more force and the psoas and soleus produced less force to compensate for the weakness. Our results agree with those of van der Krogt et al. This gives further confidence to the results from our simulations.

Chapter 5: Conclusions

5.1. Major Findings

Muscle weakness and atrophy has been associated with both aging [5-9] and knee osteoarthritis [17-23]. One of the major limitations associated with muscle weakness in both the elderly and osteoarthritic populations is difficulty walking. It is known that elderly adults have altered gait kinematics and kinetics but it is unknown how lower extremity muscle weakness contributes. Additionally, knee osteoarthritis becomes more common with age, which leads to a larger percentage of the population that has increased difficulty walking and performing other activities of daily living. Therefore, if the scientific and clinical community can gain a better understanding of lower extremity muscle weakness in the elderly population, future work can develop training programs that seek to strengthen certain lower extremity muscles so that normal gait be maintained.

In this study, we analyzed the gait of eight healthy, elderly adults by looking at the joint kinematics, kinetics, and muscle forces produced during stance and swing. We then compared our results with those of other studies that have analyzed gait kinematics and kinetics in both young and elderly healthy populations and studies that have analyzed muscle forces in young populations. We found that our joint kinematics and kinetics results compare well with other healthy, elderly gait published results [10]. However, there were differences

in the average free speed between our elderly population and that of Kerrigan et al. [10], which makes a direct comparison more difficult as Liu et al. [2] found that walking speed affects gait kinematics and kinetics. When comparing our gait results to those of speed- matched younger populations, the elderly subjects’ hip, knee, and ankle joints were more extended. Also, we found that the elderly subjects in our study reached higher peak flexion or extension moments during stance. Therefore, we have found that the healthy, elderly population in our study walked differently than younger populations.

Our analysis of muscle forces during gait in healthy, elderly subjects lead to several key findings, as well. We found that that the quadriceps in elderly subjects are active at different points during the gait cycle when compared to younger populations. We found that the rectus femoris was primarily active during swing and the vasti were primarily active during stance and that the gastrocnemius was favored more than the soleus, whereas the opposite is true in younger populations. Because we found differences in the gait kinematics and kinetics between young and elderly populations, it follows that the lower extremity muscles would behave differently in elderly adults during gait.

The next phase of our analysis was to determine the effect of lower extremity muscle weakness on other lower extremity muscles while maintaining normal gait kinematics and kinetics. As the quadriceps were systematically weakened, we found that the gluteus maximus was the primary compensator during stance for weakness in the rectus femoris and the vasti. The rectus femoris produced less force during swing and the vasti produced less force during stance. Overall, elderly gait was relatively insensitive to quadriceps weakness.

As the plantarflexors were systematically weakened, the gastrocnemius produced less force while the soleus produced more force. Other muscle groups in the lower extremity also 85

increased or decreased their force production during late stance, when the plantarflexors produce their peak force. The compensatory mechanisms of the lower extremity in response to plantarflexor weakness were closely related to the primary action of each muscle group.

Overall, elderly gait was very sensitive to plantarflexor weakness. As the gluteus muscles were systematically weakened, a more dynamic set of compensatory mechanisms was exhibited because the gluteus muscles are active during both stance and swing. Therefore, certain muscle groups produced more force (or less) during certain parts of gait while producing the same amount of force in others. Therefore, we hypothesize that more neurological control is required to respond to gluteus weakness. Overall, elderly gait was sensitive to gluteus weakness, especially during early stance. A summary of the compensation strategies in response to quadriceps, plantarflexor, and gluteus weakness can be found below in Table 17.

Table 17: Summary of muscular compensations that occur with weakness of different muscle groups

Weak muscle group Compensations Force produced Muscles that Muscles that by the weak produced more force produced less force muscle/muscle group itself RF Down GMAX QUADS VAS Down ILPS, GRA, SAR, RF, TA, PERT, SOL Up TFL, BFL, BFS, SMM, EXTD, EXTH PF SMT, FLD, FLH, GAS Down PERB, PERL, TP GEM, PIRI, ADDB, ILPS, QF (sw), GMAX Down ADDM, SAR, RF, ADDL, PEC, GRA, VAS, TFL, BFS, BFL, SMT GLUT GMED Down SMM, GAS, SOL, FLD, FLH, PERB, GMIN Down PERL, TP, TA, PERT, EXTD, EXTH

Abbreviations: QUADS: quadriceps femoris, RF: rectus femoris, VAS: vastus lateralis, intermedius, and medialis, GMAX: gluteus maximus, PF: plantarflexors, SOL: soleus, GAS: lateral and medial heads of the gastrocnemius, ILPS: iliopsoas (iliacus and psoas), GRA: gracilis, SAR: sartorius, TFL: tensor fasciae latae, BFL: biceps femoris long head, BFS: biceps femoris short head, SMM: semimembranosus, SMT: semitendinosus, FLD: flexor digitorum, FLH: flexor hallucis, PERB: peroneus brevis, PERL: peroneus longus, TP: tibialis posterior, TA: tibialis anterior, PERT: peroneus tertius, EXTD: extensor digitorum, EXTH: extensor hallucis, GLUT: gluteus muscles, GMAX: gluteus maximus, GMED: gluteus medius, GMIN: gluteus minimus, GEM: gemellus, PIRI: piriformis, ADDB: adductor brevis, ADDM: adductor magnus, QF: quadratus femoris, ADDL: adductor longus, PEC: pectineus, (sw): only in swing.

Our compensation strategies largely agree with those found by van der Krogt et al.

[27] and Thompson et al. [28], who studied compensation strategies in younger populations.

Both Thompson et al. and van der Krogt et al. found that the soleus muscle was a compensator for quadriceps weakness, whereas we found that the soleus did not alter its force production. However, we found very similar compensation strategies for plantarflexor and gluteus muscle weakness when compared to van der Krogt et al. Additionally, van der

Krogt et al. found that young gait is very sensitive to plantarflexor and gluteus medius weakness, which agrees with our findings. 87

5.2. Contributions

No other study has examined the role of individual lower extremity muscles during gait in healthy, elderly subjects. Additionally, the compensation strategies of lower extremity muscles in response to functional muscle weakness have not been studied in an elderly population. Our findings have identified key differences between healthy elderly and healthy young gait as well as identify when muscles produce force during gait in healthy, elderly subjects. We also investigated how lower extremity muscles compensate for functional muscle group weakness during gait in an elderly population. We have shown that elderly gait is robust against quadriceps weakness and that elderly gait is sensitive to plantarflexor and gluteus weakness. These results are an important first step in understanding how elderly adults with muscle weakness from either aging or knee osteoarthritis can regain normal gait in everyday life.

5.3. Future Work

In order to gain a better understanding of the complex relationship between knee osteoarthritis, lower extremity muscle weakness, and lower extremity muscle function during gait in elderly subjects, future work should be completed in this area. Previous studies [5, 43] have shown that not only do the quadriceps muscle experience muscle atrophy in patients with osteoarthritis, but patients also experience activation failure. Future work should examine the compensatory strategies of lower extremity muscles in response to activation failure in the quadriceps. This work might show that other muscles, in addition to or instead

of the gluteus maximus, increase their force production in response to quadriceps activation failure.

This thesis has shown how lower extremity muscles contribute to force production during gait in healthy, elderly subjects; however, it remains unknown how the lower extremity muscles contribute to vertical support and forward progression during gait [3, 44,

45]. Therefore, future work should utilize the Induced Acceleration Analysis (IAA) within

OpenSim to determine the contributions of lower extremity muscles to vertical and horizontal acceleration of the body mass center during gait in healthy, elderly subjects.

To verify that the results of these weakening simulations represent what is being seen in elderly subjects that exhibit quadriceps weakness, a study should look at the contributions of lower extremity muscles to vertical support and forward progression in a population of elderly patients that have been diagnosed with osteoarthritis and quadriceps weakness. This would verify that the static optimization and induced acceleration analyses accurately predict the mechanisms of quadriceps weakness compensation strategies in older adults.

Because the end goal of this work is to inform physical therapy and slow the effects of quadriceps weakness, forward dynamic simulations should be run that strengthen certain lower extremity muscles. From the results of this work and the work that verifies the compensatory lower extremity muscles in elderly subjects with quadriceps weakness, the muscles that are identified that compensate for weak quadriceps should be strengthened in forward dynamic simulations. This would help verify that the predictions from the inverse dynamic simulations would hold true in the target population. From the results of this work, physical therapy programs could be developed that would strengthen the identified compensatory lower extremity muscles to help treat quadriceps weakness in elderly subjects. 89

This work would extend to not only patients with osteoarthritis and quadriceps weakness, but also to elderly subjects that are experiencing muscle atrophy from the natural aging process.

5.4. Summary

We have determined when lower extremity muscles produce force during gait in elderly subjects and how lower extremity muscles compensate for functional muscle group weakness characteristic of aging and knee osteoarthritis. Our results suggest that the gluteus maximus is primary compensator for quadriceps weakness, which is an important implication for the osteoarthritis community. However, further work is required to understand how lower extremity muscles compensate for activation failure of the quadriceps, which has also been shown to be positively correlated with knee osteoarthritis. We have also found that elderly gait is sensitive to plantarflexor and gluteus muscle weakness. Our work is an important first step in further understanding muscle weakness in the elderly population and the effects it has on activities of daily living.

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Appendix A: Supplemental Information

Simulated Atrophy of Plantarflexors

Table 18: Individual muscle force changes in response to plantarflexor atrophy

Plantarflexor Atrophy Full Strength 70% Strength 40% Strength Change Change Muscle Original Gait Cycle 70% Peak from % change 40% Peak from % change Group Muscle Normal Normal LG 574.1 42 470.4 -103.7 -18.1% 283.2 -290.9 -50.7% Gastroc MG 1533 44.5 1136 -397 -25.9% 660.4 -872.6 -56.9% SOL SOL 882.1 52.5 946.1 64 7.3% 978.5 96.4 10.9% Iliacus 1101 45 1111 10 0.9% 1145 44 4.0% Iliopsoas Psoas 1160 45.5 1170 10 0.9% 1208 48 4.1% Knee Grac 46.8 50 54.9 8.1 17.3% 73.29 26.49 56.6% Flexors Sar 106.8 49 118.7 11.9 11.1% 141 34.2 32.0% RF 133.3 51 97.58 -35.72 -26.8% 79.95 -53.35 -40.0% Knee Ext TFL 192.4 46.5 210.5 18.1 9.4% 211.8 19.4 10.1% BFLH 277.2 40 287.1 9.9 3.6% 318.7 41.5 15.0% BFSH 648.1 41 680.3 32.2 5.0% 729.8 81.7 12.6% Hams SM 313 38.5 338.7 25.7 8.2% 391.4 78.4 25.0% ST 235.7 40.5 261 25.3 10.7% 308.8 73.1 31.0% TA TA 401.3 40 281.1 -120.2 -30.0% 32.77 -368.53 -91.8% FlexDig 24.99 56 32.02 7.03 28.1% 78.66 53.67 214.8% FlexHal 66.72 55.5 92.79 26.07 39.1% 143.1 76.38 114.5% Ankle PF PerBrev 139.3 54.5 176.8 37.5 26.9% 254.6 115.3 82.8% PerLong 388.5 53 520.2 131.7 33.9% 800.2 411.7 106.0% TP 301.4 54.5 495.9 194.5 64.5% 769.3 467.9 155.2% PerTert 92.26 40 20.05 -72.21 -78.3% 1.527 -90.733 -98.3% Ankle DF ExtDig 278.4 40.5 156 -122.4 -44.0% 9.097 -269.303 -96.7% ExtHal 69.19 40 13.44 -55.75 -80.6% 1.246 -67.944 -98.2%

Figure 41: Lateral head of the gastrocnemius force as a function of plantarflexor weakness, which decreased as the plantarflexors were weakened

Figure 42: Medial head of the gastrocnemius as a function of plantarflexor weakness, which decreased as the plantarflexors were weakened 95

Figure 43: Soleus force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened

Figure 44: Iliacus force as a function of plantarflexor weakness, which increased slightly during stance as the plantarflexors were weakened 96

Figure 45: Psoas force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened

Figure 46: Gracilis force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened 97

Figure 47: Sartorius force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened

Figure 48: Rectus femoris force as a function of plantarflexor weakness, which decreased during stance as the plantarflexors were weakened 98

Figure 49: Tensor fasciae latae force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened

Figure 50: Biceps femoris long head force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened 99

Figure 51: Biceps femoris short head force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened

Figure 52: Semimembranosus force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened 100

Figure 53: Semitendinosus force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened

Figure 54: Tibialis anterior force as a function of plantarflexor weakness, which decreased as the plantarflexors were weakened 101

Figure 55: Flexor digitorum force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened

Figure 56: Flexor hallucis force as a function of plantarflexor weakness, which increased as the plantarflexors were weakened 102

Figure 57: Peroneus brevis force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened

Figure 58: Peroneus longus force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened 103

Figure 59: Tibialis posterior force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened

Figure 60: Peroneus tertius force as a function of plantarflexor weakness, which decreased in late stance as the plantarflexors were weakened 104

Figure 61: Extensor digitorum force as a function of plantarflexor weakness, which decreased in late stance as the plantarflexors were weakened

Figure 62: Extensor hallucis force as a function of plantarflexor weakness, which decreased in late stance as the plantarflexors were weakened 105

Simulated Atrophy of Gluteus Muscles

Table 19: Individual muscle force changes in response to gluteus atrophy

Gluteus Atrophy Full Strength 70% Strength 40% Strength Change Change Original 70% Peak 40% Peak Muscle Gait Cycle from % change from % change [N] [N] [N] Group Muscle Normal Normal GMAX 564.4 11.5 434.2 -130.2 -23.1% 357.2 -207.2 -36.7% GMED 1571 15.5 1362 -209 -13.3% 903.8 -667.2 -42.5% GLUTS GMED 1050 40.5 906.6 -143.4 -13.7% 636 -414 -39.4% GMIN 422.7 14.5 418.9 -3.8 -0.9% 359.3 -63.4 -15.0% GMIN 618.3 43 484.6 -133.7 -21.6% 302.7 -315.6 -51.0% Iliacus 1101 45 1098 -3 -0.3% 1097 -4 -0.4% Iliacus 227.3 90.5 194.1 -33.2 -14.6% 133.3 -94 -41.4% Iliopsoas Psoas 1160 45.5 1142 -18 -1.6% 1104 -56 -4.8% Psoas 247.5 91 227.4 -20.1 -8.1% 156.7 -90.8 -36.7% QuadFem 90.64 41.5 57.8 -32.84 -36.2% 74.97 -15.67 -17.3% Hip Gem 3.5 21.5 10.79 7.29 208.3% 15.22 11.72 334.9% External Gem 5.491 56.5 6.704 1.213 22.1% 9.197 3.706 67.5% Rotators Peri 125.5 9 245.1 119.6 95.3% 433.6 308.1 245.5% Peri 104.5 90.5 152.6 48.1 46.0% 236.9 132.4 126.7% AddLong 115.6 58.5 111.8 -3.8 -3.3% 98.08 -17.52 -15.2% AddBrev 53.55 59.5 55.4 1.85 3.5% 54.77 1.22 2.3% Hip AddMag 70.84 59.5 80.33 9.49 13.4% 97.59 26.75 37.8% Adductors Pect 55.5 44 59.81 4.31 7.8% 14.43 -41.07 -74.0% Grac 46.8 50 23.53 -23.27 -49.7% 18.82 -27.98 -59.8% Sartorius Sar 106.8 49 131.5 24.7 23.1% 144.7 37.9 35.5% RF 82.51 21 132.6 50.09 60.7% 273.1 190.59 231.0% Knee VL 330.4 13 388.6 58.2 17.6% 452.7 122.3 37.0% Extensors VI 194.4 13 228.3 33.9 17.4% 266.4 72 37.0% VM 151.8 13.5 179.1 27.3 18.0% 208.7 56.9 37.5% TFL TFL 192.4 46.5 221.2 28.8 15.0% 250.2 57.8 30.0% BFLH 277.2 40 254.3 -22.9 -8.3% 207.8 -69.4 -25.0% BFSH 648.1 41 663.8 15.7 2.4% 732.7 84.6 13.1% Hams SM 247.2 15 357.5 110.3 44.6% 581.4 334.2 135.2% ST 235.7 40.5 217.6 -18.1 -7.7% 205.1 -30.6 -13.0% LG 574.3 41.5 601 26.7 4.6% 698.5 124.2 21.6% MG 1533 44.5 1543 10 0.7% 1557 24 1.6% SOL 882.1 52.5 876.3 -5.8 -0.7% 864.4 -17.7 -2.0% SOL 273.7 19 278.7 5 1.8% 299.4 25.7 9.4% Ankle PF FlexDig 25 56 25 0 0.0% 25 0 0.0% FlexHal 66.7 55.5 66.7 0 0.0% 66.7 0 0.0% PerBrev 111.5 44 113.2 1.7 1.5% 128.6 17.1 15.3% PerLong 388.5 53 388.5 0 0.0% 387.6 -0.9 -0.2% TP 301.2 554.5 301.2 0 0.0% 301.2 0 0.0% TA 401.3 40 412.8 11.5 2.9% 547.1 145.8 36.3% PerTert 92.26 40 96.42 4.16 4.5% 105.3 13.04 14.1% Ankle DF ExtDig 278.4 40.5 284.7 6.3 2.3% 356.4 78 28.0% ExtHal 69.19 40 72.2 3.01 4.4% 79.12 9.93 14.4% 106