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Modeling the Role of the Foot, Toes, and Vestibular System in Human Balance

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Modeling the Role of the Foot, Toes, and Vestibular System in Human Balance Modeling the Role of the Foot, Toes, and Vestibular System in Human Balance Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Laura R. Humphrey, B.S., M.S. Graduate Program in Electrical and Computer Engineering The Ohio State University 2009 Dissertation Committee: Dr. Hooshang Hemami, Adviser Dr. Ashok Krishnamurthy Dr. Andr`eaSerrani c Copyright by Laura R. Humphrey 2009 ABSTRACT The study of human balance and gait is a complex area that involves a large number of biological systems, including the musculoskeletal, somatosensory, vestibu- lar, visual, and central nervous systems. In contrast, computational models used for simulating motion of the human body tend to be relatively simple, especially with respect to the feet. Clinical research, however, has begun to more closely examine the mechanical and sensory contributions of the feet in balance and gait, leading to a disparity between the state of clinical research and models used for simulation. A model with a more complex foot would aid in the clinical diagnosis and treatment of motor control disorders, improvement of prostheses, and development of functional electrical stimulation for recovery of lost motor function. This dissertation presents a computational model of a human with a more complex foot, which uses four rigid and connected segments to represent the heel, forefoot, and toes. Derivation of physical parameters, equations of motion, actuation based on human musculature, and control based on proprioception, i.e. body segment positions and velocities, will be discussed. Computation of ground reaction forces under the heel, forefoot, and toes will also be addressed. Simulations focusing on the role of the toes and toe muscles in static balance, forward leaning, and tip-toe stading will be presented. Contributions by the vestibular system will also be considered. ii This dissertation is dedicated to all the great teachers in my life. iii ACKNOWLEDGMENTS I would first and foremost like to thank my advisor, Professor Hooshang Hemami, for his guidance, support, and knowledge, both in my research and my life. I would also like to thank Professor Barin for his work and insight on our pending publications. Additionally, I would like to thank Professors Serrani and Krishna- murthy for serving on my Graduate Studies Committee. And, I would like to thank several people at the Ohio Supercomputer Center { Alan Chalker, Judy Gardiner, Brian Guilfoos, Ben Smith, and Vijay Gadepally { for providing additional research opportunities, computing resources, and a fantastic work environment. Finally, I would like to thank Jason Parker for being a very bad hobbit. iv VITA June 2004 . B.S. Electrical and Computer Engineering, The Ohio State University March 2006 . .M.S. Electrical and Computer Engineering, The Ohio State University March 2006-present . .Graduate Research Assistant, Ohio Supercomputer Center PUBLICATIONS L. Humphrey et al. Evaluating Parallel Extensions to High Level Languages using the HPC Challenge Benchmarks. Proceedings of the 2009 DoD HPCMP Users Group Conference, 2009. B. Guilfoos, L. Humphrey, and J. Unpingco. Improvements to MPSCP. Proceedings of the 2008 DoD HPCMP Users Group Conference, pp. 376-378, 2008. J. Unpingco, J. Gardiner, L. Humphrey, and S. Ahalt. Computationally Intensive SIP Algorithms on HPC. Proceedings of the 2007 DoD HPCMP Users Group Conference, pp. 271-276, 2007. FIELDS OF STUDY Major Field: Electrical and Computer Engineering v TABLE OF CONTENTS Page Abstract . ii Dedication . iii Acknowledgments . iv Vita......................................... v List of Tables . ix List of Figures . xi Chapters: 1. Introduction . 1 2. Background . 3 2.1 Motor Control Theories . 3 2.2 The Central Nervous System . 5 2.2.1 The Spinal Cord and Brainstem . 5 2.2.2 The Diencephalon and Thalamus . 6 2.2.3 The Cerebellum . 7 2.2.4 The Primary, Secondary, Tertiary, and Association Areas . 7 2.2.5 The Basal Ganglia . 8 2.3 The Peripheral Nervous System . 9 2.3.1 The Somatosensory System . 9 2.3.2 The Vestibular System . 10 2.4 The Musculoskeletal System . 12 vi 2.4.1 Bones, Joints, and Ligaments . 12 2.4.2 Overview of Skeletal Muscles . 13 3. Review of Literature . 16 3.1 Role of Foot Sole Mechanoreceptors in Balance . 16 3.1.1 Effects of Aging . 18 3.1.2 Effects of Disease . 19 3.1.3 Effects of Inhibition . 22 3.1.4 Effects of Stimulation . 25 3.1.5 Balance on a Rotationally Disturbed Platform . 28 3.1.6 Summary . 34 3.2 Role of the Toes in Balance . 37 3.3 Role of the Vestibular System in Balance . 39 4. The Models . 41 4.1 Five-Link Sagittal Biped Model with a Foot . 41 4.1.1 Model Overview . 42 4.1.2 Model Parameters . 44 4.1.3 Muscles, Joints, and Ligaments . 47 4.2 Three-Link Sagittal Biped Model . 48 4.2.1 Model Overview . 49 4.2.2 Muscles . 50 5. Exploring the Role of the Foot Sole and Toes in Balance . 54 5.1 Control of the Five-Link Model Through the Muscles . 54 5.2 The Limits of Static Balance in a Healthy Subject . 58 5.3 The Limits of Static Balance in a Subject with Diminished Toe Mus- cle Strength . 64 5.4 Force Distribution and Foot Arch Angle during Forward Leaning . 68 5.5 Discussion . 71 6. Exploring the Role of the Vestibular System in Balance . 74 6.1 Recovery from Disturbance . 76 6.2 Fall from Disturbance . 79 6.3 Addition of a Vestibular Term . 79 6.4 Vestibular Modulation of Muscular Forces . 82 6.5 Simulation of Chorea-like Motion . 85 6.6 Discussion . 87 vii 7. Conclusions . 89 7.1 Summary . 89 7.2 Future Work . 91 Appendices: A. Nomenclature . 95 B. Deriving Equations of Motion for the Five Link Model . 98 B.1 Basic Equations of Motion . 98 B.2 Terms due to Ground Reaction Forces . 102 B.3 Terms due to the Muscle Inputs . 103 C. Deriving Equations of Motion for the Three Link Model . 104 C.1 Basic Equations of Motion . 104 C.2 Terms due to the Muscle Inputs . 105 C.3 Initial Conditions due to a Sudden Horizontal Platform Disturbance . 107 C.4 Preventing Hyperextension . 108 C.5 Estimating Center of Pressure . 109 Bibliography . 111 viii LIST OF TABLES Table Page 4.1 Lengths, masses, centers of mass, moments of inertia, and end points for major segments of the human body. Mass is given as a percent of total body weight. Center of mass is listed as a percent of the length, measured from the first listed endpoint. Abbreviations are: Cerv for cervicale, MDH for midhip, SJC for shoulder joint (center), EJC for elbow joint, WJC for wrist joint, DAC3 for tip of the 3rd digit (3rd dactylion), HJC for hip joint, KJC for knee joint, AJC for ankle joint, TTIP for tip of the longest toe. 45 4.2 Lengths, masses, centers of mass, moments of inertia, and endpoints for larger segments of the human body derived using values from Table 4.1. 45 4.3 Lengths, masses, centers of mass, moments of inertia, and endpoints for segments of the foot. Values were derived using information from [1]. Note that values are for the segments of one foot only. 46 4.4 Parameters for the five-link biped model. I is moment of inertia in kg·m2 about the center of gravity, m is the mass in kg, l is the length in meters, and k is the distance to the center of mass from one joint of the segment in meters. 46 4.5 Parameters for the three-link biped model. I is moment of inertia in kg·m2 about the center of gravity, m is the mass in kg, l is the length in meters, and k is the distance to the center of mass from one joint of the segment in meters. 50 5.1 Gains and set points used to calculate muscle torques for the five-link biped model during normal standing. 57 ix A.1 Symbols used for both models. \·" designates mixed units. 95 A.2 Symbols used for the five-link model. \·" designates mixed units. 96 A.3 Symbols used for the three-link model. \·" designates mixed units. 97 x LIST OF FIGURES Figure Page 4.1 The five-link sagittal biped is composed of five rigid links. The term ki, for i = 1 ... 5 is the distance from one end of link i to the center of mass of link i. This is shown for all links; however, it is labelled for links 1 and 5 only. The term li is the length of link i. xa and ya are the coordinates of the ankle joint. Angles θi for each link are measured clockwise from the vertical. Fh is the horizontal ground reaction force at the heel, and Gh, Gm, and Gt are the vertical ground reaction forces at the heel, metatarsals, and toe, respectively. 42 4.2 Medial (A) and lateral (B) views of a human foot skeleton. Features as numbered are 1-calcaneus; 2-sustentaculum tali; 3-talus; 4-head of talus; 5-navicular; 6-tuberosity of navicular; 7-medial cuneiform; 8-intermediate cuneiform; 9-base, 10-body, and 11-head of the first metatarsal; 12-base, 13-body, and 14-head of the proximal phalanx of the great toe; 15-base, 16-body, and 17-head of the distal phalanx of the great toe; 18-sesamoid bone; 19-lateral cuneiform; 20-cuboid; 21- base, 22-tuberosity, 23-body, and 24-head of the fifth metatarsal; and 25-tarsal sinus. Taken from [2]. 43 4.3 Muscles used in the five-link sagittal biped model.
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