Applied Science, Faculty of
Mechanical Engineering, Department of
DSpace
UBCV
Qiao, Zhuhan (Calvin)
Doctor of Philosophy - PhD
University of British Columbia
Standing balance deficits are common in aging populations and individuals with neurological disorders, including patients with traumatic brain injuries. Despite the prevalence, the neural mechanisms underlying such deficits remain unclear. Existing standing balance tests mainly focus on global postural stability metrics, often neglecting the roles of individual sensory organs and neural components. Therefore, new methods are required to better probe the standing balance circuit. The cerebellum emerges as a key neural center for managing standing balance control and its adaptability. While human-in-the-loop robotic balance platforms have been used to test balance adaptability, they are limited to the anteroposterior direction and lack direct cerebellar measurements. To address these limitations and investigate the underlying mechanisms of standing balance control deficits, this thesis has the following objectives: (1) conduct a literature review to summarize standing balance deficits, current test paradigms and their limitations, with a focus on patients with concussions, (2) achieve multidirectional control on a human-in-the-loop balance robot by adding mediolateral (ML) capabilities, (3) develop an accurate kinematics model for ML balance simulation, and (4) develop an experimental protocol that combines electroencephalography (EEG) with the robot to measure cerebellar activity during adaptation. The literature review confirmed relatively consistent post-concussion global balance stability changes and highlighted the need to develop more specific methodologies to probe the balance control circuit. After upgrading the balance robot to include ML control, its motion tracking performance achieved delays under 15 ms and submillimeter errors. A multi-segmental kinematics ML balance model was developed, validated through experiments, and improved through data-driven refinements. The refined model reduced root mean squared errors of the estimated trunk/pelvis position by 37.4-47.4%. Additionally, a balance adaptation study combining the balance robot and an EEG device revealed cerebellar power increases in delta, beta, and gamma bands during early adaptation followed by decreases to baselines post-adaptation in healthy individuals. These advancements enable the study of standing balance adaptability in multidirectional contexts and could help quantify deficits in standing balance adaptation and cerebellar function in various patient groups, leading to more tailored balance assessment and recovery management.
INVESTIGATING CEREBELLAR INVOLVEMENT IN THE ADAPTABILITY OF STANDING BALANCE CONTROL USING A ROBOTIC PLATFORM AND ELECTROENCEPHALOGRAPHY by Zhuhan (Calvin) Qiao M.S., Carnegie Mellon University, 2019 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) June 2024 © Zhuhan (Calvin) Qiao, 2024 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: Investigating Cerebellar Involvement in the Adaptability of Standing Balance Control Using a Robotic Platform and Electroencephalography submitted by Zhuhan (Calvin) Qiao in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Examining Committee: Lyndia Wu, Assistant Professor, Department of Mechanical Engineering, UBC Supervisor Jean-Sébastien Blouin, Professor, School of Kinesiology, UBC Co-supervisor Bryan Gick, Professor, Department of Linguistics, UBC University Examiner Peter Cripton, Professor, School of Biomedical Engineering, UBC University Examiner Jean Blouin, Professor, Laboratoire de Neurosciences Cognitives, Aix-Marseille University External Examiner Additional Supervisory Committee Members: Agnes d’Entremont, Associate Professor of Teaching, Department of Mechanical Engineering, UBC Supervisory Committee Member Julia Schmidt, Assistant Professor, Department of Occupational Science and Occupational Therapy, UBC Supervisory Committee Member iii Abstract Standing balance deficits are common in aging populations and individuals with neurological disorders, including patients with traumatic brain injuries. Despite the prevalence, the neural mechanisms underlying such deficits remain unclear. Existing standing balance tests mainly focus on global postural stability metrics, often neglecting the roles of individual sensory organs and neural components. Therefore, new methods are required to better probe the standing balance circuit. The cerebellum emerges as a key neural center for managing standing balance control and its adaptability. While human-in-the-loop robotic balance platforms have been used to test balance adaptability, they are limited to the anteroposterior direction and lack direct cerebellar measurements. To address these limitations and investigate the underlying mechanisms of standing balance control deficits, this thesis has the following objectives: (1) conduct a literature review to summarize standing balance deficits, current test paradigms and their limitations, with a focus on patients with concussions, (2) achieve multidirectional control on a human-in-the-loop balance robot by adding mediolateral (ML) capabilities, (3) develop an accurate kinematics model for ML balance simulation, and (4) develop an experimental protocol that combines electroencephalography (EEG) with the robot to measure cerebellar activity during adaptation. The literature review confirmed relatively consistent post-concussion global balance stability changes and highlighted the need to develop more specific methodologies to probe the balance control circuit. After upgrading the balance robot to include ML control, its motion tracking performance achieved delays under 15 ms and submillimeter errors. A multi-segmental kinematics ML balance model was developed, validated through experiments, and improved iv through data-driven refinements. The refined model reduced root mean squared errors of the estimated trunk/pelvis position by 37.4-47.4%. Additionally, a balance adaptation study combining the balance robot and an EEG device revealed cerebellar power increases in delta, beta, and gamma bands during early adaptation followed by decreases to baselines post-adaptation in healthy individuals. These advancements enable the study of standing balance adaptability in multidirectional contexts and could help quantify deficits in standing balance adaptation and cerebellar function in various patient groups, leading to more tailored balance assessment and recovery management. v Lay Summary The mechanisms underlying standing balance deficits are poorly understood in certain clinical populations, including patients with brain injuries. This thesis aimed to improve existing balance testing techniques to enable the study of the role of the cerebellum in such deficits. Specifically, I upgraded the robotic balance platform by adding side-to-side control and developing a kinematics model to simulate body segment movements in this direction. In addition, I combined neural sensors with the balance robot to measure cerebellar activity during balance adaptation in healthy individuals. The results showed excellent motion tracking performance of the robot, improved model accuracy, and increased cerebellar activities during early adaptation. These technological advances could improve the specificity of balance assessment and rehabilitation programs for patients with standing balance deficits. vi Preface This dissertation represents a collaborative effort between the Sensing in Biomechanical Processes Laboratory in the Department of Mechanical Engineering and the Sensorimotor Physiology Laboratory in the School of Kinesiology at the University of British Columbia (UBC). The formulation and execution of the research project, as well as the content development for each chapter, were completed by me, Zhuhan (Calvin) Qiao, under the guidance of Dr. Lyndia Wu and Dr. Jean-Sébastien Blouin. This encompassed conducting a comprehensive literature review, enhancing a human-in-the-loop robotic balance system, validating a mediolateral balance model, integrating electroencephalogram technology to study cerebellar involvement in balance adaptation, and conducting extensive data and statistical analyses. The experiments conducted in this thesis were approved by the ethics behavior board and clinical board at UBC under application numbers: H18-03702 and H22-00523. This dissertation presents advancements and findings that have been disseminated through various publications and conference presentations: • C.Z. Qiao, A. Chen, J.S. Blouin, L.C. Wu, Potential mechanisms of acute standing balance deficits after concussions and subconcussive head impacts: a review. Annals of Biomedical Engineering. 49.10 (2021): 2693-2715. • C.Z. Qiao, A. Chen, J.S. Blouin, L.C. Wu, Mechanisms of acute standing balance changes after concussion and subconcussive head impacts. Poster Presentation at the Biomedical Engineering Society Annual Meeting. (2021). vii • C.Z. Qiao, A.M. Nasrabadi, R. Partovi, P. Belzner, C. Kuo, L.C. Wu, J.S. Blouin, Multidirectional human-in-the-loop balance robotic system. IEEE Robotics and Automation Letters (2023). • C.Z. Qiao, J. Chalton, T. Pan, C. Aitken, C. Kuo, L.C. Wu, J.S. Blouin, Modeling multi-segmental kinematics of mediolateral standing balance: validation and refinement of a whole-body center of mass decomposition approach. Manuscript under preparation. • C.Z. Qiao, R. Partovi, C. Kuo, L.C. Wu, J.S. Blouin, Developing and validating a mediolateral balance model for a robotic balance platform. Oral Presentation at the 9th World Congress of Biomechanics. (2022). • C.Z. Qiao, C. Kuo, L.C. Wu, J.S. Blouin, Multi-segmental model of the mediolateral kinematics of standing balance. Poster Presentation at the Neural Control of Movement Annual Meeting. (2023). • C.Z. Qiao, R. Qiu, J.S. Blouin, L.C. Wu, A novel methodology to investigate cerebellar involvement during adaptation to an unexpected delay in standing balance control. Oral Presentation at the Biomedical Engineering Society Annual Meeting. (2023). • C.Z. Qiao, C. Aitken, R. Qiu, J.S. Blouin, L.C. Wu, A novel methodology to investigate cerebellar involvement during adaptation to an unexpected delay in standing balance control. Manuscript under preparation. This thesis could not have been accomplished without the help and participation of many people: Dr. Anthony Chen was involved in revising the literature review article, especially the section on the human standing balance system; Dr. Calvin Kuo proposed the first algorithm for the center-of-mass decomposition model and was involved in designing the validation experiments for the mediolateral balance; Amin Mohammadi Nasrabadi, Reza Partovi, and Paul Belzner were viii involved in the development of the robotic system. Dr. Jesse Charlton and I completed the human balance data collection for the mediolateral model validation experiment. Tianyue Pan was involved in analyzing some of the balance data. Ruixin Qiu helped design and improve the robotic-electroencephalography (EEG) experimental protocol and participated in early data analysis. Caroline Aitken assisted in the data analysis of the robotic-EEG experiment, especially the sway velocity variance part. ix Table of Contents Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ......................................................................................................................... ix List of Tables ................................................................................................................................xv List of Figures ............................................................................................................................. xvi Acknowledgements .................................................................................................................. xviii Chapter 1: Background and Motivation .....................................................................................1 1.1 Standing Balance Deficits ............................................................................................... 1 1.2 Prevalence of Standing Balance Deficits Following Concussions ................................. 2 1.3 Biomechanics of Concussions and Subconcussive Head Impacts .................................. 5 1.4 The Human Standing Balance System ............................................................................ 7 1.5 The Cerebellum and Its Potential Damages Post-Concussion ...................................... 13 1.6 Robotic Balance Platforms and Delay Adaptation Paradigm ....................................... 15 1.7 Electroencephalogram (EEG) ....................................................................................... 16 1.8 Current Technological Limitations ............................................................................... 18 1.9 Thesis Objectives .......................................................................................................... 19 1.10 Thesis Overview ........................................................................................................... 20 Chapter 2: Potential Mechanisms of Acute Standing Balance Deficits After Concussions and Subconcussive Head Impacts – A Review ..........................................................................21 x 2.1 Standing Balance-Related Sensorimotor Assessments for Concussion and Subconcussive Head Impacts .................................................................................................... 21 2.2 Acute Standing Balance-Related Sensorimotor Changes After Concussions and Subconcussive Head Impacts .................................................................................................... 25 2.2.1 Acute Standing Balance-Related Sensorimotor Changes After Concussions ...... 26 2.2.2 Acute Standing Balance-Related Sensorimotor Changes After Subconcussive Head Impacts ........................................................................................................................ 35 2.3 Discussion ..................................................................................................................... 56 2.3.1 Summarizing Standing Balance Deficits After Concussions and Subconcussive Head Impacts ........................................................................................................................ 56 2.3.2 Limitations and Recommendations in Standing Balance Testing After Concussions and Subconcussive Head Impacts .................................................................... 59 2.3.3 Linking Between Neural Damages and Higher-Level Standing Balance Deficits 62 2.4 Summary ....................................................................................................................... 65 Chapter 3: Design and Development of a Multidirectional Human-in-the-Loop Robotic Balance Platform ..........................................................................................................................68 3.1 Introduction ................................................................................................................... 68 3.2 System Architecture ...................................................................................................... 71 3.2.1 Design Requirements ............................................................................................ 71 3.2.2 Mechanical Architecture ....................................................................................... 72 3.2.3 Software Architecture ........................................................................................... 77 3.2.4 Details of the Whole-Body Center of Mass Decomposition Model ..................... 79 3.2.5 Electronic Architecture ......................................................................................... 83 xi 3.3 Balance Motion Tracking Performance ........................................................................ 84 3.3.1 Multi-Sine Standing Balance Trajectory .............................................................. 84 3.3.2 Natural Unperturbed Standing Balance Trajectory ............................................... 85 3.3.3 Performance Qualification .................................................................................... 85 3.3.4 Experimental Results ............................................................................................ 86 3.4 Human-Robot Interactive Balance Performance .......................................................... 88 3.4.1 Experimental Procedure ........................................................................................ 88 3.4.2 Data Recording and Analysis................................................................................ 89 3.4.3 Experimental Results ............................................................................................ 89 3.5 Discussion ..................................................................................................................... 92 Chapter 4: Modeling Multi-Segmental Kinematics of Mediolateral Standing Balance: Validation and Refinement of a Whole-Body Center of Mass Decomposition Approach ....94 4.1 Introduction ................................................................................................................... 94 4.2 Materials and Methods .................................................................................................. 97 4.2.1 A Brief Overview of the Center of Mass Decomposition Model ......................... 97 4.2.2 Participant Recruitment ...................................................................................... 100 4.2.3 Experimental Apparatus and Data Collection..................................................... 100 4.2.4 Experimental Procedure ...................................................................................... 101 4.2.5 Data Preprocessing.............................................................................................. 102 4.2.5.1 Stance Width ................................................................................................... 102 4.2.5.2 Trunk/Pelvis Position ...................................................................................... 102 4.2.5.3 Trunk-Pelvis Angle ......................................................................................... 102 4.2.5.4 Force Plate-Estimated Whole-Body CoM Angle ........................................... 103 xii 4.2.5.5 The Slope Between Segmental Kinematics and CoM Angle ......................... 104 4.2.6 Model Accuracy Analysis ................................................................................... 104 4.2.6.1 Root Mean Squared Error ............................................................................... 105 4.2.6.2 Slope Ratio ...................................................................................................... 105 4.2.7 Data-Driven Model Refinement ......................................................................... 105 4.2.8 Cross-Validation Analysis .................................................................................. 107 4.2.9 Statistical Analysis .............................................................................................. 107 4.2.10 Exploratory Analyses of Movement Mechanisms .............................................. 108 4.3 Results ......................................................................................................................... 109 4.3.1 Measured Trunk-Pelvis Angle ............................................................................ 109 4.3.2 Estimation Errors of the Original Model ............................................................ 110 4.3.3 Results of the Cross-Validation Analysis ........................................................... 113 4.3.4 Measured Head Position and Trunk Angle In Space .......................................... 116 4.4 Discussion ................................................................................................................... 118 4.4.1 Trunk-Pelvis Perpendicular Assumption ............................................................ 119 4.4.2 Sources of Model Estimation Errors ................................................................... 120 4.4.3 Potential Mechanisms of the Observed Trunk/Pelvis Movements ..................... 121 4.4.4 Application and Limitations of the Model .......................................................... 122 4.5 Conclusion .................................................................................................................. 123 Chapter 5: Applying a Robotic Balance System and Electroencephalogram to Investigate Cerebellar Involvement During Adaptation to Unexpected Delays in Standing Balance Control ........................................................................................................................................125 5.1 Introduction ................................................................................................................. 125 xiii 5.2 Materials and Methods ................................................................................................ 128 5.2.1 Participant Recruitment ...................................................................................... 128 5.2.2 EEG Instrumentation .......................................................................................... 128 5.2.3 Delayed Balance Control Adaptation Paradigm ................................................. 129 5.2.4 Experimental Procedures .................................................................................... 130 5.2.4.1 Anthropometric Measurements ....................................................................... 131 5.2.4.2 Robot Setup and Familiarization .................................................................... 131 5.2.4.3 Experimental Protocol .................................................................................... 132 5.2.5 Data Synchronization and Collection ................................................................. 133 5.2.6 Data Analysis ...................................................................................................... 133 5.2.6.1 Standing Balance Velocity Variance Analysis ............................................... 133 5.2.6.2 EEG Data Preprocessing ................................................................................. 134 5.2.6.3 Cerebellar EEG Data Analysis........................................................................ 135 5.2.6.4 Statistical Analysis .......................................................................................... 136 5.3 Results ......................................................................................................................... 137 5.3.1 Results of Sway Velocity Variance Analysis .................................................... 137 5.3.2 Results of EEG Cleaning .................................................................................... 138 5.3.3 Cerebellar Power Change and Its Association with Adaptation Progress .......... 141 5.4 Discussion ................................................................................................................... 147 5.4.1 Cerebellar Neural Oscillations and Their Implications ...................................... 147 5.4.2 Muscular Contamination in Cerebellar EEG Signals ......................................... 149 5.4.3 Limitations and Future Work .............................................................................. 150 Chapter 6: Conclusions and Future Work ..............................................................................153 xiv 6.1 Conclusions ................................................................................................................. 153 6.2 Limitations .................................................................................................................. 157 6.3 Future Work ................................................................................................................ 158 6.3.1 Multidirectional Control of Standing Balance .................................................... 158 6.3.2 Standing Balance Adaptation in Patients ............................................................ 158 6.3.3 Integration of Advanced Neuroimaging Techniques .......................................... 159 6.3.4 Development of Personalized Rehabilitation Strategies ..................................... 160 6.3.5 Translation into Clinical Practice ........................................................................ 161 6.3.6 Summary and Outlook ........................................................................................ 161 Bibliography ...............................................................................................................................163 Appendices ..................................................................................................................................207 Appendix A Verbal Instructions for the Mediolateral Balance Experiment ........................... 207 Appendix B Results of Individual Fitting and Statistical Parametric Mapping ...................... 208 Appendix C Summary - Linear Mixed-Effects Model for Mediolateral Balance Analysis ... 209 Appendix D Verbal Instructions for the Delay Balance Experiment ..................................... 210 Appendix E Summary - Linear Mixed-Effects Model for Cerebellar Power Analysis .......... 213 xv List of Tables Table 2.1 Acute global standing balance deficits after concussions. ............................................ 27 Table 2.2 Acute visual/vestibular sensory deficits after concussions ........................................... 33 Table 2.3 Acute standing balance-related sensorimotor changes after subconcussive head impacts....................................................................................................................................................... 37 Table 3.1 Results of balance motion tracking ............................................................................... 86 Table 3.2 Results of the human-robot interactive balance experiment ......................................... 90 Table 4.1 Average root mean squared errors and slope ratios of trunk/pelvis positions estimated by the original model vs. the refined model ............................................................................... 112 Table 5.1 Post-cleaning results ................................................................................................... 139 xvi List of Figures Figure 1.1 Overview of potential mechanisms of head impact-induced standing balance deficits 9 Figure 1.2 Standing balance measurements and frequency characteristics .................................. 11 Figure 2.1 CoP Entropy calculation and the influences of hyper-parameters .............................. 22 Figure 3.1 Mechanisms of the balance robotic system ................................................................. 73 Figure 3.2 Angular-to-linear mappings for anteroposterior balance control ................................ 76 Figure 3.3 Human-in-the-loop balance control ............................................................................. 78 Figure 3.4 The mediolateral whole-body center of mass decomposition model .......................... 80 Figure 3.5 Balance motion tracking performance ......................................................................... 87 Figure 3.6 Interactive balance performance .................................................................................. 91 Figure 4.1 Experimental setups ..................................................................................................... 99 Figure 4.2 Measured trunk-pelvis angle and center of mass angle across stance widths ........... 109 Figure 4.3 Estimation errors using the original model ............................................................... 111 Figure 4.4 Comparison between the original model vs. the refined model ................................ 114 Figure 4.5 Error comparison of estimated trunk/pelvis positions with respect to the range of center of mass angle using the original and refined models ....................................................... 115 Figure 4.6 Final fitting results ..................................................................................................... 116 Figure 4.7 Results of exploratory analyses ................................................................................. 129 Figure 5.2 Robot-induced standing balance delays .................................................................... 130 Figure 5.3 Experimental procedure ............................................................................................. 130 Figure 5.4 Velocity variance across participants ........................................................................ 138 Figure 5.5 Examples of pre- vs. post-cleaning cerebellar EEG signals ...................................... 140 xvii Figure 5.6 Delta cerebellar power changes ................................................................................. 142 Figure 5.7 Beta cerebellar power changes .................................................................................. 143 Figure 5.8 Gamma cerebellar power changes ............................................................................. 144 Figure 5.9 Theta cerebellar power changes ................................................................................ 145 Figure 5.10 Alpha cerebellar power changes .............................................................................. 146 xviii Acknowledgements I would like to express my deepest gratitude to my supervisors, Lyndia Wu and Jean-Sébastien Blouin, for their unwavering support, guidance, and invaluable mentorship throughout this research endeavor. Their expertise, encouragement, and constructive feedback have been instrumental in shaping the direction of this dissertation. I also extend my gratitude to my committee members, Agnes d’Entremont and Julia Schmidt, for their insightful comments, suggestions, and expertise, which have significantly enhanced the quality of this work. This research was made possible through the generous support of various sources, including the Natural Sciences and Engineering Research Council of Canada (NSERC), Michael Smith Health Research British Columbia, and UBC’s four-year fellowships. I am immensely thankful for their financial assistance, which enabled me to undertake this study. I extend my heartfelt appreciation to my fellow students, lab mates, and colleagues for their camaraderie, encouragement, and collaborative spirit. Their support and camaraderie have made this journey both fulfilling and enjoyable. My family deserves special recognition for their unwavering love, encouragement, and understanding throughout my academic pursuit. I am particularly grateful to my parents for their moral and financial support over the years. Lastly, I would like to acknowledge the contributions of all individuals who directly or indirectly supported me during this research endeavor. Your assistance and encouragement have been invaluable, and I am truly grateful for your contributions. Thank you all for being an integral part of this journey. 1 Chapter 1: Background and Motivation 1.1 Standing Balance Deficits Standing balance deficits are a common issue in aging populations and various clinical conditions, leading to increased fall risks and affecting quality of life [1]–[4]. For example, aging is associated with a progressive loss of sensorimotor function, including structural and functional changes in the somatosensory, visual, and vestibular sensory systems, along with declines in central neural processing and muscular strength [1], [5]. These sensorimotor changes could result in slower reaction times and reduced postural stability, impairing standing balance control, especially under cognitive loads and in reaction to unexpected postural disturbances. In clinical populations, standing balance deficits could arise from a variety of neurological conditions, including stroke, Parkinson's disease, multiple sclerosis, Alzheimer's disease, Huntington's disease, cerebellar ataxia, and traumatic brain injuries [3], [6]–[11]. Understanding the mechanisms of these observed deficits is crucial for enhancing standing balance assessments and rehabilitation strategies. The pathophysiological mechanisms responsible for such deficits can be mainly organized into the following three categories: • Abnormal acquisition, transmission, or perception of sensory signals, • Abnormal sensorimotor integration and planning in the neural controller in the brain, • Impaired transmission of motor output or musculoskeletal system damage. With a better understanding of the specific injury mechanisms underlying higher-level balance deficits, tailored interventions, such as neuro-modulation [12], strength training [13], and sensory rehabilitation [14], can be developed to target the source of injuries with higher specificity. To improve the specificity of standing balance assessments, this thesis research aims to develop new technologies and methodologies for a deeper investigation of the mechanisms 2 behind standing balance deficits. The initial focus is on patients with concussions, a common condition that leads to such deficits. Given the cerebellum's crucial role in achieving standing balance control and its adaptability, it has been identified as one of the key areas of interest in concussion mechanism research and thus a target region of interest of this thesis. To address several technological limitations, I have enhanced existing robotic balance platforms and integrated them with electroencephalography (EEG) technology. This integrated approach allows a detailed examination of the cerebellum's role in standing balance adaptation tasks. While the initial focus is on patients with concussions, the developed technology has the potential to be generalized and applied to other populations with standing balance deficits, broadening its impact and utility in various clinical and research settings. 1.2 Prevalence of Standing Balance Deficits Following Concussions Among the various clinical conditions that can lead to standing balance deficits, concussion stands out as a significant public health concern in recent years with increasing public attention due to its prevalence and potential long-term impacts. In Canada, the average annual concussion incidence was reported to be 1,153 per 100,000 residents [15]. In the United States, approximately 1.7 to 3 million sports- or recreation-related concussions occur each year with higher incidence in collision sports such as American football and ice hockey [16]. Concussions, most formally referred to as mild traumatic brain injury (mTBI), usually result in transient neurological symptoms without apparent structural brain changes in standard clinical neuroimaging [17], [18]. The Concussion in Sport Group (CISG) published a new consensus statement at the 6th International Conference on Concussion in Sports in 2022, which provides a concise and widely accepted definition of sports-related concussion: 3 “A traumatic brain injury caused by a direct blow to the head, neck or body resulting in an impulsive force being transmitted to the brain that occurs in sports and exercise-related activities. This initiates a neurotransmitter and metabolic cascade, with possible axonal injury, blood flow change and inflammation affecting the brain. Symptoms and signs may present immediately, or evolve over minutes or hours, and commonly resolve within days, but may be prolonged. No abnormality is seen on standard structural neuroimaging studies (computed tomography or magnetic resonance imaging T1- and T2-weighted images), but in the research setting, abnormalities may be present on functional, blood flow or metabolic imaging studies. Sport-related concussion results in a range of clinical symptoms and signs that may or may not involve loss of consciousness. The clinical symptoms and signs of concussion cannot be explained solely by (but may occur concomitantly with) drug, alcohol, or medication use, other injuries (such as cervical injuries, peripheral vestibular dysfunction) or other comorbidities (such as psychological factors or coexisting medical conditions). [19]” Individuals with concussions commonly experience deficits in sensorimotor function. Around 30% of sports concussion patients exhibit acute balance problems [20], [21]. Although the majority of balance symptoms usually resolve within 2 weeks for adults and within 4 weeks for children and adolescents following concussions, several studies have documented persistent balance deficits extending beyond these time frames [22]–[24]. Vestibular and vision symptoms may be even more common, with 67-77% of patients with concussion reporting dizziness [25] and 69% exhibiting visual disorders [26]. These symptoms play a significant role in contributing to balance problems by impacting sensory input essential for maintaining balance. Thus, balance assessments are commonly integrated into concussion evaluation protocols. For example, standing balance testing is a major component of the standardized Sports Concussion Assessment Tool (SCAT) 4 [27]–[29], and the balance function is the main determinant of return-to-play/work/school decisions after concussions [30]. More recently, attention has been drawn to subconcussive head impacts, which are milder head traumas that do not result in clinical concussions [31]. Athletes can sustain up to thousands of subconcussive head impacts per sports season [32], [33], raising concerns about their cumulative effects. Notably, balance deficits have been observed in collegiate football players without clinical concussions [34]–[36]. This underscores the importance of comprehensively understanding the impact of both concussive and subconcussive events on balance function and overall neurological health. Concussions are thought to affect brain function through mechanical deformations of brain tissue often resulting from direct impacts to the head [37]–[40]. Considerable concussion research has focused on identifying biomechanical parameters to quantify the risk of sustaining clinical concussions; however, few studies have identified mechanistic links between the biomechanical inputs and the highly variable types and severities of trauma outcomes, including balance deficits. Several review articles have questioned the diagnostic sensitivity of sideline balance tests for concussion [20], [41], [42], prompting the question of why balance deficits may be clearly observed in some patients with concussions, but not others. As such, some have advocated for more comprehensive post-concussion evaluations looking at different aspects of balance function, namely, postural stability [43], postural complexity [20], and sensory deficits associated with postural control [44]–[46], which may elucidate the origins and mechanisms of sensorimotor or neural trauma. Overall, there exists a gap in bridging the biomechanical mechanisms of concussion with resulting post-concussion standing balance deficits. Given the known variability in the biomechanics of concussive and subconcussive head impacts [31], [47]–[52], a key research question is, can we link head impact biomechanics to the 5 presence/absence of balance deficits, or even to the characteristics of these deficits based on the underlying mechanisms of trauma? One of fundamental theoretical frameworks we can use to formalize the problem is by viewing the control of standing balance as an intricate multi-sensory feedback control circuit, the subcomponents of which may get mechanically disrupted by concussive and subconcussive head impacts producing observable balance deficits. 1.3 Biomechanics of Concussions and Subconcussive Head Impacts The biomechanics of head impacts are typically quantified through head/skull kinematics, assuming the skull experiences little deformation and undergoes rigid-body motion. The head/skull accelerations exhibit an impulse response, with short impulse duration on the order of tens of milliseconds [49], [51], [53]. Peak linear and rotational accelerations are usually reported as gross representations of head impact severity. Impacts leading to clinical concussions generally produce higher magnitude head kinematics than subconcussive head impacts. According to head impact exposure data from football, soccer, lacrosse, rugby, and hockey studies, peak linear and rotational head accelerations inducing concussive symptoms were generally between 50-100 g or higher and 5000-10,000 rad/s2 or higher, respectively [47]–[49], [54]–[56], whereas subconcussive head impacts exhibited kinematics typically between 10-30 g or lower and 1,000-3,000 rad/s2 or lower, respectively [31], [50]–[52]. Despite these general observations, it is important to note that there is no clear skull kinematic threshold for predicting concussion risk [57]. Prior studies have reported concussion cases with lower head kinematics (e.g., 15-30 g and < 1000-3000 rad/s2) [56], [58]–[60] and high kinematics impacts (e.g., > 90 g and > 5000 rad/s2) that did not result in clinical concussion diagnoses [36], [61], [62]. Instead, concussions are likely influenced by factors such as the impact response of the skull, material properties, tolerance of brain structures, as well as the vulnerability of neural structures 6 and sensory end organs within the head. Due to challenges in using simple head kinematic thresholds for identifying injury, researchers have explored other predictors of injury risk through brain biomechanical parameters based on direct brain deformations. Generally, head linear accelerations have been associated with focal brain deformation and pressure gradients across brain tissue [63], [64], whereas head rotational velocities and accelerations have been mainly associated with diffuse brain tissue strains that may disrupt neural connectivity [37], [38], [65], [66]. Agreeing with the observation that injury severities and symptoms are highly variable across concussions and individuals, the directionality [67], [68], dynamics (e.g. impact duration) [69], [70], and magnitudes of impacts can influence brain deformation patterns. For example, in primates, coronal (lateral plane that divides the body or its components into anterior and posterior portions) head rotation induced more severe diffuse axonal injury compared with head rotations in other planes at similar head kinematics magnitudes [67]. A centripetal theory of concussion also hypothesized that diffuse strains propagate from the surface of the brain towards deeper centers, and the severity of injury correlates with increasing centripetal progression of tissue strains [71]. Considering the complexity of brain geometry and material properties, investigations of injury mechanisms based on brain loading parameters are supported by finite element model (FEM) analysis. To date, a number of human head FEMs incorporating biofidelic brain geometry and material properties have been developed and used for concussion analyses [72]–[76]. These FEMs simulate the mechanical behaviour of the brain as a soft deformable body and quantify resultant brain tissue deformations given external head kinematics inputs. Most prior modeling studies have extracted peak brain strain metrics [40], [77]–[79] and regional strain metrics in the cerebral cortex [40], [75], [80], corpus callosum [40], [78], [80], [81], basal ganglia [77], [79], thalamus [40], [77], [79], brainstem [40], [77], [82], [83], and cerebellum [40], [78] as potential correlates of 7 concussion risk. However, there are limited concussion head impact data available for FEM analyses, and so far, no clear injury threshold for concussion has been defined using FEM-derived brain deformation metrics. It should be noted that concussion biomechanics analyses and FEMs typically do not quantify stresses and strains experienced by sensory end organs or cranial nerves, yet these components may also be deformed by head trauma and could play a role in commonly observed concussion symptoms (e.g., dizziness, visual disruptions). The sensorimotor control of standing balance requires sensing of whole-body motion via peripheral visual/vestibular sensors located in the head as well as synergistic activation of multiple brain regions. Mechanical blows to the head may result in damages in one or more sensory end organs and neural components involved in keeping an upright stance, resulting in standing balance deficits. In the following section, the anatomy, function, and biomechanics of the human standing balance control system are briefly reviewed. 1.4 The Human Standing Balance System The primary goal of standing balance is to keep the unstable body upright. To achieve this, the nervous system must coordinate the activity of appendicular and axial muscles to stabilize the body within a base of support defined by the outer edge of both feet. Mechanically, the maintenance of an upright stance is accomplished by actively modulating the self-generated torque to counterbalance the torque induced by gravity acting on the upright body. Given that the gravitational torque and the reaction torque are not perfectly balanced, the whole-body experiences motion (termed postural oscillations) when upright. From a control perspective, human standing balance can be modeled as a closed-loop feedback system consisting of three major components 8 (Figure 1.1): peripheral sensors, a balance controller consisting of a network of brain structures, and motor dynamics [84]–[86]. The peripheral sensors mainly include the vestibular, visual, auditory, and somatosensory subsystems. The vestibular end organs encode linear (gravito-inertial), and rotational head accelerations via the otoliths (utricle and saccule) and semicircular canals, respectively [87], [88]. Vestibular, visual and directional auditory cues are integrated to form self-motion perception [89]–[93]. In contrast to the head-centered nature of the vestibular, visual, and auditory signals, the somatosensory system relies on mechanoreceptors distributed in muscles, joints, tendons, and skin throughout the body to perceive relative limb position and movement [94]–[96]. Sensory signals encoded by sensory receptors are transduced into neural impulses and transmitted to multiple neural structures including the spinal cord, cerebellum, brainstem, basal ganglia, thalamus, and cortex. Together, these structures are referred to as the central neural balance controller and are responsible for integrating multi-sensory information, forming internal representations of body motion, and generating corrective motor commands to remain upright [84], [97]–[99]. Interestingly, these structures have been implicated in concussion biomechanics studies, as mentioned in the previous section, and may thus warrant a closer investigation into their functional links to concussion-related balance deficits. 9 Figure 1.1 Overview of potential mechanisms of head impact-induced standing balance deficits. (A). Concussive and subconcussive head impacts may mechanically deform soft tissue on the head, including sensory and neural components that could be critical for standing balance function. (B). Soft tissue deformation may disrupt one or more components of the close-loop feedback control circuit of human standing balance. This circuit involves central integration of the sensory cues from peripheral sensors (vestibular, visual, somatosensory, and auditory) to calculate the necessary motor commands for the purpose of maintaining the body’s balance set-point. (C). Mechanical disruption of this balance control loop could result in global standing balance deficits (e.g. greater postural sway). The brainstem houses a critical network of neurons for sensorimotor integration and control with deep interconnections to multiple parts of the brain (including the cerebellum and sensorimotor cortex) and multisensory systems. Critical brainstem structures for the control of standing balance include the vestibular nuclei and reticular formation [100]. The convergence of inputs occurring in the brainstem provides it with crucial capacities to manage and modulate reflexes of vestibular origin, anticipatory/reactive postural adjustments, and muscle tone [100]. The thalamus, acknowledged as a relay hub, contributes to sensorimotor control by processing sensory signals from various sources before transmitting them to cortical regions [101], [102]. The cerebellum receives inputs from somatosensory receptors via the spinocerebellar tracts and exhibits interconnectivity with the brainstem, thalamus, and cerebral cortex. By combining peripheral sensory signals with motor signals, the cerebellum has been proposed to act as a 10 comparator between motor commands and their resulting sensory consequences, a process integral to our internal probabilistic representation of self-motion and the control of standing balance [100]. The cerebellum is also thought to contribute to reactive balance control in response to imposed sensory perturbations, motor adaptation/learning, and refinement of motor commands [100], [103], [104]. The basal ganglia network contains the motor circuitry thought to be important for the selection/inhibition of competing movement patterns as well as reward-oriented motor learning [105]–[107]. Cortical components such as the primary motor cortex, premotor cortex, and supplementary motor cortex work together to modulate voluntary muscular movements (e.g., planning, initiation, control, execution) [108], [109]. Cortical motor commands are integrated with subcortical centers to activate interneurons and lower motoneurons within the spinal cord, leading to coordinated muscle activation for the production of restorative torques required to maintain an upright posture [110], [111]. The kinematics and dynamics of standing balance can be modeled using an inverted pendulum [112]. For small body angles, anteroposterior (AP) balance dynamics can be simplified into an inverted pendulum pivoting around the ankle joint (Figure 1.2 panel A). The corresponding dynamical equation Tθ= −mgL relates the body angle (θ) to a given ankle torque (T) required to maintain balance at the current state, where m, g, L refer to the body mass, gravity constant, and the distance from the whole-body CoM to the ankle joint, respectively [113]. The mediolateral (ML) dynamics differ from AP, requiring a multi-segment inter-connected model (Figure 1.2 panel A), where the lower body is modelled as a closed-chain four-bar linkage and the trunk as an additional inverted pendulum connected at the midpoint of the pelvis [86], [114]. Consequently, the dynamics of ML standing balance varies as a function of stance width [86], [114]. In such multi-segmental ML balance models, one important assumption is that the trunk stays 11 perpendicular to the pelvis at all times during ML sway across narrow to wide stance widths. Although this assumption simplifies the modeling, it has not been rigorously verified yet. Due to the intrinsically different biomechanics underlying the control of AP and ML balance, their characterization is often decoupled for balance assessments. Figure 1.2 Standing balance measurements and frequency characteristics. (A) Biomechanically, anteroposterior (AP) standing balance is typically modeled as an inverted pendulum where the ankle torque actuates the body angle, while 12 mediolateral (ML) standing balance usually requires a more sophisticated four-bar linkage model. Standing balance behaviors can be quantified by measuring the ankle torque exerted on a force plate to derive the Center of Pressure (CoP). (B) Here we illustrate the bird’s eye view of typical 2-D CoP data measured over 120 seconds. Patients with concussion exhibit greater postural oscillations (simulated data). (C) The 2-D CoP can be further broken down into AP (top row) and ML (bottom row) components. (D) CoP data of both AP (top row) and ML (bottom row) have most of the power concentrated in the lower frequency ranges, where 90% of the power is below 0.5 Hz. Researchers often describe postural oscillations using the displacement of the whole-body CoM and CoP. In the context of standing balance, CoM refers to an equivalent virtual point at which the total body mass is concentrated, while CoP represents an equivalent virtual point where the resultant ground reaction force is applied. In a laboratory or in the field, the CoP is typically estimated using a force plate, while the CoM can be estimated with motion capture, inertial motion sensors, or derived from force plate data [115]–[117]. Panel B of Figure 1.2 illustrates a bird’s-eye view of typical 2-dimensional CoP displacements measured during standing balance, while panel C of Figure 1.2 further breaks down the CoP displacements into its AP and ML components. Random CoP displacements occur while standing upright (typical magnitude ≤ ~1 cm) [111], [118], [119], and are expected to increase in persons with balance deficits after concussions or subconcussive head impacts (Figure 1.2 panel C). The biomechanics of standing balance reveals that, due to the whole-body inertia, postural oscillations exhibit dominant components at low frequencies. Indeed, over 90% of the power in CoP displacements is contained below 0.5 Hz [120]–[122]. The power of CoM displacements may be concentrated in even lower frequencies, with mean frequency at 0.1-0.2 Hz compared to 0.4 Hz for CoP displacements [123]. Consequently, standing balance CoP/CoM needs to be recorded over a sufficient duration to characterize the low-frequency characteristics of postural oscillations [121], [122], [124]. For example, 50 seconds of data are required to quantify postural 13 oscillations occurring at 0.02 Hz. A prior study found that increasing the sampling duration from 15 to 120 seconds shifted the relative power of the CoP signals to lower frequencies (mean power frequency shifting from ~0.36 to ~0.15 Hz) [121]. Hence, clinical evaluations that rely on brief assessments of standing balance (< 30 seconds) may lack low-frequency data to fully characterize the upright balance behavior. Although most of the postural oscillations occur at frequencies below 0.5 Hz, the power in the signals may extend to ~3-5 Hz. The higher frequency CoP oscillations may arise from the net whole-body acceleration, muscular contractions generating small-amplitude postural adjustments or tremors, as well as somatosensory feedback mechanisms [125]–[127]. 1.5 The Cerebellum and Its Potential Damages Post-Concussion The human standing balance control circuitry involves a myriad of sensory end organs and neural centers. Concussive and subconcussive head impacts may strain and stress one or more of these components, causing them to function abnormally. Among these components, the cerebellum acts as a neural center that plays a pivotal role in standing balance control and adaptation. Therefore, probing the cerebellum in the circuit may be an important step forward in uncovering the intrinsic neural mechanisms of standing balance issues post-concussion and subconcussive head impacts. Situated below the cerebral hemispheres at the base of the brain, the cerebellum comprises numerous neuronal circuits and connections. Its role in balance control and sensorimotor adaptation is paramount. The cerebellum maintains standing balance control by integrating sensory information from various sources [104]. It detects head position and acceleration through connections to vestibular organs, coordinates eye movements and spatial perception via visual 14 inputs, and senses body position and motion through signals from muscles, tendons, and joint receptors [100], [128]. In addition to processing sensory signals, the cerebellum receives efferent copies of motor commands. These copies are believed to be integrated with sensory signals through a forward model within the cerebellum, generating anticipated sensory feedback. By comparing anticipated feedback with actual sensory input, the cerebellum can generate corrective signals to adjust ongoing motor control commands, ensuring smooth, precise, and stable movement of the body [129]–[131]. This unique ability of the cerebellum to update motor signals using sensory feedback enables humans to adapt to changes in both external environments and internal body conditions [132]–[134]. Examples of such adaptation include walking on uneven terrain, compensating for delays in motor control, and acquiring new motor skills. Following concussions or subconcussive head impacts, the cerebellum may sustain damages from focal impacts resulting from linear head kinematics or diffuse brain strain deformations caused by rotational head kinematics. For instance, finite element method (FEM) studies have shown that concussive head impacts can induce maximum principle strains on the cerebellum of up to 0.22±0.08 [40], [78]. Furthermore, a magnetic resonance imaging study has demonstrated that concussive head impacts significantly reduce axial diffusivity in the cerebellar region, indicating altered microstructure of cerebellar tracts [135]. These damages can lead to structural and functional changes in the cerebellum. In fact, deficits have been observed in visuomotor adaptation tasks post-concussion [136]–[139], However, investigations into adaptation functions in the context of standing balance control with direct measurements of cerebellar activity are still lacking. 15 1.6 Robotic Balance Platforms and Delay Adaptation Paradigm Robotic balance platforms have emerged as a promising technology for assessing and rehabilitating standing balance in individuals. These platforms come in two main types: conventional and human-in-the-loop. Conventional robotic balance platforms are equipped with motors and sensors. These motors can provide precise and repeatable mechanical perturbations to participants during standing, while sensors measure their reactions such as joint angles and applied forces. Perturbations may be applied to various body parts, including the pelvis and standing support surface, and can take the form of controlled rotations, translations, or combinations of both [140]. However, it's crucial to recognize that these unexpected mechanical perturbations introduce error signals external to the ongoing control of standing balance. The compensatory responses triggered by the perturbations aimed at preventing falls differ from the natural internal challenges encountered during quiet standing, and thus may not engage the typical neuromuscular circuitry involved in maintaining quiet standing balance [84] [141]. In contrast, human-in-the-loop robotic balance systems mimic human balance control principles and engage core neural processes driving muscle actions during balance. Early versions of such robots required participants to balance an actual inverted pendulum [141], [142], while later iterations combined computer simulations with mechatronics platforms [143]–[145]. In these platforms, the body of the participants are usually secured to a motion platform while standing on a force plate measuring their ankle torque. A computer calculates the expected body motion using an inverted pendulum model and drives the platform accordingly. Participants then sense their body motion synced with the platform to adjust ankle torque continuously. Previous validation studies have shown that the load stiffness (i.e., the relationship between 16 ankle torque and body angle) of these platforms in the AP balance direction was not significantly different from those observed during natural quiet standing [143], [145]. Human-in-the-loop robotic balance platforms uniquely enable researchers to manipulate the standing balance control loop by altering motion feedback corresponding to participants' actions. As a result, these manipulations require participants to adapt to the altered sensory-motor relationship within the context of ongoing balance control to maintain and restore their balance. These platforms have been crucial in investigating standing balance adaptation tasks, providing insights into the mechanisms underlying human balance learning and control. For instance, standing balance is influenced by inherent delays in the control circuit between sensory feedback and muscle reaction. These delays, estimated to range between 100 to 160 milliseconds, stem from various factors such as sensory signal processing time and the duration of nerve/muscle signal transmission [84], [146], [147]. Aging and neurological injuries, such as concussions, may exacerbate these delays, resulting in impaired balance function [148], [149]. Using human-in-the-loop robotic balance platforms, researchers were able to impose additional delays on the standing balance control loop to study the effects of delayed balance control. They have shown that healthy adults can adapt to additionally imposed delays of up to 400 ms on top of their inherent delays in standing balance control [149]. Given that the cerebellum plays a key role in the ability to adapt while balancing, human-in-the-loop robotic balance systems offer a novel approach to specifically investigate cerebellar involvement in the adaptability of standing balance control. 1.7 Electroencephalogram (EEG) To allow researchers to delve deeper into the neural mechanisms of standing balance adaptation, functional neuroimaging techniques can be applied. EEG, a non-invasive and increasingly more 17 portable neuroimaging method, holds promise for such standing balance experiments. EEG can reveal insights into the underlying neural oscillations in the brain across various frequency bands, including delta (< 4 Hz), theta (4-8 Hz), alpha (8-13 Hz), beta (13-30 Hz), and gamma (> 30 Hz) frequency bands [150], [151]. This is achieved through placing electrodes on the scalp to record synchronized electrical activity generated by neurons in different brain regions [150]. Furthermore, the emergence of wearable EEG devices has improved portability and usability in various clinical and research settings [152]. EEG has been instrumental in studying sensorimotor adaptation in humans, typically through visuomotor adaptation tasks [153], [154]. These investigations examined EEG signals in both temporal and spectral domains, shedding light on the brain’s neural oscillation patterns and neural markers involved in these adaptation processes. Although EEG has been traditionally used to measure cortical activity, recent advancements have expanded its applicability to study subcortical structures such as the cerebellum. This is done by placing arrays of electrodes with specific configurations on the scalp in the vicinity of the cerebellum to capture its signals [155]–[157]. Additionally, advanced EEG pre-processing and denoising algorithms have been developed aimed at removing various artifacts, especially muscle noises, from recorded EEG signals [158]–[160]. Using cerebellar EEG, researchers have investigated the cerebellum’s role in sensorimotor control, learning, and adaptation [161]–[164] as well as its contributions to motor control diseases such as Parkinson's disease and essential tremors [165]–[167]. The integration of cerebellar EEG with human-in-the-loop robotic balance platforms can provide researchers with a novel methodological framework for understanding cerebellar mechanisms underlying standing balance adaptation. This blend of neuroimaging techniques with interactive robotic systems facilitates the exploration of the interplay between cerebellar 18 activity and corresponding standing balance adaptation performance. Through this approach, insights into cerebellar dysfunction related to standing balance control and adaptation may be gained in clinical populations such as patients with concussions, potentially informing the development of more targeted interventions for standing balance recovery. 1.8 Current Technological Limitations Despite the prevalence of standing balance deficits following concussions and/or subconcussive head impacts, the precise injury mechanisms underlying these issues remain unclear. The human standing balance control circuit is complex, involving an array of sensory end organs and neural centers. Concussions and subconcussive head impacts may stress and strain these components, affecting their function and leading to abnormalities. Among these, the cerebellum stands out as a crucial neural center for standing balance control and adaptation. Therefore, exploring the role of the cerebellum in standing balance can provide valuable insights into the neural mechanisms underlying post-concussion balance deficits. A promising avenue for investigating the cerebellum's role in standing balance is through the use of human-in-the-loop robotic balance platforms in combination with cerebellar EEG. However, before applying this approach to quantify and assess standing balance deficits and associated cerebellar injuries in patients with concussions, several technological limitations must be addressed. One significant limitation lies in the absence of ML balance control in current robotic platforms. This constraint arises from the lack of integrated hardware, electronics, and software systems, as well as the absence of an accurate model for simulating multi-segment kinematics during ML balance. Additionally, there is a gap in the experimental design and protocol for integrating the robotic balance system with EEG to measure cerebellar activity during standing balance adaptation. Bridging these technological gaps is crucial for enabling 19 researchers to gain deeper insights into the neural mechanisms underlying standing balance control and its adaptability, particularly targeting the cerebellum following head impacts. With advances in the understanding of the neural mechanisms underlying standing balance deficits, more effective rehabilitation interventions may be developed tailored to patients with standing balance deficits. 1.9 Thesis Objectives Given the overarching goal to investigate the mechanisms of standing balance deficits after concussions and subconcussive head impacts as well as the identified technological limitations outlined in the preceding section, the specific objectives of the thesis are: • Objective 1: Conduct a literature review to summarize acute standing balance deficits observed after concussions and subconcussive head impact exposure, explore potential correlations between head impact kinematics and changes in the standing balance circuitry, identify limitations in existing standing balance assessments, and propose recommendations for improved standing balance test specificity and sensitivity. • Objective 2: Further develop a multidirectional robotic balance platform to incorporate ML control capabilities in addition to AP capabilities, assess the system's ability to track motions simulating both small unperturbed and large perturbed balances, and evaluate its real-time performance in the ML direction with human-in-the-loop experiments. • Objective 3: Validate the accuracy of a CoM decomposition model in representing multi-segmental kinematics during ML balance with in-vivo experiments, including a trunk-pelvis perpendicular assumption utilized by the model, and improve its accuracy using data-driven approaches. 20 • Objective 4: Apply EEG with the robotic balance platform to investigate the role of the cerebellum in adapting to unexpected delays in standing balance control. 1.10 Thesis Overview Chapter 2 addresses Objective 1 by presenting the findings of a comprehensive literature review, summarizing standing balance deficits post-concussion and subconcussive head impacts. This chapter synthesizes existing knowledge regarding potential injury mechanisms and identifies major limitations in the current standing balance assessments post-concussion, laying the groundwork for subsequent investigations. In Chapter 3, Objective 2 is addressed by introducing the addition of ML control capabilities to existing robotic balance platforms. A novel CoM decomposition model is also presented, which is designed to simulate multi-segmental kinematics during ML balance. Chapter 4 focuses on addressing Objective 3 through a validation experiment of the developed CoM decomposition model, including data-driven model refinements to improve its estimation accuracy. Chapter 5 presents the design and results of an experiment combining the robotic balance platform with a portable EEG device to investigate the role of the cerebellum in adapting to unexpected delays in standing balance control, addressing Objective 4. Finally, Chapter 6 concludes the thesis by summarizing key contributions and outlining possible future research directions. 21 Chapter 2: Potential Mechanisms of Acute Standing Balance Deficits After Concussions and Subconcussive Head Impacts – A Review This chapter begins with reviewing commonly employed standing balance testing paradigms post-concussion. Then, I delve into a comprehensive review of studies examining standing balance function in the acute phase following concussions and subconcussive head impacts. Subsequently, I synthesize the observations and gaps within the reviewed literature. In light of the findings, future recommendations are made aimed at addressing the limitations in current research practices. This includes advocating for increased sensitivity and specificity for assessing standing balance deficits resulting from concussions and subconcussive head impact exposure. This chapter has been published in Qiao et al., 2021 [4]. 2.1 Standing Balance-Related Sensorimotor Assessments for Concussion and Subconcussive Head Impacts For sports concussions, the Balance Error Scoring System (BESS) has emerged as a primary balance evaluation [41], [168], where the participant quietly stands with eyes closed during six different conditions varying in standing surface (foam/firm) and stance (single/double/tandem). A shortened modified BESS (mBESS) that only assesses standing balance on the firm surface condition [169] is integrated into the SCAT [27], [28]. In each BESS/mBESS test, the participant is asked to stay as still as possible for 20 seconds while an evaluator counts balance errors. Such balance errors include excessive sway, arm/leg movements, or the participant opening their eyes, which are taken as hallmarks of losing postural stability during quiet standing. The errors can also be obtained via video analysis or instrumented sensors. One recent study has shown poor 22 agreements between human and instrumented ratings suggesting using only one method for maintaining the test consistency [170]. Figure 2.1 CoP Entropy calculation and the influences of hyper-parameters. (A). Raw CoP displacement time series data is typically coarse-grained by the time scale parameter, which is a part of the multi-scale analysis to examine varying time scales. Prior single-scale concussion studies usually set the time scale to 10 for analysis. (B). The Approximate Entropy (ApEn), the most used entropy metric for single-scale analysis in prior concussion entropy studies, can then be computed based on the sequence length (m) and tolerance (r) where m determines how many data points are contained in one data segment for segment-wise comparison and r is the tolerance threshold for assessing the similarity (typically quantified as a distance function, e.g., the maximum distance) between every two data segments. m and r are usually selected as 2 and 20% of the time-series standard deviation in prior concussion studies, respectively. (C). The selection of time scale, sequence length, and tolerance may all influence the final CoP displacement ApEn value to vary between ~0.2 and ~0.8. 23 Aside from counting balance errors, postural stability during standing balance can also be quantified using CoP/CoM displacements and their derivatives such as velocity and acceleration. Time and frequency domain metrics derived from CoP and CoM such as sway path, sway area, range, and standard deviation of the oscillations, as well as mean or median frequency, are typically used to quantify standing balance [171]. These metrics have been frequently applied to assess postural stability in concussion patients. In addition, postural complexity metrics estimate the nonlinear time-varying postural movement pattern. Approximate entropy (ApEn) [172], sample entropy (SampEn) [173], Shannon/Renyi entropy[174], and multivariate multiscale entropy (MMSE) [175], [176] of CoP displacements have been applied, where lower entropy indicates less complex and more regular systems [177], [178]. At its core, entropy calculation involves comparing the similarity between data segments throughout the time series as an assessment of regularity (Figure 2.1 panel B). The entropy calculation process involves a multitude of post-processing parameters such as the time scale, sequence length, and tolerance. Selections of these parameters influence the resulting entropy value (Figure 2.1 panel C) [179]. Single-scale entropy only examines the complexity of CoP signals at one fixed frequency, whereas multi-scale entropy provides insights across a range of frequencies. Another frequently used clinical assessment of standing balance is the Sensory Organization Test (SOT). This test assesses six sensory conditions that vary the visual input (eyes open/ eyes closed/sway-referenced) and standing surface (fixed/sway-referenced) while participants stand upright for 20-second trials [23], [180], [181]. The various sensory conditions assess the individual’s ability to use reduced or altered sensory information (e.g., visual, vestibular, and somatosensory). The test score for each condition is quantified by comparing the anteroposterior (AP) maximum sway angle against a 12.5-degree sway limit [182]. Vestibular, visual, and 24 somatosensory scores are quantified as the ratio of the score in the altered sensory condition relative to the unaltered sensory condition, and the overall composite score represents the weighted average of all conditions [181]–[183]. The Clinical Test of Sensory Interaction and Balance (CTSIB) and the modified CTSIB (CTSIB-M) are simplified forms of the SOT by replacing the sway-referenced vision and support surface with a visual conflict dome and foam surface [184], [185] or fully removing the visual conflict dome condition [186], respectively. Beyond standing balance testing, some clinical sensory tests can directly probe sensory dysfunction relevant to standing balance. For instance, the vestibulo-ocular reflex (VOR) can be assessed by computing the gain of the eye compensatory response to head movements, evaluating the vestibular contributions to extraocular muscles for stabilizing the visual image on the retina [187]–[190]. The VOR can be assessed for all planes of linear and rotational motion but clinical VOR testing typically involves imposed head rotation stimuli (e.g., head thrust test [191], [192]), active head rotation stimuli (e.g., horizontal/vertical VOR test [193], [194]), or both (dynamic visual acuity test [189], [195], [196]). When direct ocular measurements are not possible, the vestibulo-ocular function can be assessed using the vestibular/ocular motor screening (VOMS) test [193], [194], [197]. VOMS involves participants performing (1) saccade, (2) convergence, (3) smooth pursuit, (5) horizontal/vertical VOR, and (5) visuomotor sensitivity (VMS) and subjectively rating provoked symptoms such as headache, dizziness, nausea, and fogginess on a scale that ranges from 0 to 10 [198]. Other stand-alone visual /oculomotor tests for potential concussion screening tests include the King-Devick (K-D) test [199], [200] and ocular near point of convergence (NPC) [201], [202]. In addition to clinical or sideline assessment of the vestibulo-ocular function, in-laboratory evaluations of eye movements during saccades and smooth pursuit can quantify gaze positional 25 and timing errors post-concussion [203], [204]. Also, artificial activation of the vestibular system using currents applied in a binaural bipolar configuration over the mastoid bone (i.e. galvanic vestibular stimulation - GVS or electrical vestibular stimulation - EVS) induces well-defined VOR, perceptual, postural, and navigation responses in participants [205]–[210]. The percutaneous current modifies the neural firing pattern of vestibular primary afferents and consequently provides an isolated vestibular error signal with minimal activation of other sensory signals involved in standing balance control [211]–[213]. Researchers have recently used this method to assess standing balance function after subconcussive head impacts [214], [215]. 2.2 Acute Standing Balance-Related Sensorimotor Changes After Concussions and Subconcussive Head Impacts A comprehensive literature search of peer-reviewed English journal articles was performed on MedLine/PubMed, Compendex Engineering Village, and Google Scholar using search terms “(balance OR vestibular OR visual OR ocular OR sensorimotor) AND (concuss* OR subconcuss* OR mTBI)”, with the Google Scholar search limited to the first 100 articles. Only articles observing acute standing balance-related changes within 4 weeks (the majority within 2 weeks) after concussions or subconcussive head impacts were included. I excluded studies with unspecified testing timeframes and studies that only examined persistent sensorimotor deficits (beyond 4 weeks post-concussion/impacts) with potential secondary physiological or biomechanical contributors. In addition, studies that focused on instrument validation, walking and gait analysis, blast-induced injury, neuroimaging assessments, blood biomarkers, biochemical/cellular analysis, and non-human models were excluded. The primary search was conducted in February 2020, along with a secondary search of the bibliographies of the selected 26 papers. In total, my search led to 43 original research articles (concussion: 34; subconcussive head impacts: 9). 2.2.1 Acute Standing Balance-Related Sensorimotor Changes After Concussions Patients with concussions have shown mostly consistent standing balance deficits immediately after injury, followed by recovery within 14-30 days of injury (Table 2.1). For example, BESS error scores significantly increased to 14-20 from baseline (<12) within 24 hours of injury, followed by a gradual decrease in the next 1-5 days [216]–[218]. Instrumented BESS/mBESS IMU tests have also revealed acute increases in sway velocity, acceleration, and area [219]–[222]. Participants showed higher AP and mediolateral (ML) CoP area/displacement followed by a gradual return to baseline within 14-30 days of injury [223]–[228]. In addition, researchers assessing standing balance with the SOT identified an acute decline in the composite equilibrium score on day 1 in the concussion group compared to the control group, and such group differences usually resolved within the next 1-9 days [43], [56], [188], [217], [229]–[232]. Furthermore, researchers using SOT sensory analyses have typically demonstrated reductions in vestibular and visual ratios in concussion patients on day 1 of injury, followed by a gradual return to baseline in the next few days [43], [229], [230], [232]. Despite the acute balance impairment-and-recovery pattern commonly observed in the first 2 weeks after injury, abnormal balance performances were still detected beyond the 2-week time frame when participants were asked to perform a cognitive task, suggesting persistent subtle balance deficits that may be exposed with increased cognitive load [233]. 27 Table 2.1 Acute global standing balance deficits after concussions. ↑ denotes measurements became higher, ↓ lower, ↔ no significant differences; EO: eyes-open, EC: eyes closed; F: female participants, M: male participants; NS: not specified. Article Patients (Sex, Avg. Age) Post-Injury Test Time Protocol (Duration, Comparison Method) Key Observations Postural Stability McCrea et al.[216] 94 football players (M, 20.0 yrs) 0, 3 hrs, 1, 2, 3, 5, 7, 90 days BESS (20s, baseline) Error score ↑ at 0 hr and mostly recovered by day 5 Teel et al.[218] 352 high school/college athletes (NS, NS) 0, 3 hrs, 1-7, 90 days BESS (30s, baseline) Error score ↑ at 0 hr and returned by day 4 Parrington et al.[219] 23 athletes (F/M, 20.1 yrs) ≤ 24-48 hrs Instrumented BESS (30s, controls) Error score ↔and sway (mm/s2) ↑ King et al.[220] 52 athletes (F/M, 20.4 yrs) 2.2 days (avg.) Instrumented mBESS (30s, controls) Error score ↔, while sway area, ML RMS acc, acc range, power ↑ (double stance) Baracks et al.[221] 48 athletes (F/M, 20.6 yrs) ≤ 72 hrs Instrumented mBESS (30s, controls) RMS sway acceleration and 95% sway area ↑ Gera et al.[222] 38 athletes (NS, 20.6 yrs) ≤ 23 days Instrumented CTSIB-M (20s, controls) Postural sway area measured by IMU ↑ in 3/4 conditions Guskiewicz et al.[56] 13 football players (M, 20.2 yrs) ≤ 24-48 hrs SOT (20s, baseline) Composite score ↓ in 8/13 patients; no relationship identified between head kinematics and composite score changes Guskiewicz et al.[217] 36 athletes (F/M, 19.5 yrs) 1, 3, 5 days SOT (20s, baseline/controls) Composite score ↓ on day 1 and did not fully return by day 5 Guskiewicz et al.[229] 11 athletes (F/M, 18.6 yrs) 1, 3, 5, 10 days SOT (20s, controls) Composite score ↓ on day 1 and ↔ by day 10 28 Article Patients (Sex, Avg. Age) Post-Injury Test Time Protocol (Duration, Comparison Method) Key Observations Peterson et al.[230] 28 athletes (F/M, 20.2 yrs) 1, 2, 3, 10 days SOT (20s, baseline/controls) Composite score ↓ from day 1-10 and returned by day 10 Register-Mihalik et al.[231] 108 athletes (F/M, 18.8 yrs) 1.44 days (avg.) SOT (20s, baseline/controls) Composite score ↓ in the headache group Christy et al.[188] 28 athletes (F/M, 20.7 yrs) ≤ 72 hrs or ≤ 2 weeks SOT (20s, controls) Composite/individual score ↓ Resch et al.[234] 40 athletes (F/M, 20.2 yrs) ≤ 24 hrs SOT (20s, baseline/controls) Composite score ↔ Cripps et al.[232] 7 athletes (NS, 17.1 yrs) 24-48 hrs, 10 days SOT, CTSIB-M (20s, baseline/controls) Composite score ↓ on day 1 than 10 and ↑ with visual distractions than without; CTSIB-M sway ↔ McDevitt et al.[191] 12 athletes (F/M, 20.5 yrs) ≤ 490 days (6 acute: 210 days) SOT, BESS (20s, controls) Scores in condition 3/4 ↓ while error score ↔ Wright et al.[192] 12 athletes (F/M, 21.7 yrs) ≤ 10-120 days (avg. 36 days) EO/EC, foam/firm surface, with/without rotating visual scene, BESS (20s, controls) CoP area and variability ↑ especially for rotating visual scene/foam while CoP velocity and error score ↔ Wright et al.[227] 11 athletes (F/M, 20.4 yrs) 2-90 days (6 subacute: > 10 days) EO/EC, foam/firm surface, with/without rotating visual scene, SOT (20s, controls) CoP area ↑ especially for rotating visual scene/foam, while only the condition 3 score in SOT ↓ Rhine et al.[224] 13 children (F/M, 12.8 yrs) ≤ 6 hrs EO/EC double/single limb (60s/30s, controls) CoP displacement ↑ for double-limb EO, and CoP range ↑ for double-limb EO/EC 29 Article Patients (Sex, Avg. Age) Post-Injury Test Time Protocol (Duration, Comparison Method) Key Observations Dierijck et al.[225] 12 athletes (M, 19.0 yrs) 72 hrs, 2 weeks, and 1 month EO/EC (60s, controls/72hr) AP RMS CoP displacement ↑ at 2 weeks than 72 hrs, ↔ compared to controls Powers et al.[226] 9 football players (M, 20.2 yrs) 1-13 days. EO/EC (60s, controls) CoP RMS displacement and velocity ↑ Munce et al.[223] 1 football player (M, 12 yrs) 1 hr, 2, 6, 12, 20, 27 days EO/EC with/without cognitive tasks (20s, baseline) CoP area ↑ at 1hr, peaked on day 6, and returned by day 27 Dorman et al.[233] 18 children (F/M, 16.6 yrs) 1st visit ≤ 10 days (4 visits) EO/EC with/without dual cognitive task (20s, controls) CoP area remained different in the 2nd visit but only with the dual cognitive task Hides et al.[235] 54 rugby players (NS, 24.4 yrs) ≤ 35 days EC: narrow/single leg/tandem stance on foam/firm surface (20s, controls) Sway velocity ↓, muscle cross sectional area and contraction ↑, cervical proprioception score ↔ Slobounov et al.[228] 48 athletes (M, 20.9 yrs) 3, 10, 30 days With/without visual variation (30s, baseline) CoP area ↔ without visual variation, while ↑ on day 10 and ↓ on day 30 with visual variation Postural Complexity Gao et al.[236] 10 collegiate athletes (NS, NS) Daily test (avg. 11.8 days) Normal (120s, day 1) Renyi entropy ↓ nonmonotonically from day 1 to recovery Fino et al.[237] 6 college athletes (NS, NS) Weekly test (1-6 weeks) Normal (120s, controls) CoP MMSE SampEn ↓ except week 5 and was more consistent than other entropy metrics Purkayastha et al.[176] 31 athletes (F/M, 21.0 yrs) 3, 21, 90 days EO/EC (60s, controls) CoP MMSE SampEn ↓ until day 90, while AP CoP range and variability ↑ on day 3 and returned by day 21 30 Article Patients (Sex, Avg. Age) Post-Injury Test Time Protocol (Duration, Comparison Method) Key Observations Cavanaugh et al.[238] 27 athletes (F/M, 19.5 yrs) ≤ 48 hrs SOT (20s, baseline) AP and ML ApEn ↓ ≤ 48 hrs Cavanaugh et al.[239] 29 athletes (F/M, 19.1 yrs) 48, 48-96 hrs SOT (20s, baseline) AP and ML ApEn ↓ ≤ 48hr; ML ApEn remained ↓ at 4896 hrs in those whose instability recovered 31 While postural sway generally increases post-concussion, the complexity metrics point toward more regular and predictable postural movements that may persist longer than postural stability changes (Table 2.1). Cavanaugh et al. reported smaller AP and ML CoP displacement ApEn within 48 hours of concussion compared to baseline [238], [239]. These authors further showed that ApEn for ML CoP displacement declined for a longer duration post-concussion (up to 96 hours vs. 48 hours) and more consistently across all SOT conditions compared to the ApEn estimated for AP CoP displacement. Other researchers identified decreases in entropy metrics up to 10 days (CoP area Renyi entropy) [236] and 6 weeks (CoP MMSE SampEn) [237] post-concussion. Despite showing lower CoP MMSE SampEn at 3, 21, and 90 days after concussions, Purkayastha et al. observed that the AP CoP range/variability recovered by day 21 [176]. From a methodological perspective, these studies have generally digitized CoP at 100 Hz and selected a time scale parameter of 10 for single-scale or 1-20 for multi-scale analysis with a sequence length of 2 [176], [237]–[239]. Consequently, the frequency range of postural oscillations considered in the CoP entropy estimates was typically > 2.5-5 Hz. These approaches would not capture complexity changes of the dominant low-frequency (< 0.5 Hz) component of standing balance movement. Sensory dysfunction was frequently identified by symptom provocation from vestibular and visual testing post-concussion (Table 2.2). Clinical symptoms were identified in 16.8-53.6% of the participants with concussions in various tests of VOMS within 14 days post-injury [194]. Another study found that VOMS symptom score substantially increased from 0.1 on average at baseline to > 2 for the saccade, smooth pursuit, and convergence tests, and to > 3 for the VOR and VMS tests within 21 days post-concussion [193]. Two clinical chart reviews reported around 30% of concussed children displayed vestibular-ocular dysfunction (VOD) within 30 days of injury [240], [241]. Other studies found significant increases in NPC distance [193], [242], [243], VOR 32 cancellation gains [188], subjective visual variances [188], and K-D test completion times with higher error counts [199], [200], [244] acutely following concussions. Although most researchers have observed acute standing balance and vestibular/visual deficits post-concussion, some have reported conflicting results using common sideline/clinical tests. Some studies did not find significant changes in the BESS/mBESS error scores but found significant differences in sway acceleration from IMU sensors97,149 and in select visual or vestibular tests [191], [192]. Of note, two of these studies [191], [192] combined acute (≤10-14 days) and chronic (≤90-120 days) patients in the concussion group. Another group of researchers did not find significant differences in CTSIB-M postural sway between day 1 and 10 post-concussion or between the concussion and control groups [232]. Interestingly, these authors found improved SOT scores in concussion patients when visual perturbation was applied. Similarly, three other studies found improvements in postural stability [235], [238], and the SOT vestibular ratio score [234] compared to baseline in concussion patients. The authors of one study argued that the increased stability, instead of indicating an improvement, may result from a decreased willingness to use body sway for sensory stimulation to gather information about the environment[235]. Aside from this hypothesis, the evaluation of standing balance over short durations (primarily 20 seconds) [20], [236] and potential learning effects [245]–[248] could contribute to inconsistent findings. 33 Table 2.2 Acute visual/vestibular sensory deficits after concussions. ↑ denotes measurements became higher, ↓ lower, ↔ no significant differences; EO: eyes-open, EC: eyes closed; F: female participants, M: male participants. Article Patients (Sex, Avg. Age) Post-Injury Test Time Key Observations Sensory Organization Test (SOT) Sensory Analysis Guskiewicz et al.[217] 36 athletes (F/M, 19.5 yrs) 1, 3, 5 days Vestibular and visual ratio ↓ on day 1 than baseline/controls and did not fully return by day 5 Guskiewicz et al.[229] 11 athletes (F/M, 18.6 yrs) 1, 3, 5, 10 days Vestibular and visual ratio ↓ than controls on day 1 and ↔ by day 10 Peterson et al.[230] 28 athletes (F/M, 20.2 yrs) 1, 2, 3, 10 days Vestibular ratio ↓ on days 1, 2 than controls and gradually returned by day 10 Register-Mihalik et al.[231] 108 athletes (F/M, 18.8 yrs) 1.44 days (avg.) Vestibular and visual ratio ↓ than baseline/controls in the headache group Resch et al.[234] 40 athletes (F/M, 20.2 yrs) ≤ 24hrs Vestibular ratio ↑ while visual ratio ↔ compared to baseline/controls McDevitt et al.[191] 12 athletes (F/M, 20.5 yrs) ≤ 90 days (6 acute: 210 days) Visual ratio ↓ while vestibular ratio ↔ compared to controls Cripps et al.[232] 7 athletes (NS, 17.1 yrs) 1, 10 days Vestibular ratio ↓ on day 1 than controls; sensory ratios ↑ in visual-distraction conditions Vestibular/Oculomotor Motor Screening (VOMS) Mucha et al.[193] 64 athletes (F/M, 13.9 yrs) ≤ 21 days VOMS symptom scores ↑ than controls Anzalone et al.[194] 167 sports patients (N/A, 15.0 yrs) ≤ 14 days 36.8-53.6% provocation rate for saccade, smooth pursuit, and VOR; 16.8% for convergence. Elbin et al.[243] 63 athletes (F/M, 15.5 yrs) 1-7, 8-14 days NPC distance and VOMS symptom scores ↑ in days 1-7 and ↓ in days 8-14 than baseline Other Clinical VOR and Visual/Oculomotor Tests Ellis et al.[240] 77 sports patients (F/M, 13.7 yrs) ≤ 30 days 29% of patients met the clinical VOD criteria Ellis et al.[241] 306 sports patients (F/M, 13.9 yrs) ≤ 30 days 30% of patients met the clinical VOD criteria 34 Article Patients (Sex, Avg. Age) Post-Injury Test Time Key Observations McDevitt et al.[191] 12 athletes (F/M, 20.5 yrs) ≤ 90 days (6 acute: 210 days) Horizontal VOR and optokinetic stimulation symptom score ↑, while horizontal eye saccade, NPC distance, K-D, and dynamic visual acuity line difference ↔ Wright et al.[192] 12 athletes (F/M, 21.7 yrs) 10-120 days (avg. 36 days) NPC distance, symptom scores of horizontal VOR, optokinetic stimulation, horizontal eye saccade, and dynamic visual acuity line difference ↑ than controls while K-D score ↔ Hides et al.[235] 54 rugby players (NS 24.4 yrs) ≤ 35 days Asymmetry (%) of the video head impulse test ↔ compared to controls Christy et al.[188] 28 athletes (F/M, 20.7 yrs) ≤ 72 hrs VOR gains ↑ than baseline 35 Few studies attempted to relate head impact biomechanics information with acute standing balance deficits. Guskiewicz et al. used instrumented helmets to measure head linear and rotational accelerations during concussive impacts and did not find any significant association between impact location/magnitude and post-concussion (< 48 hours) SOT composite score change from baseline in 13 concussed college football players [56]. J. Dierijck et al. applied skin-mounted head impact sensors and found no clear correlations between head impact data and balance changes (estimated from CoP metrics) in 12 concussed college athletes [225]. The authors of these studies have suggested that the inability to identify potential links between mechanical head inputs and balance deficits may be due to the complex and uncontrolled characteristics of concussive impacts (e.g., varying frequency, magnitude, and location), the time elapsed between the injury and assessment, and other interfering factors such as one’s concussion history and repeated subconcussive exposure. 2.2.2 Acute Standing Balance-Related Sensorimotor Changes After Subconcussive Head Impacts Although subconcussive head impacts are considered milder than concussive head impacts, they have also been associated with subtle changes in standing balance and vestibular/visual function (Table 2.3) – albeit less consistently. Indeed, only 44% (4/9) of the subconcussive impact studies reviewed showed at least one statistically significant change in standing balance or related sensorimotor assessments, compared to 97.1% (33/34) of the concussion studies. Soccer heading is commonly used as a controlled head impact model in laboratory settings. A typical header paradigm is to have participants perform 10-20 soccer headers at 1-2 minute intervals [52], [214], [249], [250] using a sports ball launcher to reproduce similar head kinematics as soccer games/practices (10-30g in linear accelerations) [251], [252]. Launching soccer balls 40 feet away 36 from the participants, Caccese et al. reported elevated CoP velocities immediately after headers compared to both baseline and controls; however, there were no significant changes in CoP area or AP and ML CoP ApEn [250]. At a relatively short ball launch distance of 22 feet, potentially corresponding to higher ball velocity upon head impact, Haran et al. identified significant increases in AP CoM displacement (at 1 hour and 24 hours) and ML displacement (at 24 hours) in the heading group compared to the control group, with a subsequent return to baseline at 48 hours for both AP and ML displacements [249]. In the 2 hours following soccer headers, participants exhibited lower responses (smaller trunk angle, leg angle, and CoM movement) to isolated perturbations (GVS) during standing balance [214]. Finally, Nowak et al. reported longer NPC distances and increased KD time/errors at 0, 2, and 24 hours post-headers [52]. On the other hand, a number of soccer heading studies that varied the number of headers, ball launching parameters, or testing time frames did not find significant changes in standing balance parameters such as the CoP area/velocity or SOT scores [253]–[255]. It should be noted that the soccer heading studies reviewed did not measure the head impact kinematics to allow for comparisons of impact mechanics or severity across studies. In a field study where instrumented helmets were applied, Mccaffrey et al. did not find significant changes in SOT scores following either a low (< 60 g) or high (> 90 g) head impact in college football players at the end of a practice or game [61]. Lastly, Caccese et al. perturbed the visual (virtual reality), vestibular (GVS), and Achilles tendon (vibration) of standing participants but did not observe significant changes in weightings between the sensory systems after 10 headers[215]. A notable distinction with previous work from the same group [214] was that here they did not blindfold participants or ask them to stand on a foam surface. 37 Table 2.3 Acute standing balance-related sensorimotor changes after subconcussive head impacts. ↑ denotes measurements became higher, ↓ lower, ↔ no significant differences; EO: eyes-open, EC: eyes closed; F: female participants, M: male participants. Article Participants (Sex, Avg. Years) Intervention Test Time Protocol (Duration, Comparison Method) Key Observations Postural Stability and Complexity Schmitt et al.[254] 31 soccer players (F: 19.4 yrs, M: 20.7 yrs) 18 headers in 40 min (30 mph, 82 ft) 0, 24 hrs EO/EC (20s, controls) CoP area and velocity ↔ Caccesse et al.[250] 160 soccer players (F/M, 12-24 yrs) 12 headers in 12 min (25 mph, 40 ft) 0 hr EO/EC (120s, baseline/controls) CoP sway velocity ↑ while CoP area, AP and ML ApEn ↔ Mangus et al.[255] 10 soccer players (F/M, 21.4 yrs) 20 balls kicked by a teammate (82 ft) 0 hr SOT (20s, baseline) Composite score ↔ Mccaffrey et al.[61] 43 football players (M, 20.7 yrs) < 60 g or > 90 g ≤ 24 hrs SOT (20s, baseline) Composite score ↔ Broglio et al.[253] 40 soccer players (F/M, 19.5 yrs) 20 headers in 20 mi (55 mph, 80 ft) 0 hr EO/EC, with/without visual dome, foam/firm surface (20s, baseline) Total and mean CoP displacement ↔ Haran et al.[249] 16 soccer players (F/M, 21.0 yrs) 10 headers in 10 min (25 mph, 22 ft) 1, 24, 48 hrs Dark, still/rotating visual scene, still/ moving surface (30s, controls) AP RMS CoM displacement ↑ at 1hr, while ML ↑ at 24 hrs; both returned at 48 hrs Caccesse et al.[215] 30 soccer players (F/M, 21.8 yrs) 10 headers in 10 min (25 mph, 40 ft) 0, 24 hrs GVS, visual translating scene, vibration surface (20s, controls) Weightings between vestibular, visual, and somatosensory body movement gains ↔ Vestibular and Visual/Ocular Sensory Functions Hwang et al.[214] 20 soccer players (F/M, 21.0 yrs) 10 headers in 10 min (25 mph, 40 ft). 0, 2, 24 hrs GVS (135s, controls) Body angles relative to GVS inputs ↓ at 02 hrs and returned at 24 hrs 38 Article Participants (Sex, Avg. Years) Intervention Test Time Protocol (Duration, Comparison Method) Key Observations Nowak et al.[52] 78 soccer players (F/M, 20.4 yrs) 10 headers with 1-min interval (25 mph, 40 ft) 0, 2, 24 hrs NPC measure, K-D test (duration N/A, controls) NPC distance and KD time/errors ↑ at 0, 2, 24 hrs 56 2.3 Discussion Head impacts can lead to mechanical loading of sensory and neural components situated in the head, which may adversely affect multiple structures contributing to the sensorimotor control of standing balance. In this review, I have identified consistent acute standing balance change patterns such as increased postural oscillation/sway and reduced postural complexity post-concussion. In addition, vestibular and visual deficits are commonly observed in patients with concussions, while the vestibular and visual systems are often neglected in mechanistic studies. Only a few research groups have measured and correlated concussion impact biomechanics information with standing balance outcomes without identifying conclusive relationships. Consequently, the exact pathophysiological relationship between head impact biomechanics, neurotrauma, and standing balance deficits remains an open question. Compared to acute concussion, researchers examining the effects of subconcussive head impacts have shown conflicting standing balance outcomes. Through this review, I have highlighted potential limitations associated with standing balance testing such as trial duration, which should be considered for the design of future studies to improve our fundamental and clinical understanding of balance deficits following acute concussions. 2.3.1 Summarizing Standing Balance Deficits After Concussions and Subconcussive Head Impacts Based on the studies reviewed, acute standing balance changes post-concussion have been assessed with postural stability (70%), postural complexity (14%), and sensory testing including SOT sensory analysis and other direct visual/vestibular sensory tests (42%). Taken together, one or more statistically significant post-concussion sensorimotor deficits were identified in 97.1% 57 (33/34) of the reviewed concussion studies. In most of these studies, participants exhibited increases in balance errors (BESS: 30-58%) or postural oscillations (IMU angular sway and power: 21-97%; CoP/CoM displacement, velocity, area: 25-120%) and decreases in SOT composite equilibrium scores (7-14%) acutely post-concussion compared to baseline or healthy controls [176], [216], [217], [223]–[226], [229]–[231], [233]. While changes in standing balance are often assessed using stability indicators, these metrics have limited specificity to identify the underlying deficit. Postural complexity metrics, assessed mainly with CoP entropy, decreased by 19-33% post-concussion, corresponding to an increased regularity in CoP oscillations during standing balance [176], [237]–[239]. Decreases in CoP entropy were observed for longer periods following concussion than the increases in CoP oscillations (up to 90 vs < 30 days) and some authors have hypothesized the increased regularity is due to decreased brain connectivity or altered muscle contraction patterns after concussions [237]–[239], [256]. However, to verify such hypotheses, future work is needed to explore if/how brain connectivity or muscle contraction patterns affect the entropy of CoP displacements. Finally, some authors have reported that ML CoP entropy showed more consistent reductions across test conditions and persisted longer than changes in AP entropy [238], [239]. These results imply potentially different postural control changes between the AP and ML balance [238], [239], [249] that may be related to their distinct biomechanical constraints, dynamics, and sensorimotor control strategies. Approximately 30-50% of adult and pediatric patients show VOD or provoked symptoms with vestibular/visual testing [193], [194], [240], [241], [243], and SOT sensory tests revealed 12-20% and 7-14% declines for vestibular and visual ratios relative to baseline or controls, respectively [191], [217], [230]–[232]. While direct sensory assessments have been increasingly applied in the past 5-10 years in concussion testing and have shown frequent abnormalities, potential trauma to 58 the sensory end organs is rarely considered in concussion mechanism studies. Theoretically, mechanical head impact forces do not just affect the brain but could also deform/damage the sensing elements of the vestibular and visual end organs and/or their associated cranial nerves. For example, head impacts may dislocate otoconia from the utricle to the semicircular canals and result in Benign Paroxysmal Positional Vertigo (BPPV) [45], [257], [258]. Davies et al. have reported a BPPV rate of ~15% in patients with varying degrees of traumatic brain injury (from mild, to moderate to severe) [259]. Other research groups have reported lesions in the optic nerve and retina as a result of transmissions of mechanical energy from head impacts, mostly for severe head injury cases [260]–[263]. It appears possible that, for milder concussive or subconcussive head impacts, structures of the vestibular and visual systems may experience inertial loads that result in temporary sensory dysfunction. Few researchers have included head impact biomechanics information measured through the helmet and skin-mounted IMUs [56], [223], [225] or reconstructed concussion impacts through medical reports from the hospital’s emergency department [264]. In three out of these four studies, the authors have attempted to link head impact exposure or simulated brain tissue strain data to acute standing balance deficits but failed to identify clear associations. All studies, however, had a relatively small sample size (N = 12, 13, and 34) for correlation analysis. In addition, head kinematics from helmets and skin-mounted sensors are prone to kinematics measurement errors due to sensor decoupling from the skull [51], [265]–[267], while medical reports may be affected by recall and reconstruction errors. More accurate and comprehensive head impact exposure data along with other information such as concussion history are critically needed to shed light on the possible relationship between mechanical head impact inputs and induced acute standing balance deficits. 59 Few studies have investigated standing balance changes after subconcussive head impacts and reported inconsistent results, with only 44% (4 of 9) of studies identifying at least one post-impact standing balance-related sensorimotor deficit. As expected, based on the relative severity of subconcussive impacts, the authors of these studies reported more subtle balance changes compared with concussion studies. For example, CoP sway velocity increased by 47% or more acutely following concussions [232], while less than a 3% increase was reported after soccer headers [250]. Considering most balance deficits dissipate gradually post-concussion, subtle balance changes after subconcussive head impacts are also likely to be more transient and may or may not be detectable depending on the test time point. In addition, exposure levels varied from single football impacts to 10-20 soccer headers between studies. While head impact kinematics were not quantified, they also likely varied between studies due to factors such as soccer ball launcher distance, angle, and speed. These factors could all contribute to inconsistent findings in the reviewed subconcussive head impact studies. 2.3.2 Limitations and Recommendations in Standing Balance Testing After Concussions and Subconcussive Head Impacts Despite the general agreement regarding acute post-concussion balance changes, there are some factors that may contribute to varied outcomes between studies. First, the initial assessment time point post-concussion was inconsistent and ranged between 0 to ≥72 hours, as were follow-up assessments. I note that assessment time point selection can contribute to variance in study outcomes. For example, postural sway changes may be more detectable acutely and gradually dissipate by 14-30 days post-concussion. Second, about 41% of studies (14/34) included baseline balance measurements, while the other studies compared participants with concussions to matched healthy controls. One recent study has cast doubt on the benefit of using baseline in BESS due to 60 the higher within-subject than between-subject variance identified over two football seasons [268]. As such, test-retest reliability and individual variance need to be further assessed for any selected tests to determine the need for baseline testing and threshold to indicate a significant change. Third, among the 34 reviewed concussion studies, age, and sex considerations were under-explored for interpreting the results of acute post-concussion standing balance assessments. Given the physiological, anatomical, geometrical, and potential tissue mechanics variances across different ages and sexes, these factors may influence the severity of balance impairments induced by similar head impacts as indicated by some prior studies [269], [270]. Finally, current studies have used a range of different sample sizes, which could also contribute to variance in study findings. In the 34 concussion studies reviewed, sample sizes differ: 18 studies had < 30 participants, 11 had 30-90 participants, and 5 had > 90 participants (Table 2.1). Sideline and clinical diagnosis of concussions often require rapid and large-scale testing. As such, simple and fast tests such as BESS have been commonly used. While the BESS has demonstrated reasonable utility in concussion diagnosis, it may not be suitable at detecting subtle balance deficits, nor at detecting the origin of observed balance deficits. Even if a sub-component of the neural control of balance is disrupted, compensatory mechanisms may activate and achieve seemingly normal standing balance performance [111], [271]. For example, if the vestibular system is impaired, the visual, auditory, or somatosensory inputs may compensate and provide adequate information to avoid gross balance errors quantified by the BESS. Direct sensory perturbations or manipulations may thus increase test sensitivity and reveal specific sensory abnormalities that contribute to standing balance deficits. In addition, applying a dual-task paradigm and increasing the cognitive load during a standing balance task may reduce the brain’s capacity to cognitively compensate for subtle balance deficits [233], [272]. 61 The frequency characteristics of standing balance should be carefully considered when designing clinical or laboratory test paradigms. Standing balance is composed of a wide range of frequencies with most of the power contained in the low-frequency range [120]–[122]. Based on data from healthy participants, researchers have suggested that the CoP measurement duration should be at least 60 seconds for quiet standing trials and 300-360 seconds for altered vision conditions [121], [122]. Nonetheless, most concussion studies only used 20-30 seconds for each trial, limiting the balance assessment to a single oscillation at 0.03 to 0.05 Hz. Only a few of the reviewed studies applied longer trial times such as 60 seconds [176], [224]–[226] and 120-135 seconds [214], [236], [250]. Gao et al. showed that both CoP area and entropy increased linearly and sometimes even exponentially as the sampling duration increased from 20 to 120 seconds one-day post-concussion, which further motivates longer testing time (at least 60-120 seconds) [20], [236]. The characterization of postural oscillations complexity using entropy-based metrics has revealed a potentially higher sensitivity for balance assessment and longer-persisting changes post-concussion than stability-based CoP metrics (e.g. variance, range, area). Careful study designs and signal processing considerations are required because the results from entropy metrics are sensitive to the selection of post-processing hyper-parameters [273]. To illustrate this, I show how the key hyperparameters (e.g., time scale and sequence length) influence the entropy estimates from a 120-second CoP dataset (Figure 2.1 panel C). In existing concussion entropy studies, authors have often chosen parameters that examine entropy over a 2.5-5 Hz frequency band, avoiding over 90% of the CoP signals that are contained below 0.5 Hz. Thus, future CoP entropy analysis may need to reconsider the selection of post-processing parameters to capture and compare low-frequency complexity changes following concussion. 62 Fundamental investigations to understand the underlying mechanisms of standing balance deficits can benefit from more specific and quantitative testing paradigms. For example, VOR tests involve a three-neuron neural circuit, and quantitative instrumented tests may reveal specific impairments in this circuitry. Also, electrical activation of the vestibular system enables specific activation of the vestibular afferents without applying a motion to the head and activating other sensory afferents. This approach, along with other sensory-specific signals (e.g. virtual reality), can help in determining the sensory contributions to the balance deficits observed post-concussion. While such tests often involve specialized equipment, they may be necessary to further probe the specific effects of head impacts on critical neural circuitry and pinpoint the cause of sensorimotor symptoms or balance deficits. Emerging standing balance robotic devices can be used to create mechanical/sensory perturbations and manipulate the constraints/relationship between sensory cues and motor control outputs (e.g. altering the brain representation of the body and environment), thus providing researchers with unique opportunities to explore and probe the standing balance circuitry, its adaptability and the underlying components impaired post-concussion [84], [143], [145], [274]–[276]. In addition, accurate head impact biomechanics information paired with the mechanistic sensorimotor/balance tests are required to start understanding the chain of events from mechanical head impact to functional disruptions. 2.3.3 Linking Between Neural Damages and Higher-Level Standing Balance Deficits Given limitations in existing studies, there is insufficient evidence to establish the mechanisms of head impact-induced standing balance deficits. Further evidence may be drawn from a broader range of mechanical modeling, neuroimaging, and sensorimotor assessment studies to hypothesize potential neural components key to such balance deficits. As mentioned earlier, several brain 63 regions implicated in concussion biomechanics studies are intricately linked with standing balance function. The brainstem has been identified as a region of interest in concussion mechanism studies and is linked with severe concussion outcomes such as loss of consciousness [38], [277]. FEM simulations of concussive head impacts have proposed shear stress at the brainstem as a predictor of concussion [40], [82]. Supporting these modelling studies, participants exhibited prolonged inter-peak latency in brainstem auditory-evoked potentials within 48 hours after a mild head injury [278]. Also, participants with chronic concussion and loss of consciousness at the time of injury exhibited white matter integrity and abnormalities in the brainstem compared to controls [277], [279]. Brainstem structures, and in particular the vestibular nuclei and reticular formation, are thought to be critical for the control of standing balance. Indeed, researchers have found strong correlations between brainstem lesions in MRI and participants’ inabilities to maintain balance using single-leg stance conditions [280]. Some researchers have examined the vestibular control of balance using EVS methods and reported conflicting outcomes, with either larger motor responses to a vestibular error signal after a bout of 10 headers [214] or no upregulation of the vestibular control of balance for high heading exposure compared to low heading exposure soccer players [281]. Anatomically, the brainstem and cerebellum are in close proximity, and the cerebellum is another key structure implicated in concussion mechanisms as well as standing balance function [104]. Guskiewicz et al. hypothesized that a coup-countrecoup mechanism caused by crown impacts can indirectly concuss the cerebellum resulting in postural stability deficits [56]. Some concussion FEM studies have reported mean maximum principal strains > 0.2 in this region [40], [78]. Using diffusion tensor imaging, Mallott et al. identified abnormality in the cerebellar tracts 64 acutely post-concussion [135]. Standing balance deficits have been consistently identified in patients with cerebellar lesions [282]–[284] and, depending on the location of the lesions, different balance deficits have been reported [283]. Specifically, increased postural sway of high velocity/low amplitude and low frequency/high amplitude was identified in patients with anterior lobe atrophy and vestibulo-cerebellar impairments, respectively. The cerebellum also plays an important role in sensorimotor adaptation and learning. For example, in common balance test conditions where sensory inputs are manipulated (e.g. sway-referenced vision or somatosensory information), the cerebellum is thought to re-calibrate motor actions when consistent errors are encountered [285], [286]. Cerebellar deficits could indeed lead to an increased difficulty for patients with concussions to adapt to sensory manipulations during standing balance (e.g., SOT test). Indirectly supporting this possibility, visuomotor adaptation difficulties involving upper limb tasks have been confirmed in concussion patients, revealing larger within-subject variance and greater differences compared to controls, and such adaptation deficits persisted up to 18 months post-concussion [136], [139]. Notably, there is a lack of tissue displacement data for the brainstem and cerebellum to validate FEMs, leading to uncertainties in brain deformation modeling studies to further examine these areas of interest [287]. The basal ganglia is in tight connections with the cerebellum contributing to reward-based sensorimotor reinforcement learning [288]. Lesions in the basal ganglia have been associated with reduced sensorimotor adaptation and learning [289]–[291]. One computed tomography study identified focal impairments in the basal ganglia area in 55.2% of patients with mild or moderate brain trauma [292]. The thalamus is situated at the intersection between multiple neural regions including the cortex, cerebellum, and brainstem. Patients with unilateral thalamic lesions were reported to suffer from sensory loss and inabilities to stand [293]. Several functional magnetic 65 resonance imaging studies have found abnormalities in this area in concussion patients [294], [295]. Strains in the thalamus have also been strongly associated with concussions in FEM analysis. Zhang et al. hypothesized that the high strains induced by coronal head rotations in the thalamic-midbrain area were due to the motion-impinging effect exerted by the falx cerebri. Aside from regional considerations, diffuse brain deformations could potentially lead to widespread axonal connectivity disruptions. Researchers using diffusion tensor imaging have frequently found diffuse connectivity disruptions post-concussion [135], [296], [297]. The potential diffuse decoupling of brain regions has been hypothesized to manifest as decreases in neural complexity that could be identified using postural entropy [238], [239]. Some researchers have proposed that concussions and subconcussive head impacts may inhibit the neural transmissions inside the corticomotor regions, resulting in the dampening of neural muscular control [298]–[301]. Increased latencies between primary motor cortex activation and lower leg muscles were identified using transcranial magnetic stimulation in university boxers/Muay Thai athletes following three rounds of sparring bouts [301]. Similar observations have also been reported after repeated concussive exposure [298]–[300]. 2.4 Summary Research into the mechanisms of concussion has mostly focused on brain mechanics and function, despite increasingly broad definitions of concussion that consider a wide range of neurocognitive, sensorimotor, neuropsychological, and physiological symptoms. Given the prevalence, investigating the mechanisms of standing balance deficits could be one major step toward explaining the variance seen in post-concussion outcomes. The understanding of the underlying acute injury mechanisms will inform more effective practices in applying standing balance testing for diagnosis, monitoring, and management of mild traumatic brain injury. 66 Overall, there remain major gaps in the data available to investigate the mechanisms underlying acute standing balance-related sensorimotor changes after concussions and subconcussive head impacts. The key points from my findings are summarized below: • Standing balance testing after concussions has demonstrated prevalent and consistent acute increases in postural sway within 1-2 days post-injury, followed by recovery to baseline up to 14-30 days of injury. Subconcussive studies have shown subtle and inconsistent standing balance changes. • Postural complexity, specifically CoP entropy changes, may persist for longer than postural stability changes post-concussion; however, the physiological relevance of such changes remains unclear. In addition, hyperparameters need to be carefully selected for entropy calculation. • Clinical and laboratory standing balance testing should consider the low-frequency characteristics of standing balance dynamics and increase trial duration from 20 seconds to 60-120 seconds or longer. • Concussion mechanisms studies should consider the potential role of sensory end organs and their neural connections, especially vestibular and visual end organs, in common concussion deficits. • Brain regions such as the brainstem, cerebellum, basal ganglia, thalamus, and cortex have been identified as regions of interest in concussion mechanism studies and are known to be critical for standing balance function, but their links to standing balance deficits need further confirmation. 67 • More accurate head impact biomechanics measurements are needed to link head impact kinematics and damages in sensory/neural components related to global balance changes as well as local functional changes in subcomponents of the balance control circuit. • Investigations of the mechanism of standing balance deficits should consider emerging sensorimotor testing paradigms (e.g. robotic balance systems and electroencephalogram) that can quantitatively target and characterize the components underlying the neural deficit. 68 Chapter 3: Design and Development of a Multidirectional Human-in-the-Loop Robotic Balance Platform Based on the comprehensive review presented in Chapter 2, it is evident that conventional post-concussion standing balance assessments lack the specificity needed to uncover the underlying mechanisms of standing balance deficits. To bridge this gap, I propose integrating innovative sensorimotor testing technologies, such as robotic balance systems and electroencephalogram (EEG), which offer precise identification and evaluation of the neural components implicated in the deficit. In this chapter, I detail the design and development of a next-generation human-in-the-loop robotic balance platform enabling multidirectional control by adding mediolateral (ML) control functionalities. I evaluated the system’s performance tracking both perturbed and unperturbed standing balance motions as well as its human-in-the-loop real-time control performance when participants balanced in the ML direction. This new robot offers novel research avenues for investigating sensorimotor principles and biomechanical interactions underlying multidirectional balance control, with potential applications in assessing and rehabilitating standing balance deficits in patients with concussions. The rest of this chapter has been published in Qiao et al., 2023 [302]. 3.1 Introduction Multisensory information is essential for generating motor commands that enable us to balance our body upright [84]. Many previous researchers exposed standing participants to sensory and/or mechanical perturbations in anteroposterior (AP) [303]–[305] and/or ML directions [306]–[308]. Such perturbations, however, are imposed externally on the ongoing balance control loop that enables active standing [84]. Hence, there is a pressing need for alternative methods and 69 technologies that manipulate the control of human standing balance while engaging the neural circuits that drive muscle actions for balance control [84], [145]. One promising approach is to use interactive robotic balance systems [142], [143], [309] that mimic whole-body balance kinematics in response to forces/moments applied by a person to the ground. Besides enabling traditional perturbations and system identification approaches, balance robots can uniquely manipulate, delay, or reverse the expected sensory consequences of self-generated balance motor commands, creating novel adaptation and learning tasks for revealing the neuromechanical principles (such as causal/probabilistic inference or internal models) underlying balance control in humans [84], [149], [275], [310]. Existing robotic balance systems are limited to controlling AP balance [142], [143], [145], [309], [311], [312]. Given that balance motion in the AP and ML directions of balance is not independent [313], building a multi-directional robotic system would bring us one step closer to mimicking a natural human balance task. The unperturbed control of AP balance (involving small whole-body oscillations) was modeled as an inverted pendulum in a real-time robotic system [113], [143], [145]. This system recreated the angular motion of the whole-body center of mass (CoM) in response to plantar- and dorsi-flexion ankle torques generated by upright participants firmly secured to the robot. For unperturbed ML standing balance, the angular motion of the whole-body CoM can also be modeled by an inverted pendulum [112]. The ML torso/pelvis kinematics vary with stance width, however, even for unperturbed standing [114], [314], making the assumption of an inverted pendulum kinematic model rotating about the ankles inadequate. To address this limitation, a decomposition model was developed that simulates the ML torso/pelvis kinematics based on the whole-body CoM angular position under different stance width conditions (a key improvement over a prior Stewart robotic 70 balance system that only simulates AP balance control [143]) and integrated it with the original AP balance control model. This chapter presents the design of a novel multidirectional robot, describes how its motion performance meets the requirements of human standing balance, and demonstrates its ability to reproduce balance motions with participants in the robotic control loop. In previous studies validating robotic balance systems, motion errors and motion delays were not systematically quantified [143], [145], [149], [315], and the real-time human-robot interactive performance was only verified for AP balance [7], [12]. Here, I 1) quantified the robotic motion error/delay for tracking motions simulating both small unperturbed and large perturbed balance with the standalone robot, and 2) characterized the human-in-the-loop real-time performance of the robot while participants performed voluntary postural oscillations at 0.05 and 0.3 Hz in the ML direction. In summary, the main contributions are: • Novel development of a robotic system to replicate both the AP and ML control of standing balance. • An original model that decomposes the ML whole-body CoM angle to lateral torso/pelvis translations for various stance widths. • Motion delays between 9.4-13.9 ms when tracking multi-sine balance trajectories and submillimeter root mean squared errors when tracking natural balance trajectories (0.01-0.05 mm, corresponding to 0.001-0.009°), both below human-level standing balance thresholds. • Submillimeter errors between the predicted and robotic motion (0.08-0.37 mm, corresponding to 0.003-0.028°) as well as between robotic and human motion (0.55-0.68 71 mm, corresponding to 0.003-0.039°) when participants interacted with the robot in real-time. With these contributions, our proposed novel system opens up scientific research on the interaction between AP and ML balance and its clinical use. 3.2 System Architecture In this section, I present the design requirements of the robot and detail its mechanical, electronic, and software architectures. 3.2.1 Design Requirements The primary requirement was to add key degrees of freedom (torso/pelvis kinematics) to simulate the ML control of balance while preserving AP balance [142], [143], [145], [309]. • Mechanical structural design (Figure 3.1): Similar to previous robotic systems [142], [143], [145], [309], [311], AP CoM motion is realized by the control of a backboard with a pivot at the ankle mimicking an inverted pendulum, while the AP ankle motion is achieved by the control of a foot platform. To achieve ML balance motion with the ability to independently control the pelvis and torso, two horizontal tracks were designed for torso/pelvis motion control and mounted on the AP backboard. These tracks are mounted on linear bearings (Rollon TLC43CSW-1200) and supported by carefully adjusted torsion springs matching the entire weight of the rails so that they can free float (Figure 3.1). Consequently, the height of each track can be adjusted based on the anatomy of participants while eliminating vertical loads. Each track is connected to the participant’s pelvis and torso using a free-rotating bracket to accommodate pelvis and torso rotations. When participants control the robot, foam-padded brackets are tightly 72 strapped to their trunk and pelvis (Figure 3.1). Seat belts passing through slots of the two brackets are used to firmly secure participants to the robot. • Motion design: Based on prior literature, whole-body CoM typically oscillates within an amplitude of 0.5° while the velocity is ~1°/s during quiet standing [142], [316], [317]. For larger sways (or when small perturbations are applied), these values may increase tenfold to 5° and 10°/s [310], [318], [319]. To ensure that the system can replicate a variety of desired balance movements including situations of both quiet standing and small perturbations, all motion axes were designed to exhibit kinematic limits of ±20° and ±60°/s. • Software and electronic system design: Real-time robotic software was designed to estimate the CoM motion in AP and ML directions in response to net torque inputs. To enable ML balance control at different stance widths, an additional whole-body CoM decomposition model was developed to predict the positions of the pelvis and torso from the whole-body CoM angular position. A two-layer electronic architecture was designed to coordinate the lower-level servo motor control with the higher-level robotic balance simulation. 3.2.2 Mechanical Architecture The four axes of the robot enable ankle and whole-body motions for AP balance and pelvis/torso motions for ML balance. To ensure participant safety, limit switches are installed on each axis. E-stops and mechanical brakes of the servo motors can immediately stop the robot’s motion while holding the load in place. 73 Figure 3.1 Mechanisms of the balance robotic system. The robot is controlled by four independent axes: backboard/foot platform for anteroposterior balance motion, and torso/pelvis for mediolateral balance motion. Torsion-spring mechanisms matched to the weight of the torso and pelvis rails with brackets enable them to free float and participants to sway mediolaterally as in natural balance. Lockable brackets and seat belts firmly secure participants to the device to ensure tight human-robot coupling. The whole-body AP motion is implemented as a single-link inverted pendulum rotating around the ankle joint center of rotation: the anterior-distal part of the medial malleolus [320]. The robotic system has a fixed rotation center assuming an ankle height of 8.50 cm. The angle of the backboard directly corresponds to the angle of the whole-body CoM in the AP direction. The AP body angular motion is driven by a rotary servo motor (OMRON R88M-K1K530H-BS2; self-contained encoder: 131072 counts and 16 mm per revolution) and a linear actuator (Rollon TH 110 SP4 16 dia×16 lead) coupled to the backboard. The peak torque about the ankle is 7918 Nm (continuous torque: 74 2641 Nm). Using the resolution of the encoder (131072 counts for a 16mm displacement), the angular resolution of the backboard axis is [4.69e-6°, 8.21e-6°], depending on the position of the linear actuator. The AP angular motion of the ankle is driven by a rotary servo motor (OMRON R88M-K40030L-BS2; self-contained encoder: 262144 counts and 10 mm per revolution) and a linear actuator (Rollon TH 110 SP4 16 dia×10 lead). The peak torque about the ankle is 860 Nm (continuous torque: 294 Nm). Based on the resolution of the encoder (262144 counts and 10 mm per revolution), the angular resolution of the foot platform axis is [3.50e-6°, 6.07e-6°], depending on the position of the linear actuator. Given the 5-μm mechanical accuracy of each linear actuator, the repositioning accuracy of AP robotic balance motion is [1.92e-4°, 3.36e-4°] for the backboard and [4.59e-4°, 7.96e-4°] for the foot platform. The mapping between the angular and linear motion of the AP backboard is given by (Figure 3.2 panel A): �dbb = zbb − abb3 sin(θbb2 + θbb3) − abb2 sinθbb2θbb2 = cos−1 �−xbb − abb3 cos�θCoMAP + 90°�abb2 � (3.1) where parameters are annotated by the Denavit–Hartenberg representation [321]: abb2, abb3 are linkage lengths, θbb2, θbb3 are rotational variables, dbb is the linear variable, xbb, zbb are the vertical and horizontal distances between the origins of reference frames 1 and 3, θCoMAP is the AP CoM angle. The mapping between the angular and linear motion of the foot platform is given by (Figure 3.2 panel B): 75 �dfp = afp3 sin�θfp2 + θfp3� − afp2 sinθfp2θfp2 = cos−1 �xfp + afp3 cos�θCoMAP + 90°�afp2 � (3.2) where afp2, afp3 are linkage lengths, θfp2, θfp3 are rotational variables, dfp is the linear variable, xfp is the vertical distance between the origins of reference frames 1 and 3. To enable rotation of the whole-body CoM in the ML direction about the ankles, the robot imposes translational motions to the pelvis and torso brackets via two linear actuators (Rollon TH 110 SP4 16 dia×10 lead) driven by two servo motors (OMRON R88M-K40030L-BS2; each with self-contained encoders: 100,000 counts and 10 mm per revolution). Peak torques about the ankle for ML robotic balance motion are 2229 Nm (continuous torque: 597 Nm) for the pelvis axis and 3536 Nm (continuous torque: 947 Nm) for the torso axis (based on 95th percent male). Considering the resolution of the encoder (100,000 counts and 10 mm per revolution) and body heights from 148.9 cm (5th percent female) to 190.1 cm (95th percent male) to cover the range of participants expected to use the robot [110], [322], the angular resolution is between [5.41e-6°, 7.84e-6°] and [3.67e-6°, 4.94e-6°] for the pelvis and torso axis, respectively. The repositioning accuracy is [2.70e-4°, 3.92e-4°] for the pelvis axis and [1.85e-4°, 2.47e-4°] for the torso axis, respectively, due to the 5-μm mechanical accuracy of the linear actuators. 76 Figure 3.2 Angular-to-linear mappings for anteroposterior balance control. (A) backboard and (B) foot platform. 77 3.2.3 Software Architecture The robotic balance simulation loop (implemented in LabVIEW 2019) was designed to run independent state-space models of AP and ML standing balance in parallel (Figure 3.3). Based on the torques estimated at the mid-point of the ankle joints and the current motion state of the system, these two state-space models simultaneously solve for the whole-body CoM angles related to standing balance. The body dynamics of both directions (for small motions) were modeled as: �?̇?𝛉𝐂𝐂𝐂𝐂𝐂𝐂?̈?𝛉𝐂𝐂𝐂𝐂𝐂𝐂� = � 𝟎𝟎 𝟏𝟏𝟎𝟎.𝟗𝟗𝟗𝟗𝟏𝟏𝐦𝐦𝐛𝐛𝐂𝐂𝐛𝐛𝐛𝐛𝐠𝐠𝐋𝐋𝐂𝐂𝐂𝐂𝐂𝐂𝐈𝐈−𝐛𝐛𝐈𝐈� �𝛉𝛉𝐂𝐂𝐂𝐂𝐂𝐂?̇?𝛉𝐂𝐂𝐂𝐂𝐂𝐂� + �𝟎𝟎𝟏𝟏𝐈𝐈� [𝛕𝛕] (3.3) where θCoM is the CoM angle of the body (AP/ML), τ is the ankle torque (AP/ML), I is the mass moment of inertia of the body measured around the ankle joint (AP/ML), 0.971mbody is the approximated whole-body mass above the feet, g is the gravitational acceleration, LCoM is the distance between the body CoM and the mid-point of the ankle joints, and b is the viscous damping factor. I is defined using a distributed-mass model and is equivalent to the sum of the mass moment of inertia of each segment normalized to one’s body height (I = 0.35∙ mbodyH2, where H is the body height) [110], [143]. b is set to zero for typical human standing balance situations. 78 Figure 3.3 Human-in-the-loop balance control. The robotic simulator produces whole-body motions via the balance model using torques applied by participants. Participants adjust their motor commands to the sensory consequences associated with robotic motions to maintain their upright balance. 79 The AP CoM angle of the inverted pendulum solved in real-time controls the angle of the backboard and foot platform, enabling different motion combinations (e.g., normal balance, ankle-only balance, and sway referenced [312]). To achieve ML balance motions at different stance widths, the angular ML CoM kinematics is further decomposed into linear movements of the pelvis and torso (Figure 3.4). The origin of the ML motion coordinate system is defined as the midpoint of the two ankle joints. The CoM decomposition process is detailed in the next section. The AP body angle and linear pelvis/trunk positions calculated by the robotic balance simulator are translated into target encoder counts to drive the four motors. Virtual limits are implemented in the software for participant’s safety: the position of the AP whole-body CoM is limited to [−3°, 6°] and up to [−7°, 7°] for ML direction. The velocities of the whole-body CoM are limited to [−15°/s, 15°/s] for both AP and ML directions. These limits cover most motions typically related to standing balance [142], [310], [316]–[319]. 3.2.4 Details of the Whole-Body Center of Mass Decomposition Model The ML CoM decomposition model was implemented in the real-time robotic balance simulator software. This model uses the whole-body CoM angle in the ML direction as an input to estimate position of the trunk/pelvis in the ML direction. Within the decomposed multi-segmental pose, the lower body is modeled as a four-bar linkage mechanism consisting of the pelvis, legs, and distance between the two ankle joints, while the upper body is modeled as an additional linkage connected at the midpoint of the top of the pelvis (Figure 3.4). The trunk is assumed to be perpendicular to the pelvis in the decomposed multi-segmental pose. 80 Figure 3.4 The mediolateral (ML) whole-body center of mass (CoM) decomposition model. The multi-segmental pose consists of a four-bar linkage at the bottom and a linkage on top representing the trunk. The kinematics of the whole-body CoM is modeled as an inverted pendulum. The CoM angle can be decomposed into a multi-segmental structure accommodating different stance widths: wide (B) vs. narrow (C). Based on the definition of the CoM, the following link exists between the measured whole-body CoM angle (θCoM) and the estimated positions of the CoM of individual body segments: mbodyLCoMθCoM − mlegx�l_legCoM − mlegx�r_legCoM−mpelvisx�pelvisCoM − mtrunkx�trunkCoM = 0 (3.4) 81 where θCoM represents the measured angle of the ML whole-body CoM, x�l_legCoM, x�r_legCoM , x�pelvisCoM , and x�trunkCoM represent the estimated positions of the CoM of the left leg, right leg, pelvis, and trunk in the ML direction. Their corresponding masses are denoted as mleg, mpelvis, mtrunk, and mbody denotes the total body mass. LCoM represents the measured distance between the whole-body CoM position and the midpoint of the two virtual ankle joints. In the motion capture coordinate system, the positions of each body segment’s CoM in the ML direction can be explicitly written as follows: ⎩⎪⎪⎨⎪⎪⎧ x�l_legCoM = lcl sin�θ�leg� − da2x�r_legCoM = �ll sin�θ�leg� + cos�θ�pelvis� lHJC − da� lclll + da2x�pelvisCoM = ll sin�θ�leg� + lHJC2 cos�θ�pelvis� − lcpsin�θ�pelvis� − da2x�trunkCoM = ll sin�θ�leg� + lHJC2 cos�θ�pelvis� + lct sin�θ�trunk� − da2 (3.5) where θ�leg denotes the estimated angle of the person’s right leg relative to the vertical axis of the motion capture coordinate system, θ�trunk denotes the angle of the trunk relative to the vertical axis of the motion capture coordinate system, and θ�pelvis denotes the pelvis angle relative to the horizontal axis of the motion capture coordinate system, ll is the length of the leg, lHJC is the distance between the two hip joint centers, lcl, lcp, lct are the proximal distance of the CoM of the leg, pelvis, and trunk segment, and lastly, da is the distance between the two ankle joints. Due to the perpendicular assumption between the trunk and pelvis, θ�trunk = θ�pelvis. Considering that the model aims to capture kinematic characteristics of balance motion within a limited range of whole-body CoM angles, a few approximations can be made here to simply the computation process. First, considering the kinematic constraints of the four-bar 82 linkage mechanism, the pelvis angle (θ�pelvis) can be linearized around the upright body posture (θCoM = 0°) using a function of the change of the person’s right leg angle (∆θ�l) as: θ�pelvis ≈ f ′�θleg�|θleg=θleg0 ∙ ∆θ�leg = lHJC − dalHJC + da ∆θ�leg (3.6) In conjunction with the linearization, the trigonometric terms in equation (3.5) can be simplified as: ⎩⎪⎨⎪⎧sin(θ�leg) = θ�leg = θleg0 + ∆θ�legsin(θ�pelvis) = θ�pelvis = lHJC − dalHJC + da ∆θ�legcos�θ�pelvis� = 1 + θ�pelvis22 = 1 + �lHJC − dalHJC + da�2 ∆θ�leg22 (3.7) These approximations can transform equation (3.4) to a quadratic function (A∆θ�leg2 + B∆θ�leg +C = 0) with respect to ∆θ�l: ∆θ�leg2 �lHJC2 �lclll mleg + mpelvis2 + mtrunk2 � �lHJC − dalHJC + da�2� +∆θ�leg �2mleglcl + mpelvis �ll − lHJC − dalHJC + da lcp� + mtrunk �ll + lHJC − dalHJC + da lct��−mbodyLCoMθCoM = 0 (3.8) where the first- and second-order coefficients A and B can be precomputed to enhance the computational efficiency. ∆θ�leg is solved analytically, given the specific measured whole-body CoM angle during the ML sway. In the special case where the distance of the two ankle joints equals the distance of the two hip joint centers (da = lHJC), θ�pelvis remains constant at zero, 83 turning the four-bar linkage mechanism into a simple parallelogram. Consequently, equation (3.8) is reduced to: ∆θ�leg�2mleglcl + mpelvisll + mtrunkll� − mbodyLCoMθCoM = 0 (3.9) where the change of the leg angle can be solved as: ∆θ�leg = mbodyLCoMθCoM2mleglcl + mpelvisll + mtrunkll (3.10) With the estimated values of θ�l and θ�p obtained above, the corresponding estimated positions of the pelvis (x�p) and trunk (x�t) in the ML direction can be calculated: ⎩⎪⎨⎪⎧ x�pelvis = ll sin�θ�leg� + lp cos�θ�pelvis�2 − da2x�trunk = ll sin�θ�leg� + lHJC cos�θ�pelvis�2 + ltrunk sin�θ�pelvis� − da2 (3.11) 3.2.5 Electronic Architecture A two-layer electronic architecture was designed (Figure 3.3). At the higher layer, an embedded controller (NI PXIe-8133) with a data acquisition module (NI PXI-6289) digitizes the forces and moments sensed by two 6-axis force plates (AMTIBP250500-2K-3847) and simultaneously runs the robotic balance simulation at 500 Hz. Forces and moments exerted by participants on the left and right force plates are combined and transformed to the midpoint of ankle joints. The net ankle moments are used as inputs to the state space equation (3.3) with τx and τy respectively driving CoM motion in the AP and ML directions. Target encoder counts from the higher layer are sent to the Field Programmable Gate Array (FPGA) module (NI PXI-7846R) at the lower layer. The FPGA communicates directly with the four motors. Based on the current and target 84 encoder count, it sends a target velocity command as a digital signal via a pulse train to each motor’s servo drive. Running at a 40 MHz base frequency, the FPGA counts the encoder pulses of all motors (i.e., measured position) and executes a four-axis velocity-feedforward proportional-integral-derivative controller to actuate motions at 2000 Hz. 3.3 Balance Motion Tracking Performance Two distinct target motions were used to quantify the system: 1) multi-sine trajectories that simulate perturbed balance and 2) trajectories of natural quiet standing balance. 3.3.1 Multi-Sine Standing Balance Trajectory To estimate the gain, delay, and error when tracking larger perturbation-like balance motions, multi-sine signals including 0.02, 0.04, 0.08, 0.2, 0.4, 0.8, 2, and 4 Hz frequencies were used to mimic the characteristics of human standing balance [323]. The power spectrum of the multi-sine signal was designed to mimic that of the natural standing balance with higher power contained at lower frequencies [112]. The ranges of the CoM motion in AP and ML directions were set to ±8.0° to test the upper limits of the system. Rotation of the AP foot platform induces unwanted gravito-inertial components on the force plates that can be partially compensated, leaving residual 0.03 Nm (τx) and 0.20 N (Fy) root mean squared error (RMSE) - data not shown. The length of each segment of the signal was 50 seconds (due to the 0.02 Hz component). Twenty-five segments were concatenated to generate a target trajectory of 1250 seconds for each axis. To enable real-time robotic simulation, anatomical measurements of a 50th percent female (body height = 157 cm, weight = 58 kg) and a 0.17 m preferred stance width (typical narrow stance width [324]) were selected as human parameters for the robotic balance simulator. Note that the tracking performance (e.g., motion errors and delays) of the robotic system for other stance widths will not change substantially. 85 3.3.2 Natural Unperturbed Standing Balance Trajectory To evaluate the tracking of natural unperturbed balance, 60-second of quiet standing balance motions recorded from 16 healthy participants were used (8 females; body height: 170.6±8.7 cm; weight: 68.9±11.1 kg) with their stance widths approximately equal to their hip joint center distances. Their whole-body kinematics were recorded by a motion capture system (OptoTrak 3020, Waterloo, CA) with markers placed at their ankle joints, anterior superior iliac spine, iliac crest, and manubrium. The AP CoM and pelvis/trunk motions were calculated from the marker data. The range of AP CoM position/velocity were [−0.9°, 0.9°] and [−2.5°/s, 1.7°/s]. The range of pelvis position/velocity were [−21.8 mm, 19.5 mm] and [−2.4 mm/s, 1.8 mm/s]. The range of trunk position/velocity were [−23.3 mm, 37.1 mm] and [−2.1 mm/s, 2.3 mm/s]. For each axis, the motion of each participant was concatenated and sent to the robot as the target motion. 3.3.3 Performance Qualification The target and measured motions were saved by the real-time controller (NI-PXIe-8133) at 500 Hz. For multi-sine trajectories, coherence, gain, delay, and positional error were calculated to quantify the tracking performance. Coherence, gain, and phase were estimated using the frequency spectrum averaged over the 25 data segments. Coherence was calculated as the squared magnitude of the cross-spectrum between measured and target positions divided by the product of the measured and target positions auto-spectra [325][326]. The gain was calculated as the cross-spectrum divided by the auto-spectrum of the target position. The phase was estimated by the angle of the cross-spectrum. The delay between the target and measured position was estimated by computing the linear slope of the phase-frequency signal and divided by 2π to convert it to seconds. To get the errors of multi-sine and natural balance, the RMSE between the target and measured positions was calculated. Angular equivalent errors of natural balance tracking were 86 calculated to provide interpretations of linear errors within the context of natural standing balance: AP equivalents using equations (3.1) and (3.2) as well as ML equivalents for the 5th percent female and 95th percent male using: eθ = ±tan−1 �elR� (3.12) where el is the linear error (mm), R is the ankle-pelvis or ankle-torso distance, eθ is the angular error (°) [110], [322]. 3.3.4 Experimental Results For multi-sine tracking, coherence was near unity for all axes. Gains of all axes were also near unity: 1.00 for 0.02-0.2 Hz, 1.00-1.01 for 0.4-0.8 Hz, 1.02-1.07 for 2 Hz, and 1.01-1.29 for 4 Hz. Delays estimated using the multi-sine trajectories were between 9.4-13.9 ms for all axes. The average RMSE of multi-sine tracking was 0.08-0.23 mm. The average RMSE of natural motion tracking was 0.01-0.05 mm (corresponding to 0.001-0.009°; Table 3.1 and Figure 3.5). Table 3.1 Results of balance motion tracking. *RMSE: root mean squared error; AEE: angular equivalent error. Natural Multi-Sine Metric RMSE (mm) AEE (°) RMSE (mm) Delay (ms) Gain Foot Plate 0.05 0.006−0.009 0.08 13.90 0.99 (1-1.02) Pelvis 0.02 0.001−0.002 0.12 11.80 1.02 (1-1.09) Trunk 0.01 < 0.001 0.18 11.20 1.02 (1-1.09) Backboard 0.03 0.001−0.003 0.23 9.40 1.05 (1-1.29) 87 Figure 3.5 Balance motion tracking performance. Results of natural (A) trajectories from one person and multi-sine (B) trajectories for each axis with insets showing target and actual motions at finer resolutions. 88 3.4 Human-Robot Interactive Balance Performance Given that previous studies have quantified the real-time AP robotic interactive performance [143], [145], I focused on evaluating the performance of the device to transform in real-time the torque inputs generated by participants into ML trunk/pelvis motions predicted by the model. The robot was tested for slow and fast frequencies (0.05 and 0.3 Hz) expected to occur for natural ML balance sway. Errors were quantified between the predicted, robotic, and measured human motions. Six healthy participants (3 females; body height: 171.8±10.8 cm; weight: 69.1±9.8 kg) were recruited. The experiment was approved by the Behavioral Research Ethics Board (H18-03702) at the University of British Columbia. 3.4.1 Experimental Procedure The participant’s body height, weight, CoM height, trunk length, leg length, pelvis depth, and pelvis width were measured. The hip joint center distance was estimated using the leg length, pelvis depth, and pelvis width by a regression method [327]. Each participant’s anatomical parameters were inputted into the robot software for simulation. Participants were instructed to sway mediolaterally on the robot at their preferred magnitude. Participants performed 10 whole-body oscillations guided by a metronome at 0.05 and 0.3 Hz given that nearly 80% of the CoM power during balance is below 0.3 Hz [112][123]. The AP and ML controls were both enabled during the experiment to ensure natural unconstrained balance motion. Before the start of each trial, practice time (up to 5 min) was given until participants felt confident with the target frequency. The medial malleoluses (the antero-distal part) of the participant were aligned with the robot’s AP axis of rotation and adjusted the depth of torso/pelvis brackets to align their vertical CoM projection with the ankle rotational axis, resulting in an initial torque (τx/τy) < 5 Nm and force (Fx/Fy) < 15 N. 89 3.4.2 Data Recording and Analysis Six active infrared markers were attached to the body of the participant: three on the pelvis (bilateral anterior superior iliac spines and right-side iliac crest midpoint) and three on the trunk (bilateral clavicles – medial third – and manubriosternal junction) tracked by a motion capture system (OptoTrak 3020, Waterloo, CA) at 100 Hz during voluntary balance oscillations. To describe the linear position of the pelvis and trunk, two points on the participant's body (relative to the 6 markers) aligned with the rotational axes of the pelvis and trunk brackets were digitized. This allowed me to calculate the linear positions of the pelvis and trunk using rigid body transformations while avoiding potential bias from the rotation of the brackets. The predicted and measured robotic motions were saved by the real-time controller (NI-PXIe-8133) at 500 Hz and down-sampled to 100 Hz to match the frequency of the marker data. The RMSEs between the predicted and robotic motion and between the robotic and measured human motion were calculated to quantify the real-time robotic control errors and the relative motions between the human and robot (due to compliance of the foam in the brackets). To interpret the errors in a standing balance context, equation (3.12) was used to calculate the angular equivalent error corresponding to the average RMSE based on a 5% female and 95% male. For the slow–quasi-static–oscillations (0.05Hz), the slope of the torque/angle relationship for ML balance was estimated. 3.4.3 Experimental Results The average ML CoM motion magnitude ranged from −5.5±0.4° to 5.3±1.2° at 0.05 Hz and −3.8±1.7° to 4.2±1.5° at 0.3 Hz. Across participants and sway frequencies (Table 3.2 and Figure 3.6), the average RMSE between the predicted and robotic motion was 0.08-0.36 mm (corresponding to 0.005-0.028°) for the pelvis and 0.08-0.37 mm (corresponding to 0.003-0.018°) for the trunk. The average RMSE between the robotic and measured motion was 0.55-0.64 mm 90 (corresponding to 0.034-0.050°) for the pelvis and 0.65-0.68 mm (corresponding to 0.025-0.034°) for the trunk. The torque/angle relationship calculated from the ML torques and CoM angles generated by the participants swaying at 0.05Hz on the robot was on average (617 ± 95 Nm/rad), less than 2% from the predicted values (605 ± 87 Nm/rad). Sound pressure increased by 3 dB relative to quiet room levels when participants swayed on the robot. Table 3.2 Results of the human-robot interactive balance experiment. RMSE: root mean squared error; AEE: angular equivalent error. Pelvis Position Condition Metric Predicted-Robotic Robotic-Human 0.3 Hz RMSE (mm) 0.36±0.16 0.64±0.36 AEE (°) 0.022−0.028 0.039−0.050 0.05 Hz RMSE (mm) 0.08±0.01 0.55±0.12 AEE (°) 0.005−0.006 0.034−0.043 Trunk Position 0.3 Hz RMSE (mm) 0.37±0.16 0.68±0.19 AEE (°) 0.014−0.018 0.026−0.034 0.05 Hz RMSE (mm) 0.08±0.01 0.65±0.22 AEE (°) 0.003−0.004 0.025−0.032 91 Figure 3.6 Interactive balance performance. A participant’s torque (𝛕𝛕𝐛𝐛), CoM angle (𝛉𝛉𝐂𝐂𝐂𝐂𝐂𝐂𝐛𝐛 ), and the mediolateral position of the trunk (𝐱𝐱�𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭)/pelvis (𝐱𝐱�𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩) predicted vs. robotic motion and robotic vs. human motion when swaying within the real-time robotic control loop at 0.05 Hz (A) and 0.3 Hz (B). Insets show oscillations at finer resolutions. 92 3.5 Discussion In this chapter, I described the mechanical, electronic, and software design of a multidirectional robotic balance system. The design was informed by the physiological requirements of standing balance motion, the need to control AP and ML motions simultaneously, and the kinematics of the pelvis and torso changing as a function of stance width. Given this novel system, I quantified its motion-tracking performance using trajectories replicating both perturbed and unperturbed natural standing balance. The robot showed delays of less than 15 ms, near-unity gain, and submillimeter tracking errors. Delays between the target and the actual robot motion can lead to feelings of controlling a foreign object, but the observed 9.4-13.9 ms delays are below human perception thresholds (150 ms [149], [315]) and automatic balance-correcting responses (15-60 ms [328], [329]). The delays of AP motion are also shorter than the 20-117 ms reported in previous robotic systems [143], [145]. Near-unity gains were shown for all motion axes and frequencies. The overall gain metrics of the system are excellent, meeting the application requirements because nearly 80% of the CoM power during balance is below 0.3 Hz with peak power below 0.5 Hz [112], [123]. In complementary experiments using a multi-sine trajectory with frequencies up to 20 Hz, gain decreased above 12 Hz and 8 Hz for the ML and AP backboard axes, respectively. Both multi-sine and natural balance motion tracking showed submillimeter (0.01-0.23 mm) errors across all motors. Based on expected users ranging from the 5th female to 95th percent male, the errors of natural motion tracking correspond to balance oscillations of 0.001-0.009° for AP motion and < 0.002° for ML motion, which are 0.8-5.0% and 0.3-0.9% of the perception threshold of human postural AP sway (0.17° at 0.06°/s) [330]. 93 The robotic system was further evaluated when a human controlled the robotic motion in real time. The robotic system again showed submillimeter RMSE (0.08-0.37 mm; corresponding to 0.003-0.028°) between the predicted and robotic motion. In addition, the robotic motion was well transferred to the participants, with RMSE relative motion between the robot and participants also remaining submillimeter (0.55-0.68 mm, corresponding to 0.025-0.050°). The 2% deviation between the measured and predicted torque/angle matched the property of the previous robot [143], while the 3 dB sound pressure increase as the robot actuated the participants was unlikely to disturb standing balance [331]. This reveals that the system not only achieves high real-time robotic motion control accuracy but also ensures tight motion coupling between the participant and robot in human-in-the-loop scenarios. Limitations of the robot include the absence of segmental hip motion for replicating the kinematic responses to large AP perturbations, the lack of independent ankle/lower leg actuation for ML balance, and the need to validate the ML CoM decomposition model (described in detail in Chapter 4). Despite these limitations, this innovative system opens new avenues for research including the possibility to characterize biomechanical interactions between the control of AP and ML balance and their consequences for adaptation and learning. Paired with electromyography and electroencephalogram, this robot can also help unravel the sensorimotor principles underlying the multidirectional control of standing balance. Future studies may also target learning protocols to assess/improve balance in older adults and persons with concussions [4]. 94 Chapter 4: Modeling Multi-Segmental Kinematics of Mediolateral Standing Balance: Validation and Refinement of a Whole-Body Center of Mass Decomposition Approach Chapter 3 focused on achieving novel mediolateral (ML) control for the robot. However, there remains a crucial gap in confirming the accuracy of the proposed center of mass (CoM) decomposition model in representing human ML balance kinematics. Specifically, the model assumes that the trunk remains perpendicular to the pelvis at all times, a hypothesis that requires rigorous validation. Therefore, in this chapter, I shift the focus to verifying both the ML CoM decomposition model and the trunk-pelvis perpendicular assumption through a human participant experiment. This validation process aimed to ensure that the robotic system faithfully replicates multi-segmental kinematics during ML balance. 4.1 Introduction Balance impairments can restrict mobility and daily functioning in patients with concussions [4], [44], [332]. Building precise standing balance models emerges as a key approach in quantifying the biomechanical changes in balance impairments as well as advancing biomedical devices that can used for balance assistance, rehabilitation, and fall prevention [333]–[335]. By simulating the dynamics and kinematics of standing balance, engineers can develop control algorithms that enable robotic exoskeletons to provide support and stability, thus improving mobility for individuals with musculoskeletal disorders [336]–[338]. Similarly, in rehabilitation settings, standing balance models contribute to the development of effective interventions for individuals recovering from musculoskeletal or neurological injuries. Understanding the biomechanics and associated underlying mechanisms of standing balance control enables clinicians to tailor 95 rehabilitation protocols to address specific deficits in postural stability, potentially leading to faster recovery and improved functional balance outcomes [339]–[342]. Additionally, these models inform the design of home-based monitoring systems that detect early signs of balance impairment, enabling timely interventions [335], [343]. Traditionally, the inverted pendulum model has been used as the primary framework for understanding and describing the dynamics and kinematics of the whole-body CoM motion during natural standing balance sway in both anteroposterior (AP) and ML directions in humans [113], [344], [345]. While the inverted pendulum model effectively captures the main characteristics of AP balance sway, it becomes inadequate for accurately depicting the multi-segmental kinematics and dynamics of the body during ML sway. In AP balance, the body is represented as an inverted pendulum pivoting at the ankle, aligning individual body segment motions with the whole-body CoM [112], [346]. However, during ML sway, the kinematics of individual body segments are influenced by stance width due to the configuration of the lower body modeled as a four-bar linkage. Consequently, differences may arise between the motions of the whole-body CoM and individual body segments [86], [114], [314]. In response to these challenges, B. L. Day and his colleagues introduced a closed-chain four-bar linkage mechanism to model the lower body and added a linkage on top of the pelvis to represent the trunk, which has served as a main framework for subsequent researchers [313]. For example, Bingham et al. applied hip torque to this model to simulate postural responses to perturbations at altered stance widths during ML sway [114]. Additionally, the novel whole-body CoM decomposition model was developed in the previous chapter, capable of decomposing the whole-body CoM into a corresponding multi-segmental pose at different stance widths [302]. However, a critical aspect to consider in such models is the assumption that the trunk remains 96 perpendicular to the pelvis during ML sway. While this assumption simplifies the multi-segmental modeling by reducing the system to a single degree of freedom (1DoF), it lacks rigorous verification and may yield erroneous estimates of trunk/pelvis positions in space. Day’s verification of the model only accounted for quiet standing scenarios where minimal trunk-pelvis rotation occurs, thus not fully addressing the impact of the trunk-pelvis perpendicular assumption during voluntary sway [313]. Goodworth examined the model more from a dynamic control perspective by applying torques to both the trunk and pelvis, without directly measuring this trunk-pelvis angle and focusing only on sway at narrow stance widths [86]. However, the constraint of trunk-pelvis perpendicularity may become more pronounced at larger CoM angles and wider stance widths. For instance, this assumption can result in the estimation of the trunk rotating in the opposite direction to the whole-body CoM at a given wide stance width (see Figure 4.1 panel A). In addition, my pilot experiment contradicted such estimation, as I observed that at wide stance widths, the rotational direction of the trunk typically aligned with the whole-body CoM. Therefore, a direct investigation of this perpendicular kinematics assumption covering a greater range of whole-body CoM angles and stance widths is needed. In light of these considerations, this study was designed to validate, in vivo, the accuracy of the trunk-pelvis perpendicular assumption between balance limits at a wide range of stance widths and its implication on the accuracy of the whole-body CoM decomposition model. Participants were instructed to sway between their comfortable balance limits in the ML direction from narrow to wide stance widths (50-200% hip joint center distance) that replicate various stance conditions that may occur in daily living. The observed deviation from the perpendicular assumption and its consequent inaccuracy in the CoM decomposition model prompted us to refine the model using actual trunk-pelvis angle changes extracted from the 97 measured data while still preserving the 1DoF system constraint, only driven by the whole-body CoM angle. Then, I validated the robustness of this data-driven model improvement through a cross-validation analysis. By addressing this key limitation of the existing ML balance model through proposed model refinements, this study contributes to advancing the understanding of multi-segmental kinematics during ML sway and developing practical applications using the improved model. 4.2 Materials and Methods 4.2.1 A Brief Overview of the Center of Mass Decomposition Model The model (Figure 4.1 panel A) decomposes the whole-body CoM angle (θCoM) in the ML direction to generate a corresponding multi-segmental pose. It works at different stance widths and estimates the positions of the trunk and pelvis in the ML direction as the final outputs. Here, θCoM is used as the independent variable that drives the entire system. The estimated position of the trunk (x�trunk) is the highest point of the trunk linkage in the model (corresponding to the position of the manubrium), while the estimated position of the pelvis (x�pelvis) is the midpoint of the left and right hip joint centers in the model (Figure 4.1 panel A). The estimated angle between the trunk and pelvis is fixed at 90°, due to the perpendicularity assumption adopted by the prior literature [86], [114], [119], [313]. The stance width is the distance between the two ankle joints in the ML direction. The following body parameters are used as constants by the model: body mass, the distance between the whole-body CoM and midpoint of the two ankle joints (CoM length), the distance between the two hip joint centers, the distance between the midpoint of hip joint centers and manubrium, the distance between the hip joint center and ipsilateral ankle joint, and the distance between the two ankle joints. 98 The guiding principle for the CoM decomposition process relies on its definition, as expressed by: θCoM ∙ LCoM =mlegx�llegCoM + mlegx�rlegCoM + mpelvisx�pelvisCoM + mtrunkx�trunkCoMmbody (4.1) where θCoM represents the measured whole-body CoM angle, and LCoM represents the measured CoM length. On the right-hand side of the equation, x�llegCoM, x�rlegCoM, x�pelvisCoM , and x�trunkCoM denote the positions of the CoM of the left leg, right leg, pelvis, and trunk in the ML direction estimated by the model, respectively, while mleg, mpelvis, and mtrunk denote their corresponding masses. Lastly, mbody is the total measured body mass. The mass of each segment is calculated by multiplying mbody with its relevant ratio according to the previous anthropometric data [110]. Note that in this model, the total trunk mass is considered to include the masses of the head and arms. Within a small angular range of body sway, equation (4.1) can be transformed into an equation with respect to the angle of the leg θ�leg, defined from the positive vertical (+z) axis to the person’s right leg, and the angle of the pelvis θ�pelvis, defined from the positive horizontal (+x) axis to the pelvis. Based on these two angles, the positions of the trunk (x�trunk) and pelvis (x�pelvis) in the ML direction are estimated. Throughout the chapter, a positive angle is defined as rotating counterclockwise from the participant’s first-personal view. Detailed step-by-step derivation of this model can be found in Section 3.2.4 of the previous chapter. In this model, the estimated angle from the vertical axis to the trunk vector (θ�trunk) is related to determining x�trunkCoM , thus affecting the entire CoM decomposition. There exists a relationship between this angle, the angle from the trunk to the pelvis (θ�trunk−pelvis), and θ�pelvis: 99 θ�trunk = 90° + θ�pelvis − θ�trunk−pelvis (4.2) In the previous literature, the trunk is assumed to be perpendicular to the pelvis: i.e., θ�trunk−pelvis is equal to 90°, leading to θ�trunk = θ�pelvis. Lastly, letters with hats (^) are used to denote kinematic variables estimated by the model, and letters without hats are used to denote measured kinematic variables in this chapter. Figure 4.1 Experimental setups. (A) The CoM angle estimated by the force plates was decomposed by the model to get the estimated trunk-pelvis angle (𝛉𝛉�𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭−𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩), trunk position (𝐱𝐱�𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭,), and pelvis position (𝐱𝐱�𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩). These values were compared with the ones obtained from the markers (𝛉𝛉𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭−𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩, 𝐱𝐱𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭𝐭, 𝐱𝐱𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩𝐩). (B) Left: Time-series trajectories of the measured/estimated trunk-pelvis angle, trunk position, and pelvis position. Right: These trajectories were plotted against the trajectory of the CoM angle, showing the kinematic characteristics in the spatial domain. Such spatial-domain plots looked linear and can be characterized/quantified by their corresponding slopes. 100 4.2.2 Participant Recruitment This study was reviewed and received approval from the Behavior Research Ethics Board at the University of British Columbia (number: H18-03702) and adhered to the Declaration of Helsinki (except principle 35 - registration to the public database before recruitment). A total of 21 healthy adult participants with no known history of musculoskeletal injury were recruited. All participants gave informed written consent for participation in the experiment. One female participant did not complete the study protocol, leaving the data of 20 participants (10 males and 10 females, age: 24±3 years, height: 173.9±12.0 cm) for analysis. 4.2.3 Experimental Apparatus and Data Collection To record multi-segmental kinematic data during ML balance, a 13-camera high-speed motion capture system (Motion Analysis Inc., CA, USA) at 100 Hz was used for sampling marker positions. Passive, retroreflective markers were securely attached with double-sided tape to key anatomical landmarks on the participant's body, including bilaterally over the anterior superior iliac spines (ASIS), posterior superior iliac spines (PSIS), lateral and medial malleoli (used for determining ankle joint positions), tragus, and bilateral inferior orbital bones. A single marker was placed on the manubrium. The marker-based kinematics were used as a gold-standard comparison to the model-estimated kinematics. Participants stood on two identical force plates (OR6-6 AMTI, Advanced Mechanical Technology Inc., MA, USA) placing one foot on each. The ground reaction forces and center of pressure signals in the ML direction were calculated using the product’s standard software and sampled at 2000 Hz. 101 4.2.4 Experimental Procedure The participant’s anthropometric data were collected first, including their height, body mass, ipsilateral ASIS-to-medial malleoli distance (leg length), bilateral ASIS distance (pelvis width), ipsilateral ASIS-to-PSIS distance (pelvis depth). I used these anthropometric measures to estimate the hip joint centers using the Harrington regression equations [347]. Subsequently, participants performed a 30-second quiet standing trial at a self-selected stance width to familiarize themselves with the experimental environment. Considering that the original CoM decomposition model estimates different trunk/pelvis positions depending on the stance width, seven different stance width ratio conditions were investigated from narrow to wide, including 50%, 75%, 100%, 125%, 150%, 175%, and 200% (stance ratio w = dalHJC∙ 100% where da denotes the stance width and lHJC denotes the distance between the two hip joint centers). These ratios were chosen to encompass a comprehensive spectrum of (extremely narrow: 50% to wide: 200%) stance widths that may be encountered during standing in daily living. In each stance width condition, participants performed two postural sway trials guided by a metronome: one at 0.1 Hz (10 oscillations/100 seconds per trial) and one at 0.2 Hz (10 oscillations/50 seconds per trial). These frequencies were selected to emulate the range of sway rates typically encountered during natural ML standing balance in real-world scenarios. To acquaint participants with the whole-body movement frequency, they engaged in approximately 1 minute of practice before each trial officially started. During the trials, participants were instructed to sway naturally from side to side within their maximum comfortable range of their base of support, gradually shifting their body weight from one foot to the other, while 102 maintaining full contact with the ground and keeping their legs straight. Specific verbal instructions provided to the participants during the experiment can be found in Appendix A. 4.2.5 Data Preprocessing 4.2.5.1 Stance Width The positions of the left and right ankle joints were calculated as the virtual midpoints of the markers attached at the corresponding medial and lateral ankle joints. The stance width (da) was then calculated as the actual mediolateral distance between the two virtual midpoints. 4.2.5.2 Trunk/Pelvis Position At each frame, the measured position of the trunk (xtrunk) was obtained directly as the position of the marker attached to the manubrium. At the same time, a local pelvic coordinate system was built using the vector from the person’s left ASIS to the right ASIS as the x-axis, the vector from the midpoint between left/right PSIS to the midpoint between left/right ASIS as the y-axis, and the z-axis obtained via cross-product following the right-hand rule. Using the regression method developed by Harrington et al. [327], the coordinates of the biliteral hip joint centers in the local pelvic coordinate system were estimated and subsequently transformed to the motion capture coordinate system. In the motion capture coordinate system, the midpoint between the two hip joint centers (xpelvis) was chosen to represent the position of the pelvis. 4.2.5.3 Trunk-Pelvis Angle The angle between the trunk and the pelvis (θtrunk−pelvis) was defined as the angle from the trunk vector to the pelvis vector. The trunk vector was defined as from the pelvis position to the manubrium marker, while the pelvis vector was defined as from the person’s left hip joint center to the right hip joint center. Finally, θtrunk−pelvis was calculated by dividing the inverse cosine function of the dot product between the two vectors by the product of their norms. 103 4.2.5.4 Force Plate-Estimated Whole-Body CoM Angle The force plate data was downsampled from 2000 Hz to 100 Hz to align with the sampling rate of the marker data. Utilizing a previous technique established by Winter et al. [119], the net center of pressure movement in the ML direction was merged from the center of pressure measurement recorded by each force plate, while the net ground reaction force in the ML direction was determined by summing the individual forces measured by each force plate. Subsequently, a zero-point-to-zero-point double-integration technique developed by prior researchers, King et al. [115], was employed to estimate the whole-body CoM position (xCoMFP ) based on the net center of pressure movement and the net ground reaction force in the ML direction. Finally, the ML CoM angle (θCoM) was calculated by taking the inverse tangent function of the ML CoM position divided by the length of the CoM: θCoM = arctan�xCoMFPLCoM� (4.3) This CoM angle was used as the input of the model to estimate the positions of the trunk and pelvis. The whole-body CoM length, LCoM, was digitized using the marker data collected from the 30-second quiet standing trial as: LCoM = �xCoM2 + (zCoM − za)2 (4.4) where za is the average height of the left/right ankle joints. xCoM and zCoM were the whole-body CoM position in the horizontal and vertical direction estimated from the markers. Specifically, they were estimated using the position of each body segment (trunk, pelvis, legs) obtained from the markers and their respective CoM positions and masses estimated according to previous anthropometric data [110]. 104 4.2.5.5 The Slope Between Segmental Kinematics and CoM Angle Through exploratory data analysis, a linear relationship was observed between segmental kinematics variables xtrunk/xpelvis/θtrunk−pelvis as a function of θCoM (Figure 4.1 panel B). Therefore, the slope between these segmental kinematics variables with respect to θCoM was extracted through linear regression and denoted as: ⎩⎪⎪⎨⎪⎪⎧ Kxtrunk = ∆xtrunk∆θCoM Kxpelvis = ∆xpelvis∆θCoMKθtrunk−pelvis = ∆θtrunk−pelvis∆θCoM (4.5) Kxtrunk, Kxpelvis, and Kθtrunk−pelvis can be used to describe the rate of change of the translational motion of the trunk/pelvis in space and the angular motion between them with respect to the change of the whole-body CoM angle during ML balance. The kinematics data from each trial were divided into ten equal segments corresponding to ten full sway cycles. A cycle starts when a person’s whole-body CoM angle was zero and ends when it returned to zero for the second time. Then the average value of the ten cycles was used as the final value of the slope for each trial. The same slope analysis can be applied to trunk/pelvis kinematics estimated by the original or refined model as well to capture their corresponding relationship with respect to the model input θCoM. 4.2.6 Model Accuracy Analysis θCoM estiamted by the force plates was fed into the decomposition model to estimate the positions of the trunk and pelvis in the ML direction. These estimated positions were compared against the gold standard: their corresponding positions measured by the markers. 105 4.2.6.1 Root Mean Squared Error The root mean squared error (RMSE) between the trunk/pelvis position (x�trunk, x�pelvis) estimated by the model and their corresponding measured one (xtrunk, xpelvis) was calculated. This reflects the degree of agreement between model-estimated and measured values along the temporal series trajectories. 4.2.6.2 Slope Ratio The slope was employed to quantify the model accuracy in the spatial domain (irrelevant of time). Specifically, the ratio between the slope of the estimated trunk/pelvis position and the slope of the measured trunk/pelvis position was calculated: ⎩⎪⎨⎪⎧Rtrunk = Kx�trunkKxtrunkRpelvis = Kx�pelvisKxpelvis (4.6) When this ratio was equal to one, the estimated and measured positions were identical, showing that the model can perfectly predict the measured positions at different CoM angles. If the ratio was greater than one, the model overestimated the positions of the trunk and pelvis compared to their measured values at different CoM angles. In contrast, if the ratio was less than one, the model underestimated the measured positions of the trunk and pelvis at different CoM angles. 4.2.7 Data-Driven Model Refinement After I observed that θtrunk−pelvis did not stay perpendicular during balance motions and that the amplitude of this angle increased with increasing stance widths (more details can be seen in Section 4.3.1 in this chapter), I used a data-driven refinement approach to remove the constraint of trunk-pelvis perpendicularity in the CoM decomposition process. This was done by first fitting 106 an empirical second-order function to estimate K�θtrunk−pelvis that is dependent on the stance width ratio (w): K�θtrunk−pelvis = b0 + b1w + b2w2 (4.6) As a result, θ�trunk−pelvis was expressed as: θ�trunk−pelvis = 90° + (b0 + b1w + b2w2) ∙ θCoM (4.7) Then, θ�trunk−pelvis was used to update θ�trunk: θ�trunk = 90° + θ�pelvis − θ�trunk−pelvis = θ�pelvis − (b0 + b1w + b2w2) ∙ θCoM (4.8) Lastly, θ�trunk was substituted back in equation (3.5) to update the subsequent CoM decomposition process. The following new quadratic equation was obtained as a function of the change of the leg angle: ∆θ�leg2 ��lHJC − da�22�lHJC + da�2 (mleglcllHJCll + mpelvislHJC + mtrunklHJC2 + mtrunkltcos((b0 + b1w + b2w2) ∙ θCoM)�+∆θ�leg �2mleglcl + mpelvis(ll − lHJC − dalHJC + da lcp) + mtrunk(ll + (lHJC − da)ltlHJC + da cos((b0 + b1w + b2w2) ∙ θCoM))�−mbodyLCoMθCoM − mtrunkltsin((b0 + b1w + b2w2) ∙ θCoM) = 0 (4.9) In the special case where da = lHJC, equation (4.9) was reduced to the following form: ∆θ�leg�2mleglcl + mpelvisll + mtrunkll� −mbodyLCoMθCoM − mtrunkltsin((b0 + b1w + b2w2) ∙ θCoM)) = 0 (4.10) producing the analytical solution as: ∆θ�leg = mbodyLCoMθCoM + mtrunkltsin ((b0 + b1w + b2w2) ∙ θCoM))2mleglcl + mpelvisll + mtrunkll (4.11) 107 With the refined estimated values of θ�l and θ�p, the same equation (3.11) can be used to get the corresponding x�p and x�t in the ML direction. This improved CoM decomposition model will be denoted as the “refined” model throughout this chapter. 4.2.8 Cross-Validation Analysis A leave-one-out-cross-validation analysis was performed to evaluate the refined model. During each fold of the cross-validation, nineteen participants were used as the training set. Their measured Kθtrunk−pelvis of the two frequency conditions was averaged for a measured stance width ratio (w). The averaged Kθtrunk−pelvis was then fitted against w to obtain an empirical 2nd-order nonlinear function relating K�θtrunk−pelvis to w. The three regression coefficients of the 2nd-order fit obtained from each participant were averaged across all nineteen participants and this fitted function was used to refine the rest of the CoM decomposition process. The refined model was tested on the remaining one participant: i.e., each fold corresponded to a different participant. RMSEs and slope ratios were calculated for the refined model at each fold and averaged across folds, which were compared to the corresponding results of the original model. 4.2.9 Statistical Analysis θtrunk−pelvis was assumed to stay perpendicular by the original model. Although this measured value may slightly deviate from an exact 90° due to individual anatomical differences, measurement noises, and minor errors in marker placement, it should remain constant without displaying significant deviations from the perpendicular value. In other words, Kθtrunk−pelvis = 0 at all times. Therefore, to evaluate the perpendicular assumption, Kθtrunk−pelvis was selected and compared against the model-assumed value at zero using one-sample t-tests at different stance width conditions (α = 0.05, MATLAB, version: 2023b, Mathworks Inc., Natick, MA). 108 Bonferroni-Holm corrections were applied to adjust the p-values due to multiple comparisons. Then, a linear mixed-effects model (Jamovi, version: 2.3.28) was used to investigate whether the amplitude of trunk-pelvis angle oscillation was influenced by stance width and sway frequency with the following form (α = 0.05): Kθtrunk−pelvis~1 + f + w + (1|id) (4.12) where f represents the sway frequency, w is the stance width ratio, and id denotes the participant’s ID. Here, Kθtrunk−pelvis was chosen as the dependent variable. w and f were chosen as fixed-effects parameters, and id was included as a random component. To examine whether estimated trunk/pelvis positions were significantly different between the original model and refined model, Statistical Parametric Mapping (SPM) (two-tailed, α = 0.05) was used to compare the cycle-averaged positional trajectory estimates of trunk/pelvis across all participants at different stance width conditions [348]. 4.2.10 Exploratory Analyses of Movement Mechanisms Exploratory analyses were conducted to explore potential mechanisms that may explain the observed trunk and pelvis motions during ML sway. First, the position of the head in space (center of the bilateral tragus and inferior orbital markers; xhead) was calculated with respect to the bilateral ankle joint positions. This allowed the determination of whether the participant’s head position was related to the edges of their base of support. Second, it is plausible that ML sway does not abide by the trunk-pelvis perpendicular assumption because people prefer to maintain a vertical trunk. Therefore, the angle from the measured trunk vector to the vertical axis (θtrunk) was calculated. 109 4.3 Results 4.3.1 Measured Trunk-Pelvis Angle θtrunk−pelvis exhibited an oscillatory pattern around the perpendicular pose throughout the balance sway cycle under different stance width conditions (Figure 4.2). Although the amplitude of the oscillation remained relatively consistent between 50% and 75% narrow stance widths, it increased substantially at stance widths ≥100%. The mean amplitude of θtrunk−pelvis across participants spanning 50-200% ranged from 0.84±0.94 to 5.23±2.39°. Multiple one-sample t-tests confirmed that Kθtrunk−pelvis at different stance width conditions were significantly higher than the assumed value at zero (p-values < 0.004). Figure 4.2 Measured trunk-pelvis angle and center of mass (CoM) angle across stance widths. The measured trunk-pelvis angle is showcased in the first row, with the yellow line depicting estimations made by the original model. The second row displays the corresponding whole-body CoM angle. The linear mixed model analysis revealed a significant impact of stance width on the amplitude of the trunk-pelvis angle oscillation (characterized by Kθtrunk−pelvis), with wider stance widths resulting in greater magnitudes (p < 0.001). Conversely, sway frequency did not significantly 110 affect Kθtrunk−pelvis (p = 0.731). Plotting Kθtrunk−pelvis relative to the stance width ratio demonstrated an overall nonlinear increase trend between these two variables. Individual plots of each participant can be seen in panel A of Appendix B. Detailed summary of the linear mixed-effects model can be found in Appendix C. 4.3.2 Estimation Errors of the Original Model Under the trunk-pelvis perpendicular assumption, the model was found to consistently underestimate the trunk position while overestimating the pelvis position (Figure 4.3 panel A). These discrepancies became more pronounced as the stance width increased, as indicated by the progressive increase in the mean RMSE across participants (Figure 4.3 panel B). Over the range from a stance width of 50% to 200%, the mean RMSE ranged from 8.0-19.2 mm for the estimated trunk position and from 4.3-10.1 mm for the estimated pelvis position, while the mean slope ratio ranged from 0.82-0.86 for the estimated trunk position and from 1.06-1.11 for the estimated pelvis position (Table 4.1). 111 Figure 4.3 Estimation errors using the original model. Panel (A) shows an example plot of trunk/pelvis positions estimated by the original model compared against their measured ones. Panel (B) displays errors in trunk and pelvis positions, calculated as the measured value subtracted by the estimated value. In both panels, Each thin gray line represents a different participant, while the thick black line depicts the average trace across participants. 112 Table 4.1 Average root mean squared errors (RMSE, unit: mm) and slope ratios (SR, from 0-1) of trunk/pelvis positions estimated by the original model vs. the refined model. Segment Model Metric 50% 75% 100% 125% 150% 175% 200% Trunk Original RMSE 8.0±4.8 10.2±5.6 13.3±7.9 14.7±9.4 17.8±12.3 18.3±12.1 19.2±11.8 SR 0.86±0.07 0.85±0.07 0.85±0.08 0.85±0.09 0.83±0.10 0.83±0.14 0.82±0.16 Refined RMSE 6.3±4.3 7.3±4.7 9.3±6.4 9.7±7.0 12.1±8.5 12.6±7.6 13.1±7.0 SR 0.92±0.07 0.92±0.07 0.92±0.09 0.94±0.09 0.95±0.12 0.98±0.16 1.00±0.19 Pelvis Original RMSE 4.3±2.6 4.7±2.4 5.8±3.2 6.6±3.8 8.5±5.3 9.3±5.7 10.1±5.8 SR 1.11±0.10 1.08±0.06 1.07±0.07 1.07±0.08 1.09±0.10 1.09±0.12 1.11±0.13 Refined RMSE 3.4±2.1 3.5±1.5 4.6±2.3 5.6±2.3 7.1±2.8 7.9±4.0 8.2±4.0 SR 1.05±0.09 1.03±0.06 1.00±0.06 1.00±0.70 1.00±0.90 0.98±0.10 0.98±0.12 113 4.3.3 Results of the Cross-Validation Analysis Unlike the original model, the refined model accurately depicted θtrunk to always rotate in the same direction as θCoM at wider stance widths, while also compensating for the greater trunk-pelvis angle oscillations observed at narrow and medium stance widths (Figure 4.4 panel A). Overall, the refined model successfully reduced estimation errors of both trunk and pelvis positions using the original model. Throughout the balance cycle at different stance widths, mean RMSEs of trunk/pelvis positions averaged across participants both decreased substantially (Figure 4.4 panel B). From 50% to 200% stance widths, the mean trunk RMSE decreased by 22-32% (from 8.0-19.2 mm to 6.3-13.1 mm) and by 18-23% for the mean pelvis RMSE (from 4.3-10.1 mm to 3.4-8.2 mm). Correspondingly, the mean Rtrunk increased by 7-22% from 0.82-0.86 to 0.91-1.00, while the mean Rpelvis decreased by 5-12% from 1.06-1.11 to 0.98-1.05, both getting closer to the ideal ratio of 1.0 (Table 4.1). 114 Figure 4.4 Comparison between the original model vs. the refined model. (A) Skeleton plots using the original and refined models at various stance widths (50%-200%). The yellow color corresponds to the original model, while the green color corresponds to the refined model. (B) Comparison of participant-average errors of trunk/pelvis position estimates throughout the balance cycle using the original and refined models at different stance widths. Additionally, across various stance widths, SPM analysis revealed significant differences (p-values < 0.001; detailed figures can be found in Appendix B panel B) between the original model vs. the refined model, encompassing approximately 98% of the balance sway cycle deviating from the central standing posture (θCoM = 0°). 115 Figure 4.5 Error comparison of estimated trunk/pelvis positions with respect to the range of center of mass angle using the original and refined models. Further examination of the relationship between the trunk/pelvis RMSE and the amplitude of the CoM sway (Figure 4.5) showed that discrepancies between the original model and the refined model tended to diminish at narrower stance widths and at smaller CoM angles. However, these errors became more pronounced with increasing stance widths and CoM angles. For instance, considering a 10 mm RMSE benchmark, both models exhibited mean pelvis RMSEs <10 mm from 50% to 125% stance widths. However, at wider stance widths (150% to 200%), mean pelvis RMSEs exceeded 10 mm at CoM angles of 9-10° using the original model, while still being kept under the benchmark using the refined model. This characteristic was more evident in the trunk position estimation. Both models maintained mean trunk RMSEs below 10 mm only for narrow stance widths (50% to 75%). From 100-200% stance widths, mean trunk RMSEs 116 exceeded 10 mm starting from CoM angles of 5-6° using the original model vs. starting at a wider range of CoM angle, 7-10°, using the refined model. After confirming that the 2nd-order-fitting-based refined model can effectively and robustly reduce overall estimation errors by the leave-one-out-cross-validation analysis, the final values of these coefficients were fitted on the entire dataset, resulting in the following expression: θ�trunk = (0.25 − 1.4 × 10−3w + 1.66 × 10−5w2) ∙ θCoM + θ�pelvis (4.13) The final fitting of K�θtrunk−pelvis as a function of stance width ratio (w) was shown below: Figure 4.6 Final fitting results. The slope of the trunk-pelvis angle with respect to the CoM angle was fitted against the stance width ratio. Each thin gray line represents the fitted result of one participant (N = 20), while the thick black line represents the final fitting result with its three coefficients obtained as the average values across the twenty participants. 4.3.4 Measured Head Position and Trunk Angle In Space The experimental results revealed that xhead consistently remained within the base of the support area delineated by the two feet and moved in the same direction as CoM (xCoMFP ) across various 117 stance widths (Figure 4.7 panel A). The mean amplitude of xhead increased with expanding stance widths from 50% to 125%: 75.4 to 131.2 mm. However, this increase was not as prominent at wider stance widths of 150% to 200%, with the mean head motion amplitude remaining stable at 141-142 mm for 150-175% stance widths and then slightly decreasing to 133.4 mm at 200% stance width. Similarly, the mean amplitude of xCoMFP exhibited a comparable trend, increasing from 42.6 to 57.8 mm between 50% and 125% stance widths, plateauing at 97-99 mm for 150-175% stance widths, and slightly decreasing to 91.6 mm at 200% stance width. Despite this trend of increase, plateau, and slight decrease, the difference between the mean amplitude of xhead and xCoMFP remained relatively consistent, contained within a narrow band of 33.0 to 44.7 mm, showing only a slight increase from narrow to wide stance widths (Figure 4.7 panel B). Additionally, θtrunk also displayed minor changes, ranging from 2.89-2.94° at 50-100% stance widths, 2.42-2.56° at 125-150% stance widths, and 1.94-1.95° at 175-200% stance widths (Figure 4.7 panel C). These differences varied by only 1-2° across the range of 50%-200% stance widths. Regardless of stance width, θtrunk consistently rotated in the same direction as θCoM. This observation contradicted the perpendicular assumption of the original model, particularly at wider stance widths where θtrunk was anticipated to rotate in the opposite direction to θCoM (Figure 4.7 panel C). At narrow stance widths, θtrunk exhibited slightly greater rotational amplitudes than estimated ones by the perpendicular assumption. At a 100% stance width, where θtrunk was expected to remain vertical in space, angular oscillations were observed relative to the perpendicular/vertical pose. 118 Figure 4.7 Results of exploratory analyses. (A) Positions of head (𝐱𝐱𝐡𝐡), trunk (𝐱𝐱𝐭𝐭), and center of mass (𝐱𝐱𝐂𝐂𝐂𝐂𝐂𝐂) of one cycle averaged across participants at different stance widths. (B) The difference between 𝐱𝐱𝐡𝐡 and 𝐱𝐱𝐂𝐂𝐂𝐂𝐂𝐂 of one cycle averaged across participants. (C) The center of mass angles (𝛉𝛉𝐂𝐂𝐂𝐂𝐂𝐂) and trunk angles (𝛉𝛉𝐭𝐭) relative to the vertical axis of one cycle averaged across participants: measured values versus the ones estimated by the original model. 4.4 Discussion In this chapter, I tested the fixed perpendicular orientation between the trunk and pelvis during ML balance sway as assumed by previous studies. The empirical measures of this model assumption show that the trunk and pelvis did not stay perpendicular, negatively impacting the estimation accuracy of the originally proposed CoM decomposition model. To resolve this issue, a second-order function was fitted to express the measured trunk-pelvis angle and put it back into 119 the decomposition process to refine the original model. The cross-validation analysis showed that the accuracy of the refined model was robust and significantly improved across stance widths compared to the original model that utilizes the perpendicular assumption. 4.4.1 Trunk-Pelvis Perpendicular Assumption The findings of this study highlight significant deviations from the traditional assumption of perpendicular alignment between the trunk and pelvis during ML balance sway [86], [114], [313]. Instead of adhering to this expected alignment, θtrunk−pelvis displayed an oscillatory pattern around the perpendicular pose. Moreover, this oscillation exhibited a nonlinear increase with wider stance widths, indicating that stance width substantially influences the angular kinematic characteristics between these two segments. The deviations from the traditional model unveiled a more complex biomechanical coordination between the trunk and pelvis during ML sway than the previously assumed one. Consequently, there was a need to refine θ�trunk utilized in the CoM decomposition process by incorporating the observed pattern of trunk-pelvis angle oscillation and stance width effects. The refinement resulted in more accurate trunk/pelvis estimations across diverse stance width conditions while preserving the 1DoF system constraint driven by θCoM. Future modeling should emphasize broader stance widths and larger CoM angles, as indicated by the increasing gaps between the original and refined models. These observations also align closely with Goodworth's model in which trunk rotational control involves both passive and active mechanisms, with the passive component exerting a predominant influence on segmental motion [86]. This passive component, governed by intrinsic mechanical stiffness and damping properties within muscles, tendons, joints, and ligaments, generally conforms to the perpendicular assumption. In contrast, the active component arises from muscle activation-induced torques. 120 4.4.2 Sources of Model Estimation Errors The investigation indicates that refining the expression for the trunk-pelvis angle in the CoM decomposition process can lead to a reduction in RMSEs of trunk and pelvis positions by 18-32%. Significant differences were revealed in the estimated trunk/pelvis positions between the original and refined CoM decomposition models. Aside from this major factor, measurement errors represent a significant source of estimation errors. I evaluated the influence of these errors across various stance widths using a broad spectrum of body parameters ranging from 5% female to 95% male [349]. Specifically, measurement errors to the original body parameters were introduced and their impact on subsequent estimations by either the original or refined model were analyzed. For instance, a 1 mm error in leg length measurement yielded a maximum of 0.04/0.2 (original/refined) mm absolute error in the trunk position and 0.1/0.2 mm absolute error in the pelvis position. A 1 mm error in trunk length measurement resulted in a maximum 0.3/0.1 mm absolute error in the trunk position estimate, and 0.1/0.1 mm absolute error in the pelvis position estimate. Moreover, the application of regression-based techniques for hip joint center estimation, as utilized in our study, has been documented to introduce errors of up to about 20 mm [350]. Such errors translate to potential absolute errors of up to 0.8/1.2 mm in the trunk position and 1.4/1.3 mm in the pelvis position. Furthermore, the utilization of imperfect anthropometric ratios in estimating the mass and CoM position of individual body segments may introduce inaccuracies. A 1 kg error in the leg mass resulted in up to 0.8/1.5 mm absolute error in the trunk position and 1.8/2.1 mm in the pelvis position. A 1 kg error in the pelvis mass led to up to 1.3/1.2 mm absolute error in the trunk position and 0.9/1.8 mm absolute estimation error in the pelvis position. A 1 kg error in the trunk 121 mass produced up to 0.5/0.8 mm absolute error in the trunk position and 0.7/1.1 mm absolute estimation error in the pelvis position. Additionally, inadvertent movements by participants, such as foot lifting or knee bending, can deviate from the four-bar linkage assumption of the model, thereby leading to errors, both of which were occasionally observed at the peaks of the CoM sway. Finally, slight fluctuations in the intended fixed stance width may contribute to estimation errors. Notably, higher absolute errors were found at wider stance widths, ranging from 7 to 20 mm across participants across stance widths from 50% to 200%. Incorporating the maximum absolute error of 20 mm into the model at the widest 200% stance width revealed corresponding absolute estimation errors of up to 3.1/2.5 mm for the pelvis position and 15.9/5.8 mm for the trunk position both occurring at the peaks of the CoM sway. 4.4.3 Potential Mechanisms of the Observed Trunk/Pelvis Movements The observed trunk-pelvis rotation pattern could be attributed to a variety of biomechanical, physiological, or other factors. One influential factor contributing to these movements is the shifting position of the CoM. As the stance width widens, the base of support broadens, facilitating a greater range of motion for the whole-body CoM. Despite the overall increase in CoM motion amplitude, a consistent translation and rotation of the trunk in alignment with the whole-body CoM was observed. This alignment likely serves a stabilizing function, preventing other body segments with lower masses, such as the pelvis and legs, from reaching extreme positions during sway. Additionally, sensory inputs provided by the head in standing balance may play a crucial role. Positioned directly above the midpoint of the shoulders, the head houses essential sensory organs (e.g., visual and vestibular) that contribute vital information to balance control [84], [85]. 122 A general trend of increasing amplitude of head and CoM movements as the stance width changed from narrow to wide was found and such increases plateaued at about 125% stance width (Figure 4.7 panel A). Despite this similar trend, the analysis revealed that positional differences between the head and CoM positions at peaks remained within 33-44.7 mm, showing only slight increases that differed by only about 10 mm (Figure 4.7 panel B). This may suggest an intrinsic link between the sensory information gathered from the head and the perception of the whole-body CoM position for guiding balance adjustments. The question of whether the trunk tends to maintain a vertical orientation in space during ML sway was also investigated. The data indicated a decreasing angle of the trunk relative to the vertical axis as stance width increased, implying a greater inclination towards staying upright at wider stances (Figure 4.7 panel C). 4.4.4 Application and Limitations of the Model The refined model developed in this study offers valuable applications across a spectrum of contexts. It can easily and conveniently interface with any device that provides reliable estimations of the whole-body CoM and efficiently simulates in < 0.005 ms for a single round of CoM decomposition process (executions of equations (4.13)-(4.11) and (3.11), benchmarked by using the timeit function in MATLAB 2023b and run on windows 10, RAM: 16 GB, processor: Intel i5-7600 CPU @ 3.50GHz). This model holds significant potential for integration into human-in-the-loop robotic balance platforms [302], robotic exoskeletons [140], [339], and assistive devices [351], [352], offering real-time segmental motion estimates alongside sensory feedback. Through this integration, robotic exoskeletons can dynamically adapt their support and stabilization mechanisms, assisting users in maintaining ML balance during various daily activities and even industrial tasks. 123 Moreover, the model's capability to generate precise corrective trunk/pelvis motions lends itself to developing rehabilitation exercises aimed at improving balance function, particularly in the ML direction [339]–[341]. This could be helpful for clinical populations where balance deficits persist longer in the ML direction than in the AP direction [4]. Importantly, the model accommodates individual body parameters, allowing for the customization of robotic exoskeletons to match the unique biomechanical characteristics of each user. This personalization also enhances the efficacy of rehabilitation interventions by promoting more targeted outcomes. Additionally, the model's potential application extends to facilitating markerless motion capture systems [353]. By leveraging force plate-based platforms, accurate real-time segmental kinematics during ML sway can be estimated without the need for cumbersome markers, thus streamlining data collection processes and expanding the applicability of motion analysis techniques. While the model holds promise, it's essential to acknowledge the model's inherent limitations. Positional errors of the model are influenced by both the range of the CoM angle and stance width. Excessive positional errors may be perceptible to humans. The perception threshold of the CoM angle in the anteroposterior balance direction was shown to be 0.17° at 0.06°/s [330], while the perception threshold for the ML direction remains undetermined. Future investigations employing human-in-the-loop robotic balance platforms or similar devices can rigorously determine if the remaining errors of the refined model can be perceived and/or influence normal balance control in the ML direction [302]. 4.5 Conclusion This chapter examined a previous assumption of trunk-pelvis perpendicularity for modeling multi-segmental kinematics of ML balance. I found a nonlinear motion pattern between these 124 two body segments dependent on the stance width but did not find any motion pattern in relation to the sway frequency. Leveraging these findings, the accuracy of multi-segmental kinematics estimated by the CoM decomposition model was improved by incorporating a cross-validated function that captures the changing pattern of the trunk-pelvis angle. This model offers promising implications for real-time robotics, rehabilitation, and fall-monitoring devices that employ ML balance models. 125 Chapter 5: Applying a Robotic Balance System and Electroencephalogram to Investigate Cerebellar Involvement During Adaptation to Unexpected Delays in Standing Balance Control The work described in Chapter 3 and Chapter 4 contributes to the further development of the robotic balance platform for future multidirectional standing balance experiments. In this chapter, I will describe the design and results of an experiment aimed at combining the robot and electroencephalogram (EEG) to investigate the role of the cerebellum in adapting to unexpected delays in standing balance control. This chapter describes the methodology used in the experiment and pilot results from healthy participants, with the potential of extending it to future studies in post-concussion populations. 5.1 Introduction Recent advancements in robotic balance systems offer a unique approach to manipulating the relationship between muscle actions and whole-body sensory feedback in balance control (discussed in Section 1.5 in Chapter 1) [144], [145], [302]. For example, this innovative "human-in-the-loop" design enables researchers to systematically introduce controlled delays into the standing balance control loop, specifically between ankle torques applied by the participant and resulting whole-body angles (see Figure 5.2). Rasman et al. conducted a study in 2021 demonstrating that, healthy individuals can successfully adapt to these robotic-induced delays of up to 400 milliseconds through a training protocol over five consecutive days consisting of two 10-minute trials per day [149]. I provided an overview of the general function of the cerebellum in sensorimotor adaptation in Section 1.4 in Chapter 1. A limited number of studies have also explored the connection 126 between the cerebellum and balance adaptation. For instance, patients with cerebellar dysfunction were found to exhibit impaired adaptation function in the context of postural control [354], [355]. The cerebellum is believed to play a crucial role in movement timing, facilitating the timely execution of multi-joint movements required for maintaining postural stability [354], [356]. On the other hand, cerebellar EEG (discussed in Section 1.6 in Chapter 1) has enabled new opportunities for studying cerebellar engagement in sensorimotor adaptation tasks and its implications for movement disorders. Previous cerebellar EEG studies have mostly focused on investigating cerebellar activities in visuomotor-related adaptation tasks. In these studies, cerebellar activities were typically found to substantially increase in various frequency bands such as theta and beta bands during early stages of adaptations, reduce in later stages, and quickly re-adjust to baseline levels post-adaptation [161], [162], [164]. Similar activation patterns have been noted in a functional magnetic resonance imaging (fMRI) study of the cerebellum in a visuomotor adaptation task [163]. Despite prior investigations in visuomotor-based adaptation, little exploration has been undertaken to measure cerebellar involvement more directly during adaptation tasks involving standing balance control. The cerebellar EEG approach provides a promising pathway for investigating cerebellar neural activity during standing balance adaptation tasks, especially when integrated with human-in-the-loop robotic balance systems. In both visuomotor and standing balance adaptation tasks, the cerebellum can play a pivotal role, yet it may be involved in different neural pathways. Visuomotor control heavily relies on the visual cortex for processing visual input, while standing balance control integrates sensory inputs from the visual, vestibular, and proprioceptive systems. In balance control, key regions such as the cerebellum, brainstem, 127 and motor cortex may be more engaged in coordinating the multi-segmental adjustments necessary to maintain whole-body balance. Thus, while the cerebellum may contribute to both types of adaptation tasks, variations in its degree of involvement and activation patterns likely exist due to the unique processing demands of each task. Therefore, I conducted this study to investigate how the cerebellum contributes to adapting to unexpected delays in standing balance control scenarios specifically. To achieve this, two specific objectives were outlined: • To examine the cerebellar power changes across the pre-adaptation, adaptation, and post-adaptation phases. • To examine the association between cerebellar power changes and the adaptation progress. Building on these objectives, the following hypotheses were formulated: • H1: Significant increases in cerebellar powers across multiple frequency bands were expected during the early adaptation phases compared to pre-adaptation baseline levels. This hypothesis was formulated based on observations from prior EEG and fMRI studies that found increases in cerebellar activity during early adaptation • H2: Cerebellar powers would return to baseline levels post-adaptation since the cerebellar power changes were expected to be mainly related to the adaptation process and to not persist beyond the adaptation task. • H3: Cerebellar powers were correlated with the progression of balance adaptation and would decrease gradually as adaptation progressed, consistent with findings from visuomotor adaptation studies. 128 5.2 Materials and Methods 5.2.1 Participant Recruitment This study was approved by the Clinical Ethics Board at the University of British Columbia (number: H22-00523) and adhered to the Declaration of Helsinki (except principle 35 - registration to public database before recruitment). I recruited twenty healthy adults with no neurological and musculoskeletal injuries (different participant cohort from Chapter 4, 10 males and 10 females, age: 23±3 years, body height: 1.73±0.11 m, body mass: 67.3±11.7 kg). All participants gave informed consent for participation in the experiment. 5.2.2 EEG Instrumentation A portable EEG system (LiveAmp32, BrainVision, Germany) equipped with 32 Ag/AgCl active electrodes was employed to record EEG signals, which were conducted by gel (SuperVisc) and amplified using the Brain Products LiveAmp amplifier. The initial EEG cap design followed the International 10-20 system but was adapted to incorporate three additional cerebellar electrodes: cerebellar central (CBZ), cerebellar left (CBL), and cerebellar right (CBR), in accordance with cerebellar EEG setups described in prior literature [155]. The CBZ electrode was positioned 15% below the Oz electrode, while CBL and CBR were situated 15% apart on the left and right sides of the CBZ electrode, respectively. This arrangement allowed for targeted monitoring of cerebellar activity alongside conventional EEG measurements (Figure 5.1). 129 Figure 5.1 EEG cap setup. The EEG cap was modified to include three cerebellar electrodes (CBZ, CBL, CBR). 5.2.3 Delayed Balance Control Adaptation Paradigm The delay adaptation task was facilitated by a custom-built human-in-the-loop robotic balance system, the detailed technical specifications of which can be found in Chapter 3. Since the validation of the mediolateral balance model (Chapter 4) was conducted in parallel, for this study, the control of the robot was constrained to the anteroposterior (AP) direction. Specifically, a 250-ms delay was implemented in the AP direction of balance control. Within the robotic balance simulation software, the participant’s ankle torque inputs were buffered such that the resulting whole-body motions of the torques were delayed (Figure 5.2). 250-ms delay was chosen because, during pilot experiments, I found participants could typically adapt to this delay 130 within 20 minutes of adaptation time, which allowed the total experimental time, including set up / take down and breaks between trials, to be 1.5-2 hours. Figure 5.2 Robot-induced standing balance delays. The time delay was added in the robotic balance simulator between the ankle torques applied by the participants and the resulting robotic body motions. The range of balance positions was constrained between 6° (anterior) and −3° (posterior), with maximum velocity limits set at ±12.5 °/s to mimic the limits experienced during overground standing balance [143]. Should the participant exceed the angular limit, it was considered a virtual fall on the robot. Trials were restarted following each fall. 5.2.4 Experimental Procedures The entire experimental procedure is visualized in Figure 5.3, consisting of six main phases: anthropometrics measurements, robot setup and familiarization, pre-adaptation quiet standing, adaptation, transition, and post-adaptation quiet standing. Figure 5.3 Experimental procedure. 131 I provided standardized verbal instructions to the participants through the experiment. The specific instructions provided in these phases can be found in Appendix D. 5.2.4.1 Anthropometric Measurements At the beginning of the experimental procedure, I collected anthropometric measurements, including body height, body weight, ankle height, CoM height, trunk length, leg length, and pelvis width/depth. These parameters served as fixed inputs for the subsequent robotic balance simulation. The CoM height was determined by using a pivot board apparatus, comprising a wooden board and a hollow steel pipe acting as a fulcrum. Participants lay supine on the wooden board while the experimenter held the pipe steady and adjusted their position on the board until the entire apparatus achieved balance. The measured CoM (CoMmeasured) was adjusted to exclude the contribution of participants' feet to their total mass and height. This adjustment was necessary to align the calculated center of mass with the inverted pendulum model integrated into the robotic simulation, which considers the ankle joint as the axis of rotation. This correction was computed using a specific equation: CoMadjusted = �(CoMmeasured + Hankle) ∙ mbody� − CoMfeet ∙ mfeetmbody − mfeet − Hankle (5.1) where mfeet = 2 ∙ 0.00145 ∙ mbody and CoMfeet = 0.039 ∙ Hbody ∙ 0.5 [110]. Hankle denotes the measured height of the ankle joint and mbody denotes the total body mass. 5.2.4.2 Robot Setup and Familiarization Then, participants were securely strapped onto the backboard of the robotic balance platform, aligning their ankle joints with the robot’s center of rotation. Shoulder and pelvis fixation was achieved using two brackets, further fastened with seatbelts. Prior to commencing the actual experiment, participants were given up to 5 minutes to familiarize themselves with controlling 132 the robot. I instructed them to maintain a normal balance and explore the virtual limits imposed by the robotic platform. If participants reached these limits, the robot took over the control and automatically returned them to the initial central position to familiarize them with what was expected to happen in the actual experiment. 5.2.4.3 Experimental Protocol The main part of the experiment began with a quiet standing session, consisting of two trials, each lasting two minutes, aimed at establishing the baseline of cerebellar activity. Subsequently, participants entered the adaptation phase of the study, lasting a cumulative total of 20-minute balancing time. During this phase, whenever participants reached the angular limit of the robot (6° and −3°), the trial was stopped, signifying a virtual fall on the robotic balance platform. If they could balance five minutes without falling, the trial was also terminated. Before the adaptation phase began, I informed the participants that the goal was to maintain balance within the virtual limits of the robotic platform while standing as naturally as possible. They may sway more and experience virtual falls during the adaptation period, but they could always control their body motion by adjusting the pressure under their feet. I also instructed them to relax their legs before each trial, focus on a visual target in front of them, and avoid unnecessary head movement and speaking during the task to minimize interferences with the EEG signals. Standardized 2-minute rests were provided to participants between each phase of the experimental protocol. Participants may also request breaks at any time during the experiment. After completing the adaptation phase, participants engaged in two additional trials of quiet standing. In the first trial, the delay was removed after 15 seconds of balancing, followed by a 133 two-minute quiet standing period. The second trial mirrored the pre-adaptation quiet standing condition, with no delays imposed. 5.2.5 Data Synchronization and Collection The robotic balance and EEG system data collection processes were synchronized via trigger signals sent at the start and end of each experimental trial. The robot captured digital signals from the linear servomotor encoder through a Field Programmable Gate Array (FPGA) board (PXIe-7648R), which were subsequently transformed into the participant's whole-body angular position and differentiated to derive the corresponding angular sway velocity. These data were saved in real time on a local computer at a sampling rate of 500 Hz. Meanwhile, the EEG system recorded data from all channels directly onto an internally installed SD card at a sampling rate of 1000 Hz. 5.2.6 Data Analysis 5.2.6.1 Standing Balance Velocity Variance Analysis The whole-body angular velocity data was imported in MATLAB (version: 2023b, Mathworks Inc., Natick, MA). The stability of standing balance control was assessed by calculating the variance of sway velocity over 2-second non-overlapping windows. During the early stages of standing balance adaptation, it was anticipated that velocity variance would be high, indicating instability and minimal adaptation. However, as adaptation progressed, velocity variance was expected to gradually decrease, indicating improved balance control as individuals learned to adjust and regain stability [149]. To model the velocity variance curve during the adaptation phase for each participant, an exponential function was employed: Var(θ̇) = a ∙ expb∙t (5.2) 134 where t represents the time in second, a and b are coefficients to be fitted. The b coefficient determined the decay constant of the fitted exponential curve: τ = −1b (5.3) Here, τ denotes the fitted decay constant, signifying the time it takes for the velocity variance to decrease by 63.2%. To enhance the robustness of the fitting against velocity variance noises, the exponential fitting was performed with the velocity variance smoothed using 30-second averaging windows. 5.2.6.2 EEG Data Preprocessing The EEG data were imported into MATLAB (version: 2023b, Mathworks Inc., Natick, MA) and processed using EEGLAB [357]. As a first step in the preprocessing pipeline. Initially, the EEG signals were re-referenced to the Pz electrode [166] and band-pass filtered between 1 and 50 Hz. Data from one participant had to be removed from the analysis due to significant contamination of the Pz channel. Following this, I applied independent component analysis (ICA) and ICLabel classifier to the signal to identify and remove various artifact components associated with eye blinks, heartbeats, muscle activity, channel noise, and line noise with probabilities exceeding 80% [158], [160], [358]. Given the susceptibility of EEG signals during large balance movements to muscle artifacts, an additional step was taken to mitigate noises associated with muscle activation, where a state-of-the-art ensemble empirical mode decomposition-canonical correlation analysis (EEMD-CCA) algorithm was employed with an autocorrelation threshold set at 0.95 (utilizing the ReMAE toolbox), a parameter value suggested by previous research [159], [359]. 135 Subsequently, the ICA-ICLabel classifier was rerun on the finalized cleaned dataset to evaluate the effectiveness of the cleaning process The traditional method of assessing the effectiveness of cleaning relies on quantifying the number of brain components identified through techniques such as ICLabel [360]. However, this method may not provide sufficient detail, e.g., muscle vs. brain probability comparison, and does not consider the variance of the identified component. To address this limitation, I used a novel approach. Specifically, the top 10 components contributing the most to the reconstructed signal of each cerebellar channel (CBL, CBZ, CBR) were identified based on their respective inverse ICA weighting matrices. For each channel, the probability that a component was muscle-related was calculated by weighting the probability of muscle artifact by the relative variance of the component: P(muscle) = ∑ pk(muscle) ∙ variancek10k=1∑ variancek10k=1 (5.4) Here, P denotes probability, k denotes the kth component ranked by the inverse ICA weighting, and variance represents the percent variance accounted for (PVAF) by the component with respect to the total variance of data across all EEG channels. The final probability was computed as the average across the three cerebellar channels. This same methodology was employed to calculate the weighted probability that the component was brain-related as well. Participants were excluded from subsequent analysis if either their final muscle probability exceeded 0.05 or their brain probability fell below 0.6 after cleaning. 5.2.6.3 Cerebellar EEG Data Analysis Average band powers were computed across various frequency bands using 2-second windows with a 50% overlap for each channel in the cerebellum. The frequency bands examined were categorized as follows: delta (1-4 Hz), theta (4-8 Hz), alpha (8-13 Hz), beta (13-30 Hz), and 136 gamma (30-50 Hz). The average power within each frequency range was calculated by integrating the power spectral density estimated using Welch’s method, with the integral approximated by the rectangular approach (utilizing the “bandpower” function in MATLAB version 2023b). The final band power estimate was derived by averaging the results from channels CBZ, CBL, and CBR. 5.2.6.4 Statistical Analysis Since participants had varying rates of adaptation, τ was used to normalize the time axis and quantify the progress of balance adaptation. To analyze the EEG signals in relation to the time constant τ, I further averaged the band power estimates within every 0.1τ increment, covering the range from 0 to each participant’s τ at the end of the 1200-sec adaptation period (with a maximum value of 2τ). The early adaptation phase was defined as the period from 0 to 0.3 τ, where the velocity variance decreased by approximately 25%. The mid-adaptation phase was defined as the period from 0.3 to 1.4τ, where at 1.4τ the velocity variance decreased by approximately 75% from time zero. The late adaptation phase was defined as the period beyond 1.4τ. Paired t-tests were conducted to examine (1) whether cerebellar powers were significantly higher during early adaptation stages compared to pre-adaptation baselines (α = 0.05), and (2) whether no significant differences exist in cerebellar powers between pre- and post-adaptation phases (α = 0.05). Bonferroni-Holm corrections were applied to adjust the p-values for multiple comparisons. To assess the correlation between cerebellar power variations and the adaptation progress quantified by τ, a linear mixed-effects model (Jamovi, version: 2.3.28) was employed within each frequency band with the following form: 137 Power(f) ~ 1 + tτ + (1|id) Here, Power(f) is the dependent variable and represents cerebellar power at a specific frequency band, tτ is the fixed-effect parameter and represents the adaptation progress, and id denotes the participant ID, which was treated as the random component. Each band was analyzed independently, with the significance level set at 0.05. Bonferroni-Holm corrections were applied to adjust the p-values for multiple tests. 5.3 Results 5.3.1 Results of Sway Velocity Variance Analysis During the pre-adaptation phase, the velocity variance was found to be low and typical of natural quiet standing balance: 0.03±0.01 (°/s)2 (Figure 5.4). It increased to 4.53±2.35 (°/s)2 during the early-adaptation phase (0-0.3τ), decreased to 2.44±1.44 (°/s)2 during the mid-adaptation phase, and further reduced to 1.08±0.53 (°/s)2 during the late-adaptation phase. In the post-adaptation quiet standing phase, the velocity variance was back to baseline levels 0.03±0.01 (°/s)2 (Figure 5.4). τ values ranged from 348 seconds to 1696 seconds, with a mean of 773 seconds and a standard deviation of 364 seconds. By the end of the adaptation phase, on average, participants reached 1.84±0.74 τ, with 1.84 τ representing a reduction in the velocity variance by about 84%. 138 Figure 5.4 Velocity variance across participants. The light red traces represent each individual’s velocity variance, while the solid red trace represents the mean velocity variance averaged across participants. The red circles represent the mean velocity variance averaged across participants during pre- and post-adaptation quiet standing. By the end of the adaptation phase, not all participants reached 2𝛕𝛕. In such cases, their velocity variance was plotted up until their maximum adaptation progression, quantified by 𝛕𝛕, was reached. 5.3.2 Results of EEG Cleaning The cleaning results of the 19 participants involved were summarized in Table 5.1 (one participant was already removed before the cleaning step due to noise in the reference channel). After the ICA-ICLabel cleaning, the mean muscle probability of the cerebellar electrodes decreased from 0.092±0.122 to 0.06±0.043 while the mean brain probability of the cerebellar electrodes increased from 0.722±0.177 to 0.747±0.155. Subsequently, after the EEMD-CCA cleaning, the mean muscle probability further decreased to 0.022±0.018, while the brain 139 probability remained relatively stable around 0.744±0.191 (Table 5.1). Example plots of artifact cleaning are shown in Figure 5.5. Table 5.1 Post-cleaning results. Participant ID Pre-Cleaning Post-ICA-ICLabel Post-EEMD-CCA P(muscle) P(brain) P(muscle) P(brain) P(muscle) P(brain) 1 0.015 0.847 0.016 0.838 0.007 0.877 2 0.558 0.256 0.110 0.599 0.056 0.552 3 0.108 0.850 0.012 0.958 0.010 0.955 4 0.113 0.769 0.077 0.786 0.013 0.836 5 0.083 0.779 0.077 0.830 0.018 0.812 6 0.132 0.773 0.133 0.789 0.038 0.823 7 0.032 0.690 0.035 0.694 0.011 0.754 8 0.011 0.453 0.011 0.373 0.008 0.533 9 0.074 0.783 0.086 0.755 0.015 0.872 10 0.132 0.730 0.067 0.791 0.021 0.695 11 0.069 0.806 0.104 0.735 0.006 0.835 12 0.065 0.505 0.044 0.536 0.062 0.335 13 0.010 0.844 0.006 0.928 0.006 0.881 14 0.134 0.747 0.136 0.749 0.003 0.869 15 0.102 0.799 0.087 0.830 0.042 0.778 16 0.010 0.874 0.011 0.827 0.024 0.778 17 0.030 0.451 0.031 0.457 0.025 0.253 18 0.059 0.850 0.070 0.819 0.044 0.800 19 0.012 0.918 0.018 0.900 0.004 0.893 Mean 0.092 0.722 0.060 0.747 0.022 0.744 140 Figure 5.5 Examples of pre- vs. post-cleaning cerebellar EEG signals. In both panels, cerebellar signals (CBZ, CBL, CBR) during the initial ten seconds into the adaptation phase are depicted. Panel (A) shows an example of a participant whose signals contain muscle-like artifacts (highlighted in the dashed box), while Panel (B) displays an example of a participant whose signals appear relatively clean before the cleaning process. 141 As a result of the cleaning criterion, four participants, specifically participants 2, 8, 12, and 17, were removed. After the removal of participants with reference channel noise (N = 1) and ineffective cleaning (N = 4), data of a total of 15 participants were retained for the band power, velocity variance, and statistical analysis. 5.3.3 Cerebellar Power Change and Its Association with Adaptation Progress During the initial adaptation phase, participants generally exhibited increased cerebellar powers, particularly evident in delta, beta, and gamma bands. As adaptation progressed, these powers decreased with increasing tτ, eventually returning to baseline levels during the post-adaptation standing balance phase. Cerebellar powers demonstrated significant increases by 41-146% across delta (p = 0.01), beta (p = 0.04), and gamma (p = 0.03) bands, but not observed in theta (p = 0.14) and alpha (p = 0.16) bands, in the early-adaptation phase compared to their pre-adaptation baseline levels (Figure 5.6 – 5.10). The increases in the delta, beta, and gamma bands were followed by gradual decreases. Powers during the post-adaptation phase were found to not significantly differ from their pre-adaptation baseline values across all frequency bands: p-values ranged from 0.22-0.81. During the main 20-min adaptation phase, cerebellar powers were found to significantly decrease with respect to the progression of adaptation (tτ) across delta (p = 0.005), beta (p = 0.012), and gamma (p = 0.018) bands, but not theta (p = 0.434) and alpha (p = 0.715). Detailed results of the linear mixed-effects model analysis for each band can be found in Appendix E. 142 Figure 5.6 Delta cerebellar power changes. Each subplot corresponds to a different participant. Blue traces depict band powers averaged over every 0.1τ, while red traces represent the corresponding velocity variances. Circles indicate the mean band power and velocity variance during pre- and post-adaptation quiet standing. 143 Figure 5.7 Beta cerebellar power changes. Each subplot corresponds to a different participant. Blue traces depict band powers averaged over every 0.1τ, while red traces represent the corresponding velocity variances. Circles indicate the mean band power and velocity variance during pre- and post-adaptation quiet standing. 144 Figure 5.8 Gamma cerebellar power changes. Each subplot corresponds to a different participant. Blue traces depict band powers averaged over every 0.1τ, while red traces represent the corresponding velocity variances. Circles indicate the mean band power and velocity variance during pre- and post-adaptation quiet standing. 145 Figure 5.9 Theta cerebellar power changes. Each subplot corresponds to a different participant. Blue traces depict band powers averaged over every 0.1τ, while red traces represent the corresponding velocity variances. Circles indicate the mean band power and velocity variance during pre- and post-adaptation quiet standing. 146 Figure 5.10 Alpha cerebellar power changes. Each subplot corresponds to a different participant. Blue traces depict band powers averaged over every 0.1τ, while red traces represent the corresponding velocity variances. Circles indicate the mean band power and velocity variance during pre- and post-adaptation quiet standing. 147 5.4 Discussion In this chapter, I introduced a novel experimental approach combining a robotic balance system with EEG measurements to monitor cerebellar neural signals during adaptations to unexpected delays in standing balance control. I applied advanced EEG cleaning algorithms to reduce potential artifacts from the raw cerebellar signals, especially targeting muscular noises. In the results, substantial increases (H1) in cerebellar powers were observed across low-to-high frequency bands (delta, beta, and gamma) during the initial adaptation phase, followed by gradual decreases to baseline levels post-adaptation (H2). The findings of the analyses also revealed a correlation between cerebellar power changes (delta, beta, and gamma) and the progression of adaptation and intra-participant variances (H3). 5.4.1 Cerebellar Neural Oscillations and Their Implications These observed changes in cerebellar power offer valuable insights into the cerebellum's role in standing balance control and adaptation. The initial heightened cerebellar activity across the delta, beta, and gamma bands suggests its active engagement in adapting to unexpected delays in standing balance control. As adaptation progressed, cerebellar activities in these three bands decreased, indicating a reduced engagement as participants became more stable in their control. No significant differences were found between pre-adaptation baseline levels and post-adaptation values across all bands, showing a return of cerebellar activities to baseline levels. Using similar cerebellar EEG measurement techniques, Edagawa et al. found beta-band cerebellar power increases in the early adaptation stage followed by decreases in an auditory-motor adaptation task, which is consistent with the beta-band power change observed in my study [161]. On the other hand, Tzvi et al. examined the cerebellar role in a visuomotor rotation adaptation task. Their findings revealed an increase in cerebellar power within the theta band 148 during the initial phase of adaptation, followed by a decrease in later stages [162]. However, my study did not observe significant cerebellar power increases in the theta band. In visuomotor adaptation, the primary visual cortex located in the occipital lobe has been hypothesized to play a direct role [163]. Notably, the occipital lobe is positioned in close proximity to the cerebellum, potentially influencing neural oscillatory patterns and in turn surface EEG band powers. Conversely, while standing balance control also partially utilizes visual inputs, it is possible that the visual cortex is not as directly involved in the adaptation process, considering the delay paradigm we implemented is distinct from the visuomotor perturbation adaptation task used in Tzvi et al. The cerebellar oscillations observed in delta, beta, and gamma bands in this study may be associated with different functions in standing balance adaptation. Delta oscillations (1-4 Hz) may be influenced by synchronized spike activities originating from the inferior olive, assisting in learning-dependent timing adjustments in response to unexpected events [361], [362]. These inputs, transmitted via climbing fibers from the inferior olive to both the cerebellar nuclei and Purkinje cells, likely convey information related to performance errors for adaptation processes. [363], [364]. Meanwhile, beta oscillations (13-30 Hz) may arise from rhythmic activity in granular cells, facilitating communication between the cerebellum and cortical regions involved in sensorimotor processing [365], [366]. Granule cells receive inputs from various sources, including the pontine nuclei and spinal cord, which also project to Purkinje cells through mossy fibers. Neural information passed via mossy fibers may be related to generating desired movements and providing sensory information to the cerebellum [367], [368]. Higher-frequency gamma (> 30 Hz) oscillations are believed to be generated by Purkinje cells located in the 149 cerebellar cortex [362]. Serving as the exclusive output source from the cerebellar cortex, Purkinje cells contribute to fine-tuning motor outputs to coordinate movements [369], [370]. 5.4.2 Muscular Contamination in Cerebellar EEG Signals Cerebellar EEG recordings are particularly vulnerable to muscular noise contamination due to the proximity of the cerebellum to muscles involved in neck movements [371]. The electrical activity generated by muscle contractions can interfere with the recorded cerebellar EEG signals, obscuring the underlying neural activity and leading to inaccurate interpretations of cerebellar function. Unlike previous studies where participants typically remained still and only moved their hands and/or arms in response to visual inputs, this study utilized an actively whole-body moving paradigm, potentially resulting in more muscle-related artifacts captured by EEG. Therefore, employing rigorous cleaning procedures is essential to mitigate muscular noise contamination and ensure the reliability of subsequent cerebellar EEG data analysis. The initial cleaning step, ICA-ICLabel, resulted in a 0.032 reduction of the mean muscle probability (from 0.092 to 0.06), coupled with a 0.025 increase in the mean brain probability (from 0.722 to 0.747). This method employs the blind source separation (BSS) technique, ICA, to decompose signals and utilizes the ICLabel classifier to detect and remove various artifacts, including electrooculogram (EOG) and electrocardiogram (ECG) artifacts, from EEG signals [372]. However, ICA is not optimized for handling muscle artifacts, and although it reduced muscular artifacts to some extent, residual noise remained noticeable upon visual inspection. The subsequent cleaning method, EEMD-CCA, further reduced the mean muscle probability from 0.06 to 0.022 while maintaining the mean brain probability at 0.744. Unlike ICA, CCA is specifically designed to tackle muscle artifacts by exploiting their broad frequency spectrum resembling white noise with low auto-correlations. Recent surveys suggest that combining 150 multiple processing procedures, such as single-channel decomposition with BSS techniques, can enhance the effectiveness of EEG artifact suppression [372]–[374]. In particular, employing data-driven single-channel decomposition methods like EEMD is beneficial for handling nonlinear and nonstationary neural signals. Together, these integrated cleaning approaches offer improved accuracy in interpreting cerebellar activity during the standing balance delay adaptation task. 5.4.3 Limitations and Future Work One limitation is that we may not be able to fully localize the observed power changes to the cerebellum given surface EEG limitations. Although electrodes were positioned in proximity to the cerebellum and based on prior cerebellar EEG studies [155], [166], more work can be done to localize the changes observed in the cerebellum. This may be achieved through the application of source localization techniques, which aim to identify the specific neural generators responsible for recorded EEG signals [375]. Source localization offers the advantage of providing spatial information about brain activity, potentially allowing researchers to distinguish between contributions from the cerebellum and other nearby neural structures. However, it's important to acknowledge the limitations of source localization methods, including their reliance on assumptions about the geometry and conductivity of brain tissues, as well as potential inaccuracies introduced by individual differences in anatomy and electrode placement. In EEG analysis, there exists a trade-off between removing muscle noise and preserving essential brain signals. Particularly for our experiment, muscle noise can distort EEG recordings and hinder accurate brain activity extraction. Techniques such as filtering and artifact rejection are commonly employed to mitigate muscle noises, yet overly aggressive noise removal may simultaneously remove valuable brain signal information. In this study, I applied the additional 151 EEMD-CCA step for muscle artifact removal, but this may also result in a trade-off with the amount of brain information retained. Recently, singular spectrum analysis (SSA) has emerged as a promising alternative [376]. SSA employs Singular Value Decomposition to map single-channel signals into a trajectory matrix. By extracting underlying signal patterns through eigenvalue and eigenvector calculations, SSA may offer improved discrimination between brain information and muscle artifacts. In future steps, SSA-CCA can be compared with the EEMD-CCA approach to determine which method better eliminates muscle artifacts while preserving more essential brain information. The cerebellum plays a crucial role in detecting errors between the predicted and actual outcomes of motor commands [377]. Adaptation, on the other hand, involves the adjustment of motor commands based on detected errors to modify ongoing movements and improve performance over time [134]. Disentangling whether the power changes observed in this study primarily stem from error detection or adaptation functions of the cerebellum requires further investigation. One potential approach could involve introducing sensory errors through robotic manipulations after participants have successfully adapted to delays, allowing us to discern whether significant cerebellar power changes persist react to such manipulation. In summary, this study established a novel experimental design and pipeline that could be used to measure cerebellar activity during robot-enabled standing balance adaptation tasks. The distinct patterns of increase and decrease observed in the delta, beta, and gamma bands in this study may serve as benchmarks for comparison in patients with concussions who have standing balance deficits. By analyzing the cerebellar power patterns exhibited by patients, abnormalities such as excessive or insufficient power during the early adaptation phase can be identified. This aids in pinpointing the underlying cerebellar damage contributing to standing balance control 152 deficits. As a result, these insights may enable clinicians to apply more targeted intervention approaches to patients, such as cerebellar transcranial direct current stimulation or cerebellar transcranial magnetic stimulation, to facilitate cerebellar and overall balance recovery [378], [379]. 153 Chapter 6: Conclusions and Future Work 6.1 Conclusions The overarching goal of this thesis was to develop novel technologies and methodologies to investigate the underpinning mechanisms contributing to impaired standing balance function. With this goal, we first recognized that standing balance issues can be formally analyzed using a sensorimotor control framework. With a special focus on standing balance deficits in the brain injury population, we hypothesized that concussive and subconcussive head impacts may exert strains and stresses on one or more sensory organs and neural centers within the control circuitry, leading to abnormal functioning. Among the various components, the cerebellum is a neural center that plays an important role in standing balance control and its adaptation. Therefore, this thesis proposed probing the cerebellum in the standing balance control circuit as a key step in unraveling the mechanisms underlying standing balance deficits caused by head impacts. Through a literature review (objective 1), I summarized current methods of standing balance assessment after concussions and subconcussive head impacts. It became evident to me that existing testing methodologies heavily rely on subjective clinical assessments, such as the Balance Error Scoring System (BESS), or quantitative measures utilizing force plates and inertial measurement units (IMUs). However, these methods are limited in their ability to provide detailed mechanistic insights, as they only yield overall standing balance stability scores, either through clinical observations or metrics derived from center of pressure (CoP) or center of mass (CoM) data. This lack of testing specificity hinders our ability to probe individual sensory or neural components, such as the cerebellum. To address this limitation, it is imperative to develop innovative paradigms for more targeted testing of components in the balance control circuit, 154 which prompted the technology and methodology development work in the following three chapters. The second objective focused on enhancing a human-in-the-loop balance robot system by integrating mediolateral (ML) control functionalities. This was achieved through the development of integrated mechatronic systems and the formulation of a novel CoM kinematic decomposition model capable of effectively breaking down ML CoM into a multi-segmental pose, which is used in real-time robotic balance simulations. During testing, the system demonstrated excellent performance metrics, exhibiting sub-15 ms delays and submillimeter accuracy in tracking both perturbed and unperturbed standing balance trajectories in both anteroposterior (AP) and ML directions. Notably, the platform showcased its ability to achieve submillimeter precision in transferring ML balance motions, estimated by the model within the balance simulator, to participants in real-time human-robot interactive control scenarios. With the newly added ML control, this robotic balance platform represents a first-of-its-kind technology enabling more biofidelic, multidirectional human-in-the-loop standing balance simulations. In addition, while the majority of past robot-based human standing balance studies have focused on and provided substantial insight in the anteroposterior (AP) balance control, our improved robot now opens a new avenue to evaluate the multidirectional control of balance. For instance, a recent study by Rasman et al. in 2024 discovered that learning to balance with imposed delays transfers across AP and ML directions [380]. Notably, a finding from our literature review was that ML balance deficits may persist longer than AP deficits in concussion patients, which further underscores the importance of developing the ML capability on the robot to further study the potential mechanistic difference between these two directions. 155 The third objective of the thesis aimed to validate the ML CoM decomposition model and verify the trunk-pelvis perpendicular assumption of the model. I conducted human participant experiments and found significant deviations from the assumed perpendicular trunk-pelvis angle, with the amplitude of the angle observed increasing with wider stance widths. My exploratory analyses offered insight into potential intrinsic biomechanical priorities, such as close positional alignment between the head and CoM, suggesting an internal encoding of CoM position relative to head sensing, or maintaining an upright torso during standing balance, possibly linked to energy minimization, that could explain the observed ML movement patterns deviating from the original model. These findings prompted a data-driven refinement of the trunk-pelvis angle estimation in the CoM decomposition model, which reduced root mean squared errors of pelvis/trunk position by 37.4-47.4%. These enhancements not only benefit the performance of human-in-the-loop balance platforms but also have implications for robotic exoskeletons and assistive devices aimed at facilitating ML balance. Moreover, the refined model may have a range of broader applications including more accurate estimates of motion targets for the trunk/pelvis during ML rehabilitation exercises, force plate-based markerless motion capture, computer vision-based pose estimation, and human movement animations in computer graphics applications [381]–[383]. The last goal of this thesis was to develop an experimental paradigm that combines robotic balance adaptation tasks with electroencephalogram (EEG) measurements of cerebellar activity. My preliminary findings obtained from healthy participants revealed statistically significant increases in cerebellar electrode powers in delta, beta, and gamma bands during early adaptation phases, followed by subsequent decreases, and the power changes were significantly correlated with adaptation progress. These findings may indicate cerebellar involvement during standing 156 balance adaptation, with EEG band power observations that may reveal unique neural oscillatory patterns associated with this cerebellar involvement. Building on this, we can develop further extensions of the experiment to investigate whether the power changes are more directly associated with the error detection or adaptation functions of the cerebellum. With the level of insight enabled by the paradigm, we may also be able to start teasing out potential specific cerebellar changes that may explain higher-level functional deficits of standing balance control observed in concussion patients. Overall, this experimental paradigm offers a novel approach to studying cerebellar neural dynamics during standing balance adaptation. In my thesis work, I set out to investigate the mechanisms underlying standing balance deficits following concussions and subconcussive head impacts, with a focus on understanding the role of the cerebellum. I identified major limitations in existing post-concussion balance testing methods and proposed an innovative approach that integrates human-in-the-loop robotic balance platforms with EEG to better understand cerebellar dysfunction contributing to these deficits. By enhancing robotic platforms with ML control capabilities and refining ML CoM decomposition models, the thesis advanced the tools that can be used to study the interaction between AP and ML balance and its implications for multidirectional standing balance control and adaptation. The improved ML model and associated exploratory analyses also deepened our understanding of ML balance coordination principles. Furthermore, I developed an experimental paradigm that merges robotic balance tasks with EEG to measure cerebellar activation during adaptation. In summary, the technological innovation in the thesis opens new avenues for fundamental studies probing the standing balance control loop with human-in-the-loop in multidirectional contexts. Furthermore, this thesis contributes to more specific methodologies for concussion management based on injury subtype and associated mechanisms [384], [385], 157 moving away from traditional approaches that have one single management protocol for patients with different symptoms and deficits. 6.2 Limitations Chapter 3 introduced a novel multidirectional robotic balance system with ML control capabilities, which advanced modeling ML kinematics across various CoM angles and stance widths. However, there are some limitations of this platform that prompt further development and improvements, including the lack of independent ankle and lower leg actuations during ML balance, which may require more sophisticated dynamical modeling of individual segments, as well as the lack of a validated ML decomposition model, which was subsequently addressed by the refined model presented in Chapter 4. Nonetheless, questions persist regarding the perceivability of remaining estimation and robot-induced motion errors, particularly at wider stance widths and greater whole-body CoM angles. Further investigation is warranted to establish whether participants can perceive the errors between their intended and robot-induced whole-body motion. In addition, the empirical data-driven model developed in this thesis relies heavily on observed data, compromising biomechanics interpretability. In Chapter 5, I successfully measured cerebellar EEG activities during balance adaptation through a combined robot/EEG approach. However, discerning whether activations stem from learning or error detection remains an open question. Future steps may involve examining cerebellar activation during transient changes in velocity variance, indicative of significant errors in balance control, during late adaptation stages and may also apply perturbations to introduce errors. 158 6.3 Future Work 6.3.1 Multidirectional Control of Standing Balance Building upon developed technologies and methodologies, the logical progression involves their application in clinical settings. The next step involves conducting patient studies to assess standing balance deficits and cerebellar neural signals in these patients using the enhanced human-in-the-loop robotic balance platforms in conjunction with EEG. By incorporating ML standing balance control capabilities and refining the multi-segmental kinematics model based on findings from natural ML balance experiments, researchers can deepen their understanding of how concussions impact standing balance across different directions. The enabling of ML control on the robotic platform is crucial, given that patients with concussions may experience lingering ML standing balance deficits for up to 48-96 hours post-injury, while AP deficits were observed to subside faster [239]. It is possible that due to the more complex biomechanics in ML balance control (e.g., with an additional factor of stance width), the neural circuitry involved in ML control may require additional elements and/or complexity and could be more vulnerable to brain trauma. Such hypotheses pose interesting and important questions for standing balance injury mechanism investigations. 6.3.2 Standing Balance Adaptation in Patients Aside from multidirectional balance assessments, the work in Chapter 5 specifically lays the foundation for further investigations of standing balance adaptation in concussion patients. Given the role of the cerebellum in standing balance control and adaptation, changes in cerebellar activity during balance adaptations in patients with concussions can be measured and quantified. Examining the correlation between cerebellar activity patterns and standing balance deficits post-concussion may shed light on how potential cerebellar impairment post-concussion contributes 159 to balance adaptation changes. If differences in cerebellar involvement during adaptation are found between concussion patients and healthy controls, it may indicate potential cerebellar injury to inform targeted rehabilitation strategies aimed at restoring cerebellar functions for patients with standing balance deficits. Additionally, this adaptation-based balance control approach is more challenging than conventional standing balance assessments, potentially increasing the sensitivity of balance assessments post-concussion, especially when balance symptoms measured by traditional postural stability metrics resolve within 1-2 weeks in patients with concussions. Notably, differences in visuomotor adaptation deficits have been observed up to 18 months post-concussion when compared with healthy controls [136]. Given potential higher sensitivity, future development of more simplified adaptation-focused balance test paradigms could also be applied in injury screening and clinical assessment. Longitudinal studies could also utilize these new technologies to quantitatively track patients' recovery trajectories in standing balance adaptation control over time, shedding light on the natural history of standing balance deficits post-concussion and the effectiveness of rehabilitation interventions. 6.3.3 Integration of Advanced Neuroimaging Techniques To enhance our understanding of the neural underpinnings of standing balance deficits post-concussion, future research may integrate other advanced neuroimaging techniques such as functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI) [386], [387]. However, to make this integration possible, the robotic system would require upgrades to enable standing balance control while participants are lying down, thus ensuring compatibility with MRI devices. By integrating neuroimaging data with findings from robotic balance assessments and EEG, researchers may be able to assess structural and functional changes in specific brain 160 regions and neural networks implicated in balance control impairments after concussions. This multi-modal approach to neuroimaging can provide a more comprehensive understanding of the complex interactions between neural circuitry and standing balance function, facilitating the development of more targeted interventions. 6.3.4 Development of Personalized Rehabilitation Strategies Future research could also explore personalized rehabilitation strategies tailored to individual concussion patients' standing balance deficits and underlying neural mechanisms. For example, multidirectional human-in-the-loop robotic balance platforms, offer promising avenues for designing customized cerebellar rehabilitation interventions that target specific balance impairments in each patient. Traditionally, cerebellar rehabilitation interventions include methods like Frenkel's exercises and rhythmic stabilization [282], [388], [389], alongside more novel approaches such as cerebellar transcranial direct current stimulations (tDCS) [378], [390], [391] which has been shown to have a positive effect on balance recovery in stroke patients [392]. These interventions can be optimized by incorporating EEG data as continuous biofeedback, enabling clinicians to monitor and refine the rehabilitation process in real time. For example, cerebellar tDCS could be tuned to operate at frequency bands corresponding to those bands with abnormalities observed in the EEG data during balance adaptation assessments. Human-in-the-loop robots can also serve rehabilitation purposes. For instance, delay adaptation training can be administered to patients to engage their cerebellar network. While traditional perturbation-based adaptation paradigms have shown improved balance control [393], further investigation is needed to determine whether human-in-the-loop robotic platforms can yield more effective balance rehabilitation outcomes. Moreover, combining cerebellar and robot-161 enabled rehabilitation with other strategies, such as vestibular rehabilitation [394], could address patients' individual needs and improve overall recovery outcomes. 6.3.5 Translation into Clinical Practice Ultimately, the aim of future research endeavors is to translate developed technologies and methodologies into clinical practice. Efforts should concentrate on establishing standardized protocols for assessing standing balance deficits in patients with concussions using multidirectional human-in-the-loop robotic balance platforms. By integrating these innovative approaches into healthcare practices, researchers can ensure that patients with concussions receive assessments and rehabilitation interventions tailored to their individual needs supported by empirical evidence. Conventional robotic therapeutic devices have already been deployed, such as for stroke rehabilitation [395]. Future developments in human-in-the-loop robotics could pay attention to reducing construction costs and further improving usability to enhance accessibility. This integration into clinical practice will facilitate improved outcomes and enhance the quality of care for patients with concussions. 6.3.6 Summary and Outlook In summary, this thesis represents collaborative and interdisciplinary research in the development of novel technologies and methodologies for understanding standing balance deficits. The advancements pave the way for more targeted interventions and improved clinical outcomes for individuals facing balance impairments. 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Move continuously and smoothly without pausing at the ends of your sway range. 208 Appendix B Results of Individual Fitting and Statistical Parametric Mapping Panel A: Fittings between the slope of the trunk-pelvis angle with respect to the CoM angle and the stance width ratio for each individual (N = 20). Panel B: Results of the statistical parametric mapping for examining the differences in estimated trunk/pelvis positions between the original and refined center of mass decomposition model. 209 Appendix C Summary - Linear Mixed-Effects Model for Mediolateral Balance Analysis 210 Appendix D Verbal Instructions for the Delay Balance Experiment Below are standardized verbal instructions mentioned in Chapter 5 that were provided to the participants for the delay adaptation experiment, including the briefing, familiarization, pre-adaptation quiet standing, adaptation, and post-adaptation quiet standing phases. • Briefing o Greet the participant. We are very happy to have you in our experiment. This experiment aims at investigating the neuromuscular mechanisms behind standing balance adaptation. o You have read the consent form before the experiment. If you are now okay and agree with our study, feel free to go ahead and sign up your name on the last page of the consent form. o The experiment has three stages.  First, we will measure your body parameters.  Second, we will prepare you for the experiment by setting up sensors and putting you on the robot.  Third, we will conduct the actual experiment which includes three phases: pre-adaptation, adaptation, and post-adaptation. o You will receive a $20 Amazon gift card as compensation for participating in this study. • Familiarization phase o Before the experiment begins, we will ask you to move forward and backward to familiarize yourself with the robot. This will represent your baseline control, but please note that balancing might get more challenging during the actual 211 adaptation trials. Remember, you can control your movement by adjusting the pressure on the force plate under your feet. o First, move your whole body to the front until you feel some resistance. This resistance is the forward limit of balance and represents a virtual fall on the robot. o Next, move your whole body to the back until you feel some resistance. This resistance is the backward limit of balance and represents a virtual fall on the robot. o When you fall virtually on the robot, you will not be in control of the robot anymore. We will stop the trial, bring you back to the center position automatically, and then start the next trial. • Pre-adaptation quiet standing phase o Please stand relaxed and balance normally in your natural standing posture for 2 minutes. o There will be two trials in total. o During the experiment, please look at the target in front of you and avoid turning your head or eyes. Since talking could affect the brain signals, please try not to speak during the balance task. Try to relax your head, neck, and face. • Adaptation phase o Before the start: We will brief the adaptation experiment here for you. o The objective is for you to remain within the virtual limits of the robot and stand as relaxed and natural as possible. o You may sway more and experience virtual falls (reach the position limits of the simulation) during the adaptation period. Although the control of balance may 212 appear more difficult, you will always be able to control your body motion by adjusting how your feet interact with the ground. o If you reach a virtual limit, we will count it as a virtual fall and bring your body back to the center position. o Before each new trial, we will ask you to relax your legs. o Then, we will start the next trial without informing you after observing you are ready. o This adaptation will last for 20 minutes in total. o You can request a break at any time during the experiment. o During the experiment, please look at the target in front of you and avoid turning your head or eyes. Since talking could affect the brain signals, please try not to speak during the balance task. Try to relax your head, neck, and face. o If you have any questions about the science behind this experiment, we are happy to discuss them after the experiment. • Post-adaptation quiet standing phase o Please stand relaxed and balance normally in your natural standing posture for 2 minutes. o There will be one last trial in total. o During the experiment, please look at the target in front of you and avoid turning your head or eyes. Since talking could affect the brain signals, please try not to speak during the balance task. Try to relax your head, neck, and face. 213 Appendix E Summary - Linear Mixed-Effects Model for Cerebellar Power Analysis Delta Band 214 Theta Band 215 Alpha Band 216 Beta Band 217 Gamma Band
Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Wu, Lyndia
Blouin, Jean-Sébastien
Investigating cerebellar involvement in the adaptability of standing balance control using a robotic platform and electroencephalography
Text