The Effects of Simulated Muscle Weakness on Lower Extremity Muscle Function during. Gait in Healthy, Older Subjects. Thesis

Transcription

1 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 By Amanda Nicole Strube, B.S. Graduate Program in Mechanical Engineering The Ohio State University 2012 Thesis Committee: Robert A. Siston, Advisor Laura C. Schmitt

2 Copyright by Amanda Nicole Strube 2012

3 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

4 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

5 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

6 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

7 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

8 Vita June 2007 Mount Notre Dame High School B.S. Mechanical Engineering, The Ohio State University 2011 to present...first Year Engineering Graduate Teaching Associate Major Field: Mechanical Engineering Fields of Study vii

9 Table of Contents Abstract... ii Acknowledgements... v Vita... vii Table of Contents... viii List of Tables... x List of Figures... xii Chapter 1: Introduction Focus of Thesis Significance of Research Overview of Thesis Chapter 2: Methods Data Collection Data Analysis Subject Specific Simulations Lower Extremity Muscle Weakness Chapter 3: Results Full Strength Model Simulated Atrophy of Quadriceps Femoris Simulated Atrophy of Plantarflexors Simulated Atrophy of Gluteus Maximus, Medius, and Minimus Chapter 4: Discussion Full Strength Model Simulated Atrophy of Quadriceps Femoris Simulated Atrophy of Plantarflexors Simulated Atrophy of Gluteus Maximus, Medius, and Minimus Chapter 5: Conclusions Major Findings Contributions viii

10 5.3. Future Work Summary References Appendix A: Supplemental Information Simulated Atrophy of Plantarflexors Simulated Atrophy of Gluteus Muscles ix

11 List of Tables Table 1: Subject anthropometric data Table 2: Quadriceps femoris muscle atrophy Table 3: Plantarflexor muscle atrophy Table 4: Gluteus muscle atrophy Table 5: Peak average forces from the seven major muscle groups obtained during Static Optimization Table 6: Muscle force changes in response to quadriceps femoris atrophy Table 7: Muscle group force changes in response to plantarflexor atrophy Table 8: Muscle group force changes in response to gluteus atrophy in early stance Table 9: Muscle group force changes in response to gluteus atrophy in late stance Table 10: Muscle group force changes in response to gluteus atrophy in swing Table 11: Comparison of gait kinematics across various subject populations 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) 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] x

12 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] Table 15: Comparison of muscle force timing during stance in various subject populations Table 16: Approximate peak forces of major muscle groups in lower extremity during stance for various populations Table 17: Summary of muscular compensations that occur with weakness of different muscle groups Table 18: Individual muscle force changes in response to plantarflexor atrophy Table 19: Individual muscle force changes in response to gluteus atrophy xi

13 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 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 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) Figure 5: Inverse dynamics joint moments averaged across all eight subjects and normalized to body weight and height; Positive: Extension (Plantarflexion), Negative: Flexion (Dorsiflexion) Figure 6: Static optimization muscle forces for full strength model averaged across all eight subjects Figure 7: Individual muscle forces from seven major muscle groups in the lower extremity from the full strength model, averaged across all eight subjects xii

14 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 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 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 Figure 13: Gluteus maximus force as a function of quadriceps femoris atrophy, which increased as the quadriceps were weakened Figure 14: Gluteus maximus activation as a function of quadriceps femoris atrophy, which increased as the quadriceps were weakened 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 xiii

15 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 Figure 19: Iliopsoas (Iliacus and psoas) force as a function of plantarflexor weakness, which increased slightly in late stance as the plantarflexors were weakened 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 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 Figure 23: Hamstrings force as a function of plantarflexor weakness, which increased in late stance as the plantarflexors were weakened Figure 24: Tibialis anterior force as a function of plantarflexor weakness, which decreased in late stance and swing as the plantarflexors were weakened 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 xiv

16 Figure 26: Minor ankle dorsiflexors force as a function of plantarflexor weakness, which decreased in late stance and swing as the plantarflexors were weakened 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 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 Figure 31: Iliopsoas force as a function of gluteus muscle weakness, which decreased in late stance and swing as the gluteus muscles were weakened 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 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 Figure 34: Sartorius force as a function of gluteus weakness, which increased in both stance and swing as the gluteus muscles were weakened 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 xv

17 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 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 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 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 = 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 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 xvi

18 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 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 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 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 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 xvii

19 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 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 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 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 xviii

20 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. 1

21 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 2

22 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]. 3

23 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 4

24 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. 5

25 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 6

26 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. 7

27 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 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. 8

28 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 reported difficulty walking, approximately 27% of people aged 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 9

29 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 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. 10

30 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. 11

31 Table 1: Subject anthropometric data Leg Length [m] Free Speed [m/s] Nondimensional Free Speed* Stride Length [m] Lower Extremity Tested (EMG) Subject Gender Age [years] Mass [kg] A141 F Right AS46 F Right BP40 M Left C139 F Right FA46 F Left J145 M Left J332 M Right KA32 F Right Average Standard Deviation *Free speed normalized by 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

32 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

33 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 , 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. 14

34 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 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 15

35 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 , 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 , 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 16

36 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 a m is the activation for muscle m: (1) 17

37 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] 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). 18

38 Table 2: Quadriceps femoris muscle atrophy Peak Isometric Force (N) Quadriceps 100% Strength 70% Strength 40% Strength Muscle (Normal) Rectus Femoris Vastus Lateralis Vastus Medialis Vastus Intermedius 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 Gastrocnemius Medial Head of Gastrocnemius Soleus 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

39 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 Gluteus Maximus Gluteus Maximus Gluteus Medius Gluteus Medius Gluteus Medius Gluteus Minimus Gluteus Minimus Gluteus Minimus

40 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. 21

41 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. 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 22

42 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 selfselected 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 ± 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 23

43 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) 24

44 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. 25

45 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

46 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 27

47 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 28

48 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 29

49 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 Stance Hams Stance RF Swing Vasti Stance Gastroc Stance Sol Stance TA 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. 30

50 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

51 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 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 Muscle Peak Force [N] Change from Change from % change Normal [N] Normal [N] % change RF % % Vasti % % GlutMax % % Hams % 0 0% Gastroc % 0 0% Sol % 0.4 0% TA % 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. 32

52 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 33

53 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. 34

54 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

55 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

56 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. 37

57 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 38

58 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 39

59 Functional Muscle Group Table 7: Muscle group force changes in response to plantarflexor atrophy Full Strength Peak Force [N] 70% Plantarflexor Strength Change from Normal [N] % change 40% Plantarflexor Strength Change from Normal [N] % change Gastroc % % Sol % % Iliopsoas % % Minor Knee Flexors % % RF % % Hams % % TA % % Minor Ankle Plantarflexors % % Minor Ankle 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. 40

60 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

61 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 42

62 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. 43

63 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 N of peak force. 44

64 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

65 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

66 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 47

67 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 48

68 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 49

69 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 50

70 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 51

71 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 Muscle Group Normal [N] Normal [N] % change GLUTS % % Iliopsoas Hip External Rotators % % Hip Adductors % % Sartorius % % Knee Extensors % % TFL % % Hams % % Ankle PF Ankle DF

72 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 Muscle Group Normal [N] Normal [N] % change GLUTS % % Iliopsoas % % Hip External Rotators % % Hip Adductors % % Sartorius % % Knee Extensors % % TFL % % Hams % % Ankle PF % % Ankle DF % % 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 Muscle Group Normal [N] Normal [N] % change GLUTS % % Iliopsoas % % Hip External Rotators % % Hip Adductors Sartorius % % Knee Extensors TFL % % Hams Ankle PF % % Ankle DF % % 53

73 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 54

74 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 55

75 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