USING BIOMECHANICS TO UNDERSTAND THE EFFECTS OF AGING AND EXERCISE ON OSTEOARTHRITIC AND HEALTHY THUMBS By Amber Rose Vocelle A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Physiology—Doctor of Philosophy 2019 ABSTRACT USING BIOMECHANICS TO UNDERSTAND THE EFFECTS OF AGING AND EXERCISE ON OSTEOARTHRITIC AND HEALTHY THUMBS By Amber Rose Vocelle Thumb carpometacarpal (CMC) motion, motion between the thumb and the wrist, is primarily responsible for our ability to grasp objects, open jars, and makes up 50% of arm function1,2. To improve hand function and the quality of life in persons with CMC osteoarthritis (OA), it is critical that we improve our ability to monitor changes in thumb function. The first step is to augment our methods to quantify the functional losses and used these methods to identify effects of treatment. The overarching goal of this work was to quantify the differences in motion and force abilities of persons with and without thumb CMC OA, and to measure the ability of hand stretching and strengthening exercises to increase thumb function in persons with CMC OA. Initial motion and force datasets were collected from young healthy persons (n = 23), older healthy persons (n = 11), and older persons with diagnosed CMC OA (n = 24). Following collection of initial datasets, study participants were given daily hand stretching exercises. After two weeks, motion and force datasets were collected a second time. Participants then were given daily strengthening hand exercises to be completed in addition to the daily stretching exercises. Following four weeks of combined stretching and strengthening exercises, participant motion and force datasets were collected a final time. For this work, there were three aims: Aim 1 was 1) to develop a method to measure isolated thumb forces in multiple directions, 2) to demonstrate this method on three populations, young healthy, older healthy, and older participants with OA of the CMC joint, and 3) to identify the effects of short-term hand exercises on thumb force production and grip strength in these three groups. Results showed that both thumb and grip forces improved in young healthy females, older healthy females and males, and older osteoarthritic females and males. In contrast, young healthy males increased their grip forces following exercise, but not their thumb strength. This suggests that thumb and strength forces are not interchangeable, and that thumb forces should be collected in a clinical setting to better track the effects of intervention (exercise, surgery, etc.) on thumb function. Aim 2 was 1) to determine differences in thumb motions across three groups of participants (i.e., young healthy, older healthy and those with CMC OA) and 2) to determine if multi-planar motions provided additional movement information in comparison to standard planar measures. Both standard thumb ranges of motion typically collected in clinic and new multi-planar motion datasets were obtained from all participants. Results indicated that motion capture was capable of detecting changes in CMC mobility due to the effects of aging and OA pathophysiology that were not detected using standard approaches, and use of multi-planar measurements have the potential to identify changes that are indicators of early stages of OA. Aim 3 was to identify changes in CMC motions as a result of a six-week exercise regimen on CMC OA participants as determined through two approaches 1) standard goniometry measures and 2) complex movements measured through the use of a motion capture system. We found that six weeks of exercise were sufficient to improve standard CMC ranges of motion using goniometry, and produce trends of improvement using motion capture. Copyright by AMBER ROSE VOCELLE 2019 TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES KEY TO ABBREVIATIONS CHAPTER 1: INTRODUCTION 1.1 Overview 1.2 Demographics 1.3 Ligaments and Muscles 1.4 CMC Joint Mechanics 1.5 Measures of Hand Function 1.6 Motion Capture and Modeling 1.7 Biomechanical Risk Factors 1.7.1 Joint laxity and instability 1.7.2 Joint malalignment 1.7.3 Joint stress 1.7.4 Muscle strength and imbalance 1.8 Pathophysiology 1.9 Treatment Options and Outcomes vi vii viii 1 1 3 5 6 8 10 10 10 11 12 12 13 15 CHAPTER 2: DETERMINING THE EFFECTS OF SHORT-TERM HAND EXERCISES ON THUMB FORCE GENERATION AND GRIP STRENGTH IN OSTEOARTHRITIC AND HEALTHY PERSONS 2.1 Abstract 2.2 Introduction 2.3 Methods 2.3.1 Participant testing 2.3.2 Exercise protocol 2.3.3 Thumb force measurement device 2.3.4 Hand grip dynamometry 2.3.5 Statistical Analysis 2.4 Results 2.4.1 Participants 2.4.2 Thumb force generation trends prior to intervention 2.4.3 Effects of exercise on thumb force generation 2.4.4 Grip strength trends prior to intervention 2.4.5 Effects of exercise on grip strength generation 2.5 Discussion 2.5.1 The relationship between thumb forces and grip strength 2.5.2 Thumb force generation trends prior to intervention 2.5.3 Effects of exercise on thumb force generation iii 18 18 18 20 20 21 23 24 24 25 25 25 27 29 29 30 31 32 32 2.5.4 Grip strength trends prior to intervention 2.5.5 Effects of exercise on grip strength generation 2.5.6 Limitations 2.6 Conclusions 33 33 33 34 CHAPTER 3: COMPLEX THUMB MOTIONS AND THEIR POTENTIAL IN IDENTIFYING MOTION CHANGES RELATED TO OSTEOARTHRITIS EARLIER THAN STANDARD MEASURES 3.1 Abstract 3.2 Introduction 3.3 Methods 3.3.1 Testing 3.3.2 Participants 3.3.3 Motion capture 3.3.4 VAS pain scores 3.3.5 FIHOA questionnaire 3.3.6 Statistical analysis 3.4 Results 3.4.1 Differences in standard clinical ranges of motion between groups 3.4.2 Multi-planar ranges of motion 3.4.3 VAS pain scores and FIHOA questionnaire responses 3.5 Discussion 3.5.1 Standard clinical ranges of motion 3.5.2 Multi-planar ranges of motion 3.5.3 VAS pain scores and FIHOA questionnaire responses 3.5.4 Limitations CHAPTER 4: THE EFFECTS OF SHORT-TERM HAND EXERCISES ON THUMB FUNCTION IN PARTICIPANTS WITH CARPOMETACARPAL OSTEOARTHRITIS 4.1 Abstract 4.2 Introduction 4.3 Methods 4.3.1 Testing 4.3.2 Exercise regimens 4.3.3 Participants 4.3.4 Standard ranges of motion measured clinically 4.3.5 Motion capture 4.3.6 Clinical questionnaires 4.3.7 Post-testing questionnaire 4.3.8 Statistics 4.4 Results 4.4.1 Standard clinical ranges of motion using goniometry and motion capture 4.4.2 Multi-planar ranges of motion 4.4.3 Clinical questionnaires 4.4.4 Post-testing questionnaires 4.5 Discussion 4.5.1 Standard clinical ranges of motion using goniometry and motion capture iv 35 35 36 38 38 38 38 44 44 44 45 45 46 49 49 49 51 53 53 55 55 56 57 57 58 61 61 62 66 66 67 67 67 68 70 70 70 71 4.5.2 Multi-planar ranges of motion 4.5.3 Questionnaire scores 4.5.4 Limitations 4.6 Conclusions CHAPTER 5: CONCLUSIONS APPENDICES APPENDIX A APPENDIX B BIBLIOGRAPHY 72 75 75 76 77 79 80 87 96 v LIST OF TABLES Table 3-1: Vectors used to calculate range of motion with vectors created from motion capture markers. 41 Table 3-2: Standard ranges of motion measures collected using motion capture. Table 3-3: Multi-planar ranges of motion. Table 3-4: Comparison of p-values between healthy groups and older groups for each motion tested, standard and multi-planar. Table 4-1: Stretching exercise regimen. Table 4-2: Strengthening exercise regimen. 45 47 48 59 60 Table 4-3: Vectors used to calculate ranges of motion with vectors created from motion capture markers. 64 Table 4-4: Comparison of goniometry and motion capture measurement of CMC ranges of motion prior to exercise. Table 4-5: The effect of exercise on multi-planar motions. 68 69 vi LIST OF FIGURES Figure 1-1: Muscles and tendons that play a role in thumb motion and stability. Figure 1-2: Dorsal view of hand anatomy. Figure 1-3: Directions of thumb movement. Figure 1-4: Goniometer example. Figure 2-1: Hand exercise regimen. Figure 2-2: Computer model of device adjustability. Figure 2-3: Load cell apparatus. Figure 2-4: Female thumb force application. Figure 2-5: Male thumb force application. Figure 3-1: Motion capture marker placement. Figure 3-2: Standard range of motions tested in a clinical setting and the associated angles measured using motion capture. Figure 3-3: Multi-planar motion tasks tested. Figure 3-4: First metacarpal tracing during circumduction. Figure 4-1: Motion capture marker placement. Figure 4-2: Standard clinical range of motions and multi-planar motions. 6 7 7 9 22 23 24 26 27 39 40 42 43 63 63 vii KEY TO ABBREVIATIONS 3D three dimensional CMC carpometacarpal DIP distal interphalangeal FIHOA functional index of hand osteoarthritis IP interphalangeal LRTI ligament reconstruction tendon interposition MCP metacarpophalangeal OA osteoarthritis OH older healthy PCA principal component analysis PIP proximal interphalangeal ROM range of motion VAS visual analogue scale YH young healthy viii CHAPTER 1: INTRODUCTION 1.1 Overview Thumb carpometacarpal (CMC) motion, motion between the thumb and the wrist, sets us apart from other species. Although humans are not the only primates capable of opposition, which is the ability to touch the thumb to another finger on the same hand, they are the only species capable of producing a pinch grasp3. Although the thumb CMC joint is relatively small, CMC joint motion is primarily responsible for our ability to grasp objects, open jars, and is necessary for nearly 50% of arm function1,2. When CMC motion and strength becomes impaired, as is the case in persons with CMC osteoarthritis (OA), hand and arm function is significantly affected. CMC OA reduces hand function abilities and impedes completion of daily tasks like buttoning shirts and unlocking doors. In extreme cases, CMC OA can impair a person’s ability to care for themselves, resulting in 24 hour care4. To improve hand function and the quality of life in persons with CMC OA, it is critical that we improve our ability to monitor changes in thumb function. The first step is to augment our methods to quantify the functional losses and used these methods to identify effects of treatment. The overarching goal of this work was to quantify the differences in motion and force abilities of persons with and without thumb CMC OA, and to measure the ability of hand stretching and strengthening exercises to increase thumb function in persons with CMC OA. For this work, initial motion and force datasets were collected from young healthy persons (n = 23), older healthy persons (n = 11), and older persons with diagnosed CMC OA (n = 24). Following collection of initial datasets, study participants were given daily hand stretching exercises. After two weeks, motion and force datasets were collected a second time. Participants then were given daily strengthening hand exercises to be completed in addition to the daily 1 stretching exercises. Following four weeks of combined stretching and strengthening exercises, participant motion and force datasets were collected a final time. This work has been divided into five chapters with chapters two-four written in the form of a publication (chapter two is under review): Chapter one is a literature review that discusses some basic anatomy of the hand, CMC joint function, osteoarthritis presentation and statistics, clinical treatment and outcomes, and knowledge gaps that must be addressed to further our understanding of CMC OA development and successful treatment. Chapter two describes the development of new methods for thumb force data collection, and force data prior to and following six weeks of hand exercises. The goals of this study were to 1) develop a method to measure isolated thumb forces in multiple directions, 2) demonstrate this method on three populations, young healthy, older healthy, and older participants with OA of the CMC joint, and 3) identify the effects of short-term hand exercises on thumb force production and grip strength in these three groups. Datasets were collected at three time points: week 0 (prior to intervention), week two (following two weeks of stretching exercises) and week six (following an additional four weeks of stretching and strengthening exercises). Results showed that both thumb and grip forces improved in young healthy females, older healthy females and males, and older osteoarthritic females and males. In contrast, young healthy males increased their grip forces following exercise, but not their thumb strength. This suggests that thumb and strength forces are not interchangeable, and that thumb forces should be collected in a clinical setting to better track the effects of intervention (exercise, surgery, etc.) on thumb function. 2 Chapter three focuses on motion evaluation and testing prior to exercise intervention in the same participants described in chapter two. The goals of this research were 1) to determine differences in thumb motions across three groups of participants (i.e., young healthy, older healthy and those with CMC OA) and 2) to determine if multi-planar motions provided additional movement information in comparison to standard planar measures. Both standard thumb ranges of motion typically collected in clinic and new multi-planar motion datasets were obtained from all participants. Results indicated that motion capture was capable of detecting changes in CMC mobility due to the effects of aging and OA pathophysiology that were not detected using standard approaches, and use of multi-planar measurements have the potential to identify changes that are indicators of early stages of OA. Chapter four compared pre- and post-exercise motion datasets (i.e., goniometry and motion data) in the CMC OA participants. All participants completed the same stretching and strengthening exercises over six weeks with testing occurring at week zero, week two, and week six. The goal of this research was to identify changes in CMC motions as a result of a six-week exercise regimen. These changes were determined through two approaches 1) standard goniometry measures and 2) complex movements measured through the use of a motion capture system. We found that six weeks of exercise were sufficient to improve standard CMC ranges of motion using goniometry, and produce trends of improvement using motion capture. Chapter five contains the overall conclusions of the entire body of work and suggestions for future work. 1.2 Demographics Osteoarthritis (OA) is characterized by articular cartilage wear and damage to the underlying bone. Although considered a disease of aging, long-term joint use alone is not sufficient to cause 3 OA onset5,6. Incidence and prevalence increase with age, and women are more likely to be affected, primarily due to hormone differences between the sexes6–14. Persons with OA also have higher medical costs, increased risk of hospital admittance and re-admittance, and more missed work than persons without OA15–18. OA can affect any joint, but most commonly involves the hips, knees, and the hands. Hand OA, and more specifically OA of the carpometacarpal (CMC) joint located at the base of the thumb, has a significant impact on hand function and quality of life1,2,4,11,19–24. The goal of this chapter is to summarize and interpret the currently available research on OA of the hand and thumb CMC joint. This chapter will encompass thumb CMC joint mechanics, measures of hand function, OA risk factors, and gaps of knowledge in these areas. Radiographic changes associated with hand OA, or changes that are visible on radiographic examination such as joint space narrowing, the presence of bone spurs, and subchrondral sclerosis, are present in over 40% of American adults25,26. However, evidence of OA on radiographs is found in populations worldwide, with the prevalence in some populations approaching 80%25,27,28. In the U.S., hand OA presents symptomatically in seven to 22% of the population; in other countries such as Israel, symptomatic OA affects over 75% of the aging population7,25. Genetics are believed to be a strong component of OA incidence in countries like Israel; for example, Ashkenazi Jews had three times the rate of OA as Sepharadi Jews in that study29. The thumb CMC joint is one of the most common joints affected by OA with 21% of the population exhibiting OA changes on radiographs30–32. The population most affected by thumb CMC OA is post-menopausal women where two thirds to one-half with CMC OA report symptoms33. Additionally, as the aging population continues to increase, the number of patients affected by thumb CMC OA also increases34. 4 Loss of hand function can lead to loss of self-reliance and independent living4. This is because 50% of upper limb function comes from the thumb, primarily from the CMC joint. OA of the CMC joint is associated with poor range of motion (ROM), reduced ability to complete activities of daily living, and difficulty performing tasks like opening jars1,2,4,11,19–24. However, few have investigated the kinematic and biomechanical changes that alter hand function in these persons. 1.3 Ligaments and Muscles Ligaments play a crucial role in CMC joint stability. Multiple ligaments and muscles have been identified as key supports to prevent dorsoradial subluxation of the first metacarpal35–38. The ligament structure itself is quite complex; even the number of ligaments reported to attach to the CMC joint is conflicting39,40. It is generally agreed that the anterior oblique ligament, the deep anterior oblique ligament, the posterior oblique ligament, the dorsoradial ligament, the intermetacarpal ligament, the ulnar collateral ligament, and the radial collateral ligament are all important for CMC joint stability35,39,41–43. Of these, both the anterior oblique ligament and the dorsoradial ligament have consistently been identified as the primary stabilizers of the CMC joint35,39,42,44. The thumb CMC joint relies heavily on peri-CMC joint muscles to produce joint motion and maintain joint stability (Figure 1-1). The abductor pollicis longus and abductor pollicis brevis, located on the dorsoradial side of the thumb, move the thumb during radial and palmar abduction. The opponens pollicis, located radial to the abductor pollicis brevis, aids thumb movement into palmar abduction and opposition. On the ulnar side of the thumb, the adductor pollicis moves the thumb into radial and palmar adduction. Wrist stabilizers, both extrinsic flexors and extensors, are also important for CMC joint and thumb function. Both the first dorsal 5 interosseous and the opponens pollicis have been shown to protect against subluxation of the first metacarpal37,38. In short, peri-CMC muscles help maintain healthy joint alignment and preserve joint motion. Figure 1-1: Muscles and tendons that play a role in thumb motion and stability. Muscles and tendons are shown from a) dorsal and b) palmar views of the hand. Abbreviations are as follows: adductor pollicis (AP), abductor pollicis brevis (APB), abductor pollicis longus (APL), extensor carpi radialis brevis (ECRB), extensor carpi radialis longus (ECRL), extensor capri ulnaris (ECU), extensor pollicis brevis (EPB), extensor pollicis longus (EPL), first dorsal interosseous (FDI), flexor pollicis brevis (FPB), and opponens pollicis (OP). ECRB, ECRL, ECU, and EPLshown in panel a are also considered extensor tendons. 1.4 CMC Joint Mechanics The bones of the hand include the metacarpals, proximal phalanges, middle phalanges, and distal phalanges (Figure 1-2). Although OA can affect the joints between any of these bones, hand OA most often affects the thumb CMC joint, the proximal interphalangeal (PIP) joints, and 6 the distal interphalangeal (DIP) joints45. Figure 1-2: Dorsal view of hand anatomy. The thumb carpometacarpal joint is shown as the dashed line between the first metacarpal (shaded blue) and trapezium (shaded orange). Interphalangeal joints are located between the phalanges (shaded purple) and metacarpophalangeal joints are located between the metacarpal and the phalanges. The CMC joint has the ability to move in four directions: palmar abduction, palmar adduction, radial abduction (also known as flexion), and radial adduction (extension; Figure 1-3). When these motions are coupled, rotation occurs allowing for opposition and reposition46. Figure 1-3: Directions of thumb movement. a) radial abduction, b) palmar abduction, c) radial and palmar adduction, and d) opposition. In opposition, the thumb rotates about its long axis so the palmar surface of the thumb can touch the palmar surface of other fingers. In retroposition, the thumb rotates away from the other fingers, extending toward the dorsoradial side of the arm. The average ROM is 40-70° in palmar 7 adduction-abduction, 40-63° in radial adduction-abduction, and 17-31° in opposition- retroposition47–50. CMC joint motion is necessary to perform various grips. During key pinch, the CMC joint moves in a palmar direction by palmar abduction and opposition, and while grasping a jar, the CMC joint moves in a distal ulnar palmar direction combing radial and palmar abduction51. The CMC joint’s ROM comes from its unique structure. The CMC joint is one of only three saddle joints found in the body. The first metacarpal and trapezium have concavity differences between their dorsovolar and radioulnar sides. Specifically, the metacarpal is concave in the dorsovolar direction and convex in the radioulnar direction, while the convex and concave shapes are found in opposite planes of the trapezium13,39,52. Multiple contact planes allow the metacarpal to move over the trapezium, producing a loose, unstable fit between the bones52–55. Thus, the large ROM of the CMC joint comes at a price—reduced joint stability. 1.5 Measures of Hand Function Current clinical measures are not sufficient to detect the multi-directional motion and force deficits that alter thumb function in early CMC OA. While it is clear that motion and force play a critical role in OA pathophysiology, standard clinical measures lack the specificity to detect them1,5,55–58. This led to the development of a multitude of prescription philosophies, prescribed exercise regimens, patient outcomes, and lack of best practice recommendations59–61. Further quantification of the improvements associated with treatment interventions is necessary to shape treatment protocols, change therapy prescription, and improve decision-making, thereby reducing treatment costs62,63. In a clinical setting, goniometers are typically used to measure joint ROM (Figure 1-4). Goniometers have a planar design that measures ROM in a single axis, but they cannot measure 8 the full three-dimensional motion of the thumb CMC joint8,42,64. Goniometers have low accuracy and poor inter-rater reliability65–67. Figure 1-4: Goniometer example. An example of a goniometer used to measure range of motion of the joints in the hand. Hand strength is typically measured using a hand grip dynamometer. Although dynamometers measure total hand strength, they cannot measure the strength contributions of individual digits. Currently, no device can measure individual digit or joint specific strength in multiple directions. The lack of such a device makes it difficult to track the effect of therapy in joint specific pathologies like CMC OA. Additional measures are necessary to identify the motion and force changes associated with thumb CMC OA. Motion capture technology can measure ROM and joint alignment in three- dimensions with high levels of accuracy, making it a superior method to measure thumb CMC motion65,68,69. Unlike grip dynamometers, a multi-axis load cell with an appropriately designed interface, can measure both force magnitudes and directions of the isolated thumb. When used concurrently, motion capture and load cell technologies can quantify motion and force with high accuracy and repeatability that are not possible with standard clinical approaches. 9 1.6 Motion Capture and Modeling Due to the complexity of the hand, motion capture and modeling are used in a laboratory setting to gain insight into the complex motions and forces at play. A few small studies have used modeling to evaluate interphalangeal (IP) joint and CMC joint motion in everyday tasks1,51,58,70–73. Although several studies have used motion capture and modeling to divide complex hand motions into component movements, only a few have applied modeling to pathological changes in the hand58,72–76. A few studies suggest that CMC joint kinematics, alterations in ROM, and joint deformities can be evaluated using motion capture1,58,70,72,73. Additional research is needed to further elucidate the pathophysiology of OA development and motion deficits. Such information would be useful to develop CMC joint specific OA diagnostic criteria, track OA progression, and quantify treatment success. 1.7 Biomechanical Risk Factors Altered biomechanics (e.g. altered motions and forces) play a critical role in both OA development and progression. Most cases of OA develop after years of joint use, often in an environment of suboptimal biomechanics11,54,77–79. Biomechanical contributors to OA include joint laxity and instability, joint malalignment, elevated joint stress, and muscle strength and imbalance6,11,56,80–82. 1.7.1 Joint laxity and instability Joint laxity predisposes the joint to instability, leading to joint damage and increasing the risk for OA development83. Diseases that predispose individuals to increased joint laxity, or loose ligaments, frequently result in subsequent OA diagnosis6,8. For example, early onset OA is a well-known consequence of Ehlers-Danlos Syndrome, a genetic disorder characterized by altered 10 collagen and connective tissue. Hypermobility and increased joint laxity are, by definition, associated with reduced joint stability, and increase the risk of joint injury6,41,52,83. Laxity can also lead to joint movement outside of normal ROM, resulting in inadequate transfer of loading forces and increased forces directed through the joint77,84. Joint laxity increases the contact area between articular surfaces, forcing new areas to experience abnormally high loads and subsequent cartilaginous wearing53,77,85. Additionally, research in the knee suggests that laxity may not only be a risk factor but also a consequence of OA86. Joint laxity creates an environment that adds stress to the other soft tissue supports surrounding the joint. If the non-ligamentous supporting tissues are not able to compensate for the loose ligaments, the joint will become unstable. The remaining soft tissue supports are especially important in the CMC joint because even a healthy CMC joint has relatively loose ligaments to allow for its large range of joint motion54,87. In the thumb, specific postures are linked with CMC joint instability. For example, key pinch tasks correlate with reduced CMC joint stability and translation of the trapezium54,88. CMC joint instability, defined by altered joint surface alignment, surface contact, and abnormal muscle actions, and has also been shown to lead to CMC OA42,89. 1.7.2 Joint malalignment Improper joint alignment is another biomechanical risk factor. Malalignment results in uneven joint wear, articular cartilage damage, and increased risk of OA56,90–92. For example, in the knee, malalignment is a well-described risk factor for OA development and progression8,81,90,93. Although the mechano-pathology is less researched in the thumb, dorsoradial subluxation of the first metacarpal and associated joint malalignment in the CMC joint, becomes more common as 11 healthy individuals age94. More importantly, dorsoradial subluxation increases one’s risk of CMC joint OA80,94. 1.7.3 Joint stress Increased joint load and high frequency of use stress the joint, predisposing one to OA development1,8,10,11,23,41,52,95,96. Excess joint stress can alter joint mechanics and cause abnormal joint loading1. Elevated joint stress leads to irreparable mechanical tissue damage and alternations to chondrocyte metabolism and gene expression which lead to downstream biochemical and local environmental changes11,93,96,97. 1.7.4 Muscle strength and imbalance Increased muscle strength is also a risk factor for hand OA development. When the hand grips an object, the forces felt by the joints increase as you move proximally. That is, the thumb IP joint experiences the least force, with increasing force in the metacarpophalangeal (MCP) joint, and finally the CMC joint, which is under the greatest magnitude of force13. Men with greater grip strength are at increased risk to develop OA in the first CMC joint and the MCP and PIP joints98,99. In women, this is associated with increased risk to the MCP joints98,99. Similarly, joint overuse increases the risk of OA development100. For example, regular chopstick use is associated with increased prevalence of OA in the thumb MCP joint and IP joint as well as the PIP and DIP of the 2nd and 3rd fingers100. Muscle balance and activation patterns are related to OA. Co-activity, or the activation of both agonist and antagonist muscles, is thought to be important for joint stability97,101. In the leg, increased ratio of quadriceps to hamstring strength and altered quadriceps muscle activation have been observed in patients with knee OA97,102,103. Although muscle atrophy was previously thought to be a consequence of disuse in OA patients, in the knee it has become evident that a 12 muscle strength imbalance occurs much earlier104,105. Similar research to investigate the role of muscle in hand OA is needed. Although increased grip strength is a risk factor for OA development, grip strength reduction is a well-known consequence of OA. Poor grip strength and muscle imbalance can be observed in hand OA patients106. Looking specifically at the thumb CMC joint, OA is also associated with reduced key pinch strength, tip strength, and tripod strength88,106. However, research investigating the effect of CMC OA on the relative strength of peri-CMC joint muscle groups is lacking. 1.8 Pathophysiology Regardless of the risk factors involved, OA disease pathophysiology is similar. Years of repetitive use causes wear and tear on the articular cartilage. Due to its avascularity, cartilage cell turnover is very slow and its ability to regenerate is extremely limited. As one ages, the body’s minimal ability to repair and renew articular cartilage if further limited and the cartilage may become compromised6,107,108. As OA progresses, the articular cartilage wears away, joint space distance changes, and nearby structures like subchondral bone are exposed to new stresses107. Attrition of the cartilage and joint can distort the already compromised biomechanics, altering thumb CMC joint surface alignment and reducing joint movement and force generation44,56,84,109,110. These changes lead to patient reports of inflammation, tenderness to touch, reduced ROM, and joint pain that worsens with movement9,11,61. Inflammation occurs in early stages of hand OA8. When measured over a three month period, ultrasound revealed that inflammation features are consistently present in almost all hand OA patients over this time period111. However, lower rates of inflammation (10%) have been reported at a single time point112,113. 13 In the hand, clinical diagnosis and staging are based upon the presence of hand pain or stiffening, tissue joint enlargement, and joint deformity. Early OA presents with joint effusion widening of the joint space and minimal subluxation. As OA progresses, the CMC joint space begins to narrow, articular cartilage becomes worn, the joint capsule becomes lax, joint debris begins to accumulate, and osteophytes start to appear on the dorsal portions of the trapezium. Later in the disease, CMC joint degeneration becomes evident on radiographic imaging and subluxation worsens. Osteophytes enlarge and the bone underlying the articular cartilage begins to show wear. The final stage of CMC OA presents with more significant joint space narrowing, degeneration of both the CMC and scaphotrapezium surfaces, and subchondral bone degeneration114–116. Future work to investigate earlier signs of OA development such as functional changes (changes in motion abilities and force production) or local inflammation could be useful to identify OA related changes, and thus provide treatment more quickly. Long term studies suggest that joint space narrowing and osteophyte development continue to deteriorate joints in approximately 20% of patients for a minimum of two to 10 years8,117. Osteophyte progression seems to be more common in women, and is more likely to occur within 10 years of menopause117. This timeline further supports the potential role of hormones in OA and specifically osteophyte development; the dramatic reduction in estrogen that occurs at the onset of menopause may lead to osteophyte progression117. Radiographic changes are not synonymous with clinical deficits or pain. Although many studies have investigated the relationship between radiographic findings, pain, and functionality, few have found an association between imaging and the latter two117,118. However, numerous studies have shown a strong relationship between pain and functional deficits117,118. 14 1.9 Treatment Options and Outcomes OA diagnosis and treatment are generally initiated when the patient expresses joint pain concerns. First line treatment is most commonly acetaminophen or a non-steroidal anti- inflammatory prescription. Although the focus of OA treatment is pain management, early diagnosis and intervention can reduce long-term treatment costs and mitigate the impact of OA on hand function25,41,119. In lieu of the benefits of early treatment, conservative treatment frequently includes exercise therapy, lifestyle modification with a joint protection plan, and splinting of the affected joint(s). Exercise in the form of physical and occupational therapist recommendations is the most cost-effective treatment for OA and is a cornerstone of treatment62,63,120. However, exercise prescription and the specific exercises prescribed are inconsistent5,22,32,61,121–125. The discrepancy between prescription and patient need is likely due to the lack of unbiased, high quality research studies evaluating the effects of specific exercise regimens24,59,126. When discussed in broad terms, most exercises fall into two categories: ROM (stretching, muscle release, etc.) and strengthening (resistance-based). In early stages of disease, most therapists prescribe both stretching and strengthening exercises. In later stages of disease, therapy prescription is based on one of two philosophies. The first is that joints with advanced OA should be treated with stretching exercises, but not strengthening exercises, as strengthening programs may worsen joint deterioration32. The second is that patients with advanced OA should be treated with stretching exercises which will increase ROM, and then can be treated with strengthening exercises5. Although care for advanced OA may be dictated by the prescribers belief in the impact of strengthening exercises on joint deterioration, no study has looked at the impact of exercise on joint angles in the thumb, and few have quantified the impact of exercise 15 on motion and strength (force application) abilities5,127–129. Additional research is necessary to validate the use of hand exercises to improve quantitative hand function in CMC OA. Studies have evaluated the effect of exercise specifically on patients who have hand OA with mixed results5,22,123–125,129–133. Those that have were rarely hypothesis driven; rather, they were developed by clinicians and therapists to substantiate their prescribed exercise regimens. This is likely the reason why most studies report outcomes based solely on validated, but subjective pain and function questionnaire scores. In the few studies that quantify hand ROM and hand grip strength changes following exercise, stretching regimens, strengthening regimens, and combined exercise regimens (with both stretching and strengthening components) have all reported similar gains5,22,122–124,134. To our knowledge, only one study was been conducted in persons with CMC OA to look at grip strength outcomes and none have looked at ROM; exercises studies have focused on subjective responses122,124,134. Further study is needed to evaluate the effects of hand exercise on objective, quantifiable function changes. Second line treatment options for OA include joint injections and further pain management. However, many with thumb CMC OA eventually have pain severe enough that they seek the last line of treatment, surgical intervention. CMC joint surgeries are most commonly modifications of trapeziectomy. Since trapeziectomy began, ligament reconstruction and tendon interposition (LRTI) has been added to traditional trapeziectomy surgery in an effort to improve patient outcomes, namely reducing pain, improving and maintaining joint function, and preventing impingement41. Several studies have found that ligament and tendon alteration results in reduced pain, and improved grip strength135,136. However, these modifications may also increase side effects and risk of adverse outcomes135. Still, LRTI is considered the gold standard surgical option and the most commonly performed surgery in CMC OA patients135,137,138. 16 In order to better improve patient care and hand function for the greatest number of patients, a thorough understanding of the benefits of early OA treatment must be determined. To help meet this overall goal, the work herein will provide evidence of the effectiveness of one key component of early OA treatment—exercise therapy. There is a strong need to develop quantitative measures to evaluate the effect of hand exercises on CMC joint function, namely the thumb and CMC joint specific kinematics and kinetics. This may aid the future development of gold standard CMC OA exercise recommendations. The specific goal of this work is to quantify the effects of exercise on both thumb motion and force application. This document will provide therapists, physicians, and patients alike with data that quantifies the benefits of exercise therapy on thumb motions and force abilities in young healthy participants, older healthy participants, and participants with CMC OA. 17 CHAPTER 2: DETERMINING THE EFFECTS OF SHORT-TERM HAND EXERCISES ON THUMB FORCE GENERATION AND GRIP STRENGTH IN OSTEOARTHRITIC AND HEALTHY PERSONS 2.1 Abstract Osteoarthritis of the carpometacarpal joint can dramatically impair thumb function resulting in the inability to complete basic tasks. Development of a measurement method to detect changes in thumb forces is essential to improving our understanding of the progression of carpometacarpal osteoarthritis and the effects of treatment. The goals of this study were to 1) develop a method to measure thumb forces in multiple directions, 2) demonstrate this method on three populations, young healthy (n = 23), older healthy (n = 11), and older participants with carpometacarpal joint osteoarthritis (n = 24), and 3) identify the effects of short-term (six weeks) exercises on thumb force production and grip strength in these three groups. Hand exercises improved thumb forces in young healthy female participants during radial (p = 0.017) and palmar abduction (p = 0.031) and female participants with osteoarthritis during palmar abduction (p = 0.010). Exercise improved grip strength in young healthy males (p = 0.028), young healthy females (p = 0.041), and females with osteoarthritis (p = 0.027). Clinical significance: Changes in grip strength do not necessarily correlate with changes in thumb strength; gathering thumb force data provides additional information for clinical assessment and treatment. 2.2 Introduction Osteoarthritis (OA) at the base of the thumb, the carpometacarpal (CMC) joint, affects nearly 50% of Americans over 65 years old8. CMC OA causes a reduction in grip strength, poor range of motion, and joint pain, resulting in significant impairment of hand function8,108,139–144. The CMC joint has a unique saddle shape that allows the thumb to move in many directions, facilitating the completion of daily activities145,146. Everyday activities such as opening pill bottles, tying shoes, and grasping a glass of water become daunting tasks with OA1,141,147. 18 Furthermore, the inability to conduct these basic tasks has the potential to result in a loss of independent living4,19–21. CMC OA alters grip strength and hand force production. Not only do individuals with CMC OA have reduced grip strength, they also have difficulties during hand opening and pinch grip88,106,108,144,148. To measure these forces, grip dynamometers are commonly used to obtain a single composite force generated from all the fingers together. A challenge with this approach is that the force data are non-specific to the digit and therefore, do not provide details with respect to the role of the thumb. Current measures of grip strength utilized by clinics are not sufficient to determine thumb force abilities. Although a few devices can measure forces generated by the thumb in specific directions, none have been used to study individuals with CMC OA145,149–157. Some research reports have used the Rotterdam Intrinsic Hand Myometer to determine thumb forces in diseased populations, but not in OA154. Since the thumb exhibits complex movement, it is necessary to evaluate the thumb in postures that represent these movements. Thus, development of a measurement method to detect thumb forces in multiple directions is essential to improve our understanding of the effects of CMC OA. To better assess the effectiveness of targeted therapeutic interventions, a method to track thumb specific force production must first be developed and implemented. Multi-directional, thumb specific force data are critical for fine-tuning rehabilitation, to improve patient care, and to provide evidence of treatment effectiveness. Exercise therapy is part of conservative OA treatment63,158–160. The goal of hand exercise is to increase hand function, namely by reducing pain, improving range of motion, and increasing grip strength. However, functional loss begins years prior to OA diagnosis. Several studies show that 19 short-term hand therapy significantly increases overall grip strength both in individuals with hand OA and elderly individuals without OA diagnosis5,22,124,125,161,162. Little research is available to determine the specific effects of hand exercises on thumb force production. Based on the gaps in research, the goals of this study were to 1) develop a method to measure isolated thumb forces in multiple directions, 2) demonstrate this method on three populations, young healthy, older healthy, and older participants with OA of the CMC joint, and 3) identify the effects of short-term hand exercises on thumb force production and grip strength in these three groups. 2.3 Methods 2.3.1 Participant testing All testing and participant data were conducted in accordance with the University's Institutional Review Board. All participants were consented prior to data collection. Participants were right-handed and all data were collected on the right hand. Participants in the young healthy (YH) group were required to be between the ages of 18-30 years old and participants in the older healthy (OH) and osteoarthritic (OA) groups were required to be between 55-80 years old. Inclusion criteria for the healthy groups: right-handed, no history of hand surgery, no hand therapy within the last three months, no medication changes within the last three months and no severe hand injuries, disease or illness, including hand OA. Inclusion criteria for the OA group: right-handed, doctor diagnosed hand OA, no history of recent hand surgery or therapy, no medication changes within the last three months, and no hand injuries, disease, or illness, other than OA. Presence of hand stiffness, aching and/or pain in our joint of interest, the right first CMC joint, was required for inclusion in the OA. 20 All participants were tested at three time points over six weeks. For each time point, data were collected at the same time of day. Time point one (week 0) data were collected at their initial visit prior to intervention. Time point two (week 2) data were collected following two weeks daily hand stretching exercises. Time point three (week 6) data were collected following four weeks of daily hand stretching and strengthening exercises. The order of dynamometry and thumb force application tests were randomized across participants. Basic demographic information, thumb force, and grip strength data were collected from participants at three time points. 2.3.2 Exercise protocol The exercise protocol included both stretching and strengthening exercises (Figure 2-1) and was developed in conjunction with a hand therapist. The first two weeks was composed of exercises designed to stretch the first web space and improve joint alignment during grip tasks. Exercises included passive range of motion (ROM), active ROM, and manual medicine techniques. After two weeks, participants were retested and given a second set of exercises to be completed in addition to the stretching exercises. 21 Figure 2-1: Hand exercise regimen. Stretching exercises included osteopathic and muscle release techniques: a) first web space release, b) first web space cone stretch, and c) bilateral web space stretch; passive range of motion exercises: d) passive radial abduction, e) passive palmar abduction; and active range of motion exercises: f) active radial abduction, g) active palmar abduction, h) okay sign, i) opposition to the base of the fifth finger, k) opposition to each fingertip, and k) finger spread. Strengthening exercises included therapy band exercises: l) resisted radial abduction and m) resisted palmar abduction; and putty exercises: n) putty roll, o) key pinch, p) okay sign pinch, q) three finger pinch grip, r) resisted finger spread, and s) putty squeeze. The second set of exercises were conducted for four weeks and designed to improve hand strength, focusing on the peri-first metacarpal muscles. Exercises included resistance-based active ROM and resistance-based grip tasks using therapeutic bands and putty. All participants were asked to complete the exercises a minimum of once daily. Additionally, participants were contacted periodically throughout the study to check for adverse effects, to remind participants to complete the exercises daily, to answer any questions they had, and to confirm future appointments. 22 2.3.3 Thumb force measurement device Thumb force datasets were collected using an AMTI multi-axis load cell (Watertown, MA) and a custom-built apparatus (Figure 2-2). The vertical height, the distance from load cell, the angle of hand inclination between the base plate and ulnar side of the hand, and the diameter of ring of the apparatus were adjustable. Tubing was positioned along the inner diameter on the ring as needed to ensure a snug fit while thumb placement was maintained in the center of the ring. Both the tubing and various sized wedges were used to ensure the thumb rested with the metacarpophalangeal joint parallel to the ring. The right hand was placed with the palm against the medially located hand support and the ulnar side of the hand flat against the base plate. Figure 2-2: Computer model of device adjustability. Adjustments can be made to a) the load cell height, b) the distance of the hand support from load cell, c) the angle between the base plate and ulnar side of hand, and d) the diameter of ring where thumb applies force. Thumb forces were collected in four directions (Figure 2-3): 1) radial abduction (RAB), 2) radial adduction (RAD), 3) palmar abduction (PAB), and 4) palmar adduction (PAD). Participants were instructed to use their thumb to press against the ring in the specified direction with as much thumb force as they could without using other parts of their body. Thumb forces were collected three times in each direction. To match the clinical protocol of dynamometry 23 (discussed below), the largest force applied from the three replicates (for each thumb direction) was used for analysis. Figure 2-3: Load cell apparatus. Forces were applied in the following directions: radial abduction (RAB), radial adduction (RAD), palmar abduction (PAB), and palmar adduction (PAD). Tubing was used to adjust the internal diameter of the ring and various sized wedge. 2.3.4 Hand grip dynamometry Grip strength was collected using a Sammons Jamar Hydraulic Hand Dynamometer (Model 31204071, Bolingbrook, IL). All dynamometry protocols were performed in the same fashion as they would be performed in a clinical setting144,163,164. All participants had their maximum grip strength measured using grip #2 (handle distance 1 7/8 in or 4.76 cm) and #3 (handle distance 2 3/8 in or 6.03 cm) in triplicate. The largest force applied from the three replicates (for each grip) was used for analysis. 2.3.5 Statistical Analysis Two main analyses were conducted. First, a repeated measures ANOVA was used to compare across time points to determine the effects of exercise for all six groups (two sexes in each of the three participant groups) and a Bonferroni t-test was used to determine significance between time points. Because prior research has shown that there are magnitude differences between sexes, the 24 sexes were evaluated separately163,165. Next, a one-way ANOVA was used to compare the force differences between sex specific YH, OH, and OA group data with SigmaStat (Systat, San Jose, CA) at each time point and Holm-Sidak method was used to determine statistical differences; a p-value < 0.05 was considered statistically significant. Data was tested for normality using Shapiro-Wilk and for equal variance using Brown-Forsythe. In the case that normality or equal variance failed, Kruskal-Wallis ANOVA on Ranks was used; Dunn’s post-hoc comparison was used to determine significant differences between specific groups. 2.4 Results 2.4.1 Participants A total of 58 individuals participated in this study with 50 completing all six weeks of exercise: 1) 23 young healthy (21 completed all six weeks), average age 22.5 years ± 3.1 years, 12 males, 2) 11 older healthy (9 completed all six weeks), average age 66.3 ± 8.4 years, five males, and 3) 24 participants with CMC OA (20 completed all six weeks), average age 69.4 ± 5.8 years, six males. 2.4.2 Thumb force generation trends prior to intervention The largest thumb forces produced by all groups were applied during radial adduction (week 0 females: 38.1 N in YH, 35.3 N in OH, and 25.2 N in OA; males: 54.6 N in YH, 49.8 N in OH, and 54.8 N in OA). Most participants had greater radial and palmar adduction forces than abduction. For all directions, females produced less forces than males. 25 2.4.2.1 Female groups Statistically, OA females produced significantly less thumb force during radial adduction and palmar abduction than YH females (p = 0.020 and p = 0.020 respectively; Figure 2-4). Prior to exercise, the largest forces in all female participant groups were produced during radial adduction, followed by palmar adduction, palmar abduction, and then radial abduction. Figure 2-4: Female thumb force application. Force application occurred during a) radial abduction, b) radial adduction, c) palmar abduction, and d) palmar adduction. * denotes a significant difference between the indicated groups at a given time point. # denotes a significant difference for a given participant group between the indicated time points. Data is shown are group averages ± standard deviation. 2.4.2.2 Male groups Prior to exercise, the forces produced by males varied by group and differences were not as large as those generated by females. YH and OA male participants produced the greatest forces during radial adduction, followed by radial abduction, palmar abduction, and then palmar 26 adduction. OH males had their greatest forces during adduction (radial adduction then palmar adduction) followed by abduction (palmar abduction then radial abduction; Figure 2-5). Figure 2-5: Male thumb force application. Force application occurred during a) radial abduction, b) radial adduction, c) palmar abduction, and d) palmar adduction. No statistically significant differences were found between groups at given time point or within groups following exercise. Data is shown are group averages ± standard deviation. In summary, the results show that participants of most generated more force when the thumb was moving towards the palm (adduction) than away (abduction) for both palmar and radial cases. The YH group produced larger forces than the older groups but statistical differences were only seen in the female groups. 2.4.3 Effects of exercise on thumb force generation 2.4.3.1 Female groups YH females produced significantly greater radial adduction and palmar abduction forces (p = 0.0001 and p = 0.033, respectively) following two weeks of hand exercises than OA participants; this was also true for radial abduction forces following six weeks of exercises (p = 0.036). OH 27 females also produced significantly greater radial adduction forces than OA females after two weeks and greater radial abduction force after six weeks (p = 0.021 and p = 0.027, respectively). When looking for the average improvement across all four directions, female participant groups had similar increases in thumb force generation (~4.5 N increase on average of all force directions). Exercise increased female force generation in all directions with the biggest effect after two weeks of stretching exercises. Exercise significantly improved radial abduction thumb force in YH female participants following two weeks of stretching exercises (p = 0.025). Increased radial abduction ability was maintained following six weeks of exercise. Additionally, after six weeks of exercise, palmar abduction force generation was significantly greater than pre-exercise (week 0) values in YH females (p < 0.001). Although both OH and OA females improved their force generation following exercise, only palmar abduction in OA females was significant (week 0-2 p = 0.039 and week 0-6 p < 0.01, respectively). 2.4.3.2 Male groups On average, YH male thumb force generation increased 0.05 N, OH increased by of 2.2 N, and OA by 5.6 N across all force directions after exercise. Exercise did not have a significant effect on thumb force generation in male participant groups, however positive trends were shown primarily in the two older participant groups. When looking at changes in specific directions following exercise, YH male participants increased force generation in palmar adduction only (3.3 N at week 6). OH participants increased their radial and palmar adduction force generation (3.8 N and 8.6 N, respectively at week 6), but not their radial or palmar abduction force. OA participants improved force generation in every direction following exercise (increases of 0.3 N in radial abduction, 9.1 N in radial adduction, 5.4 N in palmar abduction, and 7.4 N in palmar 28 adduction at week 6). However, no increase was statistically significant in our male sample (Figure 2-5). In summary, exercise increased force generation in all thumb directions for all female participants and had a limited effect on male thumb forces. Additionally, when comparing the effects of the two weeks of stretching exercises to the four weeks of combination exercises, the stretching exercises resulted in greater thumb force increases in the female participants. 2.4.4 Grip strength trends prior to intervention All participant groups had similar grip strength using both grips #2 and #3. Trends for improvement were often the same for both grips, however statistical significance varied by sex and the grip used. As expected, male participants exhibited greater grip strength than females. 2.4.4.1 Female groups Female grip strength was stratified by group. YH had significantly greater grip #2 and #3 strength than OH and OA females prior to exercises (vs. OH grip #2 p = 0.009 and grip #3 and p = 0.035; vs. OA grips #2 and 3 p < 0.001, respectively). 2.4.4.2 Male groups YH males had greater grip strength than OH or OA participants, although not statistically significant. There were no significant differences in grip strength between any male groups for either grips. 2.4.5 Effects of exercise on grip strength generation 2.4.5.1 Female groups YH participants had significantly greater grip strength than OH participants following two weeks of exercises (p = 0.022 for both grips #2 and #3), but not after six weeks (grip #2 p = 0.089 and grip #3 p = 0.080). YH participants also had significantly greater grip strength than 29 OA females for both grips following exercise (p < 0.001 for both grips at both two and six weeks). Exercise improved grip strength in all female participant groups. YH females significantly improved grip strength following exercise (grip #2 p = 0.041 and grip #3 p = 0.033, respectively). OH and OA participants also increased their grip strength following exercise, however only grip #2 was significant (OA grip #2 p = 0.0440, grip #3 p = 0.427 and OA grip #2 p = 0.027, grip #3 p = 0.058). 2.4.5.2 Male groups Two and six weeks of hand exercises increased hand grip strength significantly in YH male participants using grip #2 (p = 0.008 and p = 0.029, respectively). Although both OH and OA males had improvements in both grip strength #2 and #3 following exercise, the changes were not significant. In summary, exercise increased grip strength in all participant groups using both grips. Significant improvements were seen in both sexes following exercises when using grip #2. 2.5 Discussion The goals of this study were to 1) develop a method to measure isolated thumb forces in multiple directions, 2) demonstrate this method on three populations, young healthy, older healthy, and older participants with OA of the CMC joint, and 3) identify the effects of short- term hand exercises on thumb force production and grip strength in these three groups. To accomplish the first goal, a custom apparatus attached to a multi-axis load cell was designed and then manufactured. The device was successfully able to isolate thumb forces from other fingers and measure thumb force production in four directions: radial abduction, radial adduction, palmar abduction, and palmar adduction. The device was then tested in the three 30 groups of participants before, during and after a six-week exercise regimen. These previously unavailable datasets are clinically valuable—they provide insight into the effects of OA on thumb function and force production. Specifically, these data have the potential to provide feedback and assessments for one of most critical joints in the hand, the CMC joint at the base of the thumb. When this joint is not functioning properly, people lose the ability to complete day- to-day tasks affecting their quality of life4,19–21. This work permits focused assessments of the thumb, allowing us evaluate changes in force production and to monitor treatment success, and to determine whether modifications in the treatment strategies are necessary. In those with functional impairments, even small increases in force production or range of motion due to exercise can lead to clinically significant improvements in the ability to complete basic tasks. In individuals with CMC OA, these improvements can be the difference between successfully completing daily tasks and loss of independent living. 2.5.1 The relationship between thumb forces and grip strength Clinically, grip strength is used as an indicator of hand function in CMC OA, and thus it is assumed that a change in grip strength in persons with CMC OA is indicative of a change in thumb strength. However, thumb forces cannot be separated from the hand grip strength profile. Furthermore, our evaluation of isolated thumb data indicates grip strength does not reliably indicate thumb function. For example, hand exercises significantly improved hand grip strength in YH male participants, but this was not accompanied by an increase in thumb force generation. Therefore, our data suggests that the increased force production found in YH participants following exercise is originating from digits other than the thumb. This difference illustrates that thumb and grip trends may not be interchangeable, and suggests thumb forces are necessary in a clinical setting to follow injury and disease affecting force production in the thumb. OA males in 31 our study had similar grip strength improvements as YH males following exercise, but OA males had larger thumb force gains. This further suggests that grip and thumb force data are not equivalent. 2.5.2 Thumb force generation trends prior to intervention By measuring forces in multiple groups and sexes, we were able to identify common trends and differences between these groups. Our dataset not only adds to the no intervention male data captured by Li and Harkness, but also creates female and CMC OA datasets153. To the authors’ knowledge, no other group has published healthy and CMC OA isolated thumb force datasets within a single study149,152,153. One study by Li and Harkness obtained continuous circumferential thumb force data from seven college-aged men using a multi-axis load cell. When the thumb was in specific positions like radial abduction, the force data were extracted from the continuous dataset. The force data reported was larger than those reported in our study, however Li and Harkness indicated that “it is possible the force magnitude in a specific direction obtained by continuous exertion is different from the force generated in the same direction during a focused unidirectional effort”153. 2.5.3 Effects of exercise on thumb force generation Results indicate that the exercise regimen was sufficiently difficult to elicit changes in females, but not males. In females, OA participants improved their force application such that there was no longer a significant difference between YH and OA forces during radial adduction and palmar abduction. This suggests that the effect of exercise, in particular stretching exercises, may be clinically beneficial in OA participants. If performed early, prior to OA diagnosis, our data indicate that exercise allows individuals to regain lost force abilities. Female participant groups had a larger increase in force production with statistically significant differences between 32 time points. Healthy male participants experienced smaller improvements with no statistically significant results. Based on these sex-specific results, the exercise program may have been sufficiently difficult for female participants to elicit a change, but not strenuous enough for healthy male participants to see a similar benefit. 2.5.4 Grip strength trends prior to intervention Similar to other studies, males had greater hand grip strength than females, and younger participants had higher grip strength force generation than older individuals108,139,144,163,166. Additionally, the magnitudes of OH grip strength data reported here are similar to those published by Jensen163. It is likely that the decreased grip strength seen in OA participants is due not only to muscle weakness, but also due to the altered biomechanics and greater forces felt at the already painful CMC joint167. 2.5.5 Effects of exercise on grip strength generation Our work suggests that just two weeks of stretching exercises significantly increased grip strength in the male and female YH participants, and female OA participants. This recapitulates findings by other clinicians and researchers, and further shows improvements can occur in both healthy and diseased group in a much shorter time period than previously reported125,166,168. 2.5.6 Limitations To our knowledge, this is the first study to evaluate the effect of exercise intervention on multi-directional thumb forces. Although many of the results in this study are promising, not all the trends are statistically significant. Future studies with a larger number of participants, in particular, the inclusion of a larger number of older healthy participants, would benefit the hand research community to further validate the findings herein and aid the comparison between OH and OA participants. 33 2.6 Conclusions Understanding of the impact of exercise on thumb force application is critical to evaluate the effectiveness of CMC OA treatment on thumb function. In this study, we successfully identified changes in thumb force generation due to short-term hand exercises in YH, OH, and OA participants. These findings support the use of the stretching and strengthening exercises to target peri-first metacarpal muscles, and as little as two weeks of stretching exercises demonstrate statistically significant changes in thumb forces in females and grip strength in males and females. Based on this research, we can begin to observe the relationships between forces generated by the thumb and generalized hand strength. Grip strength is not predictive of changes in thumb forces; based on the data, collection of separate thumb forces are necessary to evaluate thumb function and intervention success. To our knowledge, this study is the first to 1) develop a quantifiable method to compare thumb forces in healthy and diseased thumbs, and 2) investigate the effect of exercise on thumb forces in both healthy and OA participants. Understanding the effects of exercise on thumb forces will allow researchers and clinicians to better develop targeted therapies and track outcomes specific to the thumb. 34 CHAPTER 3: COMPLEX THUMB MOTIONS AND THEIR POTENTIAL IN IDENTIFYING MOTION CHANGES RELATED TO OSTEOARTHRITIS EARLIER THAN STANDARD MEASURES 3.1 Abstract Early diagnosis and treatment of osteoarthritis allows for early interventions that may mitigate osteoarthritis progression and decrease severity later in life. Early identification of motion changes is limited by the clinical reliance on single planar measurements using goniometry. Multi-planar measurements using motion capture can provide insights into joint function and pathophysiology that cannot be obtained from single-plane goniometry measurements. Thus, the goals of this research were 1) to determine differences in thumb motions across three groups of participants (young healthy (n=23), older healthy (n=11), and those with carpometacarpal osteoarthritis (n=24)) and 2) to determine if multi-planar motions provided additional movement information in comparison to standard planar measures. In this study, a motion capture system was used to collect standard clinical ranges of motion and motions during three multi-planar tasks. Thus, differences in motion patterns due to aging and osteoarthritis were identified. Motions tested included palmar adduction-abduction, radial adduction-abduction, metacarpophalangeal flexion-extension, interphalangeal flexion-extension, functional adduction- abduction, opposition, and circumduction. Results indicated that motion capture was capable of detecting changes in carpometacarpal mobility that were not detected using standard approaches. Our results suggested that use of multi-planar measurements may be able to identify changes that are indicators of early stages of osteoarthritis. Early indicators are clinically useful as they will enhance patient treatment by permitting the application of treatment approaches sooner, potentially leading to reduced overall functional deficits. 35 3.2 Introduction Osteoarthritis (OA) is a prevalent disease with one in every two Americans over the age of 65 affected by carpometacarpal (CMC) OA8. OA causes cartilage attrition and can damage the underlying bone8. In the thumb CMC joint, OA presents with reduced range of motion, joint pain, and poor grip strength8,141,142. In order to oppose the thumb and to grasp objects, the large range of motion at the CMC joint is critical; loss of CMC motion significantly impacts a person’s life. This motion impairment can lead to the loss of personal independence and result in the need for nursing care1,4,19–21,75,169,170. Early diagnosis and treatment of OA can mitigate progression and disease severity later in life171. To improve outcomes in those with OA, we must first decrease the time between disease onset and diagnosis. Earlier identification of motion changes that are related to OA formation will allow for earlier treatment and preservation of hand function. Identification of motion changes in CMC OA is limited by the clinical reliance on planar measurements. In a clinical setting, a goniometer (similar to a protractor) is used to measure ranges of motion in a single plane. However, the axes of CMC motion are non-perpendicular and do not align with the planes of the body, so it is difficult to assess complete function of the CMC joint by only taking goniometer measures55,64. Goniometers have poor inter-rater reliability, and this reliability is even worse when measuring the CMC joint66,67,172,173. Joint deforming diseases like OA, along with the complex motion patterns make it even more challenging to measure CMC motion using a goniometer170. Due to these factors, it is difficult to use a goniometer to identify early CMC OA motion loss or to determine the efficacy of a given treatment. To improve measurement abilities, alternative clinical methods have been developed to obtain single movements of the thumb, specifically, thumb palmar abduction174,175. Although useful, 36 improvement in measurements for palmar abduction do not improve on the other thumb motions. Neither goniometry nor alternative clinical methods are capable of measuring the complex multi- planar motions of the CMC joint. Multi-planar measurements can provide insight into joint function and pathophysiology that cannot be obtained from planar goniometry measurements. Motion capture systems (i.e. cameras and reflective markers) are capable of measuring multi-planar motions. Marker based motion capture systems are able to measure small movements, and have been shown to be an excellent method to measure CMC motion with greater accuracy than goniometry65,68,69,176. The use of motion capture is also becoming more popular in clinical settings such as its use in the Shirley Ryan Ability lab, in surgical training programs, and post-surgery evaluation177–179. The full capacity of motion capture to study CMC OA has not been determined. Although a few studies have evaluated hand motion, these are primarily limited to a small number of participants, usually healthy persons1,2,49,58,72,75,76,176,180–191. No single study has collected standard clinical ranges of motion and multi-planar motion capture data in healthy and CMC OA participants to identify the differences between the participant groups. Three-dimensional (3D) motion data collection in both normative and diseased thumbs is necessary to better understand the complex multi-planar motion changes that occur during aging and in CMC OA pathophysiology. Thus, the goals of this research were 1) to determine differences in thumb motions across three groups of participants (i.e., young healthy, older healthy and those with CMC OA) and 2) to determine if multi-planar motions provided additional movement information in comparison to standard planar measures. 37 3.3 Methods 3.3.1 Testing All testing and participant data were conducted in accordance with Michigan State University's Institutional Review Board and all individuals consented to participation. Participant data collection included the following: American College of Rheumatology criteria, visual analogue scale (VAS) pain score, functional index for hand osteoarthritis (FIHOA) questionnaire, and motion testing107. 3.3.2 Participants All participants were right-handed. Inclusion criteria for the healthy groups was that they had no history of hand surgery or recent hand therapy ( 1 to turn on each option tic; %Starts function timer, checks to see how long to execute function %close all %Makes it so not too many plots stay open, comment out if needed FigOn = 1; %Max/Min Figures PlanePlot = 0; %Plane Plots CirclePlot = 1; %Circle Plots ScaledPlot = 0; %Scaled Plots, show circular and square SuperPlot = 1; %Superimposed Planes Plot SavePlots = 1; %This saves the plots, turn off for faster code runtime ExcelWrite = 0; no_peaks = 11; %Change this to smaller number if needed... %% File Open and Import - Reads filename -> action and sets import structure FileExt = '.mat'; %This is the extension of the matlab file ActionStr = char(strcat(action,FileExt)); %Add the extension to the action 87 A = importdata(ActionStr); %Import the File, aka Load it Trajectories = A.Trajectories.Labeled.Data; %Shorthand for Traj. calls % Rotations = A.RigidBodies.Rotations; %Shorthand for Rot. Mat. calls %% Marker Assignment - Change Marker to CMC, T2, or DIP for different calcs % Note: Each marker is a matrix of position (x,y,z) in each % column and each row representing a frame as a unit of time rad_sty=squeeze(Trajectories(30,1:3,:)); %30 us. 45,46 if virtual prox_rad=squeeze(Trajectories(32,1:3,:)); %32 us. 46,47 if virtual CMC=squeeze(Trajectories(5,1:3,:)); % us 5. if virtual 45 T2=squeeze(Trajectories(9,1:3,:)); DIP = squeeze(Trajectories(13,1:3,:)); % Had to add this to get the code to run for 1_2 CW BIG file. Not sure why % it is only an issue with this file... but should work now. rad_sty(isnan(rad_sty)) = 0; prox_rad(isnan(prox_rad)) = 0; CMC(isnan(CMC)) = 0; % These are the new markets of interest to calc the orientation of the palm Palm_UL = squeeze(Trajectories(1,1:3,:)); Palm_UR = squeeze(Trajectories(2,1:3,:)); Palm_LL = squeeze(Trajectories(3,1:3,:)); Marker1 = CMC; %This assigns the Marker of Interest for the analysis % Take the position of the marker relative to the rad_sty. % This method eliminates some of the wobble and fits actual area w/in % the idealized "possible area" Marker = Marker1 - rad_sty; Palm1 = Palm_UL - rad_sty; Palm2 = Palm_UR - rad_sty; Palm3 = Palm_LL - rad_sty; %% Max/Min Angles for Marker of Interest % This function finds the frames that represent the start of each % rotation. This is used to segment the data by each individual % revolution and is used in later calculations. [CircleStart] = MaxMinAngleV3(action,Marker,prox_rad,rad_sty,FigOn,SavePlots,no_peaks); %Now we just grab the Second Column: The Start Frames for each rotation CircleStartList = CircleStart(:,2); %% Fit Plane to Circles Drawn - Also find centroid of circle and plane normal % Function that fits a plane to each circle and plots as a figure. Plane % fitting is accomplished using the built in PCA function. [Centroids,Normals,CentroidAngles,XBasisVectors,YBasisVectors,DigitMags]... = PlaneFitDrawV3(action,CircleStartList,Marker,PlanePlot,SavePlots); 88 %DigitMags %Quick check to look at digit mags %% 2D Circle Projection and Circle Area Calculations % Here we use the data collected from the PCA analysis to project the % 3D data on to the plane of maximum area. We can then use this 2D % projection and polyfill to find the area of the circle in mm^2. [CircleAreaList,ScaledAreaCirc] = CircleProjectV3... (action,CircleStartList,Marker,Centroids,Normals,XBasisVectors,... YBasisVectors,DigitMags,CirclePlot,ScaledPlot,SavePlots); %% Superimposed Plane Plotting - Used to Compare Consistency of Plane if SuperPlot == 1 figure for i = 1:length(Centroids) plot3(Centroids(i,1),Centroids(i,2),Centroids(i,3),'ro','markersize',5,'markerfacecolor','red'); hold on [P,Q] = meshgrid(-15:15); % Provide a gridwork X = Centroids(i,1)+XBasisVectors(i,1)*YBasisVectors(i,1)*Q; % Compute the corresponding cartesian coordinates Y = Centroids(i,2)+XBasisVectors(i,2)*P+YBasisVectors(i,2)*Q; % using the tbasiso vectors in basis Z = Centroids(i,3)+XBasisVectors(i,3)*P+YBasisVectors(i,3)*Q; surf(X,Y,Z,'facecolor','blue','facealpha',0.5) %Plots the plane hold on end view(Normals(5,:)) %Change this to change the default view PlotTitle = strcat(action,'AllPlanes'); PlotTitle = strrep(PlotTitle,'_',' '); title(PlotTitle) PlotName = strcat(action,'AllPlanes','.fig'); xlabel('X')%added ylabel('Y') zlabel('Z') if SavePlots == 1 saveas(gcf,PlotName) end end %% Excel Output - Writes the Action into a SubjectNo_TimePoint File if ExcelWrite == 1 %File and Tab Naming Based on File Name FileNameArray = strsplit(action,'_'); ExcelFile = char(strcat(FileNameArray(1),'_',FileNameArray(2),'.xlsx')); PageName = char(FileNameArray(3)); %Section for CMC Angle Output HeaderCMC = {'CMC Min','Frame'}; 89 xlswrite(ExcelFile,HeaderCMC,PageName,'A1') xlswrite(ExcelFile,CircleStart,PageName,'A2') %Section for Centroid and Normal Output - Determines the plane CircleNo = (1:length(Normals))'; HeaderCircle = {'Circle No','Centroid X','Centroid Y','Centroid Z'... ,'Normal X','Normal Y','Normal Z','CentAngle','Digit Length'}; xlswrite(ExcelFile,HeaderCircle,PageName,'D1') OutputMatrix = horzcat(CircleNo,Centroids,Normals,CentroidAngles,DigitMags); xlswrite(ExcelFile,OutputMatrix,PageName,'D2') HeaderArea = {'Raw Area','ScaledAreaCirc'}; xlswrite(ExcelFile,HeaderArea,PageName,'M1') AreaOutput = horzcat(CircleAreaList,ScaledAreaCirc); xlswrite(ExcelFile,AreaOutput,PageName,'M2') %Average and SD Values for the Overall File - Start to End OutputAverage = horzcat(nanmean(Centroids(:,1)),nanmean(Centroids(:,2))... ,nanmean(Centroids(:,3)),nanmean(Normals(:,1)),nanmean(Normals(:,2))... ,nanmean(Normals(:,3)),nanmean(CentroidAngles),nanmean(DigitMags)... ,nanmean(CircleAreaList),nanmean(ScaledAreaCirc)); xlswrite(ExcelFile,{'Average'},PageName,'D15') xlswrite(ExcelFile,OutputAverage,PageName,'E15') OutputSTD = horzcat(nanstd(Centroids(:,1)),nanstd(Centroids(:,2))... ,nanstd(Centroids(:,3)),nanstd(Normals(:,1)),nanstd(Normals(:,2))... ,nanstd(Normals(:,3)),nanstd(CentroidAngles),nanstd(DigitMags)... ,nanstd(CircleAreaList),nanstd(ScaledAreaCirc)); xlswrite(ExcelFile,{'STD Dev.'},PageName,'D17') xlswrite(ExcelFile,OutputSTD,PageName,'E17') OutputVar = horzcat(nanvar(Centroids(:,1)),nanvar(Centroids(:,2))... ,nanvar(Centroids(:,3)),nanvar(Normals(:,1)),nanvar(Normals(:,2))... ,nanvar(Normals(:,3)),nanvar(CentroidAngles),nanvar(DigitMags)... ,nanvar(CircleAreaList),nanvar(ScaledAreaCirc)); xlswrite(ExcelFile,{'Variance'},PageName,'D19') xlswrite(ExcelFile,OutputVar,PageName,'E19') disp('Excel Written') end toc; end MaxMinAngle function [CircleStart] = MaxMinAngleV2(action,Marker,prox_rad,rad_sty,FigOn,SavePlots) % Function that finds the Max/Min angles of the thumb to determine the % start and end points of individual rotations %% Vector Calculations %Using the position of the marker of interest in relation to the prox 90 %rad and rad sty we can create sets of vectors that we then use to %caclulate the angle between the vectors. Serves as a crude but %accurate representation of the start and end of each circle. v1 = prox_rad - rad_sty; %Vector that represents the orientation of the wrist v2 = Marker - rad_sty; %Vector that represents the oriention of the thumb Angle = atan2d(norm(cross(v1,v2)),dot(v1,v2)); %% Find Peaks to determine starting points of revolutions no_peaks = 11; %This number is chosen to accurately identify 10 circles for both CW and CCW %Min Peaks, this represents the start of the rotation, Angle is flipped to %find the minimum instead of the maximum. [pksfm,locsfm,~,~] = findpeaks(-Angle,'MinPeakDistance', 90, 'MinPeakProminence', .1, 'NPeaks',no_peaks); % Note: MinPeakDistance and MinPeakProminence may have to be adjusted for % individual data sets. Check Max/Min plots to determine best values CMC_Min(:,1) = pksfm; %First Column of Output: these are the angle values at Min CMC_Min(:,2) = locsfm; %Second Column of Output: these are the start frames for each circle if FigOn == 1 %Figure on setting, Plots both vector and Rot. Matrix method figure plot(-Angle) %This is the plot as seen by find peaks function title('CMCMin Angles') hold on plot(CMC_Min(:,2),CMC_Min(:,1),'o') PlotName = strcat(action,'Min.png'); if SavePlots == 1 saveas(gcf,PlotName) end end %Output to Main Function CircleStart = CMC_Min; end PlaneFitDraw function [Centroids,Normals,CentroidAngles,XBasisVectors,YBasisVectors,DigitMags] = PlaneFitDrawV3(action,CircleStartList,Marker,PlanePlot,SavePlots) % Function that fits a plane to each circle and plots as a figure. Plane % fitting is accomplished using the built in PCA function. %% Initialize the Output Vectors to optimize Code Runtime NumOfLoops = length(CircleStartList)-1; %Fixes one off to account for final entry Centroids = zeros(NumOfLoops,3); %Init the Centroid Matrix Normals = zeros(NumOfLoops,3); %Init the Normals Matrix CentroidAngles = zeros(NumOfLoops,1); 91 XBasisVectors = zeros(NumOfLoops,3); YBasisVectors = zeros(NumOfLoops,3); DigitMags = zeros(NumOfLoops,1); %% Plane Fitting for Each Individual Revolution for i = 1:NumOfLoops % This is a matrix of the positions (x,y,z) in mm as a function of the % frames contained in the individual revolution. PosReltoRad = Marker(:,CircleStartList(i):CircleStartList(i+1))'; VectorAve = [nanmean(PosReltoRad(1,:)),nanmean(PosReltoRad(2,:)),nanmean(PosReltoRad(3,:))]; DigitMags(i) = norm(VectorAve); %Use PCA Function to get the normal and basis vectors for the Circle [coeff,~,~] = pca(PosReltoRad); normal = coeff(:,3); basis = coeff(:,1:2); if PlanePlot == 1 figure plot3(PosReltoRad(:,1),PosReltoRad(:,2),PosReltoRad(:,3),'r.') hold on end %Find the centroid of the circle centroid = [nanmean(PosReltoRad(:,1)),nanmean(PosReltoRad(:,2)),nanmean(PosReltoRad(:,3))]; if PlanePlot == 1 %Plot the centroid plot3(centroid(1),centroid(2),centroid(3),'ro','markersize',15,'markerfacecolor','red'); hold on %Plot the plane [P,Q] = meshgrid(-15:15); % Provide a gridwork for the plane to span X = centroid(1)+basis(1,1)*P+basis(1,2)*Q; Y = centroid(2)+basis(2,1)*P+basis(2,2)*Q; Z = centroid(3)+basis(3,1)*P+basis(3,2)*Q; surf(X,Y,Z,'facecolor','blue','facealpha',0.5) %Plots the plane hold on PlotTitle = strcat(action,' Circle ',num2str(i)); PlotTitle = strrep(PlotTitle,'_',' '); title(PlotTitle) PlaneExp = strcat(num2str(normal(1)),'*','(x- ',num2str(centroid(1)),')+',num2str(normal(2)),'*','(y- ',num2str(centroid(2)),')+',num2str(normal(3)),'*','(z-',num2str(centroid(3)),') = 0'); xlabel(PlaneExp) PlotName = strcat(action,'3DPlane',num2str(i),'.png'); view(0,0) if SavePlots == 1 saveas(gcf,PlotName) end 92 end % Look at Posotion of Radial Styloid to Find the Centroid Angle RadCentVector = centroid; %Find the Vector %Find the Angle of the Vectors using the inverse tangent function CentroidAngles(i,:) = atan2d(norm(cross(RadCentVector,normal)),dot(RadCentVector,normal)); Centroids(i,:) = centroid; Normals(i,:) = normal; XBasisVectors(i,:) = basis(:,1); YBasisVectors(i,:) = basis(:,2); end %% Plane Fitting for all circles drawn Marker = Marker(:,CircleStartList(1):CircleStartList(end))'; %Use PCA Function to get the normal and basis vectors for all Circles [coeff,~,~] = pca(Marker); allnormal = coeff(:,3); allbasis = coeff(:,1:2); %Plot the circle drawn in 3D Space if PlanePlot == 1 figure plot3(Marker(:,1),Marker(:,2),Marker(:,3),'r.') hold on end %Find the centroid of all circles allcentroid = [nanmean(Marker(:,1)),nanmean(Marker(:,2)),nanmean(Marker(:,3))]; %palm_centroid = [nanmean(Palm(:,1)),nanmean(Palm(:,2)),nanmean(Palm(:,3))]; if PlanePlot == 1 %Plot the centroid plot3(allcentroid(1),allcentroid(2),allcentroid(3),'ro','markersize',15,'markerfacecolor','red'); hold on %Plot the plane [P,Q] = meshgrid(-15:15); % Provide a gridwork for the plane to span X = allcentroid(1)+allbasis(1,1)*P+allbasis(1,2)*Q; Y = allcentroid(2)+allbasis(2,1)*P+allbasis(2,2)*Q; Z = allcentroid(3)+allbasis(3,1)*P+allbasis(3,2)*Q; surf(X,Y,Z,'facecolor','blue','facealpha',0.5) %Plots the plane hold on %This names the Plot Title and Allows for changes to filename etc. PlotTitle = strcat(action,'3DPlane','Total'); PlotTitle = strrep(PlotTitle,'_',' '); PlotName = strcat(action,'3DPlane','Total','.png'); title(PlotTitle) view(0,0) if SavePlots == 1 saveas(gcf,PlotName) 93 end end end CircleProject function [CircleAreaList] = CircleProjectV2(action,CircleStartList,Marker,Centroids,Normals,XBasisVectors,YBasisVectors ,CirclePlot,SavePlots) % Here we use the data collected from the PCA analysis to project the % 3D data on to the plane of maximum area. We can then use this 2D % projection and polyfill to find the area of the circle in mm^2. NumOfLoops = length(CircleStartList) - 1; %Number of Loops CircleAreaList = zeros(NumOfLoops,1); %Init a Area Vector for loop for i = 1:NumOfLoops % Grab the position of the marker over a circle time range MarkerXYZ = Marker(:,CircleStartList(i):CircleStartList(i+1))'; LengthOfRev = length(MarkerXYZ); %Find the number of time points % Grab the normal and centroid for the individual circle normal = Normals(i,:); %Grabs the normal for the plane of this circle centroid = Centroids(i,:); %Grabs the centroid of this circle % Initalize some vectors that we will use in the next loop. Proj_Pts = zeros(LengthOfRev,3); %Init the Projected Pts. Matrix dist = zeros(LengthOfRev,3); %Init the distance between pts and plane for j = 1:LengthOfRev dist(j,:) = MarkerXYZ(j,:) - centroid; Proj_Pts(j,:) = MarkerXYZ(j,:) - (dot(normal,dist(j,:))*normal); end %Init the "x" and "y" values that occur on the X/YBasisVectors t_1 = zeros(LengthOfRev); %x-vector for the projection t_2 = zeros(LengthOfRev); %y-vector for the projection s = zeros(LengthOfRev); % Seperation from the plane %This loop finds the distance along the X/Y Basis Vectors for the %2D Projection for k = 1:LengthOfRev t_1(k) = dot(XBasisVectors(i,:), dist(k,:)); t_2(k) = dot(YBasisVectors(i,:), dist(k,:)); s(k) = dot(Normals(i,:),dist(k,:)); end %Plot the actual 2D projection for each revolution if CirclePlot == 1 figure plot (t_1,t_2) %These are the actual x and y values of the projected circle axis([-35 35 -35 35]) hold on 94 PlotName = strcat(action,'2DProj',num2str(i),'.png'); PlotTitle = strcat(action,'2DProj',num2str(i)); PlotTitle = strrep(PlotTitle,'_',' '); area1 = polyarea(t_1,t_2); fill(t_1,t_2,'g') %Fill the Circle xlabel(strcat('Area = ',num2str(area1(1)))); title(PlotTitle) if SavePlots == 1 saveas(gcf,PlotName) end end area = polyarea(t_1,t_2); CircleAreaList(i) = area(1); end 95 BIBLIOGRAPHY 96 BIBLIOGRAPHY 1. 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