Education, Faculty of
Kinesiology, School of
DSpace
UBCV
Chen, Anthony
Doctor of Philosophy - PhD
University of British Columbia
Humans, as with other organisms, rely on sensing for survival. The principles implemented by the brain to interpret this sensory information; however, remain open for investigation. The vestibular sense provides information about self-motion and orientation, which in part allows us to properly perceive self-motion in space and to navigate the surrounding environment. The purpose of this thesis was to advance the current knowledge of how the brain processes sensory cues of motion. Because the mechanisms that govern the central integration of vestibular information are difficult to reveal through everyday experiences, we used experimentally controlled sensory stimuli to probe vestibular-related neurophysiological and psychophysical behaviours. Studies presented in this thesis emerge from a first principles approach looking at integration of signals from primary vestibular afferents using a novel sampling-based dynamical inference model. Experiment 1 characterized perceptual self-motion during and following constant vestibular stimulation and contextualized how percepts arise from the integration of differently adapting primary vestibular afferents based on the brain’s expectation about one’s self-motion. Experiment 2 examined why perception changes when different vestibular end-organs encodes the same gravity-neutral whole-body motion. We showed that vestibular otoliths provide the brain additional information of self-rotation, a role primarily attributed to the vestibular semicircular canals. Experiments 3 and 4 together evaluated electrical vestibular stimulation for probing the vestibular system in humans. Here, we used current physiological data of primary vestibular afferent responses to both mechanical and electrical stimuli to predict and evaluate their equivalence in central processing in humans. Subsequently, a real-time solution for human-in-the-loop vestibular sense modulation using electrical vestibular stimulation during active head movements was developed using our identified equivalency. Altogether, this thesis highlights that our perceptions are shaped by our past experiences. Likewise, we show that equivalent perceptual and oculomotor behaviours can be elicited by matching the predicted response of primary vestibular afferents. The novel work presented here offers new theoretical and applied principles about vestibular processing, and the sensory integration process at large. More importantly, this may lead to novel and testable hypotheses for future studies to build upon in both fundamental and clinical areas.
PHYSIOLOGICAL COMPUTATIONS UNDERLYING OUR INTERNAL REPRESENTATION OF VESTIBULAR SELF-MOTION by Anthony Chen B.Kin., The University of British Columbia, 2016 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Kinesiology) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) August 2023 © Anthony Chen, 2023 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: Physiological Computations Underlying Our Internal Representation of Vestibular Self-motion submitted by Anthony Chen in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Kinesiology Examining Committee: Dr. Jean-Sébastien Blouin Professor, Kinesiology, University of British Columbia Supervisor Dr. Robert Boushel Professor, Kinesiology, University of British Columbia Co-supervisor Dr. Christopher J. Dakin Associate Professor, Kinesiology and Health Science, Utah State University Supervisory Committee Member Dr. Miriam Spering Professor, Ophthalmology & Visual Sciences, University of British Columbia University Examiner Dr. James Enns Professor, Psychology, University of British Columbia University Examiner iii Abstract Humans, as with other organisms, rely on sensing for survival. The principles implemented by the brain to interpret this sensory information; however, remain open for investigation. The vestibular sense provides information about self-motion and orientation, which in part allows us to properly perceive self-motion in space and to navigate the surrounding environment. The purpose of this thesis was to advance the current knowledge of how the brain processes sensory cues of motion. Because the mechanisms that govern the central integration of vestibular information are difficult to reveal through everyday experiences, we used experimentally controlled sensory stimuli to probe vestibular-related neurophysiological and psychophysical behaviours. Studies presented in this thesis emerge from a first principles approach looking at integration of signals from primary vestibular afferents using a novel sampling-based dynamical inference model. Experiment 1 characterized perceptual self-motion during and following constant vestibular stimulation and contextualized how percepts arise from the integration of differently adapting primary vestibular afferents based on the brain’s expectation about one’s self-motion. Experiment 2 examined why perception changes when different vestibular end-organs encodes the same gravity-neutral whole-body motion. We showed that vestibular otoliths provide the brain additional information of self-rotation, a role primarily attributed to the vestibular semicircular canals. Experiments 3 and 4 together evaluated electrical vestibular stimulation for probing the vestibular system in humans. Here, we used current physiological data of primary vestibular afferent responses to both mechanical and electrical stimuli to predict and evaluate their equivalence in central processing in humans. Subsequently, a real-time solution for human-in-the-loop vestibular sense modulation using electrical vestibular stimulation during active head movements was developed using our identified equivalency. Altogether, this thesis highlights that our perceptions are shaped by our past experiences. Likewise, we show that equivalent perceptual and iv oculomotor behaviours can be elicited by matching the predicted response of primary vestibular afferents. The novel work presented here offers new theoretical and applied principles about vestibular processing, and the sensory integration process at large. More importantly, this may lead to novel and testable hypotheses for future studies to build upon in both fundamental and clinical areas. v Lay Summary The vestibular system detects motion and gravity during self-motion. This thesis aimed to reveal the brain’s principles when transforming sensation to perception and motor actions. We found that perception may result from what we sensed and expected. We also demonstrated that the vestibular otoliths may provide the brain additional information regarding self rotation, a role primarily attributed to the vestibular semicircular canals. We next showed that electrical vestibular stimulation can artificially stimulate the vestibular system to produce equivalent behavioural outcomes to actual motion. Following this, we developed a portable system to dynamically modulate one’s vestibular sense during movement. This form of sensory augmentation creates new potential research on the interaction between how we move based on what we sense. Overall, this research helps us better understand how our brain processes information about our movement, and how we could develop new ways of testing sensory processing in the future. vi Preface The work presented in this dissertation was conducted at the Sensorimotor Physiology Laboratory at the University of British Columbia, Point Grey Campus. All the experiments were given approval by the University of British Columbia’s Research Ethics Board. The ethical certificate numbers are: H19-00422 for Chapters 4 and 5, H09-00987 for Chapter 6, H14-01712 for Chapter 7. The study described in Chapter 4 is being prepared for submission to a peer reviewed journal with the following authors: Chen, A., Kuo, C., & Blouin J.-S. A.C. was responsible for the conception, experimental design, data collection and analysis, interpretation of results, and manuscript drafting and revisions. C.K. and J.-S.B. both assisted with experimental design, interpretation of results, and manuscript revision. The study described in Chapter 5 is being prepared for submission to a peer reviewed journal with the following authors: Chen, A., Kuo, C., & Blouin J.-S. A.C. was responsible for the conception, experimental design, data collection and analysis, interpretation of results, and manuscript drafting and revisions. C.K. and J.-S.B. both assisted with experimental design, interpretation of results, and manuscript revision. A version of Chapter 6 has been published as Chen, A., Khosravi-Hashemi, N., Kuo, C., Kramer, J. K., & Blouin, J.-S. (2020). Development of a conversion model between mechanical and electrical vestibular stimuli. J Neurophysiol., 123(2), 548-559. A.C., N.K.-H., J.K.K., and J.-S.B. conceived and designed research; A.C. conducted all experiments; A.C., N.K.-H., and J.-S.B. analyzed data; A.C., N.K.-H., C.K., and J.-S.B. interpreted results of experiments; A.C. prepared figures; A.C. drafted manuscript; A.C., N.K.-H., C.K., J.K.K., and J.-S.B. edited and revised manuscript; All authors approved final version of manuscript. The code and data for Chapter 2 has been published as Chen, A., Khosravi-Hashemi, vii N., Kuo, C., Kramer, J. K., & Blouin, J.-S. (2020). Model, code and source data for "Development of a conversion model between mechanical and electrical vestibular stimuli”. Scholars Portal Dataverse, V1. A version of Chapter 7 has been published as Chen, A., Kuo, C., & Blouin, J.-S. (2022). A portable and low-cost solution for real-time manipulation of the vestibular sense. J Neurosci Methods, 382. A.C. and J.-S.B. conceived the method. A.C. developed the code and assembled the hardware. A.C. performed the experiment. A.C., C.K., & J.-S.B. analyzed the data and interpreted the results. A.C. wrote the first draft of the manuscript and prepared the figures. All authors edited, revised, and approved the final manuscript. viii Table of Contents ABSTRACT ............................................................................................................................................................. iii LAY SUMMARY ...................................................................................................................................................... v PREFACE ............................................................................................................................................................... vi TABLE OF CONTENTS ........................................................................................................................................... viii LIST OF TABLES ................................................................................................................................................... xiii LIST OF FIGURES .................................................................................................................................................. xiv ACKNOWLEDGEMENTS ....................................................................................................................................... xvi CHAPTER 1. INTRODUCTION ............................................................................................................................... 1 1.1. RESEARCH MOTIVATION ...................................................................................................................................... 1 1.2. THE VESTIBULAR SYSTEM: A HISTORICAL PERSPECTIVE ................................................................................................ 2 1.3. THE ANATOMY AND BIOMECHANICS OF THE PERIPHERAL VESTIBULAR SYSTEM ................................................................ 3 1.4. PRIMARY VESTIBULAR AFFERENTS CODING AND RESPONSE DYNAMICS ........................................................................... 6 1.5. CENTRAL VESTIBULAR PATHWAYS AND ITS NEURAL CODE ............................................................................................ 8 1.5.1. Angular vestibulo-ocular reflex (VOR) ..................................................................................................... 9 1.5.2. Vestibular processing in discriminating between active and passive self-motion ................................ 12 1.5.3. Vestibular self-motion perception ......................................................................................................... 13 1.6. VESTIBULAR COMPUTATION AND NEURAL INTEGRATION .......................................................................................... 14 1.6.1. The velocity storage, central integrator of spatial information ............................................................ 15 1.6.2. Peripheral vestibular afferent adaptation ............................................................................................. 22 1.7. HOW CAN THE VESTIBULAR SYSTEM BE STUDIED? ................................................................................................... 23 1.7.1. Probing the integration of vestibular afferent signals .......................................................................... 24 1.7.2. Probing the integration of vestibular end-organ signals ....................................................................... 25 1.7.3. Evaluating the physiological equivalence between vestibular signals from electrical or mechanical sources ................................................................................................................................................. 25 1.7.4. Developing a real-time system for vestibular modulation using EVS .................................................... 27 1.8. OBJECTIVES & GOALS ....................................................................................................................................... 28 CHAPTER 2. FOUNDATIONS UNDERLYING THE PHYSIOLOGICAL COMPUTATIONS OF VESTIBULAR PROCESSING FOR SELF-MOTION ............................................................................................................................................... 29 ix 2.1. PREAMBLE ..................................................................................................................................................... 29 2.2. ORIENTATIONAL MODEL OF VESTIBULAR END-ORGANS ............................................................................................ 29 2.2.1. Semicircular canal orientations ............................................................................................................. 29 2.2.2. Otolith orientations ............................................................................................................................... 32 2.3. SENSORY DYNAMICS OF VESTIBULAR AFFERENT CODING ........................................................................................... 35 2.3.1. Dynamics of semicircular canal afferents ............................................................................................. 35 2.3.2. Dynamics of otolith afferents ................................................................................................................ 37 2.3.3. Dynamics of semicircular canal and otolith afferents to electrical stimulation .................................... 39 2.3.4. Neuronal variability in vestibular afferent encoding ............................................................................. 41 2.3.5. Variability in afferent background discharge ........................................................................................ 42 2.4. SUMMARY ..................................................................................................................................................... 45 CHAPTER 3. BUILDING A DISTRIBUTED PARTICLE SAMPLING MODEL FOR VESTIBULAR SELF-MOTION ............. 47 3.1. PREAMBLE ..................................................................................................................................................... 47 3.2. IMPORTANCE OF COMPUTATIONAL MODELING ....................................................................................................... 47 3.3. STEP 1: DISTRIBUTING SENSORY AND STATE PARTICLE DISTRIBUTIONS ......................................................................... 49 3.4. STEP 2: INITIALIZING SENSORY AND INTERNAL STATE PARTICLES ................................................................................. 52 3.5. STEP 3: PARTICLE SAMPLING ALGORITHM ............................................................................................................. 56 CHAPTER 4. SELF-MOTION PERCEPTION TO CONSTANT ANGULAR ACCELERATION .......................................... 61 4.1. PREAMBLE ..................................................................................................................................................... 61 4.2. INTRODUCTION ............................................................................................................................................... 61 4.3. METHODS ..................................................................................................................................................... 64 4.3.1. Participants ........................................................................................................................................... 64 4.3.2. Setup ................................................................................................................................................. 65 4.3.3. Vestibular stimuli .................................................................................................................................. 66 4.3.4. Protocol ................................................................................................................................................. 68 4.3.5. Data analysis ......................................................................................................................................... 68 4.3.6. Statistical analysis ................................................................................................................................. 71 4.3.7. Vestibular sampling model incorporating zero-motion prior ................................................................ 72 4.4. RESULTS ..................................................................................................................................................... 74 4.4.1. Rate of occurrence in adaptation response during constant angular acceleration .............................. 75 4.4.2. Rate of occurrence in post-acceleratory response during constant angular velocity ............................ 76 x 4.4.3. Perceptual adaptation to constant angular acceleration stimuli .......................................................... 76 4.4.4. Constant angular velocity post-acceleratory response ......................................................................... 78 4.4.5. Simulations of perceptual adaptation to constant angular acceleration .............................................. 79 4.5. DISCUSSION .................................................................................................................................................... 80 CHAPTER 5. SELF-MOTION PERCEPTION IS DEPENDENT ON THE ENCODING VESTIBULAR END-ORGANS .......... 89 5.1. PREAMBLE ..................................................................................................................................................... 89 5.2. INTRODUCTION ............................................................................................................................................... 89 5.3. METHODS ..................................................................................................................................................... 94 5.3.1. Participants ........................................................................................................................................... 94 5.3.2. Experimental setup................................................................................................................................ 94 5.3.3. Motion stimulus .................................................................................................................................... 96 5.3.4. Experiment 1: Manipulating the canal contribution to self-rotation encoding ..................................... 97 5.3.5. Experiment 2: Manipulating the otolith contribution to self-rotation encoding ................................... 98 5.3.6. Testing protocol .................................................................................................................................. 100 5.3.7. Data reduction and signal analysis ..................................................................................................... 100 5.3.8. Data processing ................................................................................................................................... 101 5.3.9. Bootstrap and exponential fit analysis ................................................................................................ 101 5.3.10. Bootstrap statistical analysis .............................................................................................................. 103 5.3.11. Vestibular sampling model incorporating otolith encoding ................................................................ 103 5.4. RESULTS ................................................................................................................................................... 105 5.4.1. The perception of self-rotation is longer when motion is encoded by the horizontal canals .............. 108 5.4.2. The perception of self-rotation is prolonged when more canals encode motion ................................ 109 5.4.3. Differential otolith signals encoding angular acceleration prolong the perception of self-rotation ... 109 5.4.4. Simulations of perceptual response with and without otolith encoding ............................................. 110 5.5. DISCUSSION .................................................................................................................................................. 111 CHAPTER 6. REPLICATING REAL SELF-MOTION PERCEPTION USING ELECTRICAL VESTIBULAR STIMULATION . 118 6.1. PREAMBLE ................................................................................................................................................... 118 6.2. INTRODUCTION ............................................................................................................................................. 118 6.3. METHODS ................................................................................................................................................... 123 6.3.1. Setup ............................................................................................................................................... 123 6.3.2. Vestibular stimuli ................................................................................................................................ 124 6.3.3. Protocol ............................................................................................................................................... 128 xi 6.3.4. Data analysis ....................................................................................................................................... 130 6.3.5. Statistical analysis ............................................................................................................................... 132 6.3.6. Data and software availability ............................................................................................................ 134 6.4. RESULTS ................................................................................................................................................... 134 6.4.1. Ocular slow phase velocity response to mechanical and electrical vestibular stimuli ........................ 136 6.4.2. Perceived velocity response to mechanical and electrical vestibular stimuli ...................................... 139 6.5. DISCUSSION .................................................................................................................................................. 140 6.5.1. Mechanical to electrical stimulus conversion model gain ................................................................... 141 6.5.2. Torsional exponential decay between vestibular stimuli .................................................................... 142 6.5.3. Perceptual exponential decay between vestibular stimuli .................................................................. 143 6.5.4. Initial step towards a mechanical to electrical stimulus conversion model ........................................ 144 CHAPTER 7. A PORTABLE AND LOW-COST SOLUTION FOR REAL-TIME VESTIBULAR SENSORY MANIPULATION USING ELECTRICAL VESTIBULAR STIMULATION .................................................................................................. 147 7.1. PREAMBLE ................................................................................................................................................... 147 7.2. INTRODUCTION ............................................................................................................................................. 148 7.3. METHODS ................................................................................................................................................... 152 7.3.1. Participants ......................................................................................................................................... 152 7.3.2. Hardware & software design .............................................................................................................. 152 7.3.3. Setup & instrumentation ..................................................................................................................... 155 7.3.4. Electrical vestibular stimulation model ............................................................................................... 157 7.3.5. Hardware validations .......................................................................................................................... 160 7.3.6. Validation of the hardware implementation of the EVS model .......................................................... 161 7.3.7. Experimental procedures .................................................................................................................... 162 7.3.8. Experimental data analysis ................................................................................................................. 165 7.4. RESULTS ................................................................................................................................................... 165 7.4.1. Hardware validation and performance ............................................................................................... 165 7.4.2. Comparison of the real-time to the expected EVS model output ........................................................ 166 7.4.3. Recalibration of vestibular signals ...................................................................................................... 168 7.5. DISCUSSION .................................................................................................................................................. 169 7.6. CONCLUSION ................................................................................................................................................ 175 CHAPTER 8. GENERAL DISCUSSION AND CONCLUSION ................................................................................... 176 8.1. SUMMARY OF THESIS GOALS AND DISCUSSION ..................................................................................................... 176 xii 8.1.1. Central expectation may modulate vestibular sensory integration .................................................... 176 8.1.2. Vestibular self-motion depends on encoding vestibular end-organ .................................................... 177 8.1.3. Equivalence between virtual and mechanical vestibular stimuli through matching primary vestibular afferent dynamics ............................................................................................................................... 178 8.1.4. Using physiologically-equivalent EVS to modulate vestibular sensory feedback in a real-time human-in-the-loop system ............................................................................................................................... 179 8.2. IMPLICATIONS FOR VESTIBULAR PROCESSING ....................................................................................................... 180 8.3. ADAPTING A PHYSIOLOGY-BASED SAMPLING MODEL FOR OTHER SENSORY SYSTEMS? ................................................... 182 8.4. IMPLICATIONS FOR NOVEL VESTIBULAR RESEARCH USING EVS ................................................................................. 183 8.5. LIMITATIONS AND FUTURE WORKS ..................................................................................................................... 184 8.6. CONCLUSION ................................................................................................................................................ 186 BIBLIOGRAPHY ................................................................................................................................................... 188 APPENDIX A ....................................................................................................................................................... 218 xiii List of Tables Table 1: Comparison between regular and irregular primary vestibular afferent types ......................................... 7 Table 2: Mean left and right canal plane unit normal vector coefficients ............................................................. 30 Table 3: Cost of components .............................................................................................................................. 155 Table A-1: Simulink sensor parameters .............................................................................................................. 218 Table A-2: Simulink Model Configuration Parameters ....................................................................................... 219 xiv List of Figures Figure 1-1: The structure of the peripheral vestibular system. ............................................................................... 5 Figure 1-2: Schematic of the central vestibular system pathway............................................................................ 9 Figure 1-3: Simplified angular vestibulo-ocular reflex circuitry. ........................................................................... 11 Figure 1-4: Velocity storage processing to a head angular velocity step-input. .................................................... 16 Figure 1-5: Classical control theory models used to explain oculomotor velocity storage response. .................... 17 Figure 1-6: The observer model explanation for the velocity storage. ................................................................. 19 Figure 1-7: Simplified block diagram of Laurens and Droulez’s particle filter for vestibular processing. ............... 21 Figure 1-8: Additional long-term adaptation element to early state-space models of vestibular dynamics ......... 22 Figure 1-9: Electrical vestibular stimulation and its uses. ..................................................................................... 27 Figure 2-1: 3D orientation of the left and right canal plane unit vector coefficients. ............................................ 31 Figure 2-2: Estimated Saccule and Utricle maximal tuning vector and orientation. .............................................. 34 Figure 2-3: Bode plot comparison in transfer function frequency response for primary canal afferents. ............. 37 Figure 2-4: Bode plot comparison in transfer function frequency response for primary otolith afferents. ........... 38 Figure 2-5: Bode plot transfer function for primary canal afferents to transcutaneous electrical current. ........... 40 Figure 2-6: Bode plot of fitted transfer functions for primary canal afferents. ..................................................... 42 Figure 2-7: Detection threshold simulation procedures. ...................................................................................... 45 Figure 3-1: Allocation of particles in our model. .................................................................................................. 51 Figure 3-2: Head angular velocity to canal component. ....................................................................................... 53 Figure 3-3: Illustration of tangential linear acceleration between left and right otoliths. .................................... 55 Figure 3-4: Example of sampling algorithm. ......................................................................................................... 60 Figure 4-1: Experimental setup and estimated afferent responses. ..................................................................... 67 Figure 4-2: Sampling model with prior weighting. ............................................................................................... 73 Figure 4-3: Representative participant and participant averaged response. ........................................................ 75 Figure 4-4: Participant-wise per-acceleratory time to peak and adaptation time constants................................. 77 Figure 4-5: Post-acceleratory decay time constants and relative peak amplitude. ............................................... 78 xv Figure 4-6: Sampling model simulation results. ................................................................................................... 80 Figure 4-7: Linear time-invariant model response to constant angular acceleration. ........................................... 82 Figure 4-8: Comparison between simulation for only regular or only irregular afferent type. .............................. 86 Figure 5-1: Experimental setup, conditions, and stimulus. ................................................................................... 93 Figure 5-2: Modulation of otolith tangential acceleration signal with different head orientation. ....................... 99 Figure 5-3: Perceptual response and bootstrap procedure. ............................................................................... 107 Figure 5-4: Individual and bootstrapped results for Experiments 1 and 2. ......................................................... 108 Figure 5-5: Sampling model simulation results. ................................................................................................. 111 Figure 6-1: Illustration of head orientation, rotary chair, and stimulus signals. ................................................. 122 Figure 6-2: Conceptual illustration of vestibular processing used in the mechanical-to-electrical stimulus conversion model. ...................................................................................................................................... 128 Figure 6-3: Experiment 1. ................................................................................................................................... 135 Figure 6-4: Experiment 2. ................................................................................................................................... 136 Figure 6-5: Experiment 3, Multisine vestibular stimulation between mechanical and electrical vestibular stimulations. .............................................................................................................................................. 138 Figure 6-6: Orthogonal regression analysis between mechanical and electrical vestibular stimulations. ........... 139 Figure 7-1: Illustration of electrode configuration and net-evoked EVS rotational axis. ..................................... 151 Figure 7-2: Closed-loop vestibular modulation using our real-time head-coupled EVS modulatory system. ...... 156 Figure 7-3: Standing balance experiment. .......................................................................................................... 164 Figure 7-4: Hardware validation & model output comparison. .......................................................................... 166 Figure 7-5: Bode plot of model and recorded data. ............................................................................................ 167 Figure 7-6: Sway data for the standing balance adaptation experiment. ........................................................... 168 Figure A-1: Circuit schematic of our EVS system. ............................................................................................... 218 xvi Acknowledgements First and foremost, I would like to acknowledge and thank my mentor, Dr. Jean-Sébastien Blouin, for his unwavering guidance, encouragement, and intellectual challenges my academic journey. His support has been instrumental in both shaping my research curiosity and self-efficacy. I would also like to express my appreciation to Dr. Robert Boushel and Dr. Christopher Dakin for their invaluable feedback on my work, which provided alternative perspectives that has enriched the quality of my research. I also want to especially thank Dr. Calvin Kuo, whose vital guidance and support deepened my understanding of dynamical models and the particle-based modelling approach used in my work. I am deeply thankful for the inspiring and selfless individuals within the Sensorimotor Physiology Lab and our collaborators, whom I have had the privilege to meet during my doctoral program. Their willingness to engage in inquisitive discussions and provide technical support has been invaluable to my academic and personal growth. Lastly, I want to thank my family and friends for their emotional support in both better and difficult times. My partner, Donna, thank you so much for your support and care, and being patient with me pursing this crazy path. On this farm there are no bad potatoes, just our lovely cat, Muji. 1 Chapter 1. Introduction 1.1. Research motivation The vestibular system, popularly referred to as a human sixth sense, is responsible for detecting and integrating head-centric motion cues with other available senses for gaze stabilization, self-motion perception, and motor control (reviewed in Cullen 2019). This vestibular contribution to perception is often overlooked due to our visual dominance, but despite closing our eyes, we maintain an awareness of self-motion alluding to the importance of the vestibular system. The specific computations within the brain underlying vestibular perception, however, remain unresolved. Often, carefully controlled conditions and stimuli are used to elicit unfamiliar percepts that are otherwise improbable during everyday experience, revealing central processing. By identifying how these percepts form within an experimental paradigm, we can begin to decipher the brain’s computational principles and their functional importance when framed within a conceptual or computational framework (Laurens and Angelaki 2011). Early works viewed vestibular processing through a deterministic lens using linear control systems theory (Raphan et al. 1977; Robinson 1977). Contemporary views instead shifted focus on probabilistic inference for neural integration and the role of biological noise and uncertainty, such that inferences are statistically optimal (e.g., minimize mean squared error, maximize likelihood) combinations of noisy sources of information (Ernst and Banks 2002; Karmali 2019; Karmali and Merfeld 2012; Laurens and Droulez 2007; Paulin and Hoffman 2011). Although recent work supports the idea of a 'probabilistic’ brain, the underlying assumptions from which probabilities are constructed and how inferences are drawn from them remain an open question. 2 1.2. The vestibular system: a historical perspective The first known published description of the vestibular system coincided with the anatomical characterization of the inner ear during the 18th century. The vestibular structure was initially believed to be involved in hearing due to its proximity to the cochlea. However, it was not until the late 19th century that the functional significance of the vestibular structure as sensory end-organs involved in the maintenance of balance and equilibrium was firmly established. Sensory systems in the early to mid 19th century were viewed as passive organs that facilitated the faithful reconstruction of the outside world within our brain, like a static camera projecting an image (reviewed in Paulin and Hoffman, 2019). A shift away from this perspective occurred throughout the 1950-1970s as direct recordings of neural activity revealed a diverse range of encoding responses in vestibular sensory neurons to mechanical stimuli (Fernandez and Goldberg 1971; Goldberg and Fernandez 1971a, 1971b). Furthermore, foundational works from Raphan and Cohen, and Robinson revealed a central process involving vestibular signals termed the velocity storage (Cohen et al. 1981a; Raphan et al. 1977, 1979; Robinson 1977). Since the 1970s, new theoretical paradigms within sensory neuroscience have emerged incorporating engineering (Kalman 1960; Luenberger 1971; Wolpert et al. 1995) and statistical (Arulampalam et al. 2002; Ernst and Banks 2002; Paulin 2005; Pouget et al. 2013) principles to explain central vestibular processing such as the velocity storage. Simultaneously, a more comprehensive understanding of the neural signals encoded by peripheral vestibular afferents, central neurons, and their complex neural pathways (Angelaki and Hess 1996; Cullen et al. 2011; Curthoys and MacDougall 2012; Dale and Cullen 2019; Fetsch et al. 2009; Green and Angelaki 2010a; Jamali et al. 2009; Martin et al. 2018; Massot et al. 2011; Rabbitt et al. 2005; Roy and Cullen 2002; Sadeghi et al. 2007a; Yakusheva et al. 2007) allowed further progress into the computations involving vestibular signals and their functional/clinical significance. Nonetheless, the mechanisms and 3 principles underlying how the brain centrally processes vestibular signals remain in contention (Laurens and Angelaki 2011; Raphan 2020). The following sections will highlight known vestibular morphology and neurophysiology, sensory encoding dynamics, and an overview of previously proposed modeling approaches of vestibular sensing. Together, this section will provide a working knowledge about the physiological principles and constraints of the vestibular sense allowing us to further delve into the key components of this thesis. 1.3. The anatomy and biomechanics of the peripheral vestibular system The human peripheral vestibular system is composed of a pair of five bilateral sensory end-organs located within each inner ear. Each set respectively form the left and right vestibular apparatuses. Morphologically, a vestibular apparatus is affixed to the temporal bone’s bony labyrinth cavity which is filled within by an inner membranous labyrinth layer containing an endolymph fluid medium and various end-organ cellular architectures. The membranous labyrinth is arranged as an interconnected series of sacs (vestibule) and canals (tubes) (Figure 1-1). The utricle and saccule otolith end-organs are each located within separate sacs and are responsible for sensing linear accelerations in three dimensions. Three semicircular canal end-organs each make up the three nearly orthogonal tubes and are responsible for sensing angular accelerations perpendicular to each tube’s plane thus individually encoding different rotational directions. Collectively, directional encoding during complex six-axis head motion in space is achieved by the decomposition of linear and angular accelerations components by the corresponding sensory end-organs thus serving as a biological inertial sensor for the brain (Goldberg et al. 2012). 4 Vestibular sensory end-organs encode head motion in space from the biomechanical transduction of receptor hair cell bundles occurring at their respective neuroepithelium (sensory nerve endings). Each hair cell bundle consists of a kinocilium and an array of stereocilia arranged in a staircase pattern. Directional selectivity in head motion encoding is dictated by the direction of stereocilia deflection. Deflections towards or away the kinocilium respectively lead to depolarization and hyperpolarization of the innervating primary vestibular afferent neuron. Otolith neuroepithelial hair cell bundles protrude from the lining of the two vestibular sacs and are embedded into a layer of otolithic membrane forming the utricle and saccule maculae. Hair cell bundles in each macula are dispersed in a fan-like manner, but its orientation can be subdivided into two oppositely orientated bundle regions (Curthoys et al. 1995; Dimiccoli et al. 2013; Fernandez and Goldberg 1976a). A calcium carbonate crystalline layer sits on top of the otolithic membrane and provides inertia that allows the membrane to deform relative to its neuroepithelium base. As such, the otoliths are sensitive to gravito-inertial accelerations (i.e., accelerations both due to head tilt with respect to gravity and linear head translation), as both are indistinguishable and equivalently displace the otoconia mass (Einstein 1907). Conversely, neuroepithelium in each canal end-organ is located at their respective ampulla, an enlarged region of the canal duct near the vestibule. Canal neuroepithelial hair cell bundles unidirectionally protrude from the ampulla crest and are embedded in a gelatinous mass called the cupula. The cupula itself is anchored at the ampulla forming a diaphragm-like hydraulic seal which responds to changes in endolymph fluid pressure during rotations (Hillman and McLaren 1979). Therefore, each canal detects rotations perpendicular to the fluid movement within the planar canal tube. Importantly, the three ipsilateral (anterior, posterior, and horizontal) canals are arranged in a near-orthogonal manner on both left and right vestibular apparatuses (Della Santina et 5 al. 2005), and each left/right canals with parallel orientation form co-planar pairs with opposing directional sensitivity (Figure 1-1). Figure 1-1: The structure of the peripheral vestibular system. The vestibular apparatus on one side consists of three semicircular canals (anterior, posterior, and horizontal canals) and two otolithic (utricle and saccule) end-organs. In humans, a pair of two vestibular apparatuses are present, one on the left and right inner ears. Left and right semicircular canals form three co-planar pairings: the right anterior (RA)-left posterior (LP) plane/pair (orange-dash), the left anterior (LA)-right posterior (RP) plane/pair (teal-dash), and the left horizontal (LH)-right horizontal (RH) plane/pair (not depicted; along the transverse plane). Canal afferent transduction occurs at each canal’s respective ampulla. The otoliths are located within enlarged sacs with the utricle and saccule situated in the transverse and parasagittal plane, respectively. Otolithic afferents are dispersed in a fan-like pattern along a dividing ridge of the otolithic membrane called the striola. Canal and otolithic primary afferents are directed towards the brain through the Vestibulocochlear nerve/Cranial Nerve (CN) VIII. 6 1.4. Primary vestibular afferents coding and response dynamics Primary vestibular afferents innervating vestibular end-organs transmit sensory information as a part of the brain’s vestibular neural pathway. This sensory information presumably represents a linear encoding of the input stimulus, i.e., the relationship between head motion in space and action potential firing rate. The spontaneous, resting discharge rate of the otoliths (~80 spikes/s, Jamali et al. 2013) and canals (~90 spikes/s, Sadeghi et al. 2007a) have non-zero offset biases which determines the available encoding response magnitude range (e.g., between 0 to 500 spikes/s, Sadeghi et al. 2007b). Additionally, primary vestibular afferents demonstrate variability in resting discharge interval (time between action potentials). In practice, afferents with relatively constant intervals are considered ‘regular-type’ afferents, and those with more variable intervals are considered ‘irregular-type’ afferents (Baird et al. 1988; Fernandez and Goldberg 1971; Goldberg et al. 1984b). This distinction is however arbitrary for practical purposes, and variability in internal spike interval and afferent properties should more accurately be viewed along a spectrum between the two types (Goldberg 2000a; Paulin and Hoffman 2019). Several coding strategies are used by primary vestibular afferents to transmit information about head motion in space. The first is rate coding which involves changes in afferent firing rate to encode motion (Sadeghi et al. 2007a), and the second is temporal coding where motion information is stored in the precise timing of action potentials (Jamali et al. 2016). The response dynamics of primary vestibular afferents were described through system identification techniques by measuring resultant afferent output in response to controlled head acceleration input as a function of frequency. Canal afferent frequency response, resembles a high-pass filter relative to head angular velocity (Ramachandran and Lisberger 2006; Sadeghi et al. 2007a). This is because of a 90 deg phase lag estimated within the 0.1 to 2 Hz range in response to head angular accelerations which corresponds to an in phase encoding of head angular velocity (Fernandez 7 and Goldberg 1971). An increase in phase lead below 0.1 Hz and above 2 Hz suggests that canal afferents more closely encode angular acceleration at those bandwidths (see Figure 2-3 for bode plot representation). The otolith afferent frequency response, relative to head gravito-inertial acceleration, may also be described as a high-pass filter (Angelaki and Dickman 2000; Jamali et al. 2013). Progressive increase in phase lead at higher frequencies (>10 Hz) suggests that otolithic afferents also carries information about jerk, the derivative of acceleration (see Figure 2-4 for bode plot representation). Typically, in both canal and otolith, irregular-type afferents show greater phase lead and gain for a given frequency. This tuning behaviour is believed to improve detection of transient, high frequency, movement impulses. Possibly as a consequence of their functional roles, regular afferent types are more associated with the vestibulo-ocular reflex pathway (gaze stabilization) whereas irregular counterparts are more associated with vestibulo-spinal and vestibulo-perceptual pathways (Cullen 2019). The comparison between primary vestibular afferent types is summarized in Table 1. For brevity, the mathematical transfer function equations used to describe these vestibular afferent frequency response dynamics are presented in the subsequent chapter (Section 2.3, Sensory dynamics of vestibular afferent coding). Table 1: Comparison between regular and irregular primary vestibular afferent types Regular Afferent Irregular Afferent 1. Preferential coding strategy Rate Temporal 2. Functional implication Direct head motion encoding Discriminate transient head motion stimuli 3. Preferential central pathway Predominantly vestibulo-ocular reflex Predominantly vestibulo-spinal and vestibulo-perceptual 4. Resting discharge regularity Relatively constant Relatively variable 5. Sensitivity/Gain to input Lower Greater 8 1.5. Central vestibular pathways and its neural code Primary vestibular afferent fibers travel along the vestibulocochlear nerve/cranial nerve VIII and terminate at the brainstem’s vestibular nucleus complex. This brain region serves as a central vestibular hub by integrating and relaying vestibular neural signals within a complex synaptic network interconnecting different brainstem vestibular nuclei and other regions of the brain like the cerebellum, thalamus, and cerebral cortex. This section will concentrate on central vestibular pathways pertaining to the present studies in this thesis: vestibular-driven perception (Chapters 4, 5, & 6), reflexive eye movement (Chapter 6) and vestibular internal model (Chapter 7), highlighting the neural processing involved in these three functional end goals. Primary vestibular afferents synapse onto several types of secondary central neurons at the vestibular nuclei (reviewed in: Cullen 2019; Green and Angelaki 2010b) (Figure 1-2). For example, along the vestibular-ocular reflex (VOR) circuit, synaptic connections are formed with burst-tonic (PH-BT), eye-head (EH), and with majority to position-vestibular-pause (PVP) neurons. Each, to certain degrees, correlates with eye (or head) position/velocity. Conversely, connections to vestibular-only (VO) neurons selectively encode passive motion through the gating activity of the cerebellum, such as the rostral fastigial nuclei (Brooks and Cullen 2009) and are associated with postural and perceptual pathways. Primary afferent types show preferential projections such as regular vestibular afferents preference for ocular PVP neurons providing information in their rate encoding that is necessary for gaze stabilization (Huterer and Cullen 2002; Ramachandran and Lisberger 2006). Comparatively, irregular vestibular afferents preferentially project onto VO neurons relating to the spinal cord, cerebellum, and thalamus involving the vestibulo-spinal and vestibulo-perceptual pathways. 9 Figure 1-2: Schematic of the central vestibular system pathway. Primary vestibular afferents (regular & irregular types) innervating the vestibular apparatus project onto central neurons at the medulla’s vestibular nucleus complex. Central vestibular neurons are classified into different types depending on observed functions. Two examples would be the position-vestibular-pause (PVP) and vestibular-only (VO) neurons. PVP neurons project onto pathways of the extraocular muscles, and their activity robustly matches head motion but are suppressed during gaze re-direction. VO neurons selectively encode passive motion of the head through the gating activity of the cerebellum such as the rostral fastigial nuclei (rFN). VO neurons propagate upwards toward the thalamus through the anterior ventrothalamic and posterior ventrothalamic pathways. After the thalamus, vestibular signal is shown to be involved in different cortical areas based on non-human primate studies which presumably play a similar role in human analogues. These involves the parieto-insular vestibular cortex (PIVC), ventral intraparietal area (VIP), dorsal medial superior temporal area (MSTd), and supplemental eye fields (SEF). 1.5.1. Angular vestibulo-ocular reflex (VOR) The angular vestibulo-ocular reflex (VOR) serves to stabilize gaze during head motion but is actively suppressed upon changing to goal-directed gaze (Barr et al. 1976; Cullen et al. 2004). The 10 function of the angular VOR can be demonstrated by holding up your index finger in front at a distance. When your index finger is moved left and right across the field of view at a rate of one cycle per second, the finger will appear blurry. Conversely, when the head is moved at the same frequency while keeping the finger stationary, the visual acuity of the finger is retained. This demonstrates the short latency (5-7 msec.) and high bandwidth ( >15 Hz) of the angular VOR allowing for counter-rotation of the eye relative to the head rotation to maintain a fixed point in visual space (Huterer and Cullen 2002). The angular VOR primarily involves a bilaterally symmetrical three-arc neural circuit acting in a push-pull manner. First, primary vestibular afferents, preferentially regular-type, project onto intermediate PVP neurons in the vestibular nuclei. PVP neurons, like the regular afferents, are sensitive to head angular velocity across a wide bandwidth and demonstrating a similar rate encoding strategy under active and passively applied head rotations with increasing gains at higher frequencies (Minor and Goldberg 1991; Ramachandran and Lisberger 2008; Roy and Cullen 2002). The PVP neural signal is gated and suppressed during gaze-shift or gaze pursuit by inhibitory drive from brainstem burst neurons (Roy and Cullen 1998). As such, unlike peripheral afferents, central PVP neurons demonstrate context dependent modulation reflecting changes in gaze-strategies, either stabilizing or shifting. Eye movements in response to the angular VOR is accomplished through direct excitatory and inhibitory connections to nuclei responsible for extraocular muscle activity. For example, when experiencing a counter-clockwise (leftward) head yaw rotation that elicits horizontal angular VOR, left PVP neurons will form excitatory connections with the contralateral abducens nucleus and ipsilateral oculomotor nucleus while also sending inhibitory signals to the ipsilateral abducens nucleus (Figure 1-3, blue lines). In turn, this allows the contraction of the ‘contralateral’ lateral rectus muscle and the 11 relaxation of ‘ipsilateral’ lateral rectus muscle from the abducens nuclei (Figure 1-3, red lines). Simultaneously, the ipsilateral and contralateral medial rectus are contracted and relaxed due to connections of the oculomotor nuclei (Figure 1-3, green lines). The net horizontal movement of the eyes results from the contraction and relaxation of these lateral and medial rectus muscles. Opposite actions arise for inputs from the right semicircular canals. Similar push-pull mechanisms occur for both vertical and torsional angular VORs albeit involving different extraocular muscles. Figure 1-3: Simplified angular vestibulo-ocular reflex circuitry. A simplified pathway for the angular vestibulo-ocular reflex is illustrated during a leftward head yaw rotation. Primary afferents from the left horizontal semicircular canal are excited. Opposite inhibition occurs in primary afferents from the right co-planar horizontal semicircular canal (not depicted). Left primary afferents projects to central neurons in the vestibular nuclei (dot line). Subsequent projection excites motor neurons at (1) the contralateral abducens nucleus (+ blue line) to activate lateral rectus (LR) muscle of the right eye (+ red line), and (2) at the ipsilateral oculomotor nucleus (+ green) to activate medial rectus (MR) muscle of the left eye (+ black line). Additionally, inhibitory signal from the vestibular 12 nuclei is sent to the ipsilateral abducens nucleus (- blue dash line) to inhibit lateral rectus (LR) muscle of the left eye (- red dash line). Change in ocular muscle activity results in both eyes horizontally shifting rightwards, matching the leftward head rotation. 1.5.2. Vestibular processing in discriminating between active and passive self-motion Primary vestibular afferents also project onto vestibular-only (VO) neurons in the vestibular nuclei. These VO neurons differ from PVP neurons in several aspects. (1) They are insensitive to eye movements (Cullen and McCrea 1993; Scudder and Fuchs 1992), (2) receive more projections from irregular afferents, (3) exhibit irregular afferent-like spike-timing encoding, and (4) project to the vestibular cerebellum, spinal cord, and thalamus (Marlinski and McCrea 2009; Meng et al. 2007). These characteristics suggest that VO neurons are more suited for transient, high-frequency movements and are more involved in postural control and self-motion perception; thus, the investigation of these behaviours in addition to ocular responses is important to disentangle distinct pathways. VO neurons robustly encode passively experienced head motion in space as they are inhibited during active (self-generated) movement. This ability to discern externally derived sensory inputs (exafference) from those that are self-generated (reafference) is crucial for accurate self-motion and the generation of appropriate motor actions. The suppression of VO neurons during active movement is believed to occur through a reafference cancellation signal originating from the cerebellar rostral fastigial nucleus (Batton et al. 1977; Bronstein et al. 2008). In this way, the cerebellum constitutes a forward internal model (Wolpert et al. 1995) that predicts the sensory consequences of active movement from our motor command. Importantly, internal model predictions appear to be malleable in accommodating new movement-sensory relationships at the neural level (Brooks et al. 2015; Brooks and Cullen 2014; Cullen et al. 2011) supporting observed adaptations to manipulated vestibular-feedback in human postural control (Héroux et al. 2015). Further human studies 13 incorporating real-time vestibular manipulations are necessary to reveal the mechanisms underlying the updating of the brain’s internal model. 1.5.3. Vestibular self-motion perception VO neurons from the vestibular nuclei project onto the thalamus towards the cortex through two ascending thalamocortical pathways: the anterior vestibulothalamic pathway and posterior vestibulothalamic pathway. The anterior pathway, terminating at the anterior dorsal thalamus, is involved with our sense of heading (reviewed in Cullen 2019). Conversely, the posterior pathway terminates at the ventral posterior lateral nucleus of the thalamus and selectively encodes externally applied head motion, implying that the neural information from the VO is propagated here (Dale and Cullen 2019). The ventral posterior lateral nucleus relays information to a network of cortical structures that integrates vestibular inputs with visual and somatosensory signals to generate perceived motion. Specifically, in macaque monkeys, the ventral intraparietal area (area VIP) and parietoinsular vestibular cortex (PIVC) show vestibular, visual, and somatosensory sensitivities (Bremmer 2005; Chen et al. 2013; Klam and Graf 2003). Human analogues of these regions (Bremmer et al. 2001; Eickhoff et al. 2006; Grüsser et al. 1990; Lopez et al. 2012) similarly show activity in response to vestibular, tactile, and visual stimuli. For example, diminished performance in vestibular-cued path integration (displacement estimation) and directional discrimination threshold during transcranial magnetic stimulation of the posterior parietal cortex in humans suggest a role for vestibular processing in this region (Kyriakareli et al. 2013; Seemungal et al. 2008). Another cortical region shown to receive vestibular input in the non-human primate brain is the dorsal medial superior temporal region (MSTd). Human MST also likely receives vestibular input in the anterior region as measured through functional MRI and galvanic vestibular stimulation (Smith 14 et al. 2012). MSTd neurons exhibit spatial tuning for both optic flow and inertial cues suggesting their role for heading perception (Gu et al. 2007). The combination of both stimuli leads to near-optimal integration mimicking human perceptual performance (Fetsch et al. 2009, 2010; Gu et al. 2008). Multiple cortical areas receive vestibular information from the thalamus. In particular, the area VIP, PIVC, and MST demonstrate sensitivity to visual, vestibular, and possibly somatosensory cues as shown in neurophysiological and psychophysical experiments in non-human primates and humans (Chen et al. 2011; reviewed in Cheng and Gu 2018). An emerging view suggests that during externally applied head motion, a network of cortical areas integrates passive vestibular sensory information with visual and somatosensory cues to provide an estimate of self-motion (Dale and Cullen 2019). 1.6. Vestibular computation and neural integration Our brain infers the state of the world from imprecise sensory information. The exact neural computations involved in this inference, however, remain in contention. Experiments focusing on specific behaviours or perceptual phenomena offer a way to probe these computations, and often are complemented by mathematical models that aims to replicate experimental findings. Such models advantageously provide a testable framework to further evaluate neural computations. In particular, the vestibular sense is favoured as a relatively simple sensory model to probe the brain’s processing because of its well-characterized morphology, encoding preferences, and peripheral response dynamics; all of which is necessary for building plausible dynamical models. As such, considerable work has been done in understanding central vestibular processing through incorporating engineering and mathematical concepts. This section will highlight two vestibular processes: the well-established velocity storage central adaptation and a less familiar peripheral afferent adaptation, focusing on modeling approaches and lessons learned from them. 15 1.6.1. The velocity storage, central integrator of spatial information The velocity storage is a term used to describe a well-known phenomenon believed to involve the central integration of vestibular cues (Laurens and Angelaki 2011; Raphan 2020). It can be defined as the prolongation of angular velocity information in central neurons, the angular VOR, and rotational perception (Bertolini et al. 2011; Raphan et al. 1979; Reisine and Raphan 1992; Tweed et al. 1994; Yakushin et al. 2017) beyond what is expected from the neural signals encoded by primary vestibular afferents (Cohen et al. 1981b; Dai et al. 1999; Fernandez and Goldberg 1971). This can be classically observed following a step-change in head angular velocity (Figure 1-4, black-line) in which the canal endolymph fluid motion lags (due to its inertia) behind the canal wall/ampulla thus deflecting the embedded hair cells – analogous to the motion lag of water when in a twirling glass. As such, primary canal afferents accurately capture the initial step input, but as the endolymph fluid catches up relative to the canal ampulla, the afferent response decays to its baseline firing rate in about 12 seconds (Dai et al. 1999) (Figure 1-4, red-solid). The velocity storage therefore manifests itself as the propagation of this initial peripheral response by as much as 2 to 3 times for both perception and ocular responses (Bertolini et al. 2012) (Figure 1-4, c.f., red-dashed). This creates a more accurate internal signal of constant angular velocity input than is present in the canal afferent signal. Due to the prolongation of the neural information in the absence of a peripheral signal, the observed prolongation is believed to be a manifestation of central processing, and as such, computational approaches modeling this velocity storage phenomenon may provide insight into how and why the brain integrates sensory information the way it does. 16 Figure 1-4: Velocity storage processing to a head angular velocity step-input. Upon a step-change in head angular velocity, primary canal afferent firing rate exhibits an initial burst in activity which is followed by an exponential decay with a time constant of ~4s. This peripheral response is due to the canal-cupula and afferent dynamics as the endolymph fluid medium initially lags and catches up to the canal wall due to its inertia. However, central neurons, such as position-vestibular-pause (PVP) and vestibular-only (VO) neurons, show a longer signal duration relative to the primary afferents, leading to prolongation of the angular vestibulo-ocular reflex (VOR) and rotational motion perception. This difference in the neural dynamics between primary afferent and central neurons is believed to be a manifestation of a central, multisensory integration process. The velocity storage was Initially observed through the angular VOR in nonhuman primates. Separate linear systems transfer function analyses from Raphan et al. (1977) and Robinson (1977) recognized that the brain must perform a neural equivalent to a mathematical integration of the peripheral signal to achieve the velocity storage behaviour. However, these researchers proposed distinct, but equivalent, mathematical representations of the phenomenon (Figure 1-5, c.f. A, B). The Raphan-Matsuo-Cohen model generates an angular velocity estimate from the summation over time of a direct pathway towards the oculomotor neurons and an indirect pathway processing canal afferent signal through an explicit integrator with a negative feedback loop. Comparatively, Robinson proposed a model using a single pathway with a positive feedback loop. These early linear system models identified the input-output frequency response dynamics of the angular VOR, but were limited in their capacity to explain the purpose of the velocity storage and accounting for sources of variability (MacNeilage et al. 2008). 17 Figure 1-5: Classical control theory models used to explain oculomotor velocity storage response. These models are identified as leaky integrators with model parameters used to obtain velocity storage time constants of 15-20s. Input head angular velocity is first passed through the semicircular canal-cupula dynamics modeled as a first-order high pass filter with time constant 𝑻𝒄 = 4s. (A) Raphan and colleagues (1977) proposed a leaky integrator with parameters 𝑮𝒐 = 0.25 and 𝑯𝒐 = 0.71 representing the gain of the leaky integrator and the rate of leakage respectively. (B) Conversely, Robinson (1977) proposed a model where the primary vestibular afferent signals are passed through a positive feedback loop with transfer function (𝟏𝑻𝒐+1) with a time constant of 𝑻𝒐 close to 𝑻𝒄. To link conceptual meaning for the identified signal transformations proposed by Raphan et al. (1977) and Robinson (1977), new frameworks were posited using internal models and observer theory (MacNeilage et al. 2008). The internal model is a concept pertaining to an internal knowledge of physical principles guiding sensory dynamics or motor processing within the brain. This suggests that the brain can estimate afferent responses from a given stimulus input (i.e., forward internal sensory model) or vice versa estimate stimulus input from afferent response (i.e., inverse internal sensory model) by ‘knowing’ the physical properties and/or dynamics leading to the stimulus-afferent transformation. The observer theory component, on the other hand, is a control theory application that aims to estimate the state(s) of a model’s system thereby generating the appropriate control response (Luenberger 1971). This observer design is used in engineering control problems (e.g., robotic motions) as it can advantageously estimate unmeasurable or difficult to measure states. When combined with internal models, they act as a mechanism for error monitoring by comparing known 18 internal model predictions to measured outcomes. Because neural activity in the brain exhibits behaviours consistent with the use of an internal model (Angelaki et al. 2004; Brooks et al. 2015; Kawato 1999; Shadmehr and Mussa-Ivaldi 1994; Wolpert et al. 1995), this form of error monitoring is favoured as a neural analogue within our brain. Using this principle, Borah et al. (1988) and Merfeld et al. (1993) replicated the velocity storage behaviour by estimating the ‘unobservable’ central estimate of angular velocity using an internal model of peripheral sensory dynamics. More specifically, Merfeld and colleagues (1993) implemented a model where an error resulting from the comparison of the peripheral canal signal to a internal model predicted sensory signal that ultimately replicates the velocity storage propagation when multiplied by a ‘K’ gain factor (Figure 1-6, c.f. A, B). In comparison to the implementation from Borah et al. (1988), the gain factor was defined by the modeller. Rather, Borah et al. (1988) used a Kalman filter (Kalman 1960) to derive the gain factor (called the Kalman gain in this context) mathematically by minimizing the mean square error of the prediction’s uncertainty and inverse variance of the measurement’s noise in a application of Bayes’ Theorem. Recently, Karmali and Merfeld (2012) expanded Merfeld's original observer model (Figure 1-6C) by incorporating discretized samples (termed particles) to represent prediction and measurement distributions when deriving the Kalman gain. As such, an optimal observer, whether using an analytical or sample-based method, relates the physiological sensory noise of the system to the amount of velocity storage propagation through the Kalman gain. 19 Figure 1-6: The observer model explanation for the velocity storage. These models use an internal sensory model (assumption of a central internal model of the semicircular canals that allows for a prediction of the primary afferent behaviour) within an observer error monitoring framework to replicate velocity storage behaviour. (A) Adapted from Merfeld et al. (1993), in this observer model the internal model prediction is subtracted from the measured response from the canals to generate an error. This error is scaled by a gain (K = 3) to obtain the central estimate of angular velocity. Observer models such as the one from Merfeld and colleagues (1993) posit that the gain (K) dictates the velocity storage time constant with a higher K yielding a longer propagation. (B) Adapted from Borah et al. (1988), in this optimal observer model the internal model prediction is similarly subtracted from measured response. However, the variable K (called the Kalman gain) is derived from (and proportional to) the minimization of mean square error of the prediction’s uncertainty (𝑃𝑡) and inverse variance of the measurement noise (𝑅−1). (C) Adapted from Karmali and Merfeld (2012), an extension of Merfeld’s original model derived the gain similar to a Kalman filter but used a distributed set of particles to represent model prediction and measurement distributions (and their variance). Optimal observer models imply that the noise of the system dictates the Kalman gain and, by extension, the velocity storage time constant. The Kalman filter algorithm highlights the probabilistic aspect of neural processing within the brain as it relies upon the application of Bayes theorem within a linear-Gaussian constraint (Paulin 20 and Hoffman 2011) when finding the statistically optimal gain parameter. This application of Bayesian statistics is seen in many facets of central processing such as in (multi-)sensory cue integration at both the neuronal (Gu et al. 2008) and behavioural (Fetsch et al. 2009) levels where the brain acquires information from different sources and weighs them during their combination proportional to their reliability. Building upon this idea, Laurens and Droulez (2007) implemented a Particle filter of the velocity storage that can perform Bayesian inference using Monte Carlo approximation (Figure 1-7). In such a representation, samples/particles are dynamically propagated (simulated through system dynamics) and subjected to sensory noise leading to variability in each particle. Particles together represent a full probability distribution that can be randomly sampled to generate an inference. Advantageously, particle filters provide a numerical solution to Bayesian inference in complex systems containing non-linear processes and non-Gaussian distributions that may not have a simple analytical solution. Particles in Laurens's model represent possible head motion in space which are assigned weights relative to a zero-velocity prior distribution. This prior conceptually represents a belief that the head is more likely to be at rest thus preferentially weigh particle estimates that match it. Particles, once weighted, are resampled with a probability proportional to their weight to prevent drifting of particles to improbable estimates over long time periods. Recall that in the Kalman filter optimal observer model, the velocity storage propagation is dictated by the measured sensory noise and its influence on the Kalman gain. In contrast, the velocity storage propagation in Laurens’s particle filter model is dictated by the variability in sensory noise (how much it deviates from zero) and in the zero-motion prior distribution (how much weight we give to those that deviate from zero). As such, larger variance on the zero-motion prior distribution would produce longer velocity storage propagation as particle estimates close to zero velocity are not as heavily preferred. 21 Figure 1-7: Simplified block diagram of Laurens and Droulez’s particle filter for vestibular processing. The Laurens and Droulez (2007) model similarly use an internal model to predict canal afferent activity which is compared against measured primary afferent activity. However, resampling of particles weighted to a zero-velocity prior with variance 𝜎𝛺 = 30 deg·s-1 is performed to obtain the state estimate. A major limitation in these linear system and observer models is their deterministic nature as model predictions are linear and time invariant (the same input will always produce an identical output). Deviations from this assumption are observed by Coniglio and Crane (2014) showing history-dependent perception, thus challenging predictions made by existing velocity storage models. Another issue arises from the definition of optimality as minimizing/maximizing an objective function. In the case of the Kalman filter, the objective function is to minimize the mean-squared error between the estimated and measured state of the system. Similarly, in multi-sensory integration, Bayesian integration is used to maximize the posterior distribution from separate sources of information depending on their uncertainty. However, estimated outcomes may not necessarily follow this definition of statistical optimality (Arnold et al. 2019; Fetsch et al. 2009; Meijer et al. 2019; De Winkel et al. 2018). As such, other potential operating principles within the brain may be present that are considered ‘sub-optimal’ relative to those previously stated. Additionally, sensory internal models assume that the brain has working knowledge of the physical principles of its sensory system and physical stimuli. Although we cannot preclude this notion, this brings into question the physiological practicality of internal models given the diversity of sensory experiences. 22 1.6.2. Peripheral vestibular afferent adaptation This following section shifts our focus away from the adaptation observed as a part of the velocity storage (exposure to constant angular velocity) and towards another adaptation occurring during sustained stimulation (exposure to constant angular acceleration). Recall that the semicircular canal end-organ encodes head rotation through hair-cell deflection. As such, hair-cells are continually deflected by the endolymph during a continuous angular acceleration. Early human experiments involving sustained angular accelerations showed that rotational perception decays over time (Clark and Stewart 1968; Guedry and Lauver 1961) contrary to a constant sensitivity that was predicted from an early torsion-pendulum model (van Egmond et al. 1949a). Neural recordings from primary semicircular canal afferents showed similar adaptation (Fernandez and Goldberg 1971; Rabbitt et al. 2005) with high individual afferent variability from ~1ms to hundreds of seconds suggesting this prolonged adaptation is peripherally mediated (St George et al. 2011). Changes to the torsion-pendulum model were proposed by Young and Oman (1969) and Malcolm and Jones (1970) which both added an integration of the output of the canal-cupula dynamics with an additional adaptation term – either in a feedback or feedforward manner (Figure 1-8). Figure 1-8: Additional long-term adaptation element to early state-space models of vestibular dynamics An additional long-term adaptation element that is integrated with the canal dynamics. Young and Oman (1969) proposed a feedback element, whereas Malcolm and Jones (1970) proposed a 23 feedforward element. Both elements contain a time-constant (𝑻𝒂) dictating the rate of adaptation. Experimental results suggested a wide variety of time constants depending on target behaviour. For perception, 𝑻𝒂 could be 25 to 60 sec (Mattson 1975) whereas longer time constants were observed for ocular responses (Boumans et al. 1983a, 1983b). A consequence of this constant angular acceleration adaptation is further revealed by a history-dependent aftereffect following the sudden removal of the acceleration stimulus to a zero-acceleration (constant angular velocity) rotation without decelerating/stopping. An early report from Clark and Stewart (1968) recounts the occurrence of this aftereffect as a non-veridical perception in the direction opposite of initial acceleration direction. This was observed in several subsequent experiments, but manifesting intermittently (for example: 4/8 in Luster 1972; 10/10 in Mattson 1975). Perceptual adaptation varied around 37s±20s in a perceptual study by Clark & Stewart (1968) and, in addition to the occurrence of history-dependent aftereffect, both can not be predicted by linear, deterministic models as they do not capture the variability observed in the underlying vestibular afferents (Goldberg and Fernandez 1971a). A particle/sampling approach which inherently incorporates afferent variability may better replicate the observed changes in behaviours. 1.7. How can the vestibular system be studied? To understand how vestibular signals are integrated within the brain, experimental manipulations must be performed. Firstly, we can probe the vestibular system by generating physical motion to identify time-varying adaptations to the input either (1) in the velocity storage (to prolonged constant angular velocity) or (2) through afferent adaptation (to prolonged constant angular acceleration). Such stimuli involve motions that are not frequently encountered in daily life but can be achieved using carefully controlled motion platforms to impose whole-body rotation at a fixed body posture (Bertolini et al. 2011; Peters et al. 2015; St George et al. 2011). Aside from physical motion, the vestibular system can also be activated using electrical vestibular stimulation (EVS) which non- 24 invasively activate the vestibular system independent of other sensory cues normally accompanying movement (Fitzpatrick et al. 2002a). As such, EVS can be used to generate novel experimental paradigms for investigating vestibular processing when used in a way that considers their nuances (Dakin et al. 2016; Fitzpatrick et al. 2002a; Héroux et al. 2015; Khosravi-Hashemi et al. 2019b; Mian et al. 2010b; Reynolds and Osler 2012; Tisserand et al. 2018; Toth et al. 2019; Wardman et al. 2003; Welgampola et al. 2013). The following subsections will briefly outline experimental techniques used in this thesis. 1.7.1. Probing the integration of vestibular afferent signals Variability in individual primary vestibular afferent responses to motion input is frequently observed (Goldberg and Fernandez 1971a). In the case of prolonged constant angular acceleration, primary canal afferents exhibit diversity in their adaptation rate corresponding to afferent type (as characterized by background discharge). This variability is incompatible with classical linear systems models (Malcolm and Jones 1970; Young and Oman 1969) and can not provide meaningful intuition about the brain’s processing and function. To investigate how variability in the underlying neural code (e.g., the population of peripheral vestibular afferent) may lead to observable behavioural variability such as perception, we will use a servo-controlled whole-body motion platform to probe the vestibular system. More specifically, we will use a rotary motion platform to produce a constant and continuous angular acceleration stimulus to evaluate the occurrence and time-course of perceptual adaptation and its associated aftereffect. A particle sampling model incorporating vestibular afferent variability will be created to explain the principles underlying the observed behaviour 25 1.7.2. Probing the integration of vestibular end-organ signals The vestibular end-organs are affixed to the head and encode for motion in a directionally selective manner. Depending on a person’s head orientation, a different number or combinations of end-organs can contribute to our motion sense. Cursory observations showed that velocity storage propagation is diminished when the head is in a head forward ear down position (Bertolini et al. 2012). However, these studies did not specifically target the different end-organ contributions to the velocity storage; therefore, how the encoding of vestibular stimuli influence central processing, such as the velocity storage, remains undetermined. For this question, we will once again use a servo-controlled whole-body motion platform to produce a constant angular velocity stimulus. Here, we will compare the rate of perceptual decay in the velocity storage response between different static head orientations meant to change which vestibular end-organ(s) encode the whole-body motion. An expansion of our particle sampling model will be created to account for different end-organ afferent populations and how they are integrated to provide a sense of self-motion. 1.7.3. Evaluating the physiological equivalence between vestibular signals from electrical or mechanical sources The vestibular system may be non-invasively activated using EVS leading to cranio-centric eye movements, balance responses, and virtual motion percepts (Khosravi-Hashemi et al. 2019a; Mackenzie and Reynolds 2018a; Peters et al. 2015; Reynolds and Osler 2012; Schneider et al. 2002; St George et al. 2011; Tisserand et al. 2018; Wardman et al. 2003). In humans, EVS can be delivered by placing electrodes behind the ears and over the mastoid processes. Electrical currents alter the firing rate of canal and otolithic primary afferents (Goldberg et al. 1984b) depending on the poles of the electrodes through anodal (depolarization) or cathodal (hyperpolarization) currents with increased gain at higher frequencies (Kwan et al. 2019). In the well-characterized binaural-bipolar configuration, 26 electrodes of opposing poles are placed over each mastoid causing an opposing bilateral response in the vestibular nerve on either side (Figure 1-9A). Assuming that all primary afferents are activated, a cranio-centric net EVS rotational vector oriented 18 degrees above Reid’s plane arises based on the net cancellation of otolithic components and the summation of unit vectors representing the orientations of the semicircular canals (Fitzpatrick and Day 2004; Mian et al. 2010) (Figure 1-9B). Despite mechanistic differences in vestibular hair cells and/or primary vestibular afferents activation between mechanical and electrical stimulations, the central processing from electrical stimulation is assumed to share common pathways to those underlying mechanically evoked real rotations. Here, we applied known transfer functions of transcutaneous EVS identified in nonhuman primates (Kwan et al. 2019) onto humans to compare its response to those from mechanical whole-body rotations. We compared the rate of perceptual and vestibulo-ocular reflex decay to an angular velocity step-input and to an EVS transfer function equivalent electrical current input. The question becomes whether the generation of our novel EVS stimulus would evoke physiologically equivalent responses as the stimulation by-passes the natural mechanical transduction of the vestibular end-organ. As such, we aimed to match EVS-evoked response to those experienced during natural head motion. 27 Figure 1-9: Electrical vestibular stimulation and its uses. Electrodes applied in a bipolar-binaural configuration. The cathode (+) and anode (-) electrode placements depict a cathodal right current waveform leading to rightward virtual head roll perception. Inversion of polarities leads to a virtual rotation in the opposite direction. (B) Normal unit vectors of the left-horizontal right-horizontal (blue), left anterior right posterior (green), and left posterior right anterior planes (Della Santina et al. 2005). The net electrical vestibular simulation rotational vector (purple-dash) is the vector summation of the three vector components. A small interaural linear head acceleration is also present when the virtual rotation vector has a component orthogonal to gravity (not depicted). EVS can be used to probe vestibular contributions to posture & movement, ocular reflex, and self-motion perception. 1.7.4. Developing a real-time system for vestibular modulation using EVS Building upon the known equivalence between electrical and mechanical vestibular stimulation, we aimed to create a real-time system for vestibular modulation using EVS. Although a previous implementation was realized by Héroux et al. (2015), their method was limited because they only included a motion-to-afferent transfer function (Fernandez and Goldberg, 1971; Goldberg and Fernandez, 1971) which disregarded the dynamics of afferent responses to transmastoid currents. Furthermore, their system was costly and used non-portable instrumentation which limited its use to a laboratory setting. Here, we used affordable equipment alternatives and updated the transfer function that more closely matches physiological activation of the vestibular system to implement a human-in-the-loop vestibular modulation system. We replicated the experimental balance task of Héroux et al. (2015) to evaluate the feasibility of our vestibular modulation system including new hardware and embedded motion-to-current transfer function model. 28 1.8. Objectives & Goals The overall goals of this dissertation were to build upon our understanding of how vestibular sensory code may be integrated within a probabilistic framework and to enhance current methodology for probing vestibular processing. In addition, we also aimed to provide data and models in an open-source manner. Four experiments were conducted to address different aspects of our goals asking the following questions: i. How can primary vestibular afferents encoding motion with differing adaptation dynamics combine to create a unified sense of self-motion? ii. How can varying primary vestibular afferents from distinct vestibular end-organs combine to create a unified sense of self-motion? iii. Can virtual motion induced by the electrical activation of vestibular primary afferents mimic real motion? iv. Can we build a portable device to modulate vestibular feedback by matching primary vestibular afferent physiology using electrical vestibular stimulation? 29 Chapter 2. Foundations underlying the physiological computations of vestibular processing for self-motion 2.1. Preamble As we move about our environment, we detect and perceive our self-motion using available sensory information. One critical sense is the vestibular system. This chapter focuses on providing the reader with a comprehensive understanding of the vestibular system’s morphology and physiology, as a prerequisite for explaining the construction of a computational vestibular model for self-motion in the next chapter. A particular focus will be on sources of neuronal variability, including an orientational model of the peripheral vestibular system, transfer function equations describing vestibular afferent response dynamics, and afferent discharge characteristics. 2.2. Orientational model of vestibular end-organs To model the relative encoding from each vestibular end-organ, we must first consider their preferred directional tuning sensitivity based on their orientations and position within the head. This allows us to evaluate how vestibular encoding changes as a function of head orientation. The following subsections will detail the orientations for the semicircular canal and otolith end-organs. 2.2.1. Semicircular canal orientations Canal hair cells are deflected by the movement of endolymph fluid during rotations. Because these rotations occur along the semicircular canal plane, this makes the directional tuning sensitivity of canal hair cells normal (perpendicular) to the plane itself. We used previously reported human data from Della Santina et al. (2005) to describe the relative orientation of each semicircular canal. Advantageously, Della Santina et al. (2005) reported the normal unit vectors for each of the six (left- 30 horizontal, anterior, and posterior; and right- horizonal, anterior, and posterior) canals. These vectors describe the average directional tuning sensitivity estimated from each canal plane’s measured orientation using computerized tomography scans with respect to Reid’s plane. Reid’s plane is defined as the plane intersecting the inferior orbital rim and external auditory meatus. Normal unit vector coefficients and their 3D orientations with respect to Reid’s plane are respectively summarized in Table 2 and Figure 2-1. Table 2: Mean left and right canal plane unit normal vector coefficients LA LH LP RA RH RP X -0.58954 -0.31645 -0.69611 -0.58905 -0.32891 -0.69248 Y 0.78750 -0.04108 -0.66820 -0.78928 0.03566 0.66561 Z -0.17971 0.94772 -0.26257 -0.17334 0.94369 -0.27826 Adapted from Della Santina et al. (2005). Each column lists the mean X, Y, Z coefficients of the unit length vectors normal to each semicircular canal with respect to a head orientation that has Reid’s plane parallel with Earth horizontal. The X, Y, and Z coordinate system axes correspond to the anteroposterior, mediolateral, and superoinferior axes, respectively (+X anterior, +Y leftward, and +Z superior). L =left, R = right; A, H, P = anterior, horizontal, and posterior semicircular canals, respectively. 31 Figure 2-1: 3D orientation of the left and right canal plane unit vector coefficients. Adapted from Della Santina et al. (2005). (A) Colored lines represent the unit vectors normal to the six semicircular canal planes defined in Table 2 with respect to a head orientation with Reid’s plane parallel to Earth-horizontal (grey-shaded plane). These unit vectors (LA = Blue solid line, LP = Red solid line, LH = Green solid line, RA = Blue dash line, RP = Red dash line, RH = Green dash line) denote the directional tuning sensitivity of each canal with respect to the head’s orientation (top right on each plot). (B) Changes to head-orientation can alter canal encoding with respect to experienced whole-body motion. For example, an Earth-vertical whole-body rotation at a head upright orientation (leading to head-yaw rotation; top panel) can be encoded by predominately the horizontal canals (green arrows) when pitched chin-down as it aligns the directional tuning sensitivity of the LH and RH canals. When the head is pitched further down, this head orientation (leading to head-yaw roll; bottom panel) would align the vertical- anterior and posterior canals (red and blue arrows) and minimize horizontal 32 contribution. The X, Y, and Z coordinate system axes corresponds to the anteroposterior, mediolateral, and superoinferior axes, respectively (+X anterior, +Y leftward, and +Z superior). L = left, R = right; A, H, P = anterior, horizontal, and posterior semicircular canals, respectively. These coefficients describe the near orthogonality of the three ipsilateral canals (see unit vector lines for LH, LA, LP and RH, RA, RP in Figure 2-1). Due to the near symmetry between the left and right vestibular sensory organs, contralateral canals sharing a parallel, co-planar, plane would approximately encode the same magnitude but of opposite sign due to opposing polarization in each respective hair cell bundles. In technical terms, each ipsilateral canal set defines a reference frame therefore creating two [3x3] rotation matrices. Mechanical rotation experienced by the head in space is defined by a [3x1] rotation vector where the first, second, and third elements correspondingly define head rotation in the X, Y, and Z coordinates. Following right-hand rule convention, the head in space rotation coordinate system is defined as: X positive forward, Y positive leftward, and Z positive upward. By post-multiplying a canal rotation matrix by the rotation vector, the resultant vector would be decomposed with respect to the three canals ‘axes’ hence obtaining its relative encoding contribution. When we apply a simulated head orientation change to this known canal reference frame, we are in turn changing the canals’ orientation in space as well. As such, we can simulate changes in contributing canals encoding for a given head orientation (Figure 2-1B). 2.2.2. Otolith orientations Compared to the canals, accounting for the orientation of the saccule and utricle is more challenging as they exhibit a more complex three-dimensional morphology (Dimiccoli et al. 2013). Otolithic hair-cell bundles are dispersed in a fan-like manner along a curved surface. The directional tuning sensitivity of different hair cells are also divided into two regions separated by the striola, a 33 dividing ridge of the otolithic membrane. Hair cells on each side of the striola have opposing directional tuning sensitivities. Both Tribukait and Rosenhall (2001) and Mian et al. (2010), simplified the otolith macula as a 2D plane and estimated net directional tuning sensitivity from morphological data (using data from Tribukait et al. 2005 for Mian's analysis) in the utricle and saccule, respectively. They divided each macula surface into sectors (8 for utricle, 14 for saccule) distributed evenly between the two sides of the maculae’ striola (pars lateralis and pars medialis for the utricle, pars superior and pars inferior for the saccule). Polarization vector direction within each sector is assumed to be approximately perpendicular to the striola (Lindeman 1969; Rosenhall 1972a), and the magnitude of this vector was normalized by the area of their corresponding sector over the total macula area assuming equally distributed hair cells (Lindeman 1969; Rosenhall 1972b). Net polarization vectors were summated among the sectors within each side of the striola thereby providing a directional estimate of maximal tuning sensitivity for each ‘pars’ region. 34 Figure 2-2: Estimated Saccule and Utricle maximal tuning vector and orientation. Adapted from Mian et al. (2010) & Tribukait and Rosenhall (2001). (A) Representative example of a human saccular macula divided into 14 sectors along the S-shaped striola (left) among the pars superior (purple) and pars interior (orange). Each sector’s tuning vector direction were drawn perpendicular to the striola with its magnitude equal to the sector area divided by the total macular area. With respect to a head orientation aligning Reid’s plane to Earth-horizontal, the pars superior and pars inferior show superior-posterior and inferior-anterior preferences, respectively (right). (B) Representative example of a human utricular macula divided into 8 sectors along the striola (left) among the pars medialis (red) and pars lateralis (blue). Each sector’s tuning vector and magnitude were estimated using the same procedure as the saccule. With respect to a head orientation aligning Reid’s plane to Earth-horizontal, the pars medialis and pars lateralis show anterior-medial and posterior-lateral preferences, respectively (right). (C) The saccules are oriented parallel to the sagittal plane whereas the utricles are oriented pitched up 30o from horizontal and laterally tilted down outwards by 10o. Distance between the otoliths is assumed to be 7.22cm based on inter-utricular distance from Nowé et al. (2003). In relation to the head, the orientation of the saccule plane is assumed to approximately align with the sagittal anatomical plane (Naganuma et al. 2001; Takagi and Sando 1988). The utricle plane 35 conversely is assumed to be approximately align with the transverse anatomical plane. Further, the utricle plane is oriented pitched up 30o from horizontal and laterally tilted down outwards by 10o with respect to Reid’s plane (Naganuma et al. 2003; Takagi and Sando 1988). A set of two saccular-utricular otoliths were modeled for the left and right sides and were assumed to have a radius of 3.61cm from the center of the head based on an inter-utricular distance of 7.22cm (Nowé et al. 2003). This was chosen as the closest measure because of a lack of human data. 2.3. Sensory dynamics of vestibular afferent coding In addition to describing the orientations of the vestibular end-organ, we must evaluate the afferent response of each end-organ type (canal/otolith) to head motion inputs. Transfer functions describe the linear dynamic relationship between input and output responses (e.g., angular velocity to canal afferent firing rate). The following subsections will detail the transfer functions used in our model for the semicircular canals and otoliths afferents. 2.3.1. Dynamics of semicircular canal afferents The response dynamics of primary vestibular afferents innervating the semicircular canal resembles a high-pass filter (Fernandez and Goldberg 1971) with a progressive increase in sensitivity at higher frequencies (Hullar et al. 2005; Ramachandran and Lisberger 2006; Sadeghi et al. 2007a) (Figure 2-3). Classically, the simplest transfer function representation of canal dynamics is a first-order high-pass filter (Eq: 2-1) with a time-constant (𝑇𝑐) between 4 to 6 sec. based on non-human primate afferent responses (Fernandez and Goldberg 1971). However, this equation maintains a unity sensitivity above 2 Hz which does not capture afferent responses at higher frequencies observed in more recent linear system analyses (Kwan et al. 2019; Ramachandran and Lisberger 2006). 36 𝐻𝑐(𝑠) =𝑇𝑐𝑠𝑇𝑐𝑠 + 1 Eq: 2-1 Schneider et al. (2015) fitted a higher-order transfer function to available experimental data (Ramachandran and Lisberger 2006; Sadeghi et al. 2007a) for both regular and irregular primary vestibular canal afferents (regular: Eq: 2-2 & irregular: Eq: 2-3). 𝐻𝐶𝑎𝑛𝑅𝑒𝑔(𝑠) = 2.83𝑠 (𝑠 +10.0175)(𝑠 +15.7) (𝑠 +10.0027) Eq: 2-2 𝐻𝐶𝑎𝑛𝐼𝑟𝑒𝑔(𝑠) = 27.09𝑠 (𝑠 +10.03)(𝑠 +15.7) (𝑠 +10.0006) Eq: 2-3 Further, an additional ‘long-term’ adaptation time constant (𝑇𝐴) may be added to represent a longer afferent adaptation lasting upwards from 40 seconds observed during constant rotational acceleration stimulation (Goldberg and Fernandez 1971a). This can be modeled equivalently as a negative feedforward (Malcolm and Jones 1970, Eq: 2-4) or a negative feedback term (Young and Oman 1969, Eq: 2-5). 𝐻𝐴(𝑠) =𝑇𝐴𝑠𝑇𝐴𝑠 + 1 Eq: 2-4 𝐻𝐴(𝑠) =1𝑇𝐴𝑠 Eq: 2-5 37 Figure 2-3: Bode plot comparison in transfer function frequency response for primary canal afferents. Transfer functions can be used to simulate canal afferent frequency response (gain, left / phase, right) to motion (in deg s-1). A first-order high-pass filter with a time constant (τC) of 5.7s can approximate low frequency dynamics less than 2Hz (blue) but underestimates higher frequency response. Parameters estimated from Schneider et al. (2015) more accurately capture afferent high-pass tuning behaviour (increasing gain with increasing frequency) above 2Hz for both regular (red) and irregular (orange) afferents to match physiological data in Ramachandran and Lisberger (2006) & Sadeghi et al. (2007a). Note the similar phase between the first-order (blue) and Schneider’s fitted response (red, orange) below 0.1Hz. An additional adaption term with a time constant (τA) of 40s can be used to model prolonged constant stimulation adaptation observed primarily in irregular afferents (green). This additional adaptation term captures the observed change in irregular afferents firing rate towards baseline during constant angular acceleration stimulation (Goldberg and Fernandez 1971a). 2.3.2. Dynamics of otolith afferents The response dynamics of primary vestibular afferents innervating the otoliths act relatively in phase to linear head acceleration at lower frequencies (Angelaki and Dickman 2000; Fernandez and Goldberg 1976a) (Figure 2-4). However, above 10Hz, similar high-pass tuning behaviours emerge (Jamali et al. 2013; Laurens et al. 2017), particularly for irregular afferents. Previously, authors (Borah et al. 1988; Merfeld et al. 1993; Selva and Oman 2012) modeled the otolith afferent dynamics as a low- 38 pass filter (Eq: 2-6) with a short time constant (𝑇𝑜𝑡𝑜 = 0.03-0.2), capturing the in-phase response to linear acceleration, at least for frequencies below 2 Hz. 𝐻𝑜𝑡𝑜 = 1001𝑇𝑜𝑡𝑜𝑠 + 1 Eq: 2-6 Akin to the canals, Schneider et al. (2015) fitted a fractional transfer function from Angelaki and Dickman (2000) to available experimental data in both regular and irregular primary otolith afferents from Jamali et al. (2013) (regular: Eq: 2-7 & irregular: Eq: 2-8Eq: 2-8). 𝐻𝑂𝑡𝑜𝑅𝑒𝑔(𝑠) = 0.82(𝑠0.15(1 + 0.027𝑠)1.43)(1 + 0.07𝑠) Eq: 2-7 𝐻𝑂𝑡𝑜𝐼𝑟𝑒𝑔(𝑠) = 0.70(𝑠0.27(1 + 0.0001𝑠)1.12)(1 + 0.011𝑠) Eq: 2-8 Figure 2-4: Bode plot comparison in transfer function frequency response for primary otolith afferents. Transfer functions can be used to simulate otolith afferent frequency response (gain, left / phase, right) to head motion (in G). A first-order low-pass filter with a time constant (τOTO) of 0.03s can approximate 39 low frequency dynamics (below 5Hz, blue) but underestimates higher frequency responses. Parameters estimated by Schneider et al. (2015) more accurately capture afferent high-pass tuning behaviour (increasing gain with increasing frequency) from physiological data in Angelaki and Dickman (2000) across the frequency range for both regular (red) and irregular (orange) afferents. 2.3.3. Dynamics of semicircular canal and otolith afferents to electrical stimulation Independent of head motion, the vestibular system may also be activated using electrical current applied percutaneously over the mastoid processes, termed electrical vestibular stimulation (EVS). EVS can be used to evaluate vestibular function or to manipulate the vestibular contributions to movement by decoupling the sensory consequence of movement from one’s action (e.g., amplify/attenuate vestibular feedback). A critical step to alter the vestibular consequences of head motion requires delivering electrical currents eliciting similar primary vestibular afferent dynamic responses to those from real motion. Recently, Kwan et al. (2019) measured the primary vestibular afferent dynamical responses evoked by bipolar-binaural EVS through transcutaneous electrical current (the method used in humans) in non-human primates. Even though primary otolith afferent responses were also reported, they are not considered here because it is assumed that otolith activation is cancelled during bipolar-binaural stimulation and does not (or minimally) contributes to the sense of virtual head motion evoked by EVS (Fitzpatrick and Day 2004; Mian et al. 2010b). Canal afferent responses to EVS, like physical stimulation, exhibited a monotonic increase in gain and phase as a function of frequency (Figure 2-5). Fitting their experimental data, Kwan et al. (2019) reported two transfer functions: one for regular (Eq: 2-9) and irregular (Eq: 2-10) canal afferents. Equivalent primary canal afferent responses could be achieved by carefully matching known dynamics to physical and electrical stimuli in Eq: 2-2/Eq: 2-3 and Eq: 2-9/Eq: 2-10, respectively. In turn, by developing this equivalency, we can use EVS to apply a more physiologically-consistent (at least in primary afferent response) vestibular input. This, for example, may potentially allow users to deliver EVS with clear 40 predictions regarding its mechanical equivalent as a methodological substitute to head motion stimuli in functional or clinical vestibular evaluations. Equally, we may also employ this method for real-time vestibular modulation of sensory afference which effectively allows users to amplify or attenuate the gain of primary afferent activity with respect to the net-evoked EVS rotation axis during certain head movements. 𝐻𝐸𝑣𝑠𝑅𝑒𝑔(𝑠) =98(𝑠 + 26)(𝑠 + 188)(𝑠 + 47)(𝑠 + 2578) Eq: 2-9 𝐻𝐸𝑣𝑠𝐼𝑟𝑒𝑔(𝑠) =418(𝑠 + 12)(𝑠 + 136)(𝑠 + 18)(𝑠 + 2739) Eq: 2-10 Figure 2-5: Bode plot transfer function for primary canal afferents to transcutaneous electrical current. Transfer functions can be used to simulate canal afferent frequency response (gain, left / phase, right) to transcutaneous electrical current (milliamperes, mA). Parameters estimated by Kwan et al. (2019) capture an initial flat gain (up to 1Hz) and phase (up to 0.1Hz) followed by a monotonic increase as a function of frequency for both regular (red) and irregular (blue) afferents. 41 2.3.4. Neuronal variability in vestibular afferent encoding Large variability exists in responses from different primary vestibular afferents to identical mechanical stimuli (Angelaki and Dickman 2000; Fernandez and Goldberg 1971, 1976a; Goldberg and Fernandez 1971a; Jamali et al. 2013; Sadeghi et al. 2007a). Fitted transfer functions described earlier in subsections 2.3.1 & 2.3.2 represent the averaged dynamical response of each vestibular afferent class obtained using frequency analyses. As such, directly applying a specific transfer function does not accurately simulate the distribution of afferent responses experienced by the brain. A solution would be to add sensory noise to the simulated signal (Karmali 2019; Karmali and Merfeld 2012; Laurens and Angelaki 2017; Merfeld et al. 1993; Zupan et al. 2002). However, this remains a singular ‘afferent’ signal and not representative of a distributed population of afferent signals integrated in a parallel manner observed in the nervous system (Paulin 2005; Paulin and Hoffman 2011). To simulate neuronal variability in our model, we performed a fitting procedure to generate a distributed set of transfer functions describing primary vestibular afferent responses seeded from the variability in dynamical responses observed in primary afferents innervating the otoliths (Jamali et al. 2013) and semicircular canals (Kwan et al. 2019). Pixel analyses were performed on illustrated bode plots to extract neuronal response (gain & phase) variability reported using standard error of the mean. Extracted experimental data were normally distributed across measured frequencies using the normarnd function in MATLAB (ver. 2020A) matching the reported sample size. This distributed dataset was used to fit new transfer function parameters to represent the variability in afferent responses to head motion. We used the transfer function forms and initial parameters reported by Schneider et al. (2015) as initial fitting parameters. Lower and upper fitting parameter limits were set manually. Fitting was performed with MATLAB (ver. 2020A) using the lsqnonlin function. This function solved for a set of transfer function parameters based on a custom error minimization function using 42 non-linear least squares. An additional two- and five-times weighting was respectively applied to the minimization error in gain and phase across the low frequencies (< 5Hz). Effectively, this biases the fitting to better match lower frequency response of the afferents than their higher frequency behaviour. Consequently, we solved for four (irregular/regular otolith & canal afferents) groups of transfer functions parameters (350 sets of parameters per end-organ/afferent type combination) (Figure 2-6). Figure 2-6: Bode plot of fitted transfer functions for primary canal afferents. Transfer function parameters were estimated in the form proposed for the semicircular canal (Eq: 2-2/Eq: 2-3) and the otolith (Eq: 2-7/Eq: 2-8). Parameters were fitted based on measured canal and otolith frequency response dynamics (gain and phase) from Kwan et al. (2019) [Left] and Jamali et al. (2013) [Right], respectively. 350 sets of parameters (per end-organ and respective afferent type) were estimated. The distributions of these fitted parameters are plotted (lines) with respect to published experimental data (dots) for irregular (yellow) and regular (red) afferents. Note that irregular afferents show a relatively greater increase in gain and phase compared to regular counterparts. 2.3.5. Variability in afferent background discharge We also accounted for variability in primary vestibular afferent background activity between individual afferents. Here, this variance represents the discharge regularity in regular and irregular units and can be expressed using the normalized coefficient of variation (CV*) values (Goldberg et al. 43 1984a). We use CV* as an additional noise value applied to a primary afferent firing rate response to capture individual variability. In neurophysiological studies, CV* is calculated from the mean (μISI) and standard deviation (σISI) of a sequence of recorded interspike intervals (ISI) normalized to a selected standardized mean interval (15 ms in Goldberg et al. 1984a). This procedure is commonly used to experimentally classifying regular and irregular afferents (Cherif et al. 2008; Goldberg et al. 1984a; Kwan et al. 2019; Sadeghi et al. 2007a). We used reported CV* values for semicircular canals [irregular = 0.35, regular = 0.06] from Kwan et al. (2019) and otoliths [irregular = 0.29, regular = 0.04] from Jamali et al. (2013). Our choice of CV* influences afferent detection threshold/signal-to-noise property. In other words, a lower CV* leads to less noise and improves detection threshold. As such, we wanted to evaluate how CV* affects our fitted sets of afferent transfer function parameters – how well can our simulated afferent distinguish a signal from background noise. We simulated afferent firing rate for each transfer function parameter given its corresponding CV*. In this procedure, we closely matched previously reported experimental conditions (otoliths: Jamali et al. 2013; semicircular canals: Sadeghi et al. 2007a) to simulate instantaneous firing rate from a sinusoidal input. The sinusoid waveform was 0.5Hz lasting for 100 cycles with an amplitude of ±45deg/s or ±0.15G for the canal and otolith afferents, respectively. Four series of evaluations, one per end organ and regular/irregular afferent types, were performed using transfer function parameter estimated previously in subsection 2.3.4. Within an evaluation, the estimated regular or irregular transfer function parameters were applied as equation parameters into their corresponding transfer function equation (Eq: 2-2/Eq: 2-3 or Eq: 2-7/Eq: 2-8). We simulated firing rate based on our sinusoidal input using lsim in MATLAB. The phase difference between the simulated firing rate and input mechanical head motion was calculated to shift the input in phase to obtain the output instantaneous firing rate to input (head angular velocity/linear 44 acceleration) curve. We skipped the first 5 cycles to remove starting simulation inaccuracies and extracted the last 95 cycles. To evaluate the detection/sensitivity thresholds, we first computed the mean and variance of the firing rate distribution for each discrete sample in a cycle. We then evaluated the degree of overlap between the firing rate distribution obtained for each change in input amplitude with respect to zero amplitude rest. This overlap was quantified using a signal detection measure called d’ (d-prime) (Green and Swets 1966; Figure 2-7). The d’ equation (Eq: 2-11), calculates the mean μ(𝐼) and variance σ2(𝐼) of the stimulated firing rate distribution at each head input amplitude (𝐼). 𝑑′(𝐼) =|𝜇(𝐼) − 𝜇(0)|√(𝜎2(𝐼) + 𝜎2(0))/2 Eq: 2-11 μ(0) and σ2(0) correspond to the mean and variance of the firing rate distribution at rest, (i.e., zero amplitude head input). Given that d’ increases linearly from 0 in both positive and negative input values, an absolute function 𝑑′(𝑥) = 𝐴 ∗ |𝑥| was fitted to estimate d’ values for a given input head motion amplitude. The lower the d’ value for a given head input amplitude means it is more difficult to distinguish that amplitude from background noise. A head motion input value corresponding to a d’ value of 1 was estimated using the fitted equation. ‘1’ was chosen as it represents the amplitude one standard deviation away from resting noise. Simulated detection thresholds for the semicircular canals were 4.8±1.0deg/s (irregular) and 2.4±0.3deg/s (regular). These values are consistent with the 50% larger threshold difference observed between afferent types (8.0deg/s vs. 4.0deg/s) by Sadeghi et al. (2007a). Conversely, the simulated otolith detection thresholds were 10.6±10.0 cm/s2 (irregular) and 12.6±10.1cm/s2 (regular) which followed a similar order of magnitude and within the variability to those observed by Yu et al. (2012) at 7.5 and 3.0cm/s2, respectively. 45 Figure 2-7: Detection threshold simulation procedures. Otolith and semicircular canal afferent responses were simulated given a linear acceleration (±0.2G) and angular velocity (±45deg s-1) sinusoidal (0.5Hz, 100 cycles) input, respectively. Irregular (blue) and regular (red) afferent responses were simulated for each fitted transfer functions parameters (n = 250) obtained based on experimental data from Jamali et al. (2013) and Kwan et al. (2019). Sensory noise was added to the afferent responses based on reported normalized coefficient of variance (canal: irregular: 0.35, regular: 0.04). Afferent firing rate plotted as a function of stimulus amplitude. Note that the irregular afferents show a wider variance for a given amplitude and larger firing rate range in response to mechanical stimuli. Signal detection theory was used to compare distribution of firing rates for a given stimulus amplitude to the distribution for a zero-stimulus amplitude (Gaussian curves) following the d’ equation (see Eq: 2-11). We calculated the d’ value at each discretized amplitude relative to zero and plotted it as a function of stimulus amplitude. The detection threshold was defined as the lowest absolute value of stimulus amplitude (head linear or angular acceleration) for which d’=1. 2.4. Summary In this chapter, we summarised several physiological factors when considering how the vestibular system encodes head motion. The orientation and position of the semicircular canal and otolith end-organs must be defined to estimate which afferent populations are encoding for a given 46 head motion. Furthermore, the response of these vestibular afferents to head motion or electrical current inputs are frequency dependent (e.g., high-pass tuning) and small variations in gain/phase exist between individual afferents. Transfer functions are used to mathematically describe their response dynamics by matching experimental non-human primate data, but they are often used to describe the average behaviour. We fitted four sets of transfer function parameters (one for each end-organ and afferent type) to capture this source of variability. Likewise, individual afferents also vary in their background discharge rate (categorized using CV*) which influences their ability to encode motion. We used experimental values of CV* as a noise parameter between afferent types. Altogether, these factors characterize the neural code the brain must resolves in its inference to drive perception and behaviour. 47 Chapter 3. Building a distributed particle sampling model for vestibular self-motion 3.1. Preamble Within the past decades, a prevailing view emerged about the brain’s processing as an inference system (Ernst and Banks 2002; Fetsch et al. 2009; Friston et al. 2016; Laurens and Angelaki 2011; MacNeilage et al. 2008), the so-called “Bayesian-brain”. The nuances about how our brain infers, from inherently noisy sensory signals, attributes like self-motion or spatial orientation remains an open question. Observing behavioural responses from experimental stimuli can reveal patterns that hint at the brain’s processes; however, we must also build a testable framework to contextualize how (and why) these processes come about. Computational modeling, as neural analogues, allows us to interrogate the brain operating principles by constructing quantitative hypotheses. We touched upon previous computational approaches in Section 1.6 from classical control theory, observer error-monitoring, and statistically optimal inferences. Here, this chapter will detail the computational approach used in this thesis. 3.2. Importance of computational modeling Developing computational algorithms to predict behavioural outcomes can lead to unique insight on how the brain potentially operates. Previous vestibular frameworks modeling time-varying dynamical behaviours were successful in replicating responses like the velocity storage – observed through the propagation of perceived self-motion longer than what is biomechanically expected following an angular velocity step change (Borah et al. 1988; Karmali and Merfeld 2012; Laurens and Droulez 2007; Merfeld et al. 1993). These frameworks commonly employ a predictive internal model of sensory dynamics in estimating self-motion/spatial orientation using observer theory (Oman 1982) 48 and linear optimal state estimation algorithms (Kalman 1960) wherein velocity storage propagation is influenced by a calculated observer gain parameter. For instance, Borah et al. (1988), using explicit covariance matrices, analytically solved for a statistically optimal observer gain based on sensory noise suggesting how noise may influence the velocity storage phenomenon. This optimal observer gain was similarly solved by Karmali and Merfeld (2012); however, these authors used a distributed set of samples (termed particles) forming a probability distribution that has its variance determined by sensory noise to approximate the covariance. Such particle-based approach may be applied in other computational frameworks. For example, Laurens and Droulez (2007) implemented a dynamical Bayesian optimal inference algorithm where particles encoding for motion are weighted according to how close to zero-motion they are – giving particles closer to zero more weight when averaged. This zero-motion weighting implicates the notion that the brain may rely on some sort of a priori expectation about the world. Thus, in their framework, the degree of velocity storage propagation is dependent not just on the variability of the particles (noise) but also how these particles conform to the brain’s expectation. Both particle models of vestibular processing (Karmali and Merfeld 2012; Laurens and Droulez 2007) provide similar (role of noise) yet distinct (role of expectation) insights despite implementational differences. These models critically assume strict statistical optimality which is not always the case (Acerbi et al. 2014). In the broadest sense, a model’s definition of optimality may or may not match what is optimized by biological organisms. Furthermore, it is typically assumed that the brain has explicit knowledge of the world’s physics to compute dynamics when using internal models but the implications of this requisite knowledge (and associated complexity) have been questioned (Yin 2020, 2017). As a part of this thesis, we propose an alternative dynamical vestibular inference model using distributed and physiologically-plausible signals without assuming statistical optimality (such as 49 estimations based on minimal variance in a Kalman filter) or explicit internal sensory models. Our vestibular model realizes a distributed representation using samples/particles to structure both sensory and central neural populations. These particles physiologically approximate the information encoded by a single neuron within a coding population (Paulin and Hoffman 2011). The subsequent sections will detail our modeling framework from how we distribute, simulate, and sample particles for inference. 3.3. Step 1: Distributing sensory and state particle distributions A defining feature of our model is how we represent neural activity as discrete observations (termed particles) analogous to an assortment of individual neurons. Because of neuronal variability, particles encoding the same state will produce similar, but not identical responses, mimicking neuron encoding within the brain. These particles together produce the population distribution for the encoded state unconstrained to a Gaussian distribution seen in previous analytical solutions (Borah et al. 1988; Merfeld et al. 1993). All particles within our model are divided into either sensory or internal states upon initialization depending on four factors. These are: (A) the total number of particles, (B) the ratio of sensory-to-internal states, (C) the proportion of primary vestibular afferents in each vestibular end-organ, and (D) the ratio of regular-to-irregular afferent types. An increase in the total number of particles will allow for a finer approximation of particle distributions at the cost of computational time. The latter three factors determine how many particles are allocated into which group from the available pool. As such, a greater ratio to one side would allocate more particles and consequently increase the chance of particles from that group being picked during the sampling process. Factors A and B are adjustable-parameters and have been set arbitrarily to 1000 particles with a ratio of 7-to-3. 50 Factor C was determined by quantitative analyses of primary vestibular nerve fibers in humans (Bergström 1973a; Lopez et al. 2005). Lastly, Factor D was taken from quantitative analysis of primary vestibular afferent unit types in chinchilla (Baird et al. 1988). These ratios are summarized in Figure 3-1. The allocation of particles was as follows. We first calculated the number of sensory afferent particles (NSensory = 300) by multiplying the predetermined number of total particles (NTotal = 1000) by the sensory proportion (30%) defined by the free parameter sensory-to-internal state ratio. This calculated NSensory value is then multiplied by the canal proportion (40%) and otolith proportion (60%) to respectively obtain the canal (NCanal = 120) and otolith (NOtolith = 180) particle counts. This was defined by the averaged fiber numbers identified by Lopez et al. (2005) for canals (anterior canal-1562, posterior canal-1652 & horizontal canal-1558) relative to otoliths (utricle-3369 & saccule-3100 1 ). Subsequently, NCanal was divided by 3 (assuming equal proportion) for each co-planar canal pairs (LHRH, LARP, RALP) to obtain their respective particle counts (NLHRH = 40, NLARP = 40, and NRALP = 40). Similarly, NOtolith was divided by 2 to obtain the utricle (NUtricle = 90) and saccule (NSaccule = 90) afferent (bilateral) pair particle counts. For each of the derived particle count in the three canal pairs and two otolith pairs, they were each multiplied by the proportion of regular (25%) and irregular (75%) afferent types identified by Baird et al. (1988). For the 40 particles in each canal-pair subset, 30 (NReg) and 10 (NIrreg) were classified as regular and irregular, respectively. For the 90 otolith particle pair subset, 67.5 (NReg) and 22.5 (NIrreg) were respectively classified as irregular and regular. Non-integer counts were rounded to eliminate fractional particle counts. Ultimately, the irregular and regular particles from each subgroup were summated to get the final working number of sensory particles which was 1 Saccule number calculated from ratio of utricle to saccule in Bergström (1973b). 51 subtracted from NTotal to derive the final internal state particle count [NState = 1000 – (91 + 91 + 40 + 40 +40) = 698]. Figure 3-1: Allocation of particles in our model. Our sampling model initialize a predetermined number of total particles (NTotal). Four partitions are applied to allocate each particle in the total pool. The first partition classifies particles as either sensory (NSensory) or internal state (NState) according to the ratio of sensory-to-internal states (3:7). Sensory particles are subdivided into either otolith (NOtolith) or canal (NCanal), and with each category is subdivided into their respective end-organ components (NUtricle, NSaccule, NLHRH, NLARP, NRALP) based on physiological data (Bergström 1973b; Lopez et al. 2005). Lastly, particles for each end-organ are classified as regular (NReg.X) or irregular (NIreg.X) based on the ratio of regular-to-irregular afferent types. We assumed a ratio of 3:1 regular-to-irregular based on data by Baird et al. (1988). 52 3.4. Step 2: Initializing sensory and internal state particles For a given head angular velocity (𝜔𝐻𝑒𝑎𝑑) motion input (in rad s-1) in 3D space, the relative motion encoded by each of the six semicircular canals is determined based their morphology and position with respect to the head’s current orientation (see subsection 2.2.1). This decomposes the initial 𝜔𝐻𝑒𝑎𝑑 into six separate angular velocity signals with respect to each semicircular canal (𝜔𝐿𝐻 𝜔𝑅𝐻 , 𝜔𝐿𝐴, 𝜔𝑅𝐴, 𝜔𝐿𝑃, 𝜔𝑅𝑃). These angular velocity signals are simulated as canal firing rates after each signal goes through two canal transfer functions (one for regular and irregular) with coefficients drawn uniformly at random from our two sets of fitted parameters (see subsection 2.3.4). Uniform distribution was chosen because the probability of sampling a specific set of parameters was already predetermined during the fitting procedure (i.e., there are more transfer function coefficient sets closer to the average fitted behaviour). This process was repeated using the same input signal to generate many afferent responses based on the allocated particle number for the canal in question. In the end, we generated six sensory canal particle distributions (𝐿𝐻𝑑𝑖𝑠𝑡, 𝑅𝐻𝑑𝑖𝑠𝑡 , 𝐿𝐴𝑑𝑖𝑠𝑡, 𝑅𝑃𝑑𝑖𝑠𝑡 , 𝑅𝐴𝑑𝑖𝑠𝑡 , 𝐿𝑃𝑑𝑖𝑠𝑡). Note the subscript dist in this and subsequent usages signifies a particle distribution. Generally, ~75% and ~25% of particles in each sensory distribution are respectively classified (and simulated) as regular and irregular afferents. Noise representing variability in individual background afferent discharge was next added to each particle. Background discharge noise variance for regular and irregular canal afferents were based on normalized coefficient of variation (CV*) values (see subsection 2.3.5). Individual noise value for each particle was drawn from a zero-mean Gaussian distribution given regular or irregular variance. 53 Figure 3-2: Head angular velocity to canal component. (A) Example head orientation with all canals encoding motion. The grey vector illustrates the head angular velocity (𝜔𝐻𝑒𝑎𝑑) vector experienced. 𝜔𝐻𝑒𝑎𝑑 was decomposed into six semicircular canal vector components for left horizonal (green solid line), left anterior (blue solid), and left posterior (red solid), right horizontal (green dashed line), right posterior (blue dashed), and right anterior (red dashed). (B) Time-series representation of 𝜔𝐻𝑒𝑎𝑑 decomposed into canal vector components: 𝜔𝐿𝐻 𝜔𝑅𝐻, 𝜔𝐿𝐴, 𝜔𝑅𝐴, 𝜔𝐿𝑃, & 𝜔𝑅𝑃. A series of canal angular velocity-to-afferent firing rate simulation was performed for each canal-component angular velocity. For example, 𝜔𝐿𝑃 (red line) was simulated through a canal transfer function [HCanal(s)]. The canal transfer function takes the form in Eq: 2-2/Eq: 2-3, but coefficients were selected at random with uniform probability (from 1 to ‘N’ numbers of parameter sets) within a pre-defined pool (see subsection 2.3.4). We used a uniform distribution because variability is already present within the pool; there are more coefficients closer to the fitted average. Different simulated afferent responses were generated due to sampling of coefficients. Each simulated response had noise added to obtain the final afferent response. Noise was drawn from a zero-mean Gaussian distribution with variance (𝜎2) defined by afferent background discharge experimentally reported normalized coefficient of variation. This simulation step was completed K-th times defined by the number of particles for the given class of afferent simulated (canal vs. otolith). The same procedure was performed for the otolith signal using tangential acceleration input. All simulated afferent responses together make up its respective sensory particle distribution 𝐿𝑃𝑑𝑖𝑠𝑡 The head also experiences linear acceleration tangential to the direction of circular motion during angular accelerations. This head tangential linear acceleration (𝑎𝐻𝑒𝑎𝑑 ) was calculated (in G) based on head angular acceleration (𝛼𝐻𝑒𝑎𝑑) from 𝜔𝐻𝑒𝑎𝑑 using Eq: 3-1, 54 𝑎𝐻𝑒𝑎𝑑(𝑡) =𝑟 ∗ 𝛼𝐻𝑒𝑎𝑑(𝑡)𝑔, 𝛼𝐻𝑒𝑎𝑑(𝑡) =𝑑𝜔𝐻𝑒𝑎𝑑𝑑𝑡 Eq: 3-1 where 𝑟 is the radius (~0.0361 meter) between the otolith and the axis of rotation and g is the gravitational acceleration constant (9.81 m sec-2) used to convert units from m s-2 into G. The radius distance was assumed from the human interutricular distance (Nowé et al. 2003). Similar to the canals, 𝑎𝐻𝑒𝑎𝑑 was transformed and re-referenced to each otoliths’ pars macula region (utricle left/right pars medialis & pars lateralis: 𝐴𝐿𝑃𝑀, 𝐴𝐿𝑃𝐿 / right utricle: 𝐴𝑅𝑃𝑀 , 𝐴𝑅𝑃𝐿; saccule left/right pars superior & pars inferior: left saccule: 𝐴𝐿𝑃𝑆 , 𝐴𝐿𝑃𝐼 , / right saccule: 𝐴𝑅𝑃𝑆 𝐴𝑅𝑃𝐼 ). Pars region re-referenced tangential accelerations within the same otolith are subtracted from one another (𝑎𝐿𝑈𝑡𝑟 = 𝑎𝐿𝑃𝑀 − 𝑎𝐿𝑃𝐿 , 𝑎𝑅𝑈𝑡𝑟 =𝑎𝑅𝑃𝑀 − 𝑎𝑅𝑃𝐿 , 𝑎𝐿𝑆𝑎𝑐 = 𝑎𝐿𝑃𝑆 − 𝑎𝐿𝑃𝐼 , 𝑎𝑅𝑆𝑎𝑐 = 𝑎𝑅𝑃𝑆 − 𝑎𝑅𝑃𝐼 ), and because their responses are oppositely oriented, this operation is akin to a differential amplification of the signal. This was assumed as a mechanism for pooling between otolith afferents to improve encoding observed in subsequent psychophysical behaviours (Jamali et al. 2019). The same multi-afferent simulation procedure was performed creating a sensory particle distribution for each of the four otolith tangential acceleration signals (𝐿𝑈𝑡𝑟𝑑𝑖𝑠𝑡 , 𝑅𝑈𝑡𝑟𝑑𝑖𝑠𝑡 , 𝐿𝑆𝑎𝑐𝑑𝑖𝑠𝑡 , 𝑅𝑆𝑎𝑐𝑑𝑖𝑠𝑡 ). Noise for background discharge variability was similarly added to each simulated signal (regular = 𝜎𝑟2 = 0.12, irregular = 𝜎𝑖𝑟2 = 0.21). Each particle within a canal particle distribution (e.g., 𝐿𝐻𝑑𝑖𝑠𝑡 ) is subtracted from their corresponding canal co-planar pair (e.g., 𝑅𝐻𝑑𝑖𝑠𝑡) distilling the six canal distributions into three canal paired distributions: ( 𝐿𝐻𝑅𝐻𝑑𝑖𝑠𝑡 = 𝐿𝐻𝑑𝑖𝑠𝑡 − 𝑅𝐻𝑑𝑖𝑠𝑡 , 𝐿𝐴𝑅𝑃𝑑𝑖𝑠𝑡 = 𝐿𝐴𝑑𝑖𝑠𝑡 − 𝑅𝑃𝑑𝑖𝑠𝑡 , & 𝑅𝐴𝐿𝑃𝑑𝑖𝑠𝑡 = 𝑅𝐴𝑑𝑖𝑠𝑡 −𝐿𝑃𝑑𝑖𝑠𝑡). Because each paired distribution has the same number of particles, particles at k-th index were subtracted from the other distribution at the same index location. Likewise, each particle within an otolith particle distribution is subtracted from their corresponding left and right pair distilling the four otolith distributions into two otolith paired distribution. This is possible because the left and right 55 otoliths in our experimental procedure are on opposite sides relative to the axis of rotation, thus encode oppositely oriented tangential accelerations (Figure 3-3). Bilateral difference of the two signals further provides differential amplification of the encoded tangential acceleration. Figure 3-3: Illustration of tangential linear acceleration between left and right otoliths. The otoliths (saccule and utricle) are sensitive to linear acceleration. During head angular accelerations, a linear acceleration component is present tangential to rotation direction. For example, in an Earth-vertical counter-clockwise rotation, left otoliths experience a tangential component (purple line) opposite to the right otoliths (green line). The net difference between left and right components creates a differential amplification of the encoded tangential acceleration (inset, dashed-line). Particles in the final particle distribution representing the internal state (𝐼𝑑𝑖𝑠𝑡) are initialized by randomly drawing from a normal distribution [𝑁(0, 𝜎𝐼2)] centred around zero (representing an internal representation of zero angular velocity) with a free-parameter variance of 0.1. A lower internal state variance value relative to the variance in sensory particle distributions would bias sampling towards internal state. Although this value was arbitrary, it was chosen to not create internal state variance that is far below the variance of sensory distributions (thus making sampling sensory particles 56 extremely improbable). Ultimately, upon initialization and start of the sampling algorithm, six total particle distributions are present – five forming a group of sensory distributions: 𝑆𝑑𝑖𝑠𝑡 ={𝐿𝐻𝑅𝐻𝑑𝑖𝑠𝑡 , 𝐿𝐴𝑅𝑃𝑑𝑖𝑠𝑡 , 𝑅𝐴𝐿𝑃𝑑𝑖𝑠𝑡 , 𝑈𝑡𝑟𝑑𝑖𝑠𝑡 , 𝑆𝑎𝑐𝑑𝑖𝑠𝑡}, and one for the internal state distribution (𝐼𝑑𝑖𝑠𝑡). 3.5. Step 3: Particle sampling algorithm A recursive computation was used to perform dynamical inference in our distributed particle distributions. While implemented differently, such recursive framework is commonly used for dynamical vestibular inference found in Kalman filters (Borah et al. 1988; Karmali and Merfeld 2012) and particle filters (Karmali and Merfeld 2012; Laurens and Droulez 2007; Paulin and Hoffman 2011). Here, we modeled neural integration as a sampling problem from which the brain samples particles representing available sources of information to infer the internal representation of vestibular self-motion. These sources come from afferent neurons (sensory particles) encoding motion through its firing rate (i.e., what is sensed/measured) and central neurons (internal state particles) encoding the current internal brain estimate (i.e., what was experienced). Consider two particle distributions, 𝑆𝑑𝑖𝑠𝑡 and 𝐼𝑑𝑖𝑠𝑡, representing sensory (𝑆) and internal state (𝐼) distributions. 𝑆𝑑𝑖𝑠𝑡 has 6 particles and 𝐼𝑑𝑖𝑠𝑡 has 14 particles representing a 30:70% ratio (Figure 3-4). At the start of the sampling algorithm within the current time-step, all 20 particles were assigned a probability of being sampled from, which was stored as a probability vector. Within the probability vector each number corresponded to the sampling probability of a particular particle. This probability was derived based on several factors: (1) the relative number of particles between groups, (2) relative uncertainty/variance between groups, (3) relative weighting between groups, and (4) a relative amplitude term applied on the sensory distribution (Figure 3-4, top inset). 57 1. The ‘ 𝑁 ’ term for a particular distribution ( 𝑆𝑑𝑖𝑠𝑡 or 𝐼𝑑𝑖𝑠𝑡 in this case) signifies the relative proportion of particles for a given distribution relative to the total number of particles within all distributions. As such, if more particles were within a distribution, particles from that distribution were more likely to be sampled. The 𝑁 value for particles in 𝑆𝑑𝑖𝑠𝑡 was calculated as follows: 𝑁𝑆𝑑𝑖𝑠𝑡 =# 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠 𝑆𝑑𝑖𝑠𝑡.Σ(# 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠 𝑆𝑑𝑖𝑠𝑡 , # 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠 𝐼𝑑𝑖𝑠𝑡) In practice, this term does not need to be explicitly calculated or applied to the probability vector of the particles because it is already inherent within the ratio of particle from each distribution. 2. The ‘𝛽’ term for a distribution describes the weighting applied based on relative uncertainty between distributions ( 𝜎𝑆𝑑𝑖𝑠𝑡2 , 𝜎𝐼𝑑𝑖𝑠𝑡2 in this case). This resembles a Bayesian integration approach as particles in a distribution with smaller variance (less uncertainty) were given a higher probability of being sampled. As such, the probability of being sampled is inversely related to the variance. 𝛽𝑆𝑑𝑖𝑠𝑡 = 1 −𝜎𝑆𝑑𝑖𝑠𝑡2Σ(𝜎𝑆𝑑𝑖𝑠𝑡2 , 𝜎𝐼𝑑𝑖𝑠𝑡2 ) 3. The ‘w’ term for a distribution describes a relative weighting factor applied to either sensory or internal state distribution; effectively increasing the sampling probability of one while decreasing the other’s probability. Practically, this weighting factor could be a substitute for scaling the probability change in the relative number of particles within a distribution as a higher number requires more computational power. The w term was normalized by the total weighting factor on all distributions. 58 𝑤𝑆𝑑𝑖𝑠𝑡 =𝑤𝑆𝑑𝑖𝑠𝑡Σ(𝑤𝑆𝑑𝑖𝑠𝑡 + 𝑤𝐼𝑑𝑖𝑠𝑡) 4. An additional ‘𝑎’ term was uniquely applied to particles in sensory distributions. This term was added to provide additional weighting to sensory particles that deviated from zero (i.e., particles that encodes motion greater than noise band would be more likely sampled). Because the algorithm always samples particles from each sensory distribution, this served as an indicator to focus on sensory sources that signified motion. The 𝑎 term for a given i-th particle within a distribution (e.g., 𝑆𝑑𝑖𝑠𝑡 , 𝐼𝑑𝑖𝑠𝑡) was taken as the absolute particle amplitude (Ampi). 𝑎𝑆𝑑𝑖𝑠𝑡(𝑖) = Amp𝑆𝑑𝑖𝑠𝑡(𝑖) Moreover, each particle in the internal state distribution is given a uniform weight with respect to the number of internal state particles. This prevents over weighting the internal state when all sensory signals are at zero. 𝑎𝐼𝑑𝑖𝑠𝑡(𝑖) =1# 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠 𝐼𝑑𝑖𝑠𝑡 Taken together, for a given 𝑖-th particle in a sensory distribution (e.g., 𝑆𝑑𝑖𝑠𝑡), its probability was based on a series of weights expressed as: 𝑆𝑑𝑖𝑠𝑡(𝑖) = 𝑁𝑆𝑑𝑖𝑠𝑡(𝑖) ∗ 𝛽𝑆𝑑𝑖𝑠𝑡(𝑖) ∗ 𝑤𝑆𝑑𝑖𝑠𝑡(𝑖) ∗ 𝑎𝑆𝑑𝑖𝑠𝑡(𝑖) for internal state particles it was: 𝐼𝑑𝑖𝑠𝑡(𝑖) = 𝑁𝐼𝑑𝑖𝑠𝑡(𝑖) ∗ 𝛽𝐼𝑑𝑖𝑠𝑡(𝑖) ∗ 𝑤𝐼𝑑𝑖𝑠𝑡(𝑖) ∗ 𝑎𝐼𝑑𝑖𝑠𝑡(𝑖) 59 After all factors were applied, the summated probabilities from all particles were normalized to one (Figure 3-4, bottom inset). Particles were randomly sampled with replication based on their assigned probabilities. The mean ( 𝜇𝑡𝑒𝑚𝑝 ) and standard deviation ( 𝜎𝑡𝑒𝑚𝑝 ) of the initial sampled distribution were computed. Redundantly sampled particles were removed and replaced with new particles randomly generated from this temporary sampled normal distribution 𝑁(𝜇𝑡𝑒𝑚𝑝 , 𝜎𝑡𝑒𝑚𝑝). This was performed to prevent sample degeneracy – that is a convergence of particles to one sample. Our model overall included a total of five tunable parameters: (1) uncertainty added on the primary afferents, (2) uncertainty added to the internal state, (3) the number of particles representing the afferent population, (4) the number of particles representing the internal state population, and (5) the relative weighting factor ‘w’. We note, however, that these parameters were all related and fundamentally affected the relative probability of sampling particles from the sensory or internal state distributions. Intuitively, factors increasing the probability of sampling particles for a given distribution included: 1. Increasing its relative representation (particle count). 2. Increasing the relative weighting factor ‘w’. 3. Decreasing the relative uncertainty/variance in the distribution or, conversely, increasing the relative uncertainty/variance in other distributions. 4. For sensory distributions, increasing the absolute sensory amplitude such that particles with greater amplitude are sampled from. 60 Figure 3-4: Example of sampling algorithm. Here we present an example of an iteration of our sampling model with two distributions, one for sensory (red) and internal state (blue). Within an iteration of the sampling process, 14 internal state particles at a previous time step (T-1) were propagated to the current time step (T0). Concurrently, 6 sensory particles encoding instantaneous motion were incorporated leaving a 6-to-14 (30%:70%) ratio. All sensory and internal state particles were aggregated and assigned a probability weighting that is normalized to 1 when summed (bottom inset). Weighting was based on four factors (top inset): (1) the relative number of particles from each distribution (𝑁𝑆, 𝑁𝐼), (2) the relative uncertainty/variance of each distribution (𝜎𝑆2, 𝜎𝐼2), (3) a weighting term (𝑤𝑆, 𝑤𝐼 ) applied to each distribution, and (4) the particle amplitude. Note this last factor was applied to only for sensory particles; however, internal state particles were given a uniform weight (1 over the number of internal state particles). After weights are assigned to each particle, 14 particles were sampled with the possibility of replication. The resulting sampled distribution characteristics (𝜇𝑡𝑒𝑚𝑝, 𝜎𝑡𝑒𝑚𝑝) were calculated. To prevent convergence over a prolonged period (sample degeneracy), copies of particles that are sampled more than once (non-unique) were replaced with new particles drawn from the sampled distribution (green particles). Unique and replaced particles represent the final, current estimated internal state distribution at T0 which was then propagated as the new internal state distribution for the next time step (T1). 61 Chapter 4. Self-motion perception to constant angular acceleration 4.1. Preamble Following a step-change in rotational velocity, perceived velocity rises and decays due to passive return of the semicircular canal’s cupula to its original resting state. Conversely, during constant angular acceleration, the cupula remains deflected leading to tonic deformation of the hair cells. Over time, some afferents adapt to the constant acceleration stimulus while others show little adaptation. Perception, on the other hand, tends to decay towards rest. The question as to how perception reaches no-motion despite a portion of underlying sensory signal not adapting remains unclear. In this chapter, we first estimated the dynamics of perceptual adaptation during constant angular accelerations. Subsequently, we used our vestibular sampling model discussed in Chapter 3 to understand how such percepts may result from sensory afferents adapting at different rates. 4.2. Introduction Sensory adaptation describes a gradual reduction in firing rate response encoded in sensory neurons during prolonged and constant stimulus exposure. These adaptations are ubiquitous across different sensory systems and organisms including humans (Adibi et al. 2021). Changes along neural pathways are believed to adjust sensory sensitivity when our experienced environment changes, which may confer an evolutionary advantage (Brenner et al. 2000). For instance, we are better able to detect novel odors when we adapt to the existing smell within a room (Dalton 2000). Likewise, our sense of head-motion in space, encoded by the vestibular system, adapts to continuous motion stimuli. For example. participants exposed to a constant angular acceleration in darkness initially reported a veridical motion percept which was followed by a false perception of slowing down towards rest (Guedry and Lauver 1961) within a 20s to 120s period (Clark and Stewart 1968). Such between- 62 participant perceptual variability may be reflective of how the brain centrally integrates time-varying dynamics in the firing rate of sensory neurons encoding head motion. The vestibular system provides information about our self-motion and orientation, playing a crucial role in maintaining gaze and postural stabilization. The well-characterized encoding of self-motion by primary vestibular afferents (see Goldberg et al. 2012) has guided the creation of several mathematical models related to sensory integration (Borah et al. 1988; Karmali and Merfeld 2012; Laurens and Angelaki 2011; Merfeld et al. 1993). To reveal the mechanisms underlying the brain integration processes, experiments and models often use simple, controlled stimuli that are not naturally encountered. During prolonged constant angular acceleration stimuli, the responses of primary vestibular afferents adapt at different rates despite the canal cupula remaining deflected and maintaining hair cell transduction. The decay in afferent firing rate to such stimuli may be due to mechanisms at the hair-cell/afferent synaptic complex (Rabbitt et al. 2005). Primary canal afferents exhibit highly variable adaptation rates during constant angular acceleration stimuli (Brichta and Goldberg 1996; Dickman and Correia 1989; Goldberg and Fernandez 1971a). For example, Rabbitt et al. (2005) measured adaptation time constants ranging from milliseconds to a 1000 seconds under mechanical indentation of a plugged canal. These adaptation time constants correlate with primary afferent spontaneous discharge regularity, with more adaptation observed in irregular units (Dickman and Correia 1989; Goldberg and Fernandez 1971a). Despite the presence of essentially non-adapting primary afferents, human participants do experience an adaptation in self-motion perception, although at varying rates (Clark and Stewart 1968; Guedry and Lauver 1961). After the transition from constant angular acceleration to constant velocity, participants usually reported an illusionary percept, termed aftereffect, in the direction opposite to the initial angular acceleration (Clark and Stewart 1968). 63 Variability in constant acceleration adaptation and its aftereffect warrants closer examination. An early study from Clark and Stewart (1968) reported an averaged rotational sensation lasting about 60 seconds varying by one-third (CV = 37%) among their participants (10 males), who all felt an aftereffect. Conversely, participants (8 males) in Luster (1972) reported the presence of the aftereffect in approximately 55% of trials. In both studies, participants were all men, who likely had piloting experience (Bock et al. 1979; Clark and Stewart 1968; Guedry et al. 1971; Guedry and Lauver 1961; Luster 1972; Stockwell et al. 1973). This oversampling of males highlights the need for female representation. Even though females exhibit a greater incidence of vestibular disorders (e.g., motion sickness, vertigo, and migraines, etc.), sex differences have only been reported (reviewed in Smith et al. 2019) in certain vestibular-related tasks such as subjective visual vertical detection (Cohen and Sangi-Haghpeykar 2012) and spatial orientation (Tremblay and Elliott 2007) but not for vestibular perceptual thresholds (Bermúdez Rey et al. 2016; Diaz-Artiles and Karmali 2021; Roditi and Crane 2012). As such, the lack of data from the female sex in addition to generally low sample sizes (n = 5-10) bring into question both the generalizability and the observed variability of vestibular adaptation to constant angular acceleration stimuli. Models replicating constant acceleration adaptation are based on linear control theory, expanding upon the torsion-pendulum mechanistic model of the semicircular canal (van Egmond et al. 1949b). Young and Oman (1969) and Malcolm and Jones (1970) both proposed integrating the output from the canals with an additional adaptation term to replicate the adaptation behaviour. Both models predict deterministic results, meaning their output is always the same for a given input. Further, these linear models focus on describing the average behaviour from a single input and can not link the observed variability in primary afferent adaptation to behaviour. Perceptual variability during per-acceleratory adaptation and the subsequent post-acceleration response suggest that the 64 brain may integrate peripheral signals probabilistically producing non-deterministic responses from identical input. Contemporary theory proposes that the brain employs probabilistic computations consistent with Bayesian inference using distributed signals from neural populations (Gu et al. 2008; Klam and Graf 2003) for spatial perception (Angelaki et al. 2009). Recent vestibular models (Karmali and Merfeld 2012; Laurens and Droulez 2007) proposed integrating signals using a particle filter approach (Arulampalam et al. 2002), where particles capture properties of a distribution by representing it as sampled values. These particle filtering approaches can replicate velocity storage behaviour and may serve as a framework to link variability in sensory afferents, in this case encoding self-rotations, to the perceptual variability observed during per-acceleration adaptation and post-acceleration aftereffects. The goal of this study was to evaluate the variability in perceptual self-motion adaptation that occurs during and following prolonged constant angular acceleration stimuli. We characterized and compared perceptual responses and their variability between sexes to improve generalizability. Furthermore, we contextualized our results within a probabilistic framework to investigate how different perceptions of self-rotation may arise from the integration of differently adapting primary vestibular afferents. 4.3. Methods 4.3.1. Participants 20 healthy participants were recruited; however, two participants (1 female, 1 male) dropped out within the first trial of testing. In total, 18 participants (11 females, age: 25.0 ± 3.5 years [mean ± SD]) were included in this study. All participants were screened for neurological deficits prior to their participation in this study. Participants were informed about the experimental protocol, any possible 65 discomfort associated, and the data’s public accessibility before giving their written informed consent. All procedures conformed to the standards of the Declaration of Helsinki and have been approved by the University of British Columbia’s Clinical Research Ethics Board [H19-00422 (2019-08-29)]. 4.3.2. Setup Participants were securely seated on a rotary chair within a sound- and light-proof room (Figure 4-1A). Participants were padded with dual-layered memory foam secured around their chest, arm, shanks, and feet to dampen potential vibrations from the servomotor. Participants were also fastened to the chair seat using a five-point racing harness (9411D 5-Point Harness System, RCi, USA), and their legs were strapped to the chair’s lower chassis to minimize potential movements due to centrifugal force at high angular velocities. Wind cues during rotations were masked by a wind-resistant fabric tarp placed over top the chair chassis which fully encapsulated the seated participant. Auditory cues from the chair’s servomotor were masked by wearing noise cancelling earbuds (QuietComfort 20, Bose, USA) playing auditory noise. The audio was a mix of white noise with additional power at the predominant frequencies of the motor during rotations. All experiments were performed in complete darkness to remove visual cues. We used a helmet (Classic Skate, Pro-Tec, USA) affixed to the chair carriage to secure the participant’s head at an ~18o downward pitch relative to an Earth-horizontal Reid’s plane (plane passing through the inferior orbital rim and external auditory meatus). This orientation aligned the axis of rotation with the direction of maximal activation in the horizontal canals (Della Santina et al. 2005). We tasked participants to report their perceived angular displacement using a continuous turn potentiometer (6639S-1-103, Bourns, USA) attached to a 3D-printed rotary dial. The potentiometer was powered by a 9V battery, and a linear voltage regulator integrated circuit (L7805, 66 STMicroelectronics, Switzerland) was added to keep a constant 0-5V output range. This range was mapped to one revolution of the dial. The analog voltage was digitized at 500Hz using a I/O connector block (SCB-68A, National Instruments, USA) interfaced to a multifunction FPGA module (PXI-7853R, National Instruments, USA) all controlled through an embedded controller (PXI-1031, National Instruments, USA) running a LabVIEW (ver. 2019, National Instruments, USA) custom virtual instrument program. 4.3.3. Vestibular stimuli We delivered whole-body rotations through the rotary chair programmed through our PXI embedded controller and FPGA module. Feedforward velocity commands were sent at 500Hz by the FPGA module (PXI-7853R, National Instruments, USA) via the I/O connector block (SCB-68A, National Instruments, USA) to a servo amplifier (SGDV-200A01A; Yaskawa, Japan) powering an alternating current motor (SGMCS-1EN3A31; Yaskawa, Japan; encoder angular resolution 0.00034°, continuous torque 150 Nm). Servomotor controller gains were chosen to minimize mechanical vibrations during constant angular acceleration. Such controller adjustments may not be possible in other commercial systems. Positive (+) and negative (-) angular values are conventionally defined as clockwise (cw) and counter-clockwise (ccw) rotations, respectively, from an upright seated participant's perspective. In a report by Clark (1967), angular acceleration thresholds in humans varied considerably: from 0.1deg⋅s-2 to 4.0deg⋅s-2. Considering this, our chosen acceleration amplitude was a trade-off between (1) being above vestibular threshold, (2) being able to generate prolonged stimulation to capture adaptation, and (3) retaining a low target angular velocity to prevent confounding centrifugal forces. We found that centrifugal forces were notable above 165deg⋅s-1 during pilot testing which led us to limit angular velocity to 160deg⋅s-1. For us to capture perceptual adaptation dynamics and aftereffect, we needed a prolonged angular acceleration which was followed by a period of constant angular velocity. Thus, 67 we programmed a trapezoidal angular velocity stimulus profile which consisted of a constant angular acceleration phase (+1.10deg⋅s-2 over 145s for cw rotation), a non-stationary 160deg⋅s-1 constant angular velocity phase (90s), a symmetrical constant angular deceleration phase (–1.10deg⋅s-2 over 145s), and a stationary 0deg⋅s-1 constant angular velocity (90s) phase (Figure 4-1B). A stimulus profile in the opposite direction was delivered for ccw rotations. In addition, participants were also exposed to a familiarization motion stimulus, which was ±30deg⋅s-1 multi-sine signal with equal power at 0.033, 0.050, and 0.067Hz lasting for 60s. This profile was used to provide a slow and relatively unpredictable motion signal to familiarize reporting perceived angular displacement using our instruments. Figure 4-1: Experimental setup and estimated afferent responses. (A) Participants were seated on a programmable rotary chair that can deliver Earth-vertical whole-body rotations. (B) We applied a clockwise rotation (idealized profile shown) with a stimulus profile composed of four periods: a 145s period of constant angular acceleration at 1.10deg⋅s-2, a 90s period of non-stationary constant angular velocity at 160deg⋅s-1, a 145s period of constant angular deceleration at -1.10deg⋅s-2, and a 90s period of stationary constant angular velocity at 0deg⋅s-1. (C) Predicted horizontal canal primary vestibular afferent responses for the given motion stimulus. (D) Predicted vertical canal primary afferent responses. We aligned participant’s head orientation such that only the horizontal canal responses were maximized, and the vertical canals were minimized. Irregular and regular afferents were modeled to show the relatively rapid adaptation of the irregular afferents (~25s time constant) to constant angular acceleration (yellow dots) compared to their regular 68 (~500s time constant) counterparts (blue dots). A ratio of 1 irregular to 3 regular afferents was assumed in the model. 4.3.4. Protocol We instructed participants to continuously report their perceived angular displacement throughout a trial until the end using the potentiometer dial. Participants started at a preferred starting dial position. As such, if participants perceived a 90deg rotation, the dial should reflect a 90deg turn from the starting position. Two familiarization trials, one in light and one in darkness, were performed. After familiarization, participants were rotated 6 times (3 per direction) in a randomized order. Participants were given 5 min of rest with room lights turned on between each trial. 4.3.5. Data analysis Time-varying perceived angular displacements over a given trial were recorded from potentiometer voltage changes. The raw displacement signal consisted of a linear voltage change from 0-5V reflecting a full rotation between 0 to 359deg. Rapid voltage reflecting wrapping of the voltage signal from 0 to 5V (or drop from 5 to 0V) occurred upon a full rotation in ccw (or cw direction). Raw displacement data were first zero padded for 10s at the start and end prior to signal filtering and unwrapping. We down-sampled the raw signal to 25Hz and re-interpolated using the interp1 function in MATLAB back to 500Hz which effectively filtered the high frequency components while retaining edges for better edge-detection upon differentiating the signal. A first order Savitzky-Golay filter with a 167 sample (0.33s) frame length was applied for smoothing using the sgolayfilt function in MATLAB. The Savitzky-Golay filter has a finite impulse response. It operates by iterating through each sample in the signal and smooth the data by minimizing the local least-squares polynomial defined by the (polynomial) order and frame length. Importantly, the filter is more effective at preserving high-frequency edges (Gowri et al. 2013) than a commonly used Butterworth filter. No lag was induced by 69 this filter. A custom MATLAB function was written to identify and unwrap edge-transitions. First, absolute magnitude peaks were detected from the differentiated signal using the findpeaks functions in MATLAB. The index for a detected peak was used to create a window of the edge-transition in the original, undifferentiated timeseries. We used a window length of 200 samples (0.40s) before and after the peak to find the start and end of the falling (or raising) edge. The first 5 samples in the window were used to calculate a baseline mean. The 6th sample was added to compute a comparison mean. This comparison mean was evaluated against the baseline mean by taking the sum of squared error (SSE). In effect, if the additional sample was close to baseline, it would not change the SSE; however, the SSE would increase during edge transitions. This was performed incrementally (continually adding samples) for each chronological sample until the peak indexed location. SSE above a threshold of 0.0004 was chosen as a starting edge-transition. The same procedure was performed to detect the ending edge-transition with a baseline sample from the last 5 samples of the window. The difference between the identified start and end edges was added to the wrapped signal, and samples in between were interpolated using the interp1 function in MATLAB. This unwrapped timeseries was filtered again with a first order Savitzky-Golay filter using a 5.00s frame length to remove high frequency noise while retaining low frequency perceived angular displacement for subsequent analyses. Lastly, the filtered unwrapped angular displacement was differentiated using a finite difference approach to obtain the perceived angular velocity. Our analysis of perceptual responses to angular motion for each trial was divided into two halves. The first half was the response during acceleration and non-stationary (i.e., 160deg⋅s-1) constant velocity periods, and the second was the deceleration and stationary (i.e., 0deg⋅s-1) constant velocity periods. Because we were near perceptual threshold, we did not expect a response (or adaptation) in all participants or trials. We thus identified per-acceleratory adaptations based on two 70 criteria. The peak perceived velocity must occur in the expected direction of canal stimulation and be within 45s of rotation onset (Clark and Stewart 1968; Guedry and Lauver 1961). For a cw rotation, the acceleration and following deceleration perceptual responses were expected to be cw and ccw, respectively. The opposite is true for a ccw rotation trial. Post-acceleratory responses were also systematically identified for periods of constant angular velocity. For brevity, we will refer to them as non-stationary responses or stationary responses based on the constant velocity period (160 or 0 deg⋅s-1)) each occurred in. The expected direction for non-stationary and stationary responses were opposite to previously experienced acceleration/deceleration direction (e.g., cw acceleration leads to ccw non-stationary response, or ccw deceleration leads to a cw stationary response). Because these responses were likely unattributed to our vestibular stimulus, a criterion was used to segregate responses that were an immediate reaction from transitioning to constant angular velocity from those that occurred later, that may be attributed to guessing. Responses were included when peak amplitude occurred within 45s of the transition to constant velocity and were greater than two stand deviations from a participant’s baseline fluctuation in perceived velocity. Baseline perception was defined as the last 20% (18s) of the constant velocity period where no perceived motion was expected. In the results, perceptual responses meeting these criteria are termed identified responses, and those that did not are considered guessed responses (such as cw-ccw oscillations or sensations of rotation opposite to the expected direction). Perceptual responses that did not adapt to rest were considered non-adapting. Identified per-acceleratory responses (during acceleration or deceleration) were normalized to their respective peak perceived angular velocity. Identified aftereffect responses (during non-stationary or stationary) were normalized to their respective peak perceived angular velocity during the acceleratory phase that preceded it. This was used to estimate the relative amplitude differences. 71 Peak normalized identified response for a given trial were averaged within participants (trial-averaged response). Per-acceleratory and aftereffect percepts once reaching peak amplitude were expected to exponentially decay back to zero (no motion). As such, we estimated perceptual per-acceleratory adaptation (𝜏𝐴) or post-acceleratory decay (𝜏𝐷) time constants by fitting a single-term exponential (Eq: 4-1) to perceived angular velocity ( 𝜔 ) through non-linear least squares using the fit function in MATLAB. A starting amplitude (𝐴) of 1 and a time constant of 25 (𝜏𝐴/𝜏𝐷) were used as starting points for fitting. 𝜔(𝑡) = (𝐴 ∗ 𝑒−𝑡𝜏𝐴) 𝑜𝑟 𝜔(𝑡) = (𝐴 ∗ 𝑒−𝑡𝜏𝐷) Eq: 4-1 Peak perceived angular velocity in post-acceleratory responses were normalized to the per-acceleratory peak preceding it. This normalization procedure retained the relative differences and variability in peak amplitudes with respect to the preceding acceleratory response. 4.3.6. Statistical analysis We used linear mixed model with fixed effects [sex (females & males), acceleratory phase (acceleration & deceleration), stimulus direction (cw & ccw)], interactions [sex × acceleratory phase and sex × stimulus direction] and random effect [participants]. We included sex as a factor to compare the responses between males and females but did not expect a sex effect based on previous vestibular perceptual data (Bermúdez Rey et al. 2016; Diaz-Artiles and Karmali 2021; Roditi and Crane 2012). Time-to-peak perceived angular velocity and perceived adaptation time constants were tested in our mixed model to evaluate the presence of sex differences in perceptual responses and whether stimulus phase/direction, although mechanically identically, were different. Similarly, we also assessed for post-acceleratory decay time constants and relative peak amplitude possible sex 72 differences in post-acceleratory responses using a second linear mixed model with fixed effects for sex, stimulus direction, and constant velocity phase (160 & 0deg⋅s-1). Linear mixed models were used to account for repeated measures with random intercepts for participants. Marginal means for each fix effect groups were reported. All statistical tests were conducted at an 𝛼 level of 0.05 using JASP (version 0.14, JASP Team, Netherlands). We also calculated Cohen’s d effect size of the sex effect using G*Power (version 3.1.9.7, The G*Power Team, Germany; Faul et al. 2009) based on the sample statistics (mean and standard deviations) in acceleratory time constant. 4.3.7. Vestibular sampling model incorporating zero-motion prior We used our vestibular sampling model detailed in Chapter 3 to replicate observed percepts in this experiment. Our model uses Monte Carlo sampling to infer an internal representation of self-motion by taking samples (called particles) from different neural populations. These populations represent afferent signals sensing external motion and a previously estimated internal representation of self-motion. Afferents encoding our experimental motion stimulus were primarily from the left and right horizontal canal co-planar pair. Sensory signals during integration were subjected to additional weighting representing an expectation of being at rest (stationary), akin to what was previously proposed by Laurens and Droulez (2007). This can be interpreted as the brain favouring information encoding low velocity and acceleration. Practically, this expectation was modeled as a Bayesian prior weighting distribution that was applied to each sample in the afferent distribution. The prior’s distribution took the form of a Gaussian distribution with zero mean and an adjustable variance (or its square root, standard deviation). The smaller the variance, the greater the probability samples closer to zero would be sampled. To compare effect of the prior variance on simulation adaptation time constants, we predicted results for a set of prior standard deviations: 1, 10, and 100. We did 10 simulations and reported the average behaviour. Each simulation used 1000 particles with a 73 state/sensory ratio of 7:3 and an irregular/regular afferent type ratio of 3:4. This prior weighting was accomplished by calculating the probability density value for a given sensory particle amplitude (representing instantaneous firing rate) with respect to the prior Gaussian distribution. The probability density value of each particle was multiplied by the particle sampling probability calculated based on four factors: the relative particle numbers (internal state: 700, sensory: 300), the relative particle distributions’ variance, the relative distributions’ weighting (internal state: 75, sensory: 1), and the amplitude of individual sensory particle). We scaled the sampling probability of each sensory particle with respect to the zero-mean prior distribution (Figure 4-2). Acceleration/deceleration time-to-peak and adaptation time constants were estimated from the simulated internal state result. Time constants were estimated similarly to our experimental responses using Eq: 4-2. 𝜔(𝑡) = (𝐴 ∗ 𝑒−𝑡𝜏𝐴) Eq: 4-2 Figure 4-2: Sampling model with prior weighting. In our sampling model, the probability of sampling sensory (red) and internal state representation (blue) particles are determined by the relative number of particles, relative variance, relative weighting, and sensory particle amplitude. Each particle is assigned a probability (of being sampled) shown in the 74 top right. In this experiment, we added an additional zero-amplitude weighting in the form of a Gaussian distribution that acts as a prior expectation of no-motion to sensory particles. Here we show an example of a change in sampling probability for sensory particles with respect to how close they are to zero (bottom right). 4.4. Results 18 healthy participants tracked their rotational self-motion during an 8-minute whole-body rotation. Participants rotated in the same direction throughout a trial but experienced non-veridical self-motion perception at different rotational stimulus phases (constant acceleration, non-stationary constant velocity, constant deceleration, and stationary constant velocity). Upon constant angular acceleration, 14/18 participants reported angular displacements in the same direction as the whole-body/chair angular displacements in at least one trial in either clockwise or counter-clockwise directions. On average, peak perceived angular velocity was reached ~24s into constant angular acceleration onset which adapted to no perceived motion at ~ 48s (Figure 4-3A, top row; representative participant: red, participant-averaged: blue). Altogether, the time from first perception of self-motion to perceived rest lasted ~ 75s. After transition from constant angular acceleration to a non-stationary (160deg⋅s-1) constant angular velocity, 18/18 participants reported a non-veridical displacement opposite to the chair’s rotation direction in at least one trial (Figure 4-3B, top row). This post-acceleration response on average took ~39s to decay to zero and had a ~58% relative peak amplitude difference from the preceding acceleratory response. Furthermore, 13/18 participants experienced the expected percept during constant angular deceleration which, on average, showed comparable time-to-peak (~28s) and adaptation time (~45s) to the first acceleration period but in the opposite direction (Figure 4-3A, bottom row). Similarly, when brought to a complete stop (0deg⋅s-1 rest), 16/18 participants reported a non-veridical stationary response in at least one trial that decayed to zero at ~33s with ~50% relative peak amplitude difference (Figure 4-3B, bottom row). 75 Figure 4-3: Representative participant and participant averaged response. Participant whole-body rotations were delivered in clockwise (left panel) and counter-clockwise (right panel) directions. Input angular acceleration is shown in green. Normalized perceptual responses were superimposed on top of input stimulus. Responses were normalized with respect to peak perceived angular velocity during the constant acceleration period. In a representative participant (red), perception gradually increased at the beginning of constant acceleratory period and then adapted towards a zero, no motion, percept over time. Following constant angular acceleration, participant responses showed a counter direction response (to the preceding angular acceleration period). Participant averaged responses (orange) showed similar constant angular acceleration adaptation and subsequent constant angular velocity counter percept. 4.4.1. Rate of occurrence in adaptation response during constant angular acceleration Given that participants may not perceive the stimulus acceleration (±1.10deg⋅s-2), we excluded participant responses when they reported no perception, continuous perception in the opposite direction or sinusoidal-like responses in perceived direction. These were interpreted as guessing the stimulus profile due to potentially subthreshold angular acceleration stimuli. Rather, adaptation response during constant angular acceleration was reflected by an increase in perceived angular velocity which was followed by a decrease in perceived angular velocity. All 18 participants completed clockwise (cw) trials; however, counter-clockwise (ccw) trials from one female participant were excluded due to failure to follow task-instructions. 14/18 (8 females) and 13/17 (7 females) participants exhibited perceptual responses that adapted during acceleration in at least one trial in the cw and 76 ccw directions respectively. During deceleration, 13/18 (8 females) and 12/17 (7 females) participants (in cw and ccw directions) exhibited perceived response that adapted in at least one trial. Together, 15/18 (8 female) participants exhibited adaptation in their perceptual response in either rotational direction or acceleratory phase during a least a single trial. 4.4.2. Rate of occurrence in post-acceleratory response during constant angular velocity At the transition from constant angular acceleration to constant angular velocity, we quantified how many participants perceived rotation counter to the preceding angular acceleration direction (i.e. post-acceleratory responses). Participants exhibited post-acceleratory response in 57% (60 responses / 105 trials) and 48% (50 responses/105 trials) of trials pooled between non-stationary constant angular velocity (160deg⋅s-1) and stationary velocity (0deg⋅s-1) transitions. Responses that did not occur to the expected direction (i.e., same direction as preceding acceleratory response) were excluded. 15/18 (8 females) & 14/17 (7 females) participants (in cw and ccw directions) exhibited post-acceleratory response during non-stationary constant angular velocity in at least one trial. 14/18 (8 females) and 12/17 (7 females) participants (in cw and ccw directions) exhibited post-acceleratory response during stationary, zero velocity constant angular velocity in at least one trial. 4.4.3. Perceptual adaptation to constant angular acceleration stimuli Identified perceived angular velocities from individual trials were averaged within-participants separately for constant angular acceleration or deceleration to compute time-to-peak durations adaptation time constants (Figure 4-4). We observed generally similar response profiles between sexes and minor differences remained with the response variability. Across stimulus directions during acceleration, perceptual time-to-peak response was 26.2±9.2s (mean±SD) in female participants and 77 21.1±10.3s in males. Time-to-peak perceptions were within response variability during deceleration between females (26.3±8.6s) and males (31.7±11.7s). Similarly, adaptation time constants during acceleration and deceleration observed in females (14.5±8.5s and 15.9±7.5s respectively) were similar to those observed in males (17.9±7.5s and 13.7±8.4s respectively). These observations were confirmed in our linear mixed model analyses where we found no effect of stimulus direction [F(1, 35.54) = 0.783, p = 0.382] acceleratory phase [F(1, 34.52) = 3.640, p = 0.065] nor sex [F(1, 11.90) = 0.001, p = 0.973] on time-to-peak. Likewise, no interactions between sex and stimulus direction (p = 0.706) or between sex and acceleratory phase were found (p = 0.184). The same was true for adaptation time constants: we found no effect of stimulus direction [F(1, 36.72) = 0.342, p = 0.562] acceleratory phase [F(1, 35.72) = 0.485, p = 0.491] nor sex [F(1, 12.88) = 0.048, p = 0.830]. No interactions were also found between sex and stimulus direction (p = 0.706) nor between sex and acceleratory phase were found (p = 0.184). Figure 4-4: Participant-wise per-acceleratory time to peak and adaptation time constants. Perceptual adaptation time constant (left) and time-to-peak (right) during constant angular acceleration (circles) or deceleration (triangles). Blue and red colours represent female and male participant, respectively. 78 4.4.4. Constant angular velocity post-acceleratory response We further identified perceived angular velocity responses during periods of constant angular velocity (Figure 4-5). Across stimulus directions in non-stationary constant velocity, we observed comparable response decay rates in females (14.6±12.1s) and males (12.1±7.0s). This was corroborated in our linear mixed model analysis where we found no effect of stimulus direction F(1, 37.81) = 1.685, p = 0.202, acceleratory phase F(1, 38.45) = 2.068, p = 0.159, nor sex F(1, 14.20) = 0.036, p = 0.852. No interactions between sex and stimulus direction (p = 0.504) nor between sex and stationarity were found (p = 0.628). Similarly, across stimulus directions in non-stationary constant velocity, relative peak amplitude with respect to preceding acceleratory phase were comparable in females (-59.7±26.7%) and males (-64.4±25.8%). Linear mixed model analysis showed no effect of stimulus direction F(1, 14.56) = 0.263, p = 0.616, acceleratory phase F(1, 25.88) = 2.499, p = 0.126, nor sex F(1, 26.93) = 0.007, p = 0.935. No interactions between sex and stimulus direction (p = 0.094) nor between sex and stationarity were found (p = 0.525). Figure 4-5: Post-acceleratory decay time constants and relative peak amplitude. Post-acceleratory decay time constants (left) and relative peak amplitude expressed as a percentage of the peak in the preceding acceleratory phase. Values presented during constant angular velocity at non-stationary 160 deg⋅s-1 (circles) and stationary 0deg⋅s-1 rest (triangles). Blue and red colours represent female and male participant, respectively. 79 Given the absence of sex effect, we calculated the effect size of sex on the acceleratory decay time constant by pooling the acceleratory phase and stimulus rotation direction in females (10.9±3.5s) and males (11.0±7.7s). This analysis resulted in an effect size of 0.015. 4.4.5. Simulations of perceptual adaptation to constant angular acceleration We performed computational simulations to generate an internal representation of constant angular acceleration using the motion profile experienced by participants. As such, this simulated internal representation aimed to match perceived response. Given the same head orientation, canal responses were predominately encoded by the left and right horizontal canals with no vertical canal contribution. Two sets of afferents, regular and irregular at a 3-to-1 ratio, form our model sensory distribution with irregular afferents adapting at a shorter time constant ( 𝜏𝑖𝑟 ~25s) than regular afferents (𝜏𝑟~500s). We estimated how the simulated perceptual response dynamics were influenced by the addition of a zero-amplitude prior weighting. This weighting adjusts the contribution of adapting and non-adapting afferents. If assuming a linear combination of these afferents, perceptual adaptation to our experimental stimulus would not be expected as most afferents are non-adapting. We represented the prior as a Gaussian distribution. Changes in the prior standard deviation (square root of variance) influenced the sampling probability of sensory particles in our model. Here, a decreasing variance parameter would increase the likelihood of sampling particles that are closer to zero. At a relatively high prior standard deviation (σ=100), the internal state did not completely adapt within the timeframe of our constant acceleration stimulus and more closely resembled the response of the regular afferents. The acceleration and deceleration phase had a time constant of 146.9s and 136.6s, respectively. Conversely, with a smaller prior (σ=10) the internal state in the acceleratory phase had a time-to-peak of 13.3s and did adapt towards zero amplitude. Fitted time constants for the acceleration and deceleration phases were, respectively, 20.1s and 16.0s, which were close to 80 experimental range between 14-18s (c.f., Figure 4-6B, Figure 4-3). Post-acceleratory response was present during non-stationary constant velocity and had an amplitude 35.0% of peak response during constant acceleration period. Lastly, using a very narrow prior (σ=1) the internal state did not change and remain around zero signifying no motion. Figure 4-6: Sampling model simulation results. Simulation results from our sampling model using three Gaussian distributions of different standard deviation as the prior. (A) A wide prior (standard deviation = 100) reduces the probability of sampling particle closer to zero leading to less adaptation in simulated internal state (blue). (B) As the prior variance decreases (standard deviation = 10), we see an earlier adaptation of simulated internal state with time constant ~18s. (C) A narrow prior (standard deviation = 1) samples particles closest to zero with high probability leading to no change in internal state. Unit for simulated internal state is denoted as arbitrary units as we do not have the proper scaling of responses. Note the difference in scale between A & B. 4.5. Discussion Our goal was to evaluate perceptual variability in vestibular self-motion during and following constant angular acceleration stimuli. Responses between sexes were also assessed to improve 81 generalizability of our results. Furthermore, we used a sampling-based vestibular model to describes how the brain may have an expectation of ‘no-motion’ as it integrates differently adapting vestibular afferents to produce perceptual responses observed in this study. At least 70% of tested participants were able to detect near-threshold constant angular acceleration/deceleration which consisted of an initial perception of self-motion followed by a gradual decline towards rest. Per-acceleratory time-constants, on average, were similar between acceleration/deceleration phases regardless of rotation direction; however, variability in adaptation between participants was present. Immediate post-acceleratory (constant angular velocity) responses were present in about 55% of trials which induced self-motion perception opposite to the direction of the expected preceding acceleration/deceleration. In our study, time-to-peak perceptual responses were around 15-40s. After, perceptual adaptation decreased the perceived rotation with a time constant between 10–35s which equates to ~30-100s for full return to rest. Perceptual adaptation to constant angular accelerations were initially studied by Guedry and Lauver (1961). They showed that peak perceived angular velocity was reached at about 30s which was followed by a decline in self-motion sensation over the next minute. Responses near the end were blunted in their study as the constant angular rotation stimulus was removed prior to full adaptation. Similar percepts were later reported by Clark and Stewart (1968) in longer duration constant angular acceleration stimuli, lasting between 60s±22s – defined as “the time from the first veridical report of rotation to the time when the magnitude estimates returned to zero”. Our results confirmed the reported behaviours in males and given the lack of sex difference, further extended these observations to females. During constant angular velocity, participants may report rotational percepts in the direction opposite to what was perceived in the preceding constant angular acceleration/deceleration period. In our participants, the duration of this post-acceleratory response varied around (37s±20s) and was 82 consistent with earlier reports from Clark and Stewart (1968), Luster (1972) and Mattson (1975). Critically, the relative amplitude between the per- and post-acceleratory responses suggests that they are not merely symmetrical behaviours. This symmetry is expected in previously proposed linear time-invariant model (Figure 4-7). As such, to produce this non-linear behaviour, an appropriate non-linear integration strategy must be used. In this case, our sampling approach was able to capture this relative difference (c.f., Figure 4-6B) which was ~35%. This provides further support for a sampling strategy within the brain. Figure 4-7: Linear time-invariant model response to constant angular acceleration. Simulated result of a linear time-invariant (LTI) model using transfer function 𝐻(𝑠) . The transfer function describes an irregular afferent from Schneider et al. (2015) with an adaptation term from Malcolm and Jones (1970). Expected response from this LTI model shows a symmetric response between constant acceleration and constant velocity phases. This prediction contrasts with our results and simulations using our sampling model (Figure 4-6B). We did not observe any differences between male and female participants in our study. Our results suggest that both sexes show similar response and variability. Previously, studies reported predominately from male participants with aviation backgrounds (Clark and Stewart 1968; Guedry and Lauver 1961; Luster 1972; Stockwell et al. 1973). In one report, Collins and Guedry (1967) compared nystagmus and perception during short duration (8.4s and 36s) accelerations in 4 men and 83 4 women, but sex comparison was not the focus. Morphologically, sex differences do exists as females have a significantly smaller vestibular labyrinth size (Sato et al. 1992) and a lower number of vestibular nerve fibers (Moriyama et al. 2007), but this is not reflected in vestibular-driven perceptions. For instance, no sex difference was observed in yaw rotation perceptual thresholds (Benson et al. 1989; Bermúdez Rey et al. 2016). Based on the data from Bermúdez Rey et al. (2016), we estimated their effect size for sex to be 0.25. Although larger than the sex effect size observed in this study (0.015), these data provide converging evidence that sex differences for perceptual studies are small. Considering our effect size, future studies would need a sample size of 69,334 participants per sex to achieve a power of 0.80. We acknowledge that such a large sample size poses logistical challenges and may not be feasible but also highlights the marginal size magnitude of sex differences for the perception of constant angular acceleration. Certain clinical pathologies (vestibular neuritis , Hülse et al. 2019; vestibular migraine, Radtke et al. 2012) are more prominent in females and tasks such as subjective visual vertical detection (Cohen and Sangi-Haghpeykar 2012), spatial orientation (Tremblay and Elliott 2007), and postural control (Farenc et al. 2003) may be more suitable to explore sex differences in vestibular function. In all, sex differences are multifaceted and subject to influence by sex hormones or drug interactions in addition to differing vestibular morphology (Smith et al. 2019). Future work should carefully control for these factors when comparing sexes. Vestibular primary afferents adapt across all units with adaptation rates correlating with greater background discharge irregularities (Goldberg and Fernandez 1971a; Rabbitt et al. 2005). As such, not all afferents are fully adapted within the timeframe of our experiment. This brings into question how perception reaches ‘no motion’ when a proportion of the originating neural code does not. The brain may exert a top-down modulation of available sensory information. From a probabilistic view, the brain can exert this influence by weighting signals based on certain 84 expectations. We adopted the notion that humans would have an expectation for no motion (Freeman et al. 2010; Hürlimann et al. 2002; Laurens and Droulez 2007; Stocker and Simoncelli 2006) as our head tends to be at rest. To test this, we implemented a zero-motion expectation (prior) in our model using a normal distribution with a zero-amplitude mean. This prior distribution was applied to sensory particles at each time-step. Effectively, the prior increases the likelihood of sampling particles encoding for no-motion (i.e., closer to zero). We compared model results from three different prior variance choices: a wide variance (far from the sensory particle amplitudes), a variance close to sensory particle amplitudes, and a narrow variance (well below the sensory particle amplitudes). At a wide variance, the simulated internal state (representing perception) adapts slowly (time constant >100s), more closely reflecting the behaviours of regular afferents (modeled with a time constant ~500s). In the second and smaller variance condition, we see adaptation towards zero-motion. This resembles the percepts reported by our participants (time constants range: 14-18s) with time constants between 16-20s within the variability of what we observed. In simulated responses with a narrow prior variance, this increases the likelihood of sampling particles closest to zero, resulting in effectively no changes in internal state to occur. This may suggest people who show no responses would have a narrow prior variance (strong expectation of no motion). Post-acceleratory responses were less apparent in our simulation results. In both the first (wide) and second simulation conditions, we saw a decrease in the internal state. More specifically, in the second condition, we observed post-acceleratory responses. Altogether, our sampling model suggests that the brain could employ a no-motion expectation when integrating sensory information to produce distinct adaptation time constants. Prior variance in zero motion could explain variability in perceived motion between participants. This model may provide an alternative framework in modeling vestibular integration. 85 Several theoretical interpretations can be made based on our model. First, the per-acceleration adaptation is driven by the balance between factors influencing afferent sampling (e.g., amplitude from zero, relative variance, relative number of internal states to afferent particles, & relative number of afferent types) and the influence of a zero-motion prior. This balance must allow for the sampling of afferent particles to detect changes but also allowing for the gradual return in our internal representation towards rest. Here while we implemented a static prior, other possibilities in terms of how the prior interacts with particle sampling may exist. For example, a dynamical modulation of the prior variance conditioned on past estimates (internal uncertainty related to self-motion). In this interpretation, the influence of the zero-motion prior may change over time and become history-dependent such that it diminishes during transient periods of movement. A second interpretation of our model was that we used a set (3-to-1) proportion of regular to irregular primary vestibular afferents. In our results, perceptual adaptations were considerably shorter than those previously reported for reflexive eye movements (Boumans et al. 1983c, 1983a) which had time constants upwards of 100 seconds. Discrepancies between vestibulo-ocular reflex and perception are well-known. In fast/slow alternating asymmetric rotational stimuli, ocular responses remained consistent over a prolonged duration; however, perception progressively became more asymmetric, biasing fast rotational percepts (Pettorossi et al. 2013). Differences in velocity storage decay reduction between the two behaviours following GABA-mediated inhibition suggests nonoverlapping neural networks (Shaikh et al. 2013). Divergences may occur as early as the vestibular nuclei where irregular primary vestibular afferents predominately projects onto vestibular-only neurons (Cullen 2019; Marlinski and McCrea 2009; Meng et al. 2007) involved in the vestibulo-perceptual processing. As such, we are likely underestimating irregular afferent representation in our model. Given a higher ratio of irregular afferents, more sensory particles would converge to zero thus 86 increasing sampling probability and driving internal state adaptation faster for a given prior variance. Conversely, longer adaptation is expected to occur for the vestibular control of eye movements as this is more associated with regular afferents. As such, this provides fewer adapting afferents for a given prior, or the prior variance is not narrow enough to drive signals down to zero. To highlight these differences, we simulated internal state response when sensory afferents included only regular type afferents with a prior standard deviation of 10 (Figure 4-8A). We see the internal state behaviour strongly resembling the response of regular afferents (Figure 4-1C, yellow). Contrasting this, we also simulated only irregular type afferents with the same prior (Figure 4-8B). In this case, we see a more rapid adaptation with clear post-acceleratory response resembling the irregular afferent input (Figure 4-1C, blue). Figure 4-8: Comparison between simulation for only regular or only irregular afferent type. (A) Given our experimental motion stimulus (red), we simulated (n = 10) the internal response (blue) given only regular afferent type sensory particles using a prior standard deviation of 10. In this scenario, we see minimal to no adaptation. This resembles the response of regular afferents themselves (c.f. Figure 4-1Error! Reference source not found.C, blue). (B) For the same parameters, we simulated (n = 10) the internal responses with only irregular afferents. The response adapted to near zero with time constants of 30s and 21s for acceleration and deceleration, respectively. This was close to the modeled adaptation time constant for irregular afferents (~25s) (c.f. Figure 4-1Error! Reference source not found.C, yellow). Unit for simulated internal state is denoted as arbitrary units as we do not have the proper scaling of responses. Our study had several limitations. First, we could report or not make any conclusions regarding the absolute magnitude of perceptual responses as the potentiometer tool used was not 87 systematically calibrated. However, we were able to compare relative amplitudes between per-acceleratory and post-acceleratory phases. Future studies would need to individually calibrate one’s perceived displacement to a known rotational stimulus to get absolute measures. Furthermore, we did not monitor participant’s head posture during the trial. Although we did measure head orientation while clamping their head to the chair using a modified helmet, it is possible for participants to slightly shift their head while rotating in space. Head position should be tracked during whole-body rotation in successive studies. Further work should measure ocular responses to constant angular acceleration to extend upon the modeling work done here. Our model itself also present several limitations. Responses between prior variances are scaled differently. It is unclear whether this scaling is meaningful, or a by-product of how we implemented our prior. Moreover, the central representation of our model is highly abstract and additional work must be done to clarify this. As it stands, we defined a singular group representing the internal state population. If indeed the brain implements a sampling strategy, this approach could occur in layers such as at the interface between primary afferents and central neurons (what we modeled here), and at higher-order brain areas like the thalamus. s which could be captured by our sampling approach. Finally, our model explained participant adaptation through a zero-motion prior distribution. It is conceivable that priors/expectations may also dynamically change (Chang et al. 2016) but this suggestion requires further testing. In conclusion, our results corroborate previous studies on perceptual adaptation during constant angular acceleration and confirmed similar responses in females. We contextualized our data using a sampling-based model for sensory integration from distributed signals based on available physiological evidence. This model was critically able to replicate adaptations observed in our participants’ perceptual self-motion using both adapting and non-adapting primary afferent 88 inputs distinct from what is predicted by LTI models. Predictions from this model may be used to understand how afferent information is combined within the brain and mechanistically explain vestibular-related aliments. Extension of this inferential framework may also be used for other sensory systems. 89 Chapter 5. Self-motion perception is dependent on the encoding vestibular end-organs 5.1. Preamble Self-motion perception arises in part from inertial signals encoded by the vestibular end-organs, which are comprised of the otoliths and semicircular canals. Shorter adaptation time to constant whole-body angular velocity rotation is present in a head pitched down orientation compared to a naturally upright orientation. This chapter questions why perception differs at different static head orientations. Here, we evaluated the influence of static head orientation on the perception of an angular velocity step input while systematically controlling for end-organ encoding. Findings from this study inform us about the differences we must consider when signals are encoded by differing end-organs. 5.2. Introduction The vestibular system encodes head motion in space and plays a critical role for self-motion perception and spatial orientation (Cullen 2019; Goldberg et al. 2012; Mast et al. 2014). Vestibular motion cues originate from the semicircular canal and otolith end-organs which encode angular (Goldberg and Fernandez 1971a; Della Santina et al. 2005) and gravitoinertial (Angelaki and Dickman 2000; Fernandez and Goldberg 1976b; Goldberg et al. 1990) accelerations, respectively. Six semicircular canals and four otoliths, evenly distributed between the left and right inner ears, generate inputs that are directed to the brain through firing rate changes in primary vestibular afferents. The velocity storage phenomenon describes a perceptual (or ocular) response that decays over time upon a step-change in angular velocity but prolonged from what was recorded in the originating primary afferents (Raphan et al. 1977; Robinson 1977). This prolongation, however, is 90 subject to one’s static head orientation. The reason for such differences could be explained from existing inferential models of vestibular processing. Experimentally controlled motion inputs have allowed researchers to probe the vestibular contributions to self-motion perception. Notably, following an Earth-vertical (gravity-neutral) angular velocity step-input, reflexive eye movement and perception (Bertolini et al. 2012; Okada et al. 1999; Shaikh et al. 2013; Sinha et al. 2008) decay with a time constant beyond what is expected from the dynamics of the originating canals (~3 to 7 secs) (Dai et al. 1999; Fernandez and Goldberg 1971). This prolongation in vestibular-evoked responses is believed to be a manifestation of a neural multisensory integration process termed the velocity storage (Laurens and Angelaki, 2017, 2011; Merfeld et al., 1993; Raphan et al., 1979) involving brainstem vestibular nuclei and cerebellar structures (Rühl et al. 2022). Numerous reports show that the velocity storage prolongation during Earth-vertical rotations (i.e., gravity-neutral) are influenced by one’s static head orientation in humans (Baloh et al. 1983; Bertolini et al. 2012; Fetter et al. 1986, 1992; Morita et al. 2003; Shaikh et al. 2013; Tweed et al. 1994). As such, static orientation-induced modulation of the velocity storage is not accompanied by dynamic otolith stimulation as in off-vertical axis rotations (Denise et al. 1988; Guedry 1965; Laurens et al. 2010) or post-rotatory tilt (Angelaki and Hess 1994; Benson and Bodin 1966; Raphan et al. 1981) because head orientation does not change relative to gravity during motion. Dynamical vestibular models can replicate the latter two behaviours (Hain 1986; Laurens and Droulez 2007; Merfeld et al. 1993) but can not address the influence of static head orientation on the velocity storage – notably because these models use parameters irrespective of the originating encoding end-organ thus simulating an indistinguishable net vestibular input regardless of head orientation (Borah et al. 1988; Laurens and Droulez 2007; Merfeld et al. 1993; Zupan et al. 2002). 91 Probabilistic vestibular inference models, such as the Kalman and Particle filters, alternatively suggest that the duration of velocity storage prolongation is inversely influenced by sensory noise accumulation during integration (Karmali and Merfeld 2012; Laurens and Droulez 2007; MacNeilage et al. 2008). This role of sensory noise may explain the disparity at different static head orientations due to distinct changes in the number of encoding canals. For example, the input vestibular signal during Earth-vertical rotation may be encoded by one, two or all three bilateral canal pairs depending on the head’s orientation and alignment of each canal’s directional sensitivity axis (whether there is an orthogonal component aligning with the input rotation vector). As a result, assuming similar neural noise level at each canal afferent, signal-to-noise ratio lowers when encoding is distributed among more canal pairs – predicting a shorter time constant. Alternatively, changes in velocity storage prolongation at different static head orientations are speculated (Bockisch et al. 2005; Jones et al. 1964; Seidman and John Leigh 1989; Tweed et al. 1994) to arise from alterations in encoding end-organs; particularly the difference in orientation between the vertical (anterior & posterior) and horizontal canals. The vertical canals are presumably more coupled to simultaneous otolith activation during natural head motions as we pitch or tilt the head relative to gravity (Bockisch et al. 2005). In contrast, head yaw motion when upright is mainly encoded by the horizontal canals with little change in gravitoinertial acceleration. As such, isolated horizontal canal activation would presumably need to prolong the duration of the internal signals of angular head motion to compensate for the minimal otolith contributions for typical head movements. Here, we characterized how signals from distinct vestibular end-organs are integrated during rotational self-motion perception by systematically altering the contributions of vestibular end-organs when encoding an Earth-vertical rotational step velocity input. We initially reasoned that rotational self-motion were predicated on the encoding semicircular canals leading to two hypotheses (Figure 92 5-1C). First, we expected an influence of semicircular canal type (vertical vs. horizontal) from prior head-orientation differences (Bertolini et al. 2011, 2012) and hypothesized that perceptual responses to angular velocity step stimuli would be more prolonged when encoded by horizontal canals than those from vertical canals. Second, we hypothesized that perceptual velocity storage prolongation would decrease with an increasing number of encoding semicircular canals due to a lowered signal-to-noise ratio. Our results supported the former hypothesis but not the latter. Based on these findings, we did a follow-up study analysing whether the vertical canals themselves are influenced by otolith stimulation possibly due to the biomechanics of natural head movement (Bockisch et al. 2005) leading to differences in processing pattern between horizontal and vertical canals. We hypothesized that simultaneous canal and otolithic activation would prolong perceptual step responses during vertical canal encoding due to naturalistic coupling between otoliths and vertical canals (Figure 5-1D). We compared perception adaptation to an angular step-velocity stimuli encoded by the vertical canals at head orientations with and without expected otolith components. We further contextualized our results using a probabilistic sampling model for vestibular integration by simulating the two differing otolith scenarios. 93 Figure 5-1: Experimental setup, conditions, and stimulus. (A) We used a rotary chair to deliver whole-body rotation about Earth-vertical axis to seated participants. Participants were secured to the chair’s chassis using a helmet and five-point harness. Layered foams were placed at the feet, legs, and torso to dampen possible somatosensory cues associated with motor vibration (for clarity, not all foams and straps were illustrated). Participants were asked to track their perceived rotational displacement using a handheld potentiometer attached to a crank handle. (B) The angular velocity stimulus profile delivered by the rotary chair consisted of a 10s onset ramp to a 45deg/s which was followed by a constant angular velocity period for 90s. Participants were brought back to 0deg/s stationary rest over a 1s offset ramp that was followed by a 60s stationary period. Both onset and offset ramps followed a raised cosine shape. (C) 94 Perceived rotation responses were measured in three static head orientations in Experiment 1. The head forward (2-horizontal) condition targeted the left-horizontal/right-horizontal canal pair. The head down (4-vertical) condition targeted both vertical canal pairs (left-anterior/right-posterior & right-anterior/left-posterior). The head down, 45o left turn condition targeted only one vertical canal pair (left-anterior/right-posterior). The relative change in firing rates between the first and last ‘2 canal’ conditions were similar; however, the relative change in firing rates in the ‘head down, 4 canal’ condition were lower than the others due to more encoding canals (c.f., stem plots). (D) In Experiment 2, an additional comparison in perceived rotational responses was made at two static head orientations: head down (identical to Experiment 1) and head down with left 90deg turn. The tangential acceleration experienced by the otolithic saccule (Sac) and utricle (Utr) were determined by the radius between the otoliths and axis of rotation [assumed to be ~4cm based on interutricular distance]. For the head down orientation (i.e., 0deg turn), we predicted otolith encoding of tangential acceleration that reaches a minimal predicted encoding at 90deg head turn because the otoliths are aligned with the Earth-vertical axis of rotation. Predicted canal and otolith activity is shown in the stem plot. For otolith, both conditions normalized to saccule activity at 0deg (head down). 5.3. Methods 5.3.1. Participants Sixteen healthy young participants were recruited for Experiment 1 (7 females, age: 23.7 ± 3.9 years [mean ± SD]), and another nine (6 females, age: 24.4 ± 2.3 years) participated in Experiment 2. All participants were screened for any neurological deficits prior to participation in this study. Participants were informed about the experimental protocol, any possible discomfort associated, and the data’s public accessibility before given their informed consent. All procedures conformed to the standards of the Declaration of Helsinki and have been approved by the University of British Columbia’s Clinical Research Ethics Board [H19-00422 (2019-08-29)]. 5.3.2. Experimental setup Participants in both experiments were securely seated on a motorized rotary chair using a five-point harness (9411D 5-Point Harness System, RCi, TX, USA) within a darken, sound-proof room (Figure 5-1A). Layered foams were placed around the feet, legs, and torso to dampen possible 95 somatosensory cues associated with motor vibrations. A pair of noise-cancelling earbuds (QuietComfort 20, Bose, MA, USA) playing uniform white noise at a loud, but not uncomfortable, level was used to mask auditory cues. Critically, this study necessitated participants to be in specific head orientations to target specific vestibular sensor encoding. This approach has previously been done in isolating canal contributions (Von Brevern et al. 1997). We used a six-axis inertial measurement unit (IMU; MPU6050, Invensense, CA, USA) placed on the right cheekbone with double-sided tape inferior-lateral to the right eye to capture head pitch and yaw angles. The IMU was connected to a microcontroller (Feather MO, Adafruit Industries, NY, USA) running a custom Arduino script written in the Arduino Integrated Development Environment software (ver. 1.8.8, Arduino, USA). This allowed us to monitor head orientation angles in real-time using a remote desktop enabled laptop. The transformation matrix used to convert our recorded linear accelerations data from raw IMU frame into head-centric frame was determined by measuring the 3D gravitoinertial accelerations at two poses: when the reference plane was parallel and perpendicular to the ground. The reference plane in the first experiment was defined using Reid’s plane (an imaginary line passing through the inferior orbital rim and external auditory meatus) and in the second experiment, the horizontal semicircular canal plane (19° downwards head pitched from the original Reid’s plane). These positions were visually confirmed using a spirit level measuring the angle intersecting the orbital rim and auditory meatus external landmarks. After calibration, once an appropriate head orientation was achieved, a modified helmet (Pro-Tec, CA, USA) was used to secure the participants’ head to the chair’s frame. We performed a final visual verification to confirm that the midpoint of the interaural axis intersected with the motor’s rotational axis. Participants reported their perceived rotational displacement using a handheld device with a crank handle. This handle was attached to a continuous-turn potentiometer (6637S-1-103, Bourns, CA, 96 USA) that allowed participants to report rotational perception without disruption. The potentiometer was powered by a 9V battery, and its output scaled this input voltage from 0 to 9V through one revolution. As such, the time-varying rotational displacement a participant may perceive was measured by recording voltage changes induced by handle turns. Potentiometer-modulated voltages were digitized at an 18-bit resolution with a sampling frequency of 2,000Hz using a data-acquisition board (PXI-6289, National Instruments, TX, USA) controlled through a custom code written in LabVIEW (ver. 2013, National Instruments, TX, USA). 5.3.3. Motion stimulus We used a programmable platform attached to an alternating current servomotor (SGMCS-2ZN3A-YA21, Yaskawa, Japan; encoder angular resolution 0.00034°, continuous torque 200 Nm) to deliver whole-body rotational stimulus in all experimental conditions. A National Instrument’s real-time motion controller (PXI-7350, National Instruments, TX, USA) and its motion programming suite (ver. 2013, National Instruments, USA) were used to generate torque commands for a desired angular velocity motion profile, which were digitized at 100Hz and sent to a servo amplifier (SGDV-200A01A) through a motion interface (UMI-7774, National Instruments, TX, USA). All rotations were in the clockwise direction from participants’ point of view, conventionally defined as positive (+). The angular velocity stimulus profile consisted of a 10s onset ramp, a 90s constant angular velocity period, a 1s offset ramp, and a 60s period of constant zero-velocity rest (Figure 5-1B). The onset ramp from stationary rest to 45 deg⋅s-1 followed a raised cosine profile and the 90s constant angular velocity period ensured that participant’s perception reaches motionlessness which we previously observed to occur after 45-60s (Kuo 2019). Participants were brought back to stationary rest over 1s generated from the same, but reversed, raised cosine ramp shape. We only analyzed participants’ perceptual 97 responses during the offset ramp and in the following zero-velocity period to ensure responses were not confounded by non-vestibular cues associated with motion. 5.3.4. Experiment 1: Manipulating the canal contribution to self-rotation encoding We tested two competing hypotheses in our initial experiment by comparing perceptual responses (perceived angular velocity adaptation rate to step-velocity rotation) in three static head orientations. These were designed to activate the two-horizontal, the two-vertical, and the four-vertical semicircular canal pairs (Figure 5-1B, top). All orientations deliberately aligned the maximal directional sensitivity of a co-planar canal pair, or the vector sum for multiple co-planar canal pairs, to the axis of rotation. Simultaneously, given the near orthogonal arrangement between the left-anterior/right-posterior (vertical), right-anterior/left-posterior (vertical), and left-horizontal/right horizontal canal pairings, non-targeted canal pairs were minimally activated by aligning their respective directional selectivity perpendicular to the axis of rotation. We first hypothesized that perceptual responses are longer when encoded by a horizontal pair compared to a vertical canal pair. This was tested with two head orientations: one maximizing the two-horizontal canal pair and the other maximizing one of the two vertical (left-anterior/right-posterior) canal pairs. Participants’ head orientation started at the reference position, where Reid’s reference plane was horizontally parallel with respect to the ground. We then aligned the horizontal canals to their maximal sensitivity by pitching the head downwards 19o from the reference position to get the two-horizontal canal orientation. For the two-vertical canal orientation, participants pitched their head further downwards by 109o from the reference position and then yaw rotated their head 47o leftwards. We only tested one side for practicality. Our second hypothesis predicted that increasing number of encoding semicircular canals would result in shorter perceptual responses. This is because the amplitude of each individual canal would be lowered, leading to a diminished signal-to-noise ratio. Here, we 98 performed an additional head orientation condition maximizing activity from two-vertical canal pairs. To achieve this, participants pitched their head downwards 109o from the reference position. Perceptual responses were compared against the one-vertical pair condition. Altogether participants were tasked to report their perceived self-displacement in all three head orientations. 5.3.5. Experiment 2: Manipulating the otolith contribution to self-rotation encoding We performed a follow-up experiment to expand upon the results from Experiment 1 which supported the difference between vertical and horizontal canal types. However, the signal-to-noise ratio hypothesis was not supported as perceptual responses encoded by two-vertical pair lasted longer than those encoded by a one-vertical pair counterpart. We reasoned that vertical canals may benefit from concurrent otolith contribution as they are typically coupled during head pitch and roll motions. In this case, concurrent otolith stimulation changes as a function of head yaw for our head pitched down orientation, which may influence the duration of angular motion perception. The otolith stimulation here relates to the linear tangential acceleration experienced during changes in angular velocity (Figure 5-2, top left). We can express tangential acceleration [𝑎𝑇], experienced by the saccule and utricle as the product of the angular acceleration and the distance from the axis of rotation (Eq: 5-1): 𝑎𝑇(𝑡) = 𝑟𝛼(𝑡) Eq: 5-1 where 𝑟 (in cm) is the radius between the otolithic organ and the axis of rotation, and 𝛼 (in rad/s2) is the angular acceleration experienced by the head. We assumed an interutricular distance of ~4cm using human data from Nowé et al. (2003). 99 Figure 5-2: Modulation of otolith tangential acceleration signal with different head orientation. The otoliths can detect linear tangential acceleration during angular accelerations (top left). Left and right tangential acceleration vectors are oriented in opposing directions (c.f., purple and green arrows) which, when taken the vector subtraction (differential encoding), increase the net acceleration vector (dashed line inset). When the head is pitched down at 109o (Head Down Posture in Figure 5-1C), additional head yaw leads to decrease in radius between otolith and axis of rotation as a function of the cosine of the angle (bottom left). The grey arrows denote head turn angles at 0o, 45o, and 90o. These three angles correspond to the changes in saccule and utricle position with respect to the axis of rotation (right panel). At 0o, the otoliths are at the maximal possible radius, and the otoliths are aligned with the axis of rotation leading to minimal radius at 90o. Here, we again compared perceptual responses (perceived angular velocity adaptation rate to step-velocity rotation) from two static head orientations varying the otoliths’ radius from the axis of rotation while controlling for the number of- and type of- vertical canal activation (conditions: 4-vertical with otolith and 4-vertical without otolith; Figure 5-1B, bottom). The former condition was identical to the 4-vertical condition in Experiment 1: 109o head pitch without head yaw. For the second condition, participants performed a 90o head yaw rotation after the pitch rotation to align the left and 100 right otoliths with the axis of rotation. This orientation reduced the otolith radius to near 0, leading to a predicted minimal tangential acceleration that could be encoded by the otoliths. 5.3.6. Testing protocol The protocol in both experiments followed the same procedures. Participants were exposed to each condition over three trials (9 total in Experiment 1 and 6 total in Experiment 2). Conditions were presented in randomized order; however, all three trials for a given condition were performed consecutively. Participants were always given explicit instructions to close the eyes throughout the trial and to track their perceived rotational displacement. We manually rotated the rotary chair while explaining the perceptual instructions, and a test rotation (20s 0.1Hz sinusoid) was performed prior to experimental conditions to familiarize participants to the tracking task. Rest periods with room lights turned on were provided between trials and conditions for a minimum of one minute and five minutes, respectively. 5.3.7. Data reduction and signal analysis We extracted perceived displacement time-series during and after the rotational stimulus. To evaluate the effect of head orientation on the duration of the perceptual responses, we estimated exponential adaptation decay following the transition from constant angular velocity rotation to stationary rest. All data processing and analyzes were completed using a custom-code written in MATLAB (ver. 2018b, MathWorks, MA, USA). 101 5.3.8. Data processing Raw potentiometer voltage data (between 0 to 9V) map to the angular displacement of the potentiometer handle (0 to 360o). Edge transitions between 9V and 0V therefore signifies the wrapping around of the 360-0o angle limits (and vice versa). Prior to data processing, raw voltage waveforms were zero padded for 5s at the start and end. We then applied a Butterworth low-pass filter (2nd order, 10Hz cut-off) to remove high-frequency noise and hardware artifacts allowing for better edge-detection in the first order differentiated data for phase unwrapping. Our unwrapping algorithm was based on peak detection from the differentiated data denoting transitions back-and-forth between 0° and 360°. Once a transition was identified, we took the closest before and after data points which reached a threshold value of 0.05% of peak amplitude. The region between these two points was taken as the portion to unwrap. We extracted the data points 1s before and 60s after the transition from constant velocity to stationary rest from our unwrapped data to analyze post-rotatory responses. These extracted responses were further low-pass filtered (Butterworth, 4th order, 1Hz cut-off) and then differentiated to obtain the perceived angular velocity. All velocity traces were normalized to the peak value identified within the first 5s, and these normalized velocity traces were averaged between trials for each condition. This generated a set of trial-averaged perceptual responses (one for each condition) for a given participant (i.e., participants’ trial-averaged dataset). 5.3.9. Bootstrap and exponential fit analysis Two procedurally identical, but separate, bootstrap analyzes were performed on data obtained from Experiment 1 and 2. Our bootstrap analyses randomly resampled with replication (N=10,000) the participants’ trial-averaged dataset (Chen et al. 2020). Under this procedure, we made 102 no underlying assumptions about the distribution of our data and underlying population distribution while retaining paired observations by resampling responses from all conditions from each sampled participant. Furthermore, bootstrapping provides a robust estimate of means and confidence intervals to generate reliable estimates in the presence of potential outliers (Davison and Hinkley 1997). A uniformly distributed random matrix (10,000 × N participants) was generated based on the number of iterations and the number of participants tested; therefore, at each iteration, the number of sampled participants was equal to the original dataset. For a given iteration, the trial-averaged perceived velocity time-series was extracted from all sampled participants and then averaged. This was done for each condition creating a set of ‘participant-sampled’ group-averaged perceived velocity time-series responses. These group-averaged responses (𝜔), one for each condition, were fitted to a single-term exponential function (Eq: 5-2) following the least-squares approach using the fminsearch function in MATLAB. The starting data point for a given fit was the peak amplitude identified in the perceived angular velocity traces. 𝜔(𝑡) = 𝐴 ∗ 𝑒−𝑡𝜏𝑃 Eq: 5-2 We fitted both the exponential gain (𝐴) and time constant (𝜏𝑃); however, because the data were amplitude-normalized, only the time constant was evaluated in our bootstrap analysis. At the end of our 10,000 bootstrap iterations, we estimated three sets of bootstrap time constant, one for each condition. In Experiment 1, these conditions were the two-horizontal, two-vertical, and four-vertical conditions. In Experiment 2, we had the four-vertical with otoliths and four-vertical without otoliths. These two sets of bootstrap data were used for subsequent statistical analysis. 103 5.3.10. Bootstrap statistical analysis Statistical analyses on the bootstrapped time constant data sets were performed using a custom MATLAB code (ver. 2018b, MathWorks, MA, USA). Significance level was set at 0.05. For a given statistical comparison, we calculated the group-averaged time constant difference between conditions across each bootstrap iteration. This generated a bootstrapped mean difference distribution from which we estimated a bootstrapped 95% confidence interval (95% CI*). Statistical significance was determined by comparing whether this bootstrapped 95% confidence interval overlapped zero. We computed Cohen’s d effect size between head orientations using G*Power (version 3.1.9.7, The G*Power Team, Germany; Faul et al. 2009) based on the mean and standard deviation of perceptual rebound time constants in our original sample. Two comparisons were made for Experiment 1 to test two hypotheses: the difference between canal (vertical and horizontal) types and the difference between number of canals (2 and 4) encoding. Between canal types, we calculated the bootstrapped mean difference between the 2-horizontal canal and 2-vertical canal conditions. Between number of canals, we calculated the bootstrapped mean difference between the 4-vertical canal and 2-vertical canal conditions. In Experiment 2, we hypothesized that otolith encoding of angular self-motion, through tangential acceleration, would prolong the duration of the perceived angular motion duration (4-vertical canal with otoliths would be longer than 4-vertical canals without otoliths). 5.3.11. Vestibular sampling model incorporating otolith encoding We used our vestibular sampling model detailed in Chapter 3 to replicate observed percepts in this experiment. Our model uses Monte Carlo sampling to infer an internal representation of self-motion by taking samples (called particles) from different neural populations. These populations 104 represent afferent signals sensing external motion and a previously estimated internal representation of self-motion. Afferents encoding our experimental motion stimulus were primarily from the four bilateral vertical canals and the otoliths. Vertical canals encoded for the angular acceleration of rotation whereas the otoliths detected the linear tangential acceleration component of angular acceleration. An orientational model of the vestibular end-organs and their direction tuning selectivities was necessary to map each end-organ/afferents in space to estimate the magnitudes of encoded signal for a given head orientation (Naganuma et al. 2001; Rosenhall 1972a; Della Santina et al. 2005; Takagi and Sando 1988; Tribukait et al. 2005; Tribukait and Rosenhall 2001). The proposed mechanism for the otoliths relates to the tangential acceleration encoded during angular acceleration. In our experiment, the left and right otoliths were rotating about the Earth-vertical axis. As such, the tangential acceleration detected by the left otoliths would be similar in magnitude, but of opposite direction, to the right otoliths. We reasoned that a net vector subtraction could amplify both signals akin to a differential amplifier. This vector subtraction was assumed to simultaneously occur at two points. The first would be between the striola-divided otolith surfaces (where both halves have opposite directionally tuned afferents). The second would be between the left and right otoliths themselves. Additionally, we also considered the relative number of afferents between canals and otoliths. Morphological data (Bergström 1973b, 1973a; Lopez et al. 2005) suggested that primary afferents are roughly equally distributed among canal (anterior ~1562, posterior ~1652 & horizontal ~1558) and otolith (utricle ~3369 & saccule ~3100) end-organs. These ratios were used to allocate afferents samples to each end-organs. In our model, we have sensory particle populations from the transformation of angular velocity to firing rate (for canal afferents) and from the transformation of tangential acceleration to firing rate (for otolith afferents). It is unclear, how these particles from different sensors may be combined. In our implementation, we performed two independent simulations of the internal state: one with respect to the canal sensory particles (3 sets of canal particle 105 distributions) and one with respect to the otolith sensory particles (2 sets of otolith particle distributions). This created two distributions of internal state particles and was used as the input for an additional layer of sampling to generate the final internal (perceptual) representation. We simulated conditions for an otolith signal with maximal predicted encoding and minimal predicted encoding matching the head orientations tested in Experiment 2 (Figure 5-1C). We did 10 simulations and reported the average behaviour. In the first layer, sampling was independently performed between internal state and sensory canal (or otolith) particles. The probability density value of each particle was multiplied by the particle sampling probability calculated based on four factors: relative particle numbers (internal state-to-canals: 280:120, internal state-to-otoliths: 420:180), the relative particle distributions’ variance, the relative distributions’ weighting (internal state-to-canal: 1:1, internal-state-to-otolith: 2:1), and the amplitude of individual sensory particles. In the second layer, we have two internal representation distributions from the two separate first layer samplings of canal and otolith inputs. Similarly, the internal representation distributions were treated as input ‘sensory distributions’ to generate the final internal representation distribution. Relative particle numbers were: 700 (second layer internal state), 280 (from canal), and 420 (from otolith). Relative distribution weightings between second layer particle distributions were uniform at 1. Rebound time constants were estimated similarly to our experimental responses using Eq: 5-2. 5.4. Results In the first experiment, sixteen healthy participants were instructed to track their self-motion at different static head orientations (Figure 5-1B, top) designed to selectively target separate canal encoding of head rotation. We specifically evaluated two hypotheses: 1) self-motion is influenced by encoding canal type (horizontal vs. vertical), and 2) self-motion is influenced by the number of 106 encoding canals. Based on the results from Experiment 1, a second experiment was performed to evaluate the role of the otoliths in encoding angular self-motion mainly sensed by vertical canals. Here, an additional nine participants were tested following the same rotational stimulus in static head orientations designed to target otolith contributions, from most to none (Figure 5-1B, bottom). Stereotypical perceptual responses were observed in both experiments during stimulus onset and non-stationary constant angular velocity. Participants reported angular displacements with the same heading as the clockwise rotational stimulus, and perceived angular velocity returned to a state of no-motion approximately 15-40s after reaching constant angular velocity. Following the rapid (1s) deceleration back to stationary rest (Figure 5-3A), participants perceived self-rotation in the counter-clockwise direction, opposite to the preceding chair rotation. Perceived angular velocity, estimated from the differential of reported angular displacements, reached a peak value after 1 to 4s in Experiment 1 [two-horizontal = 2.3s ± 0.9; two-vertical = 2.2s ± 1.1; four-vertical = 2.4s ± 1.1 (mean ± SD)] and Experiment 2 [four-vertical with otoliths = 1.9s ± 1.0; four-vertical without otoliths = 2.3s ± 1.5] which was followed by an exponential decay with time constants ranging from 5 to 15s [Exp. 1 pooled: 8.8s ± 5.6; Exp. 2 pooled: 5.6s ± 3.2]. 107 Figure 5-3: Perceptual response and bootstrap procedure. (A) Representative participant response to our rotational stimulus (blue) Raw individual perceived angular displacement responses were initially wrapped between 0o to 360o (orange), and an unwrapping algorithm was used to correct for these discontinuities (red). We used finite difference on the perceived angle displacement to obtain the perceived angular velocity (green). The stationary constant velocity rest period occurred immediately after the offset ramp (step-input). This period was identified for each angular velocity trial to extract the perceptual responses timeseries. Each participant’s three trials (Exp. 1: N=16; Exp. 2: N=9) were peak-normalized and then averaged for each condition to create a ‘participant trial-averaged dataset’. This dataset was used for bootstrapping group-averaged time-constant across conditions. (B) We performed a bootstrapped procedure over K=10,000 iterations. In each ‘K-th’ iteration, we first randomly sampled the same number of participants (with replication) as the original input dataset. Next, this sampled participant trial-averaged dataset was averaged across participants within the same condition. We next fitted a single-term exponential function to estimate the time constants (𝝉𝑷) and these were taken as the rebound response decay time constants. Over all iterations, three sets of 10,000 (one for each condition) time constants were estimated for Experiment 1. Two sets were generated for Experiment 2. These sets of time constants allowed us to generate condition-wise bootstrapped time-constant distributions. To generate a mean-difference distribution for statistical comparisons, we calculated the difference between conditions for each iteration’s corresponding bootstrapped time-constants. A 95% confidence interval on this bootstrapped mean-difference distribution was calculated, and statistical significance was based on whether this interval crossed zero. 108 Figure 5-4: Individual and bootstrapped results for Experiments 1 and 2. (A) Results for Experiment 1. We estimated perceptual rebound response time constants in three conditions: angular head motion encoded by 4-vertical, 2-vertical, and 2-horizontal canals. Top panel shows data for each condition: individual participant perceptual time constant is represented by dots with variability presented in the boxplot. Results from our bootstrap procedure for each condition are shown above the corresponding boxplot. The bootstrap results show the kernel smoothing function estimated probability density, and the red-line shows the bootstrapped 95% CI*. The bottom panel shows the mean difference comparison(s). Boxplot similarly shows within participant mean difference comparison conditions. The bootstrapped mean difference distribution and 95% CI* are shown above the corresponding boxplot. A mean difference 95% CI* that crosses zero was consider statistically significant. Between number of canals, the 4-vertical condition was significantly more prolonged than the 2-vertical condition. Between canal types, the 2-horizontal condition was significantly more prolonged than the 2-vertical condition. (B) Results from Experiment 2 show perceptual rebound response time constants in two conditions: angular head motion encoded by 4-vertical canals with otoliths and 4-vertical canals without otolith. Similar procedure is shown for individual participant data, and bootstrap results for each condition (top) and mean difference (bottom). 95% CI* showed that response was significantly more prolonged with otolith than without otolith. 5.4.1. The perception of self-rotation is longer when motion is encoded by the horizontal canals We first examined whether perceived angular velocity differed when rotation was encoded by horizontal or vertical canals while controlling for the number of canals encoding the motion (2-horizontal and 2-vertical canals). Perceptual rebound time constant for the 2-horizontal condition 109 [11.1s ± 6.3] was on average longer than those in the 2-vertical condition [6.6s ± 3.1]. Cohen’s d effect size was 0.91. Bootstrapped sample distributions showed similar prolongation (2-horizontal 11.7s [8.6, 15.4], 𝜇∗ [95%𝐶𝐼∗]; 2-vertical: 6.6s [5.0, 8.3]), with a significant bootstrapped mean difference of 5.1s [2.8, 8.1] supporting this difference (Figure 5-4A). 5.4.2. The perception of self-rotation is prolonged when more canals encode motion We next examined whether the duration of perceived angular velocity decreases with the number of encoding canals. While controlling for canal types, we assessed two head orientations targeting two- and four-vertical canals. The average perceptual rebound time constant was longer when angular motion was encoded by 4-vertical canals [8.7s ± 6.1] than the 2-vertical canals [6.6s ± 3.1]. Cohen’ d effect size was 0.43. This result was counter to our initial hypothesis. Bootstrapped sample distributions confirmed these results (4-vertical: 9.3s [6.5, 12.6]; 2-vertical: 6.6s [5.0, 8.3]), with a bootstrap mean difference of 2.7s [0.62, 5.48] calculated between the 4-vertical and 2-vertical conditions (Figure 5-4A). Given observed differences between canal types, and the unexpected prolongation in the 4-vertical compared to 2-vertical conditions, we subsequently evaluated the role of otoliths on our perception of self-rotation. 5.4.3. Differential otolith signals encoding angular acceleration prolong the perception of self-rotation In Experiment 2, we examined the otolith contribution to perception of self-rotation. We considered the linear tangential acceleration encoded by the otoliths during angular acceleration as a means to provide additional angular information to the brain. Following this rationale, we compared perceived angular velocity at two head orientations: angular motion encoded by 4-vertical canals and the otoliths vs by 4-vertical without otolithic stimulation. Both orientations were encoded by all four 110 vertical canals, but in the latter, the otoliths were aligned to the axis of rotation thereby eliminating any tangential acceleration (Figure 5-1C & Figure 5-2). The average perceptual rebound time constant was longer when the otoliths were not aligned to the axis of rotation (tangential acceleration present) [4-vertical canals with otolith: 6.0s ± 3.1] than when they were aligned (minimal tangential acceleration) [4-vertical canals without otolith: 4.1s ± 1.2]. Effect size estimated with Cohen’s d was 0.81. Subsequent bootstrap sample distributions supported our observations: the time constant for motion encoded by 4-vertical with otoliths (6.7s [4.5, 8.9]) was longer than those without (4.4s [3.2, 4.9]). The Bootstrapped mean difference distribution revealed a significant difference of 2.5s [0.6, 4.3] (Figure 5-4B). 5.4.4. Simulations of perceptual response with and without otolith encoding Using the framework of our sampling model, we simulated the sensing and internal representation (perceived angular velocity) results from a constant angular velocity step change input experienced by participants in Experiment 2. In the two head orientations/conditions, semicircular canal encoding of angular velocity were predominately by all four vertical canals: the left anterior/right posterior pair and right anterior/left posterior pair. Conversely, otolith encoding of tangential acceleration was only present when the head was pitched down. As the head yawed to 90o at this pitched angle, the otoliths became aligned to the axis of rotation thus minimizing the tangential acceleration amplitude detectable by the otoliths. We assumed a linear combination of bilateral otolithic afferents wherein the vector difference causes an increased signal amplification. Given a salient otolith signal, simulated internal representation responses had a time constant 5.7s (Figure 5-5, left). However, with minimal otolith signal, simulated perceptual responses had a time constant of 4.5s (Figure 5-5, right). 111 Figure 5-5: Sampling model simulation results. Simulation results from our sampling model with (left) and without (right) salient otolith signal for a clockwise step input used in our experimental motion profile. Results (internal representation) from first layers of sampling of canal (top) and otolith (middle) signal. Second layer of sampling generates the final (perceptual) internal representation (green). Both with and without salient otolith signal produced similar simulated perceptual responses. 5.5. Discussion The purpose of this study was to examine how vestibular sensory inputs from distinct end-organs contribute to our perception of self-motion. We first targeted the semicircular canals based on their type (2 horizontal vs. 2 vertical) or number (2 vertical vs. 4 vertical) using known directional selectivity of each vestibular end-organ/afferent in the vestibular apparatuses. Perceived rebound response time constants were longer when horizontal canals encoded the motion than when vertical canals provided sensory signals of head rotation. Contrary to our hypothesis, the perception of self-rotation was also prolonged when more canals encoded the angular motion. These results only partly supported our hypotheses which led us to further evaluate the potential role of the otoliths on perceptual self-rotation due to their potential encoding of linear tangential acceleration during 112 angular acceleration. Controlling for canal type and number (4-vertical canals), we observed a shorter perceptual time constant when the otoliths were aligned to the axis of rotation (i.e., expect tangential acceleration is 0), supporting a potential role of the otoliths for encoding self-rotations. Response decay in perceived angular velocity was prolonged when encoded by 2-horizontal canals (~11.0s) relative to that encoded by 2-vertical canals (~6.0s). Changes in head orientation were necessary to achieve these two conditions while remaining gravity neutral (Earth-vertical rotation). In head-centred coordinates, the 2-horizontal canal orientation resembles a head yaw motion whereas the 2-vertical canal orientation was akin to a head pitch motion. This distinction should be made as prior studies measured responses without strictly controlling head orientation. For example, head upright is assumed to activate mainly the two horizontal canals and left (or right) ear down head orientation is assumed to activate mainly two vertical canals. The difference we observed between the 2-horizontal and 2-vertical canal conditions was consistent with previously reported perceptions (Bertolini et al. 2011; Okada et al. 1999; Shaikh et al. 2013) which were about two times longer in yaw (~10.0-15.0s) compared to pitch (~4.0-6.0s). The difference between horizontal and vertical canal types were present in other conditions. For example, when evaluating the frequency response between gravity-neutral and gravity-dependent conditions in head yaw, Bockisch et al. (2005) showed that the yaw ocular response (primary encoded by horizontal canals) was similar in gravity-neutral and gravity-dependent conditions. However, differences were present in ocular responses to head roll and pitch, which suggest that otolith signals likely interact with vertical canals (and less so with horizontal). This interaction is speculated to be associated to the coupling between the vertical canals and otoliths during head pitch and roll in natural movements (Bello et al. 1991; Bockisch et al. 2005; Tweed et al. 1994). 113 While controlling for canal types (comparing only vertical canals), we evaluated head orientations that encoded Earth-vertical rotation with 4-vertical or 2-vertical canals to determine if the number of encoding canals would influence our perception of self-rotation for a given rotation. In our study, we found longer self-rotation perception when motion was encoded by 4-vertical canals (9.3s; close to head roll) compared to 2-vertical canals (6.6s; close to head pitch) encoding. These observations did not support our initial hypothesis that shorter perceptual time constants would be observed when a given head angular velocity was decomposed into multiple components encoded by multiple semicircular canals. A comparison could be made to previous studies examining self-motion perception during head roll and head pitch rotations. Head roll rotations were typically performed in a supine posture (Grunfeld et al. 2000; Seidman and John Leigh 1989; Shaikh et al. 2013) whereas our study was close to a head prone. Head pitch rotations were done with the left or right ear pointed towards the ground. Direct comparisons of self-motion perception between head pitch and roll are limited (Shaikh et al. 2013), whereas the majority of comparisons are between head pitch and yaw (Bertolini et al. 2011, 2012; Shaikh et al. 2013) or only head yaw (Okada et al. 1999; Sinha et al. 2008). In general, the reported time constants for perception of head roll motion were shorter (~6.1s) than those for the perception of head pitch motion ( ~ 6.0-7.9s). However, this difference should be approached with caution as direct comparison, such as the study by Shaikh et al. (2013), had a limited number of participants (n=6). Given the lack of support for our second hypothesis, we tested the possible involvement of the otoliths, arguing that these end-organs may provide an angular signal mediated by their encoding of tangential acceleration. This is contrary to the otolith-mediated post-rotatory head-tilts which abolish step-response perceptual prolongation as participants in our studies were held at a static orientation throughout (Waespe et al. 1985). We compared two head orientations that minimize and 114 maximize otolith tangential acceleration encoding by respectively aligning, or not, the bilateral otoliths’ position in space with the Earth-vertical axis of rotation while controlling for the number and type of canal encoding (4-vertical). We found a significant prolongation in mean perceptual time constant (2.5s) with otoliths (no alignment) relative to without otoliths (maximal alignment). Critically, because vertical canal activity was matched in both conditions, we attributed this prolongation to be a result of otolith encoding. The signal detected by the otoliths are small, but detectable as the expected tangential acceleration ( ~5.4 cm/s2) is near or above detection thresholds of otoliths afferents (Yu et al. 2012). In addition, the perception threshold for linear acceleration is lower than the detection thresholds of the otoliths suggesting that otolith afferents are pooled as a sensory integration strategy (Jamali et al. 2019). Even though the otolith hair cells are expected to transduce tangential acceleration during angular acceleration similarly to linear translational acceleration, it remains unclear if the perceptual threshold to tangential acceleration would decrease similarly. We assumed a bilateral differential computation when combining two oppositely directed signals. The vector subtraction of two opposite signals leads to an amplification of the encoding tangential acceleration thereby producing a more salient signal. Indeed, our result suggests a small, but significant, contribution of the otoliths to angular motion perception. We proposed a sampling-based model for dynamical estimation based on vestibular information. In the model, rotational information is represented by a particle ‘sample’ encoded either by primary vestibular afferents (sensory distribution) or by an internal state (state distribution) representing the central neurons. The sampling algorithm weighs each particle based on their distribution’s statistical properties comparable to other particle-based vestibular models (Karmali and Merfeld 2012; Laurens and Droulez 2007). We distributed information of rotation across the six canals, two saccules and two utricles using an orientational model of the vestibular end-organs, their 115 direction tuning selectivities (Naganuma et al. 2001; Rosenhall 1972a; Della Santina et al. 2005; Takagi and Sando 1988; Tribukait et al. 2005; Tribukait and Rosenhall 2001), and relative afferent distribution (Bergström 1973b, 1973a; Lopez et al. 2005). This allowed us to predict the expected end-organ contribution for a given head orientation. The proposed mechanism for the otoliths relates to the tangential acceleration encoded during angular acceleration. This role of tangential, not gravitational, acceleration is supported by translational otolith compensation after labyrinthectomy in mice (Khan et al. 2019). In our experiment, the left and right otoliths were rotating about the Earth-vertical axis. As such, the tangential acceleration detected by the left otoliths would be similar in magnitude, but of opposite direction, to the right otoliths. We implemented a net vector subtraction at the striola-divided otolith surfaces and between the left and right otoliths themselves. We implemented a change to our purposed model in Chapter 3. Here, we independently simulated the internal state representation with respect to the canal sensory particles (3 sets of canal particle distributions) and with respect to the otolith sensory particles (2 sets of canal particle distributions). This created two distribution of internal state particles. An additional layer of sampling was performed from these two distributions to generate the final internal (perceptual) representation. This method was done as an attempt to integrate multiple sensors (otolith and canals) within the central integration process. Simply pooling the sensory particles without this secondary layer further reduces the influence of the otoliths because of their lower overall amplitude. Despite this, our model, as it is currently constructed, was insufficient in capturing the difference observed in our experimental data. We may be underestimating the simulated amplitude of the otolith particles in either: 1) how we estimated the maximal tuning vector, 2) underestimate the otolith’s radius with respect to the axis of rotation, and/or 3) underestimate the ratio of irregular to regular afferent. All these parameters can change the salience of input otolith signal in our model. Undoubtedly, the brain’s computations and 116 structure are more nuanced in its design. This proposed sampling model attempted to add physiological context as to how our brain estimate states such as self-rotation perception. How the distributions are allocated between incoming sensory information and existing internal state information (and even the sampling process) remains contentious and arbitrary chosen. Future work should further attempt to identify models parameters supported by new intuitions about how vestibular afferents are combined (Forbes et al. 2023) in different scenarios. Limitations in our study include the evaluation of only the time profile of the perceptual response but not its magnitude. This was not done because our reporting device was not systematically calibrated. A future study should identify vestibular-only perceptual magnitude and calibrate the results to perceptions observed during experimental stimulus. Because we only recorded perception, we can not make any conclusions about the vestibular-ocular reflex, despite similar trends observed in the literature (Bertolini et al. 2012; Shaikh et al. 2013). However, given that the ocular pathways favours input from regular afferents (Cullen 2019), it may not be surprising that the transient tangential acceleration encoded by the otoliths may be weak or not considered for controlling eye motion. Lastly, we can not entirely dismiss potential effects associated with attention or positional discomfort on vestibular perception. Additional work using a more ergonomic experimental setup or addressing the influence of discomfort on velocity storage would address this concern. In conclusion, our study reveals that semicircular canals are not identically integrated by the brain to give rise to a perception of self-motion. We notably provide evidence supporting that the otoliths can detect angular motion without gravity but rather mediated through tangential acceleration. How the canal and otolithic signals combine, however, remains open. Our sampling 117 model provides a novel framework for integrating signals from multiple sensors, enabling further investigations into how sensory channels are combined within the brain. 118 Chapter 6. Replicating real self-motion perception using electrical vestibular stimulation 6.1. Preamble2 With the growing popularity of electrical vestibular stimulation (EVS) in biomedical and immersive reality applications, a direct conversion model between electrical and mechanical vestibular stimuli is needed. We developed a model to generate electrical stimuli mimicking the physiological activation of vestibular afferents evoked by mechanical rotations. We validated this model by comparing ocular torsional responses from mechanical (chair rotation) and model-derived electrical (binaural-bipolar) stimuli in separate experiments for an angular velocity step-change (±10deg⋅s-1 over 1s, ±4mA peak amplitude) [N=10] and multi-sine angular velocities (±10deg⋅s-1, ±4mA peak, 0.05-1Hz) [N=5], respectively. Perception of whole-body rotation was subsequently evaluated to our step-change stimulus [N=18]. 6.2. Introduction The central nervous system uses sensory cues such as visual, vestibular, and somatosensation to encode an internal representation of self-motion. In the absence of vision, primary vestibular afferents from the otolith and semicircular canal (SCC) end-organs are the predominant encoders of head motion and orientation in space through rate and temporal coding (Jamali et al. 2016; Sadeghi et al. 2007a; Schneider et al. 2015b). While the otolith and SCC hair cell receptors are respectively sensitive to linear and angular accelerations of the head in space, electrical current applied over the mastoid processes or directly within the inner ear can also activate the primary vestibular afferents 2 A version of this chapter has been previously published as Chen, A., Khosravi-Hashemi, N., Kuo, C., Kramer, J. K., & Blouin, J.-S. (2020). Development of a conversion model between mechanical and electrical vestibular stimuli., J Neurophysiol., 123(2), 548-559. Available at http://doi.org/10.1152/jn.00276.2019. 119 and/or hair cells (Aw et al. 2008; Curthoys and MacDougall 2012; Gensberger et al. 2016; Goldberg 2000; Goldberg et al. 1982, 1984; Kim and Curthoys 2004; Kwan et al. 2019). In nonhuman primates, transmastoid electrical vestibular stimulation (EVS) modulates the firing rate of primary vestibular afferents from both end-organs with increased gain at higher stimulation frequencies (Kwan et al. 2019). Although the irregular afferents from the otolith and SCC exhibit a larger gain than regular afferents to electrical stimuli applied percutaneously, their increased variability results in similar thresholds to the electrical stimuli (Kwan et al. 2019). Assuming that all primary vestibular afferents are activated during transmastoid EVS, the summation of unit vectors representing the orientations of the SCCs forms a net EVS-evoked rotation vector accompanied by a negligible net linear vector because of the near cancellation of otolithic components due to their hair cell orientation on the macula (Fitzpatrick and Day 2004; Mian et al. 2010). As a result of this net summation, transmastoid EVS evokes sensations of ‘virtual’ head roll rotation, as well as compensatory eye movement, balance, and navigation responses in humans (Day and Fitzpatrick 2005; Fitzpatrick et al. 2002a, 2006; Mackenzie and Reynolds 2018a; Peters et al. 2015; Reynolds 2011a; Schneider et al. 2002; St George et al. 2011; Tisserand et al. 2018). Due to the growing interest for EVS in both biomedical (Blini et al. 2018; Bunn et al. 2015; Oppenländer et al. 2015; Wilkinson et al. 2014) and immersive reality applications (Aoyama et al. 2017; Cevette et al. 2012; Nakayama et al. 2018; Preuss and Ehrsson 2019), providing a way to electrically induce virtual sensations of motion that have realistic mechanical equivalents would be a major step towards integrating EVS into those industries. Because transmastoid EVS is driven by the net-evoked virtual rotation of the head, eliciting realistic motion sensation requires the matching of sensory response with those arising from mechanical rotations of the head (Schneider et al. 2002; Day and Fitzpatrick 2005; Peters et al. 2015; St George et al. 2011). The SCC end-organs are inertial sensors responding to head angular 120 accelerations. For an impulsive head angular acceleration resulting in a step-change in head angular velocity, the endolymph lags behind the rotation of the canals because of its inertia thus exerting pressure on the cupula and activating hair cell receptors innervated by primary vestibular afferents. This causes an initial canal afferent response followed by an exponential response decay with a time constant of 3‒7s (Dai et al. 1999; Dickman and Angelaki 2004). For sinusoidal angular accelerations above 0.05Hz, the frequency at which the vestibular afferents are modulated matches the frequency of the input acceleration (Fernandez and Goldberg 1971; Ramachandran and Lisberger 2006). Additional central processing of signals originating from primary vestibular afferents prolongs the central estimate of head angular velocity through a multisensory process known as the velocity storage (Cohen et al. 1981b; Karmali and Merfeld 2012; Laurens and Angelaki 2011; Raphan et al. 1979; Raphan and Cohen 1985; Yakushin et al. 2017). The velocity storage results in a prolongation (10-20s) of the evoked vestibulo-ocular reflex (VOR) and perception of self-rotation relative to peripheral vestibular nerve activity. This, however, depends on the head orientation relative to the axis of rotation (Bertolini et al. 2011; Bertolini and Ramat 2011; Cohen et al. 1981b; Raphan and Cohen 1985, 2002; Seidman et al. 1995; Seidman and Leigh 1989). Due to the anatomical orientation of the SCCs and assuming that transmastoid EVS applied in a binaural-bipolar configuration activates all primary vestibular afferents (Kwan et al. 2019; Della Santina et al. 2005), EVS delivered at a nose-down head pitch orientation (~71‒73°) is expected to evoke ocular torsional movements and a sensation of head roll around Earth’s vertical axis (Fig. 1A; Day and Fitzpatrick 2005; Khosravi-Hashemi et al. 2019; Peters et al. 2015; St George et al. 2011). When the net EVS-evoked rotation vector has a component orthogonal to gravity, the brain infers a sensation of interaural or superior-inferior linear acceleration coupled to the sensation of self-rotation due to the integration of otolith-SCC signals and an internal representation of gravity (Khosravi-Hashemi et 121 al. 2019). Despite mechanistic differences in vestibular hair cells and/or primary vestibular afferents activation between stimulus modalities, the central processing of EVS-evoked virtual rotations would be expected to share common pathways to those underlying mechanically-evoked real rotations. Several studies have exploited these assumptions to compare ocular or perceptual responses between mechanical and electrical stimulations. St George et al. (2011), for instance, analyzed perceptual decay dynamics during a direct current EVS pulse (square wave) and a constant angular velocity mechanical pulse in standing humans. Similarly, mechanical rotations and EVS were used to compare vestibular perception in seated participants (Cutfield et al. 2011; Peters et al. 2015). Prior studies, however, focused on ocular responses to EVS (Schneider et al. 2000; Watson et al. 1998) where, notably, Schneider et al. (2002) concluded that a direct current EVS pulse was equivalent to a constant angular acceleration. In spite of these comparisons, a direct numerical relationship must be established in order for us to apply electrically-evoked and mechanically-evoked rotations interchangeably. The goal of the current study was to develop a mechanical to electrical vestibular stimulus conversion model to interchangeably derive a time-varying electrical current stimulus equivalent for a given mechanical head motion. We adapted transmastoid EVS to canal afferent transfer functions identified in nonhuman primates (Kwan et al. 2019) and tested, in humans, a mechanical to electrical vestibular stimulus conversion model that accounts for the physiological activation of primary vestibular afferents for step-change and multi-sine angular velocity stimuli. We predicted that by matching the activation of primary vestibular afferents for mechanical and electrical stimuli, the ocular and perceptual response dynamics would be similar. The present study represents a critical initial step towards generating virtual motion for a desired real mechanical motion while improving our understanding of the central processing of electrical vestibular stimulation. 122 Figure 6-1: Illustration of head orientation, rotary chair, and stimulus signals. (A) participant seated on rotary chair setup. An infrared camera is attached to a bite bar (top) and a helmet is affixed to the chair carriage (bottom) for experiment 1 and 2, respectively. Dual-layer memory foam padded participants’ feet, chest, forearms, and shanks but is not depicted for clarity. (B): net electrical vestibular stimulation (EVS)-evoked rotation vector depicting clockwise (CW) and counterclockwise rotation (CCW) for nose-forward head roll (top) and nose-down head roll (bottom). (C): electrical and mechanical vestibular stimuli produced ocular torsion and perception of whole body yaw rotation about Earth’s vertical axis. Mechanical (chair) angular velocity (top) consisted of a step change to ±10 deg/s over 30 s (experiment 1) or 45s (experiment 2) followed by a step change back to 0 deg/s rest. Note the different timescales (represented by horizontal bars) for experiments 1 and 2 (5.0 and 7.5 s, respectively) due to different stimulus durations. Time-varying model-derived electrical current stimulus that mimics the pattern of primary vestibular afferent activation evoked by the mechanical stimulus is shown at bottom. Data acquisition occurred at the start of stimulus onset, and data were analyzed following the period after the return to 0 deg/s rest. 123 6.3. Methods Two initial experiments were performed on separate days to evaluate ocular and perceptual responses between a mechanical step change in angular velocity and a model-derived electrical current equivalent. In experiment 1, ocular responses from 12 participants (7 women; age: 23.4 ± 3.9 yr; mean ± SD) were recorded through video-oculography. In experiment 2, 18 separate participants (9 women; age: 25.0 ± 3.8 yr) reported their perceived whole body angular velocities. A third experiment was performed on five participants (1 woman; age 23.4 ± 2.3 yr) to examine the generalizability of our mechanical-to-electrical vestibular stimulus conversion model by comparing ocular responses to a multisine angular velocity stimulus with its electrical equivalent. All participants had no known neurological diseases or injuries before taking part in the study. They were informed about the experimental protocol and possible discomforts involved before their written informed consent was obtained. All procedures conformed to the standards of the Declaration of Helsinki and were approved by the University of British Columbia’s Clinical Research Ethics Board [H09-00987 (2017-03-24), H19-00422 (2019-08-29)]. 6.3.1. Setup Participants were seated on a rotary chair. A series of procedures were performed to minimize non-vestibular cues of motion (Figure 6-1A). First, participants were fastened using a five-point racing harness (9411D 5-point harness system; RCi) padded with dual layered memory foam secured around their feet, chest, forearms, and shanks. This minimized potential somatosensory cues associated with whole body chair motion by dampening motor and chair vibrations. An 80-mm computer fan (KD1208PTB3-6; Sunon, Taiwan; airflow 0.85 m3/min) was positioned in front of the participant’s face to mask air movement associated with whole body motion. Auditory cues from the chair’s servomotor 124 were masked by disposable earbuds and noise-cancelling headphones (QuietComfort 25 acoustic noise cancelling headphones; Bose) playing uniform white noise. All experiments were performed in complete darkness to remove visual cues. Last, we applied anesthetic AMETOP gel (tetracaine HCl gel, 4% wt/wt; Smith & Nephew, UK) over the skin on the mastoid processes 30 – 45 min before all perceptual recordings to minimize cutaneous cues associated with the electrical stimuli. Once all sensory masking procedures were performed, the participant’s head was pitched downward by ~71–73° relative to Reid’s plane (plane passing through the inferior orbital rim and external auditory meatus) being parallel to the ground. At this nose-down head pitch orientation, the EVS-evoked rotation vector derived from the vector summation of the unit vectors normal to canal planes was parallel to Earth’s vertical axis (Day and Fitzpatrick 2005; Fitzpatrick and Day 2004; Della Santina et al. 2005). Electrical stimulation at this head orientation induced a virtual head roll perception about the Earth’s vertical axis, matching our mechanical stimulus (Peters et al. 2015, 2016; Schneider et al. 2002; St George et al. 2011). This head-down orientation avoided potential conflicts between EVS-evoked signals of head rotation from the SCCs and a lack of expected otolith signals encoding head orientation changes within the gravitational field when the EVS-evoked vector has a component orthogonal to gravity (Khosravi-Hashemi et al. 2019). Head angles were confirmed at the beginning and halfway during testing using a spirit level and protractor. We secured participant head orientation using a bite-bar fitted to the participant’s dental impression (eye movement recording; Defend vinyl polysiloxane impression material) or a helmet (perceptual recording; Classic Skate; Pro-Tec) affixed to the chair carriage. 6.3.2. Vestibular stimuli Mechanical whole body rotations (head roll in head-centred coordinates due to the nose-down posture) were delivered using a programmable rotary chair controlled through a real-time 125 motion controller at 100 Hz (PXI-7350 motion controller and Universal Motion Interface UMI-7774; National Instruments) incorporating the NI Motion Programming suite (National Instruments). Torque commands were sent by the motion controller to a servo amplifier (SGDV-200A01A; Yaskawa, Japan) powering an alternating current motor (SGMCS-2ZN3A-YA21; Yaskawa, Japan; encoder angular resolution 0.00034°, continuous torque 200 Nm). A clockwise (CW) rotation is positive (+) and a counterclockwise (CCW) rotation is negative (-) to represent, by convention, rotations around a positive Z-axis pointing to the ground. In experiments 1 and 2, the applied mechanical stimulus profile consisted of a step change in angular velocity from 0 to 10 deg/s over 1 s with a constant angular velocity duration of 30 and 45 s, respectively. A symmetrical offset step change in angular velocity from 10 to 0 deg/s brought the chair angular motion back to stationary rest (Figure 6-1C, top). In experiment 3, the mechanical stimulus profile was a multisine angular velocity oscillation of 10 deg/s peak amplitude (root mean square: 4.73) lasting 60 s with equal power at 0.05, 0.1, 0.2, 0.5, and 1.0 Hz. The 60-s motion oscillation consisted of three repeating 20-s segments. The multisine mechanical stimulus was generated using a custom MATLAB (R2017a; The MathWorks) function (Forbes et al. 2014). Virtual whole body rotations (head roll in head-centred coordinates due to the nose-down posture) were induced by electrical current applied in a binaural-bipolar configuration. Carbon rubber electrodes (9 cm2) coated with 1 mL of conductive electrode gel (Spectra 360; Parker Laboratories) were secured over the left and right mastoid processes with hypoallergenic tape (Durapore; 3M). Electrical current waveforms were digitized at 1,000 Hz using a multifunction data acquisition (DAQ) board (PXI-6289; National Instruments) and sent through a constant-current stimulus isolation unit (STMISOLA; Biopac Systems). Based on our electrode configuration and convention for mechanical rotations, a cathode right/anode left current represented a clockwise (+) virtual rotation and a cathode 126 left/anode right current represented a counterclockwise (-) virtual rotation. Time-varying mechanically equivalent electrical current waveforms were generated by using our mechanical-to-electrical stimulus conversion model implemented in MATLAB to replicate the activation of the primary SCC afferents expected from the mechanical stimulus. The electrical current waveform equivalent to our angular velocity step change mechanical stimulus consisted of an initial onset peak decaying over the mechanical constant angular velocity phase (30 s for experiment 1 and 45 s for experiment 2), which was followed by a symmetrical but inverted offset profile (Figure 6-1, bottom) to represent the transition from 10 to 0 deg/s. The multisine equivalent electrical current waveform was generated by identically passing the mechanical multisine angular velocity profile through the mechanical-to-electrical vestibular stimulus conversion model. The output current waveform resembled a multisine signal (see Figure 6-5A, top). The mechanical-to-electrical vestibular stimulus conversion model (Figure 6-2) first computed the expected primary afferent dynamics for a given input mechanical angular velocity waveform using a 4-s time constant to represent the decay in SCC afferent activity (C in Eq: 6-3; Fernandez and Goldberg 1971). The expected SCC afferent response was then passed through two inverted transmastoid EVS-to-SCC afferent transfer functions to represent the responses of the regular (Hr, 𝐻𝑟𝑒𝑔𝑢𝑙𝑎𝑟 , Eq: 6-1) and irregular (Hir, 𝐻𝑖𝑟𝑟𝑒𝑔𝑢𝑙𝑎𝑟 , Eq: 6-2) SCC afferents established by Kwan et al. (2019): 𝐻𝑟𝑒𝑔𝑢𝑙𝑎𝑟(𝑠) = 2.83𝑠 (𝑠 +10.0175)(𝑠 +15.7) (𝑠 +10.0027) Eq: 6-1 𝐻𝑖𝑟𝑟𝑒𝑔𝑢𝑙𝑎𝑟(𝑠) = 27.09𝑠 (𝑠 +10.03)(𝑠 +15.7) (𝑠 +10.0006) Eq: 6-2 127 We used a 3:1 weighting on regular-to-irregular afferent contributions based on the assumption that there were three times more regular than irregular afferents because all afferents were assumed to be activated (Baird et al. 1988; Goldberg 2000a). We multiplied the resulting output by a gain (K) to represent the scaling difference in our EVS to primary afferent transfer functions between nonhuman primates and humans due to anatomical differences in head size. Eq: 6-3 describes the relationship between electrical and mechanical stimulation: 𝐸𝑉𝑆 = 𝐾 ∗ (0.75 ∗ [𝑖𝑛𝑣(𝐻𝑟) ∗ 𝐶 ] + 0.25 ∗ [𝑖𝑛𝑣(𝐻𝑖𝑟) ∗ 𝐶]) Eq: 6-3 where K is the gain and C denotes the afferent activity resulting from the mechanical rotation. In other words, C represents the output of the transfer function representing the canal-cupula dynamics (Figure 6-2, blue dashed box). Based on previously reported direction discrimination thresholds to electrical and mechanical whole body rotations, the angular velocity-to-electrical current gain was between ~0.15 and 0.60 mA per deg/s from 0.05 to 0.5 Hz (Peters et al. 2015), differing from the 0.06 to 0.2 mA per deg/s identified in nonhuman primates (Kwan et al. 2019). For experiments 1 and 2, we used a gain K of 2.20 in Eq: 6-3 to account for these differences between nonhuman primates and humans. Consequently, the output from Eq: 6-3 will transform a 10 deg/s peak whole body rotation applied over 1 s into a 4.0-mA peak electrical stimulus (i.e., 0.40 mA per deg/s). We evaluated this proposed gain K by comparing peak ocular torsional slow-phase velocity responses between mechanical and electrical stimulations. Results from experiment 1 showed that peak ocular torsional slow-phase velocity responses were slightly higher during EVS; thus, we revised the original gain K to achieve a conversion factor of 0.37 mA per deg/s (for a step change in angular velocity) to better match responses in experiment 3. 128 Figure 6-2: Conceptual illustration of vestibular processing used in the mechanical-to-electrical stimulus conversion model. Expected primary afferent activity (firing rate) was derived for a given input head angular velocity (𝜔𝑣) by passing through canal-cupula dynamics [H(s)SCC] modeled as a high-pass filter where 𝜏𝑐 = 4s. Other sensory cues (e.g., visual, somatosensory, auditory) were assumed to be absent. Input electrical current (IEVS) was estimated from 2 inverted EVS-to-afferent transfer functions representing regular [H(s)r] and irregular [H(s)ir] units. Regular and irregular units were weighted at a 3:1 ratio and multiplied by a gain (experiments 1 and 2: K = 2.20; experiment 3: K = 2.04). In our experiments, either the electrical or the mechanical stimulus was delivered; however, both stimuli were assumed to activate primary vestibular afferents and would be additive if delivered simultaneously. Both IEVS and 𝜔𝑣 were assumed to pass through the same central processing mechanism to produce a central state estimate (?̂?) generating compensatory eye movement and perception of self-motion. 6.3.3. Protocol Experiment 1 aimed to validate our model-derived electrical stimulus and to compare central processing between electrical and mechanical stimuli through the torsional VOR. The applied electrical current waveform was designed to replicate the physiological activation of primary vestibular afferents during a step change in angular velocity to the head (see Vestibular stimuli), thereby making the two stimuli equivalent at the primary SCC afferent level (Figure 6-2). Participants were exposed to four experimental blocks: mechanical CW, electrical CW, mechanical CCW, and electrical CCW rotations; each block consisted of 10 trials with 40 trials in total. The order of these blocks was 129 randomized between participants. Right eye movements were recorded using an infrared monochromatic camera (BFSU3-16S2M-CS; FLIR, Canada) with a 16mm fixed focal length lens (16mm C VIS-NIR, Edmund Optics, USA) at 75 frames/s (minimum resolution 640x400 pixels). The acquisition of each video frame was triggered by an external 5-V pulse delivered by the DAQ board (PXI-6289; National Instruments, USA), ensuring data synchronization. The camera was placed 10 cm in front of the participant’s face, and no visual target was provided. Participants were instructed to minimize blinking while keeping their eyes wide open and looking straight ahead during each trial. Experiment 2 assessed the central perceptual processing between electrical and mechanical stimuli. Participants were exposed to mechanical and electrical vestibular stimuli in CW and CCW directions (see Vestibular stimuli) similarly to experiment 1. Each rotation was presented once in randomized order for a total of four trials. Participants were blindfolded and instructed to close their eyes throughout each trial. They were asked to track their perceived angular displacement by rotating a crank handle attached to a potentiometer. Participants were instructed to track their perceived displacement using the crank handle from a preferred starting position. As such, if participants perceived a 90-degree rotation, the crank handle should reflect a 90-degree turn from the starting position. Perceptual data for mechanical and electrical trials were respectively digitized at 2,048 and 1,000 Hz using a DAQ board (PXI-6289; National Instruments, USA). All data acquisition and synchronization for mechanical and virtual (EVS evoked) whole body rotation stimuli were achieved through a custom virtual instrument in LabVIEW (LabVIEW 2013; National Instruments, USA). In experiment 3, we evaluated the generalizability of the mechanical-to-electrical vestibular stimulus conversion model by comparing mechanical and electrical stimuli using a multisine waveform allowing for a continuum of angular velocities. Participants were exposed to a pre-generated multisine angular velocity oscillation or a model derived equivalent electrical current profile 130 (see Vestibular stimuli). Setup and instrumentation for eye recordings were identical to those used in experiment 1. Mechanical and electrical stimuli were presented five times each in a randomized order for a total of 10 trials. Additional trials were performed when video quality was deemed poor due to iris occlusion from eyelid or blinking at the beginning of trial. 6.3.4. Data analysis We only analyzed the response to an offset step change from constant 10 deg/s angular velocity to stationary rest, and its electrical equivalent, for experiments 1 and 2. This was chosen following the rationale in other studies (Bertolini et al. 2011; Okada et al. 1999) because it is possible that confounding factors, such as vibrations, may be sensed during the constant-velocity phase of the mechanical stimulus. As such, focusing on the offset response provided the closest match in sensations between the electrical and mechanical stimuli. An algorithm based on the work by Otero-Millan et al. (2015) was implemented in Python 3.6.6 using OpenCV image processing functions to estimate ocular torsional displacement from video recordings from experiments 1 and 3. Briefly, pixels within each frame were segregated into either black or white values to generate a binary video based on thresholding. The transformed video allowed for the detection of maximum contour for which a least-squares elliptical fit of the pupil was determined in each frame. The pupil’s center and radius to the iris in each frame were used to perform a polar coordinate transform of the portion of the frame containing the iris. Torsion rotation of the eye between two frames was calculated through the relative horizontal shift between two polar-transformed iris segments using cross-correlation at a resolution of 0.01 deg through interpolation of the correlation results. Shifts in each video frame were compared with the first frame, which was used as a reference. Blinks were manually removed from the analysis. Videos that had blinks within the first 131 3 s were omitted from analysis. The ocular torsional fast-phase saccades were corrected for by using an inverse nystagmus algorithm to estimate the slow-phase nystagmus and slow-phase velocity before analysis. The algorithm detected occurrences of fast phase saccades by detecting peaks in velocity based on a threshold (Barnes 1982; Krauzlis and Miles 1996). An inverted position signal was applied to the raw torsional displacement signal. Two participants were removed from the analysis of experiment 1 because they had fewer than seven analyzable videos in any condition. Ocular and perceptual displacement data were zero-padded for 5 s at the start and end before digital filtering. For experiments 1, ocular torsional displacement was differentiated, averaged across trials, and then Butterworth filtered (4th order, 1-Hz cutoff) to obtain the ocular torsional slow-phase velocity. Peak ocular torsional slow-phase velocity was identified as the absolute maximal ocular velocity occurring less than 4 s after the start of the offset phase of the stimulus (e.g., return to 0 deg/s or second EVS pulse for a trial). All perceptual data from experiment 2 were included in the analysis. Perceptual displacement was differentiated and then Butterworth filtered (1st order, 0.20-Hz cutoff). Peak perceived angular velocity was normalized to 100% to allow for averaging between participants. The exponential decay time constants for ocular torsional slow-phase velocity and perceived velocity in experiments 1 and 2, respectively, were estimated by fitting a single-term exponential using nonlinear least squares from the identified peak velocity to the end of the trial. Ocular torsional displacements obtained in experiment 3 were first sectioned into 20-s segments from the original 60-s trials and then averaged within each condition. The averaged electrical and mechanical ocular displacement responses were Butterworth filtered at a higher 2-Hz cutoff frequency (4th order) because of an expected 1-Hz component in the signal. The averaging procedure was used to avoid missing data associated with blinks and inherent noise due to the video processing algorithm. The frequency-domain magnitude spectrum was estimated for the averaged 132 ocular torsional slow-phase velocity from experiment 3 using the discrete fast-Fourier transform. The gains between ocular torsional slow-phase velocity and its stimulation types were taken at 0.05, 0.1, 0.2, 0.5, and 1.0 Hz through dividing their cross-spectral densities by the auto-spectral density of the stimulus (mechanical: velocity encoder, deg/s; electrical: current amplitude, mA). The ratio between ocular torsional slow-phase velocity evoked by both stimuli (electrical divided by mechanical) was taken as the mechanical-to-electrical response gains. All data processing was performed using MATLAB (R2017a: The MathWorks) unless otherwise stated. 6.3.5. Statistical analysis To evaluate the similarity in response between mechanical and electrical stimuli, ocular torsional response dynamics from experiment 1 (peak ocular torsional slow-phase velocity, absolute peak slow-phase velocity, and slow-phase velocity exponential decay time constants) were submitted to two-way repeated-measures ANOVAs with directionality (clockwise, counter-clockwise) and stimulus type (electrical, mechanical) as factors. Absolute peak ocular torsional slow-phase velocity and slow-phase velocity exponential decay time constants were pooled between directionality and further submitted to paired two one-sided tests of equivalence (paired TOST) because we found no significant difference in directionality. The paired TOST were performed to test the null hypothesis that two populations are dissimilar. In our paired TOST, an equivalence bound was defined as the standard deviation of the samples being compared. If the region of indifference completely encompasses the confidence interval (CI), then the two populations are deemed statistically equivalent; otherwise, the test fails to reject the null hypothesis of difference (Robinson and Froese 2004). This criterion was chosen based on its use as the sensitivity index (𝑑′) in vestibular heading experiments to determine a threshold of discrimination between two stimuli (Gu et al. 2007; MacNeilage et al. 2010a). 133 We performed orthogonal total least-squares regressions between responses evoked by mechanical and electrical stimuli. This was, for experiment 1, peak ocular torsional slow-phase velocity and slow-phase velocity exponential decay time constants, and in experiment 3, continuous ocular torsional slow-phase velocity time series. Orthogonal regressions were calculated by taking the eigenvector with the largest eigenvalue in a two-column (mechanical and electrical) matrix using the singular value decomposition algorithm (pca function in MATLAB). The orthogonal regression was chosen because it assumes both predictor and response variables were measured with error. Pearson’s correlation coefficients were calculated as a measure of linear correlation between the regressed variables. Orthogonal regression best-fit slopes were subjected to a one-sample t test to determine whether slopes were significantly different from 1. The influence of stimulus frequency on mechanical to electrical gains was also tested using a one-way repeated-measures ANOVA with frequency (0.05, 0.1, 0.2, 0.5, 1.0 Hz) as the factor. These statistical analyzes were performed using R (version 3.5.3), R Studio (version 1.1.463), and R packages “equivalence” (version 0.7.2) and “ez” (version 4.4.0). Given the variability of participants’ single-trial perceptual responses, we used a bootstrap procedure to improve the estimates of perceptual exponential decay time constants for comparisons between conditions. The bootstrap was performed by resampling with replication from the pool of 18 participants’ perceived velocity time series. Each iteration selected 18 samples, and each sample consisted of the selected participant’s perceived velocity in all four conditions, therefore retaining the paired observations. The selected perceptual responses were averaged and fitted with a single-term exponential fit starting from peak velocity as described. With this resampling procedure, perceptual exponential decay time constants were estimated over 10,000 iterations, creating a bootstrap distribution for each condition. The mean and 95% confidence intervals were derived by fitting each 134 bootstrap distribution with a Gaussian fit. For comparisons, the mean difference between two conditions was calculated for each bootstrap iteration, thus deriving a mean difference distribution. A Gaussian fit was also used to estimate the mean difference 95% confidence interval for each mean difference distribution. Means ( ?̅? *) and 95% confidence intervals (95% CI*) obtained from the bootstrap procedure are denoted with an asterisk. If a mean difference confidence interval crossed zero, this indicated that there was no statistical difference between compared bootstrap distributions. We first compared between directionality for electrical and mechanical stimuli, respectively, and then compared between stimuli for each corresponding direction. Bootstrap analyzes were performed using MATLAB (R2017a; The MathWorks). All statistical tests were performed with an 𝛼 level of 0.05. 6.3.6. Data and software availability Data from experiment 3, scripts used to generate Figure 6-5 (related to experiment 3), and our mechanical-to-electrical stimulus conversion model are available at the Scholar Portal Dataverse (Borealis)3. Data from experiment 1 and 2 were not added to the public database because of a lack of release consent at the time. 6.4. Results All participants completed the tasks with no complaints of dizziness or adverse side effects. Well-defined ocular torsion and perceptual responses to both electrical and mechanical vestibular stimuli were observed (Figure 6-3, Figure 6-4, and Figure 6-5). Ocular torsional slow-phase velocity responses exhibited an initial peak between 1.20 and 3.50 s with a subsequent exponential decay in the opposing direction for both CW and CCW conditions’ offset transition. For a representative subject, 3 Available at http://doi.org/10.5683/SP2/EZGF9H. 135 the peak ocular torsional slow-phase velocities reached similar absolute values for mechanical (CW 1.18 deg/s, CCW 1.12 deg/s) and electrical stimuli (CW 1.26 deg/s, CCW 1.22 deg/s). The subsequent ocular torsional slow-phase velocity exponential decay time constants for electrical conditions (CW 8.3 s, CCW 6.0 s) were comparable to those for mechanical conditions (CW 8.1 s, CCW 4.3 s; Figure 6-3A, left). The mean perceptual velocity exponential decay time constant averaged between participants also displayed similar response dynamics characterized by an initial peak angular velocity followed by an exponential decay ranging from 5.7 to 7.5 s (Figure 6-3A, left). Ocular torsional slow-phase velocity responses to both electrical and mechanical multisine stimulations were also observed (Figure 6-5). Figure 6-3: Experiment 1. (A) ocular torsional slow-phase velocity (SPV) across stimulation types (electrical, mechanical) and directionalities (clockwise, CW; counterclockwise, CCW) from a single participant (solid lines; left) and group averaged (solid lines; right) with ±SE (red shaded area; n = 10). (B) absolute peak ocular torsional SPV across stimulation types and directionalities. (C) ocular torsional SPV time constant across stimulation types and directionalities. In B and C, individual observations are represented as circles, and dashed vertical lines with shaded areas mark the mean ± SD. 136 Figure 6-4: Experiment 2. (A) perceived angular velocity across stimulation types (electrical, mechanical) and directionalities (clockwise, CW; counter-clockwise, CCW) from a single participant (solid lines; left) and the set mean of perceived angular velocity response used for bootstrap analysis (solid line; right) with ±SE (red shaded area; n = 18). Perception magnitudes were normalized to 100%. (B) bootstrap perceptual exponential decay time constants across stimulation types and directionalities. Dashed vertical lines indicate bootstrap means, and circles are set means with horizontal bars indicating bootstrap 95% confidence interval (95%CI*). (C) bootstrap mean difference in exponential decay time constants showing comparisons between directionalities (left 2 plots) and stimulation types (right 2 plots). Circles indicate mean differences with vertical bars indicating 95% CI*. Comparisons show no difference as indicated by the 95% CI* crossing zero (dashed line). 6.4.1. Ocular slow phase velocity response to mechanical and electrical vestibular stimuli Ocular slow-phase velocity response to mechanical and electrical vestibular stimuli. We assessed peak ocular torsional slow-phase velocity and slow-phase velocity exponential decay time constant to determine how responses evoked by electrical stimulation matched those evoked by mechanical rotations. The averaged peak ocular torsional slow-phase velocities during EVS were 1.26 ± 0.52 and 1.22 ± 0.51 deg/s (mean ± SD) for the CW and CCW directions, respectively. Similarly, the mechanically induced averaged peak ocular torsional slow-phase velocities were 1.18 ± 0.45 and 1.12 ± 0.44 deg/s for the corresponding directions. Grouped analysis of peak ocular torsional slow-phase velocity showed a significant effect of stimulus direction (F1,9 = 110.11, P < 0.001); however, analysis of 137 absolute peak ocular torsional slow-phase velocity magnitude did not reveal a significant effect of directionalities (F1,9 = 0.190, P = 0.67) or stimulus types (F1,9 = 0.430, P = 0.53), and no interaction (F1,9 0.024, P 0.88; Figure 6-3B). After the peak ocular torsional slow-phase velocity was reached, the torsional response dynamic was characterized by an exponential decay. On average, the ocular torsional slow-phase velocity exponential decay time constants in the CW rotation for electrical (6.4 ± 3.7 s) and mechanical stimulation (6.9 ± 4.2 s) were consistent. This was also observed in the CCW rotation between electrical (4.0 ± 2.4 s) and mechanical stimuli (4.1 ± 2.0 s). Grouped analysis showed no significant effect across stimulus types (F1,9 = 0.457, P = 0.52) or directionalities (F1,9 = 4.295, P = 0.07), and no interaction (F1,9 = 0.125, P = 0.73; Figure 6-3C). We further verified the equivalency between stimulation types by separately comparing peak ocular torsional slow-phase velocity and slow-phase velocity exponential decay time constants using paired TOST and correlation analyzes. Because there was no effect of directionality, we pooled the rotation directions for both electrical and mechanical stimuli. Paired TOST showed that peak ocular torsional slow-phase velocity (𝑡19 = -0.79, P < 0.002; 𝜖 = 0.47) and slow-phase velocity exponential decay (𝑡19 = 0.71, P < 0.001; 𝜖 =3.4) were both statistically equivalent. Orthogonal regression revealed a near-unity relationship for both peak ocular torsional slow-phase velocity (r = 0.93, P < 0.001, slope 1.09; Figure 6-6A) and slow-phase velocity exponential decay time constants (r = 0.80, P < 0.001, slope 0.93; Figure 6-6B). Confirming these findings, orthogonal correlation analyzes between multisine mechanical and electrical continuous ocular torsional slow-phase velocity responses revealed a regression slope close to unity across participants (slope = 1.42 ± 0.57; t4 = 1.63, P = 0.178) with positive (0.88 ± 0.10) 138 correlation coefficients (Figure 6-5B). Spectral analysis of ocular torsional slow-phase velocity responses showed peaks at the expected input frequencies of 0.05, 0.1, 0.2, 0.5, and 1.0 Hz with a high signal-to-noise ratio (Figure 6-5C). Mechanical-to-electrical gains pooled across participants at these input frequencies were close to the input conversion factor of 0.37 mA per deg/s identified in experiment 1: calculated gains were 0.32 ± 0.10 mA per deg/s at 0.05 Hz, 0.36 ± 0.15 at 0.1 Hz, 0.36 ± 0.12 at 0.2 Hz, 0.38 ± 0.14 at 0.5 Hz, and 0.36 ± 0.13 at 1.0 Hz. No significant differences were observed across stimulation frequencies (F4,16 = 0.376, P = 0.823; Figure 6-5D). Figure 6-5: Experiment 3, Multisine vestibular stimulation between mechanical and electrical vestibular stimulations. (A) 20-s segmented stimulation profiles (top), ocular torsional slow-phase position (middle), and slow-phase velocity (SPV; bottom) from mechanical (blue) and electrical (red) conditions in a representative subject. For slow-phase position, thin colored lines denote individual 20-s segment responses, and the thick colored lines denote the averaged 20-s segment response.(B) orthogonal regression analysis between ocular torsional SPV responses shown in A with best-fit (red dashed) line.(C) frequency 139 spectrum of ocular torsional SPV responses. Responses exhibited power at input frequencies (0.05, 0.1, 0.2, 0.5, 1.0 Hz) with a high signal-to-noise ratio. Black dots represent estimated magnitudes at non-stimulated frequencies within our multisine stimulus. D: pooled (n = 5) mechanical-to-electrical gains (mA per deg/s) across frequencies. Individual observations are represented as circles. Dashed horizontal lines and solid horizontal lines with shaded areas mark the means ± SD. Figure 6-6: Orthogonal regression analysis between mechanical and electrical vestibular stimulations. (A) orthogonal regression best-fit (dashed) line for peak ocular torsional slow-phase velocity (SPV) with clockwise (circles) and counterclockwise observations (crosses). (B) orthogonal regression best-fit (dashed) line for ocular torsional SPV exponential decay time constant with clockwise (circles) and counterclockwise observations (crosses). 6.4.2. Perceived velocity response to mechanical and electrical vestibular stimuli Perceived angular velocity response to mechanical and electrical vestibular stimuli. Perceived angular velocity exponential decay time constants averaged across participants (i.e., data set mean) 140 were similar for the electrical (CW 6.5 s, CCW 8.1 s) and mechanical stimuli (CW 5.3 s, CCW 6.2 s). Following the bootstrap analysis, the bootstrap mean and 95% confidence interval obtained for electrical CW [7.4 s (3.1, 11.0); X * (95% CI*)] and CCW [7.5s (3.2, 11.5)] rotations were similar to those in the mechanical CW [6.0 s (3.7, 8.2)] and CCW [5.7s (2.0, 9.0)] directions. The mean difference 95% CI* between the electrical and mechanical rotations overlapped zero for both the CW and CCW directions (Figure 6-4C), suggesting similar perceived angular velocity decay time constants between stimuli. Likewise, perceptual angular velocity decay time constants were comparable between directionality, because the mean difference 95% CI* for the CW and CCW directions within electrical and mechanical conditions also crossed zero (Figure 6-4C). 6.5. Discussion Our aim was to develop and test a mechanical-to-electrical stimulus conversion model generating electrical current waveforms that could evoke vestibular responses mimicking a mechanical rotation of interest. We used transmastoid electrical stimulation to canal afferent transfer functions identified in nonhuman primates (Kwan et al. 2019) and multiplied these transfer functions by a gain K to account for differences in EVS-evoked responses between nonhuman primates and humans. We observed similar ocular torsional responses to electrical and mechanical stimuli matched based on the conversion model (experiments 1 and 3). The time series ocular torsional velocities evoked by the multisine electrical and mechanical stimuli were well correlated, given there were peak ocular torsional slow-phase velocities evoked by a step-change mechanical stimulus or its electrical equivalent. Similarly, ocular torsional slow-phase velocity in experiment 1 showed similar rate of decay to an angular velocity step-change stimulus, which was further confirmed at the perceptual level in experiment 2. Taken together, these results suggest that a mechanical-to-electrical stimulus 141 conversion model accounting for the physiological activation of primary vestibular afferents can lead to analogous vestibular-evoked responses between electrical and mechanical stimulations. 6.5.1. Mechanical to electrical stimulus conversion model gain The mechanical to electrical stimulus conversion model depends on two transfer functions (Eq: 6-1 & Eq: 6-2), parameters that were previously identified and tuned for nonhuman primates, and a scaling gain (K; Eq: 6-3). Here we discuss our choice of K for scaling mechanical-to-electrical conversions as used in Eq: 6-3. This parameter, which was evaluated using the peak ocular torsional slow-phase velocity, dictates the gain of the conversion from angular velocity to afferent response matching the electrical current. A previous study applied EVS with a mechanical-to-electrical gain as low as 0.125 mA per deg/s (Héroux et al. 2015). These gains, however, may range from 0.1 up to 2 mA per deg/s (Peters et al. 2015). Starting with a gain K = 2.20 (which results in a conversion factor of 0.40 mA per deg/s for a step change in angular velocity) for experiment 1, we found the peak ocular torsional slow-phase velocity for mechanical and electrical stimuli in our study was similar for both stimulus types, ranging in absolute terms between 1.12 and 1.26 deg/s. Using the data from experiment 1 post hoc, we approximated the mechanical angular velocity-to-electrical current conversion factor to be 0.37 mA per deg/s. The post hoc approximated gain was then used under multisine stimulation (experiment 3), resulting in ocular torsional slow-phase velocity mechanical-to-electrical gains between 0.32 and 0.38 mA per deg/s at each input frequency component. This aligned well with the gain used in experiment 1 and with previously matched estimates ranging from 0.37 to 0.42 mA per deg/s (Schneider et al. 2000, 2002). This was further supported by near-unity regression analysis of continuous time-varying ocular torsional slow-phase velocities between stimulation types. 142 The present results allowed us to assess the relative gains between ocular torsional response to electrical or mechanical stimuli. We estimated the gain between ocular torsional slow phase velocity and electrical current at 0.31 ± 0.13 deg/s per mA in experiment 1. This was reproduced in experiment 3, where gains were between 0.33 and 0.42 deg/s per mA. Our gain estimates were within the 0.20 – 0.45 deg/s per mA range reported for electrical stimuli up to 5 mA (Jahn et al. 2003a, 2003b; Schneider et al. 2002; Mackenzie and Reynolds 2018). The gain between ocular torsional slow-phase velocity and mechanical head angular velocity was estimated at 0.11 0.04 in experiment 1. This gain closely matched those in experiment 3 ranging from 0.09 to 0.14 and previously reported values of 0.12– 0.20 (Bartl et al. 2005; Schneider et al. 2002); however, gains up to 0.40 have been reported for higher angular velocities (Groen et al. 1999; Kawato 1999; Schmid-Priscoveanu et al. 2000; Seidman and John Leigh 1989; Tweed et al. 1994). The ocular torsional gains estimated from the present data demonstrate that our observed ocular torsional slow-phase velocity responses to mechanical and electrical stimuli followed expected sensitivities. 6.5.2. Torsional exponential decay between vestibular stimuli The similar peak ocular torsional slow-phase velocity evoked by both electrical and mechanical stimuli suggested that the evoked primary afferent activation of the SCCs was comparable between stimuli. This allowed us to further analyze any differences in central vestibular processing between stimuli by comparing ocular torsional slow-phase velocity exponential decay dynamics. Ocular response dynamics will be influenced by the high-pass characteristics of the transfer functions between electrical/mechanical stimulation and SCC afferent responses (Eq: 6-1 & Eq: 6-2), that we used in the mechanical-to- electrical vestibular stimulus conversion model (Eq: 6-3). In response to both stimuli, ocular torsional slow-phase velocity exhibited an exponential decay from peak value with time constants ranging, on average, between 3 and 7 s. Schneider et al. (2002) also showed 143 comparable time constants for constant angular acceleration and its equivalent direct current electrical stimulus. Our results and those reported by Schneider et al. (2002) reflected time constants consistent with the peripheral canal-cupula mechanism rather than showing prolongation of the ocular response dynamics associated with the velocity storage mechanism. Although central prolongation of the VOR has been reported extensively in the literature, this process is dependent on the head orientation and the direction of the axis of rotation with respect to gravity (Bertolini et al. 2008; Bockisch et al. 2005; Schmid-Priscoveanu et al. 2000; Tweed et al. 1994). For example, head yaw rotation in a head-up posture evoked horizontal VOR with central processing showing time constants of 14 –20 s time constants; (Bertolini et al. 2011; Seidman and John Leigh 1989; Su et al. 2000; Tweed et al. 1994). Shorter time constants (2–7 s) were reported for head pitch or roll rotations evoking vertical and torsional rotational VOR (Bertolini et al. 2008; Bertolini and Ramat 2011; Seidman and John Leigh 1989; Tweed et al. 1994); i.e., for head rotations (roll) aligning better with the virtual rotation vector induced by EVS. 6.5.3. Perceptual exponential decay between vestibular stimuli We further investigated the applicability of our mechanical-to-electrical stimulus conversion model in replicating perception of self-motion by presenting the same stimulus pulses while recording participants’ perception of self-motion in experiment 2. Vestibular afferent information is sent to the vestibular nuclei for central processing involving the VOR (Dickman and Angelaki 2004); however, conscious self-motion perception also involves further activity at the thalamus and neocortex neurons (Büttner et al. 1977; Grüsser et al. 1990). Participants’ perceptions of angular velocity also exhibited an exponential decay in response to both stimuli with time constants between 4 and 8 s, similar to previous reports with participants rotating in a supine position or lying sideways (Bertolini et al. 2011; Grunfeld et al. 2000; Shaikh et al. 2013). Comparable to reported ocular torsional time constants, 144 these short time constants cautiously imply similar central processing between torsional VOR and self-motion perception. Given that minimal ocular torsional velocity storage was expected (Bertolini et al. 2011; Okada et al. 1999; Sinha et al. 2008) due to its dependency on head orientation and the axis of rotation relative to gravity (Bertolini et al. 2011, 2012; Shaikh et al. 2013), ocular torsional rotations may not be the best model to address this issue. 6.5.4. Initial step towards a mechanical to electrical stimulus conversion model The development of a physiologically plausible mechanical-to-electrical stimulus conversion model for human use is promising given our data suggest that we replicated both ocular responses to and perceptions of whole body rotation during a step change in head angular velocity and in multisine angular velocity oscillations. Our model, nonetheless, has some inherent limitations. First, we were limited to a low 4-mA current amplitude, in line with most EVS studies using current ±5 mA for safety and to minimize potential current leakage onto other central pathways. As such, we only compared rotations limited to ~10 deg/s. Second, our data only support the replication of ocular and perceptual responses evoked by a step change in angular velocity and ocular response to a multisine angular velocity delivered at a nose-down head roll posture. Continued research is needed to validate our model for different participant populations, head orientations, and motion pulses (e.g., constant angular acceleration, higher frequency motion). Variability in ocular and perceptual responses was captured in our data set. For example, individual data may suggest changes in response gains across stimulation frequencies, but when data from all participants are considered, the between-subject variability led to averaged gains close to our reported gain (Figure 6-5C and D). The origin of this variability is unknown. Future work should explore the potential role of anatomical variations between participants and also determine if transfer functions from physiological data (Schneider et al. 2015a) 145 may provide advantages for representing the human canal response dynamics (e.g., for stimuli including higher frequencies). Special considerations must be made when EVS is applied at head orientations that deviate from our nose-down head pitch posture used in this study. Electrical stimulation at a nose forward or an ear-down orientation results in inferences of interaural or superior-inferior linear acceleration of the head as the brain attempts to resolve the discrepancy between the EVS-induced virtual rotation of the head that changes the alignment of the head relative to gravity without the accompanying expected otolith signal (Khosravi-Hashemi et al. 2019). The combination of our present mechanical-to-electrical stimulus conversion model with the interaction between head orientation in the gravitational field and the inference of motion induced by EVS may help bridge the gap between research and clinical application of EVS (MacDougall et al., 2005; Cutfield et al., 2011; Mackenzie et al., 2018; Welgampola et al., 2013). Vestibular pathologies such as acute lesions show biases in vestibular responses (Anastasopoulos et al. 1997; Aoki et al. 1999; Bisdorff et al. 1996), which are believed to stem from otolithic imbalance. These could potentially be clinically probed to compare and understand vestibular responses in persons with these pathologies; however, future work is required to compare and understand vestibular responses in persons with these pathologies. Under ideal conditions, all non-vestibular (somatosensory, interoceptive, and auditory) cues would be eliminated. Unfortunately, we cannot disregard these additional cues of motion and how they may have influenced the responses evoked by the mechanical stimuli. We controlled for these potential confounding factors by taking precautions to minimize non-vestibular cues of motion (see Setup). Additionally, for experiments 1 and 2, we only analyzed the responses evoked from the constant angular velocity-to-stationary transition that matched the electrical and mechanical stimuli as closely as possible. Statistically, we elected to use the paired two one-sided tests (TOST) of 146 equivalence and Pearson’s correlation coefficient as measures of equivalency. The statistical framework was flipped in the paired TOST because the null hypothesis assumes a difference between populations (Robinson and Froese 2004). This, however, required us to set equivalence boundaries; i.e., how small an effect is considered meaningfully different (Lakens 2017). Overall, this study presents an initial validation for our mechanical-to-electrical stimulus conversion model toward replication of ocular torsional movements and self-motion perception for step-change and multisine head angular velocity stimuli. The current results represent an important step forward in using EVS within applied settings. The usefulness and future impact of the proposed stimulus conversion model lie in the emerging use of EVS as a clinical assessment and treatment tool. Assessing vestibular function with EVS provides a simple and portable alternative compared with the physical apparatus needed to impose whole body rotations. Our model may also allow for future commercialization within the virtual/augmented reality industries to supplement immersive experiences by generating desired self-motion. 147 Chapter 7. A portable and low-cost solution for real-time vestibular sensory manipulation using electrical vestibular stimulation 7.1. Preamble4 In this chapter, we designed an open-source electrical vestibular stimulation (EVS) modulatory system aimed at being more portable, economical, and accessible than existing implementations. We also built upon the study in Chapter 2 by embedding our validated mechanical-to-electrical stimulus conversion model within our system. Specifically, our system, in real-time, measures head-motion and estimates the motion equivalent electrical current using an inertial measurement unit kinematic sensor, Arduino microcontroller, and Simulink programming interface. Our system operated at ~200Hz(±0.005Hz) and was able to deliver head-motion-equivalent electrical currents with ∼10ms delay. The output driving the current stimulator matched the implemented linear model for physiological vestibular afferent dynamics with minimal background noise (<0.2% of ±10V range). Participants recalibrated to the modulated closed-loop vestibular feedback using visual cues during standing balance replicating earlier findings. EVS is typically used to impose external perturbations that are independent of one’s own movement. We provided a solution using open-source hardware to implement a real-time, physiology-based, and task-relevant vestibular modulations using EVS. Our portable, low-cost vestibular modulation system will make physiological closed-loop vestibular manipulations more accessible thus encouraging novel investigations and biomedical applications of EVS. 4 A version of this chapter has been previously published as Chen, A., Kuo, C., & Blouin, J.-S. (2022). A portable and low-cost solution for real-time manipulation of the vestibular sense, J Neurosci. Methods, 382. Available at https://doi.org/10.1016/j.jneumeth.2022.109709. 148 7.2. Introduction Multisensory cue integration is required to establish accurate representations of body orientation and motion in space that are critical to human movement control. For example, to maintain our upright equilibrium, the brain must integrate vestibular, visual, auditory, and somatosensory cues to distinguish internal from external sources of self-motion thus enabling balance-correcting responses only to stability-threatening stimuli. These processes rely on learned internal representations of the relationship between motor and sensory signals that adapt as we grow, age, or when faced with a health condition (e.g., vestibular loss, cerebellar degeneration). Imposed mechanical and sensory perturbations external to the control of movement may reveal how the brain integrates sensory cues following an external event (Assländer et al. 2015; Dakin et al. 2016; Koelewijn and Ijspeert 2020; Tisserand et al. 2018; Toth et al. 2017), but the error-correcting motor commands remain external to the underlying sensorimotor networks controlling self-generated movements. Thus, the application of external perturbations can not address how the brain learns and reassociates sensory feedback to self-generated actions because the relationship between motor actions and their sensory consequences remains unchanged. Instead, closed-loop manipulations of the natural sensory and motor dynamics can reveal neural adaptations underlying the active control of movements (Rasman et al. 2018). A promising approach for such sensorimotor ‘human-in-the-loop manipulations’ involves the modulation of the vestibular sense (i.e. amplification and/or attenuation of primary vestibular afferent firing rates) using electrical vestibular stimulation (EVS) as implemented by Héroux et al., (2015). Given the recent surge in popularity of EVS in biomedical applications to reveal the mechanisms of vestibular function (Dakin et al. 2016; Mackenzie et al. 2018; Schneider et al. 2009; St George et al. 2011; Wardman et al. 2003) and to assess/treat a wide range of clinical disorders (Banman et al. 2021; Blini et al. 2018; Hwang et al. 2017; Lee et al. 2021; Oppenländer et al. 2015; 149 Wuehr et al. 2017), we propose a low-cost, portable method to recalibrate, in real-time, the vestibular sensing of human self-motion. The vestibular system, critical for sensing self-motion, includes the semicircular canal and otolith end-organs each encoding head angular and gravito-inertial accelerations in space, respectively. The frequency response of primary vestibular afferents innervating these end-organs have been well characterized in animals (Angelaki and Dickman 2000; Baird et al. 1988; Goldberg et al. 1984a; Jamali et al. 2013; Kwan et al. 2019; Ramachandran and Lisberger 2006; Sadeghi et al. 2007a) leading to linear models of motion-to-afferent responses (Schneider et al. 2015a). Alternatively, primary vestibular afferents are also selectively activated by electrical currents applied over the mastoid processes (in humans and animals) or directly within inner ear (in animals) (Fitzpatrick et al. 2002b; Goldberg et al. 1984a; Kim and Curthoys 2004b; Schneider et al. 2002). Assuming all primary vestibular afferents are activated through bilaterally-applied transmastoid currents (i.e., bipolar-binaural EVS configuration, Figure 7-1), the net signal of head motion is represented by a net rotational vector directed posteriorly ∼17-19o above Reid’s plane (Fitzpatrick and Day 2004; Schneider et al. 2002). This prediction of virtual head motion corresponds well to the induced perception of head rotation (Chen et al. 2020; Day and Fitzpatrick 2005; Peters et al. 2015; Schneider et al. 2002) that may be accompanied by an inference of linear head accelerations when the rotational vector has a component orthogonal to gravity (Khosravi-Hashemi et al. 2019a). Recently, Kwan et al. (2019) characterized the frequency response of vestibular afferents to transmastoidal electrical currents in non-human primate similar to how it is applied in humans. We confirmed the applicability of this linear model (electrical current-to-afferent dynamics) to EVS-evoked perception and ocular movements in humans and identified a gain needed to evoke equivalent responses to electrical and mechanical stimuli based on the average response from all participants (Chen et al., 2020). 150 A prerequisite understanding of vestibular physiology is needed to implement closed-loop modulations of the vestibular sense with EVS to reveal mechanisms of vestibular sensory recalibration in health and disease. When initially exposed to vestibular afferent modulating electrical currents based on head motion (head-coupled EVS), Héroux et al. (2015) showed that participants standing on foam with eyes closed exhibited an increase in sway amplitude and a decrease in vestibular-evoked muscle reflex. Strikingly, participants recalibrated their balance and reflex responses which returned to baseline following a period of visual or proprioceptive availability. Notably, this recalibration of the vestibular sense occurred only for coherent head-coupled EVS and not for an identical ‘played-back’, but non-coherent, EVS signal unrelated to self-generated motor commands. This confirmed their methodological approach as being distinct from a simple downregulation of noisy vestibular signals and provides a unique opportunity to reveal recalibration processes associated with cancellation of predictable error signals (Brooks et al. 2015) and recalibration of internal sensory predictions when maintaining standing balance. Although Héroux et al. (2015) established that EVS can be used for closed-loop modulation and recalibration of the vestibular sense, their method remains limited. First, they only included the motion-to-afferent transfer function (Fernandez and Goldberg, 1971; Goldberg and Fernandez, 1971) and consequently disregarded the dynamics of afferent responses to transmastoid currents. In addition, their system required costly and unwieldy instrumentation including a real-time stationary data acquisition unit, three analog angular velocity sensors, and a customized mounting tripod to ensure the orthogonality of these angular velocity sensors. These prerequisites make it difficult to emulate their design outside of a laboratory setting. Affordable equipment alternatives (i.e., less than $100) are now commercially available which allows us to implement human-in-the-loop vestibular modulation and recalibration both within and outside of the laboratory. Notably, open-source microcontrollers can perform real-time data acquisition and computations while miniature inertial measurement units (IMU) can record 3D head motion with low 151 noise characteristics meeting our vestibular application [RMS noise; sensor: 0.033o/s, vestibular afferents: 3.2o/s (Myers and Lewis, 1990)]. The goal of this study was to design and implement a solution for real-time human-in-the-loop EVS modulation of the vestibular sense during active head-motion, thus allowing others to readily explore the mechanisms of sensorimotor recalibration in humans. This was achieved using inexpensive and commercially available components to record head motion, perform the calculations to transform head angular velocity into physiologically-relevant signals, and output these signals to a linear current stimulator. We estimated the required currents to evoke signals of head motion using physiologically-derived linear models of vestibular afferent responses to head motion (Schneider et al. 2015a) and to transmastoidal current (Kwan et al. 2019). We described our system’s hardware design, software parameters, and real-time characteristics (i.e., sampling rate, background noise, and transfer function outputs) while also providing sample code to facilitate the implementation of our solution for other potential users. Lastly, we demonstrated the effectiveness of our system to induce neural adaptation by amplifying closed-loop vestibular feedback, partly replicating the findings reported by Héroux et al. (2015). Figure 7-1: Illustration of electrode configuration and net-evoked EVS rotational axis. (A) Electrodes applied in a bipolar-binaural configuration. The cathode (+) and anode (-) electrode placements depict a cathodal right current waveform (anode left) leading to a signal of rightward virtual head roll motion. Inversion of polarities leads to a virtual rotation in the opposite direction. (B) 152 Orientation of the net-evoked EVS rotational vector axis (dash-line) directed ~17-19o above Reid’s plane (dotted-line) derived from the summation of all semicircular canal afferents in the anterior, posterior, and horizontal canals (summarily denoted as A, P, and H respectively). A small interaural linear head acceleration is also present due to an orthogonal component relative to gravity (not depicted). 7.3. Methods 7.3.1. Participants Three participants (1 female, age: 23.3 ± 3.5yr.; mean ± SD) completed the experimental protocol. All participants had no known neurological diseases or injuries before taking part in the study. They were informed about the experimental protocol and possible discomforts involved before their written informed consent was obtained. The experimental protocol conformed to the Declaration of Helsinki and was approved by the University of British Columbia Clinical Research Ethics Board (H14-01712). 7.3.2. Hardware & software design Our real-time head-coupled EVS modulatory system was composed of four primary components: a host computer, an Arduino Due microcontroller, an IMU and a voltage-controlled linear current stimulator. We used a laptop PC (IdeaPad 720S-13ARR, Lenovo, Hong Kong; spec: Windows 10, AMD Ryzen7 2700U 2.20GHz CPU, 8GB RAM) as the host computer running MATLAB-Simulink (ver. R2020b, MathWorks, USA) with the ‘Simulink Support Package for Arduino Hardware’ dependency installed. 5 Simulink and its support package provide a graphical user interface to configure and access the Arduino’s data acquisition and communication functionalities while also retaining the programmability and ease of use of MATLAB. We selected MATLAB-Simulink because of its popularity, and we anticipate that it will facilitate intuitive use or modification of our design for 5https://www.mathworks.com/matlabcentral/fileexchange/40312-simulink-support-package-for-arduino-hardware 153 other end-users. Within Simulink’s Configuration Parameters, a fixed-step discrete solver with a step size of 0.005s (200Hz) was chosen which was sufficient in capturing the frequency bandwidth of most naturalistic self-motion activities (i.e., less than 25Hz) the vestibular system experiences (Carriot et al. 2014). We used an Arduino Due (Atmel SAM3X8E ARM Cortex-M3 84MHz CPU, 32bit, 96KB SRAM) microcontroller connected to a host PC through USB2.0. This connection was required to upload compiled Simulink code to the Arduino and to perform real-time data logging or visualization. All other necessary functions to deliver EVS current can operate on the Arduino when disconnected allowing for untethered deployment once the compiled code was transferred and executed. We measured head angular velocity and gravito-inertial acceleration signals with a miniature IMU (MPU-6050, Invensense, USA; Accelerometer range = ±2G, Gyroscope range = ±500o/s, Gyroscope bandwidth = 0-98Hz) connected to the Arduino using I2C protocol. Instantaneous angular velocity was processed in real-time to estimate the equivalent electrical current (see Section 2.4). The calculated instantaneous current was converted into an analog voltage using a 12-bit digital-to-analog (D/A) converter (MCP4725, Microchip, USA) also connected to the Arduino through I2C protocol.6 We did not use the Arduino Due’s integrated D/A because its output has an effective resolution of 8 bits that was insufficient for our application (for comparison with a 0-5V range, 8-bit resolution = 19mV vs. 12-bit resolution = 1.2mV increment). The MCP-4725 D/A converter outputs analog signals between 0-5V. All relevant Simulink Model ‘Configuration Parameters’ are provided in Appendix A (Table A-1, A-2). Given that the isolated linear current stimulator (STMISOLA, Biopac System, USA) used for our vestibular application required positive and negative voltages between ±10V to provide currents between ±10mA, we built an analog circuit performing two main steps: (1) adjust for the offset of the D/A output by bringing the range from 0-5V to ±2.5V and (2) amplify the voltage output by a factor of 6 https://www.mathworks.com/matlabcentral/fileexchange/41906-arduino-s-function-for-mpc4725-i2c-dac 154 4 bringing D/A output to a ±10V range (resolution: 4.9mV increment). All hardware components are listed in Table 3, and a circuit diagram is provided in Appendix A. Briefly, our analog circuit used the 5V pin from the Arduino Due to power the D/A converter and to generate a 2.5V signal using a voltage divider (two 1kOhm resistors). The 2.5V signal was passed through a unity gain amplifier (TL072, Texas Instruments, USA; Channel A) to minimize the risk of a voltage drop given that we needed a stable 2.5V signal to adjust the offset of the D/A converter. Next, we used a differential amplifier to generate the desired output voltage. The differential amplifier was made of an operational amplifier (TL072, Texas Instruments, USA; Channel B) and four resistors (two 4kOhm and two 1kOhm). The differential amplifier provided an amplification constant of 4 after a 2.5V offset removal from the D/A converter signal (i.e., from 0-5V to ±2.5V to ±10V). The two operational amplifiers were powered with a +12V power supply and voltage inverter (LT1054, Texas Instruments, USA) to provide the required -12V. Lastly, we applied a resistor-capacitor (RC) low-pass filter (fc = 72Hz; delay = 2ms) to the commanded ±10V voltage. This filtered analog voltage was sent to a linear current stimulator to deliver the electrical vestibular stimuli using a gain factor of 1mA/V (range: ±10mA). The total delay of the system was approximately 10ms due to the solver rate (5ms), IMU digital filter (3ms), and RC filter (2ms). Considerations must be made regarding the specific linear current stimulator used. In particular, it is important to ensure maximum voltage compliance of the stimulator is sufficient to deliver the target current given the expected skin impedance. In our system the maximum voltage compliance was 200V and after applying conductive gel, skin impedance typically remained between 5-10kOhm. This was well below the 20kOhm maximum impedance given our stimulator’s characteristics and maximal ±10mA current. 155 Table 3: Cost of components Component Manufacturer Manufacturer Part Number Quantity Approx. Cost/Unit ($CAD) Arduino Due Arduino A000062 1 51.69 MPU-6050 ‘IMU’ DFRobot SEN0142 1 13.69 MCP4725 ‘D/C converter’ SparkFun Electronics BOB-12918 1 7.61 Voltage Inverter IC Texas Instruments LT1054IP 1 4.08 Op-Amplifiers IC Texas Instruments TL072IP 1 1.40 1kOhms resistor TE Connectivity YR1B1K0CC 4 0.83 4kOhms resistor Ohmite MOX70034001BYE 2 2.27 22kOhms resistor Yageo MFP25SBTE52-22K 1 0.35 0.1μF capacitor Vishay K104K15X7RF5TL2 1 0.29 2.2μF polar capacitor Panasonic ECA-1HHG2R2B 1 0.39 10μF polar capacitor KEMET ESK106M025AC3AA 1 0.32 100μF polar capacitor Panasonic EEU-FR1H101 1 0.81 Total 88.49 excl. Tax 7.3.3. Setup & instrumentation To modulate the vestibular signals of head motion in real-time, our system must: (1) measure a participant’s instantaneous head angular velocity about the net-EVS evoked rotational vector, (2) estimate the instantaneous electrical current equivalent to the measured head angular velocity, and (3) deliver the calculated current back to the participant in real-time (Figure 7-2). Instantaneous angular head velocity was recorded using an IMU that we fitted to a mouthguard. The mouthguard was made from ethylene vinyl acetate and moulded to fit the participant’s upper dentition obtained from a vinyl polysiloxane dental impression. This coupled the IMU to the participant’s head as directly as possible thereby minimizing soft-tissue motion artifacts (Wu et al. 2016). Raw angular velocity data were measured in the IMU coordinate system. Consequently, we calculated and applied a rotational matrix to re-reference these data with respect to the predicted net-evoked EVS rotational frame (Fitzpatrick and Day 2004) (Figure 7-2, see ‘Re-referencing’ inset). The transformation matrix was unique for each participant and was derived from having participants perform two calibration trials 156 in distinct head orientations: 1) a face-forward pose with the head pitched 18o up from Earth-horizontal (i.e., net-evoked EVS axis parallel to ground) and 2) a face-up pose with Reid’s plane directed 18o past from Earth-vertical (i.e., 90o pitched up from the first pose). Reid’s plane was identified as the intersection between the inferior orbital rim and external auditory meatus and its angle was visually confirmed using a ruler level and protractor. Participants were asked to hold these poses for 10s while we recorded 3D linear accelerations. The calibration matrix was calculated by taking the cross-product of the 3D gravity vector between the two poses (face-forward cross face-up) to define a Z-axis while the cross-product between the newly defined Z-axis and the 3D gravity vector for the face-forward pose established the orientation of the Y-axis. The 3-axis vectors were then concatenated row-wise to define our calibration matrix. Pre-multiplying the 3D head angular velocity data by this matrix brings the 3D head angular velocity into our EVS frame, with the Y-axis aligned with the net-EVS evoked rotational vector. Figure 7-2: Closed-loop vestibular modulation using our real-time head-coupled EVS modulatory system. 3D head angular velocities were measured using an IMU attached to the head via a mouthguard. An Arduino Due microcontroller communicating with a host computer running Simulink acquires the 157 instantaneous angular velocity signals and transforms them into the equivalent instantaneous electrical current to manipulate the vestibular sense in real-time. First, raw angular velocity data were initially referenced with respect to the IMU frame; therefore, a calibration matrix (R) was applied to obtain the angular velocity component about the net-EVS evoked rotational vector (‘Re-referencing’ inset). The calibration matrix was derived from two pre-calibration head poses (face-forward & face-up). The transformed angular velocity component about the net-evoked EVS rotational axis (red timeseries trace) was passed through a physiologically-derived transfer function EVS model to obtain the current equivalent to head motion (blue timeseries trace) in the form of a digital signal. A digital-to-analog converter transformed our digital signal to an analog voltage command which was passed to a linear current stimulator. The stimulator converted the input voltage into current at a gain of 1mA:1volt over a maximum range of ±10mA (from the ±10V input signal). Binaural-bipolar currents applied over the mastoid processes were delivered to the participants to modulate their vestibular sense as a part of the overall ‘Sensorimotor Plant’. Four validations were performed on our system: Solver Rate, Background Noise, Signal Correlation, and Model Verification, to ensure that current stimuli were satisfactorily delivered. 7.3.4. Electrical vestibular stimulation model The equivalent current required to generate a physiological angular head motion about the net EVS-evoked rotational vector was calculated in real-time using a linear model. The model components included transfer functions derived from non-human primate vestibular afferent responses to mechanical and electrical stimuli (Kwan et al. 2019; Schneider et al. 2015a) with its output gain adjusted for the net virtual motion observed in humans (Chen et al. 2020). Note that the gain used in this experiment corresponds well to the average ocular and perceptual responses across participants but does not account for between-participant variability in their responses to mechanical and electrical vestibular stimuli (see Discussion). To maintain model stability of the linear transformations, all continuous transfer functions were discretized using the first-order hold method through the c2d function in MATLAB with a sample time matching Simulink’s 200Hz solver step size for the Arduino microcontroller. Our model assumes that all vestibular afferents are activated by the electrical current applied to the mastoid processes, resulting in a net head angular velocity signal oriented ∼17-19o up from 158 Reid’s plane (our EVS frame Y-axis) (Fitzpatrick and Day 2004). Consequently, we did not model the activation of each vestibular end-organ or combination of afferents between left and right end organs but rather transformed the net head angular velocity around the EVS vector (EVS frame Y-axis) into an equivalent transmastoid electrical current applied in a binaural-bipolar configuration based on previous empirical data from human experimentations (Chen et al. 2020; Day and Fitzpatrick 2005; Schneider et al. 2002). Conceptually, our EVS model first transforms the head angular velocity input around the net EVS vector into the expected afferent discharge firing rate (i.e., motion-to-afferent) using a pair of transfer functions (Eq: 7-1 & Eq: 7-2), one for regular and irregular afferent types, weighted at a 3 to 1 ratio based on neurophysiological data (Baird et al. 1988) 𝐻𝑀𝑂𝑟𝑒𝑔(𝑠) =2.83 ∗ 𝑠 (𝑠 +10.0175)(𝑠 +15.7) (𝑠 +10.0027)∗ 0.75 Eq: 7-1 𝐻𝑀𝑂𝑖𝑟𝑒𝑔(𝑠) =27.09 ∗ 𝑠 (𝑠 +10.03)(𝑠 +15.7) (𝑠 +10.0006)∗ 0.25 Eq: 7-2 where s = i2πf. We summed the outputs from Eq. 1 & 2 and passed the summated, afferent-equivalent, response through another pair of transfer functions (Eq: 7-3 & Eq: 7-4) representing the expected current based on afferent discharge rate (i.e., afferent-to-current), again with afferent types weighted 3 to 1 in favor of the regular afferents. The summated outputs from Eq: 7-3 & Eq: 7-4 resulted in a prediction of the electrical current equivalent to a head angular velocity (i.e., motion-to-current) about the net-EVS evoked rotational vector (Y-axis) (Kwan et al. 2019). 𝐻𝐸𝑟𝑒𝑔(𝑠) = 𝑖𝑛𝑣 (98(𝑠 + 26)(𝑠 + 188)(𝑠 + 47)(𝑠 + 2578)) ∗ 0.75 Eq: 7-3 159 𝐻𝐸𝑖𝑟𝑒𝑔(𝑠) = 𝑖𝑛𝑣 (418(𝑠 + 12)(𝑠 + 136)(𝑠 + 18)(𝑠 + 2739)) ∗ 0.25 Eq: 7-4 Altogether, the net current output (I) was scaled with a gain of 4.23 to obtain a conversion ratio of 0.37mA per deg·s-1 on the full model’s step-response (Eq. 5). 𝐼 = 4.23 ∗ [ (𝐻𝑀𝑂𝑟𝑒𝑔) + (𝐻𝑀𝑂𝑖𝑟𝑒𝑔) ] ∗ [(𝐻𝐸𝑟𝑒𝑔) + (𝐻𝐸𝑖𝑟𝑒𝑔)] Eq: 7-5 This gain most closely matched the between-participant averaged EVS-evoked afferent response to that evoked by angular velocity inputs (Chen et al., 2020) which is expected to double the vestibular encoding of head motion. Conversely, inverted this gain value (−4.23) would be expected to attenuate (and potentially cancel) vestibular encoding of head motion (Peterka 2012). For the present validation of our real-time head-coupled EVS modulatory system, however, we elected to add an additional gain of 0.3381 to scale down the conversion ratio to 0.125mA per deg·s-1 to match the gain used by Héroux et al. (2015). Based on pilot experiments, an unscaled gain of 0.37mA per deg·s-1 (expected to double the sensed vestibular signal) made participants unable to perform our balance task without continuous support. Lastly, for added safety, we limited the output voltage to ±10V corresponding to ±10mA. Our current EVS model implementation presents two key differences with respect to other models previously described (Chen et al. 2020; Héroux et al. 2015). First, the motion-to-afferent transfer functions we used differ from the first-order high pass or second order bandpass torsion pendulum models (Eq. B.1) that are commonly used to model canal-cupula dynamics (Karmali and Merfeld 2012; Merfeld 1995; Ramat and Bertolini 2009; St George et al. 2011). These filters, however, are only suitable for head movement frequencies below 2Hz (Fernandez and Goldberg 1971) as higher frequencies are assumed to have a flat gain. This is in contrast to recorded afferent responses at 160 frequencies up to 50Hz (Ramachandran and Lisberger, 2006; Sadeghi et al., 2007) which showed an increased sensitivity as fitted by Schneider et al., (2015). Second, our model improves upon the one (Eq. B.2) used by Héroux et al. (2015) by incorporating the afferents’ dynamic response to transmastoid electrical currents using the transfer functions described by Kwan et al., (2019). Taken together, the transfer functions presented by both Schneider et al., (2015) and Kwan et al., (2019) describe the physiological dynamic response from motion(-to-afferent)-to-current. The Simulink implementation of our model can be found on Scholar Portal Dataverse (Borealis)7. 7.3.5. Hardware validations All current command voltage outputs from our real-time head-coupled EVS modulatory system were simultaneously recorded by a wired PXI data acquisition system (50ns timing resolution; PXI-6289, National Instruments, USA). The PXI analog inputs and outputs were programmed and controlled through a custom LabVIEW virtual instrument (ver. 2019, National Instruments, USA) and set to a 400Hz sampling rate. Command output voltages were reported rather than current due to variations in voltage to current conversion between commercially-available current stimulators. As the goal was to ensure that the command voltage derived from our circuit was suitable, we will report the expected current based on recorded command voltage assuming a constant 1mA:1V gain. We first verified the Arduino’s 200Hz fixed solver rate by comparing the number of acquired samples on our PXI over a fixed signal (90s multi-sine signal) sent by the real-time head-coupled EVS modulatory system (Validation 1: Solver Rate). This fixed signal was sent 10 times. For each cycle, we divided the expected number of samples (200 samples/s. × 90s) from our system by the number of samples acquired by the PXI. We then multiplied this ratio by the PXI sampling rate (400Hz) to calculate 7 Available at http://doi.org/10.5683/SP3/KYSIAI. 161 the actual system sampling rate. Next, we characterized the background noise in the system to determine whether the output voltage driving the linear current stimulator contained any detrimental noise characteristics that may affect the current delivered to the participant (Validation 2: Background Noise). We recorded the output voltage with our PXI system while the mouthguard instrumented with the IMU remained stationary on a table in the same orientation for 100s over 12 trials (20 min total). In our time-domain analysis, we calculated the voltage offset, voltage offset removed peak-to-peak (VPP), and voltage offset removed root mean square (VRMS) noise value for each of the 12 trials’ 100s segment. The offset removed VRMS value provides an indicator of the effective electric voltage (and subsequent current) passed to the participant, and the VPP value was used to estimate the largest noise amplitude in the applied voltage signal. These measures were conducted to ensure that our intended signal was not masked by noise or that participants would not be subjected to suprathreshold currents due to substantial offsets or spikes in the actual output signals. A frequency-domain analysis was performed on the same 12 segmented timeseries to identify the frequency components specific to the noise. We did this by calculating the segments’ magnitude response (freq. resolution 0.01Hz) using the fft function in MATLAB. 7.3.6. Validation of the hardware implementation of the EVS model We performed further validation to ensure our embedded motion-to-current conversion model was delivered accurately. We recorded 20 minutes of standing balance head motion with the IMU-instrumented mouthguard at different angular velocity amplitudes/frequencies. Within Simulink, we logged the digital signal sent to the D/A (i.e., model digital output) while simultaneously recording the analog output voltage from the D/A driving the linear current stimulator using our LabVIEW-PXI system. All signals were synchronized using a digital pulse signal sent from the Arduino recorded by 162 both systems. The analog output voltage timeseries was downsampled from 400Hz to 200Hz to match our real-time head-coupled EVS modulatory system’s sampling rate. We calculated Pearson’s correlation coefficient (r) between the model digital output (i.e., signal sent to the D/A from the Arduino) and the downsampled analog output (i.e., signal delivered to stimulator from the D/A) to quantify the similarity between the digital command and its eventual analog command (Validation 3: Signal Correlation). Next, we estimated whether the analog output command voltage driving our constant current simulator matched the theoretical frequency response of our embedded EVS model using spectral analysis (Validation 4: Model Verification). We separated the recorded 20 min angular velocity input and voltage output into 1 min segments (n=20; freq. resolution 0.017Hz). The cross spectral power density between head angular velocity and voltage (PXY) was calculated using the cpsd function in MATLAB. This function estimates the cross power spectral density using Welch’s averaged, modified periodogram. Similarly, the head angular velocity auto-spectrum (PXX) was also estimated. The output/input gain ratio was calculated as the absolute value of the cross-spectrum over the amplitude of the input auto-spectrum as a function of frequency. In addition, the relative phase between signals as a function of frequency was calculated by taking the angle of the cross-spectrum. We lastly calculated the idealized frequency response of our EVS model’s transfer function using the bode function in MATLAB. The idealized gain and phase outputs were plotted with our calculated gain and phase responses for visual comparison. 7.3.7. Experimental procedures To demonstrate how our real-time head-coupled EVS system can modulate vestibular feedback in a task-relevant manner, we partly replicated the vestibular recalibration procedures established by Héroux et al., (2015). Note that we did not expose participants to non-coherent noisy 163 EVS as Héroux et al., (2015) already showed that such signals do not induce recalibration or down-regulation of the vestibular sense even if they are identical (played-back copy) to the head-coupled EVS. Briefly, participants stood upright and performed self-generated whole-body and head movements to recalibrate the vestibular signals induced by the real-time system to their motion and related feedback. Participants instrumented with a mouthguard stood with their feet together on a 2.25” thick balance foam pad (Balance Pad, Yes4All, USA). Electrical currents were delivered in a binaural-bipolar configuration using a pair of 3×3cm carbon-rubber square electrode with a small groove that fits along the back of the ear when secured on the left and right mastoid processes with hypoallergenic tape (Durapore; 3M, USA). A layer of conductive electrode gel (Spectra 360, Parker Laboratories, USA) was applied on the electrode before placed on top of the skin. These electrode dimensions and gel were used to minimize current density and potential discomfort, and, as such, no anesthetics were used or needed for this experiment. The foam pad was used to increase the importance of vestibular cues for upright balance without making the task too unstable or difficult. Body sway was recorded at 240Hz using a 3D motion-tracking system with a sensor positioned on the C7 spinous process (TrakSTAR, Ascension Technology Corporation, USA). Because participants were performing a standing balance task, the Arduino circuit and isolated current stimulator components were placed on a tabletop. However, depending on the need, both can be placed within a small backpack and powered by a portable 12V power bank battery. Participants completed a single trial composed of four phases occurring immediately one after the other to reveal the effects of vestibular recalibration (Figure 7-3). First, participants stood upright with their eyes closed and no electrical current for 40s; this served as our baseline phase. Second, participants maintained standing balance with their eyes closed for 60s while receiving head-coupled EVS. During this pre-calibration phase, participants experienced head-coupled EVS that amplified vestibular afferent responses to their actual head rotation. Next, participants were asked to open their eyes for 240s while they still received 164 the head-coupled EVS. This recalibration phase was performed to re-associate the newly EVS modified vestibular signals to the ongoing motor actions and associated feedback (at least visual cues). To facilitate adaptation, we asked participants to explore the novel vestibular sensations by voluntarily swaying in the mediolateral direction to promote head roll at different frequencies, amplitudes, and head orientations. We also facilitated head movements by asking participants to throw and catch a tennis ball away from their midline (Héroux et al., 2015). Lastly, we asked participants to close their eyes once again and maintain standing balance while the real-time head-coupled EVS modulatory system remained on. This post-calibration phase was performed to verify whether participants indeed recalibrated to this new vestibular feedback and could maintain their balance with the head-coupled EVS (as demonstrated by Héroux et al., 2015). Figure 7-3: Standing balance experiment. Participants wearing an instrumented mouthguard stood on top of a balance foam pad. Instantaneous angular velocity about the net EVS-evoked rotational vector was recorded and transformed using a physiologically-derived motion-to-current transfer function model. The resulting electrical current was relayed back to the participant at the mastoid processes to manipulate vestibular feedback. Participants initially stood with eyes closed with no EVS for 40s to capture their baseline balance oscillations (baseline). EVS was then turned on while participants remained with eyes closed for 60s (pre-calibration). Participants were next asked to actively sway, prominently in the mediolateral direction, for 240s with eyes open (calibration). This active sway was used to promote the re-association of the novel vestibular sense with the ongoing motor actions (recalibrated using visual cues). In the post-calibration period, participants were once again asked to close their eyes 60s to quantify changes in balance performance relative to the pre-visual calibration. 165 7.3.8. Experimental data analysis Given that EVS applied in a binaural-bipolar configuration with the head forward induces mainly mediolateral balance responses (Lund and Broberg 1983; Mian and Day 2009), we calculated the mean-removed mediolateral root mean square displacement measured at the C7 spinous process as an index of sway for each condition. Specifically, we compared this variable between the No EVS (control), pre-visual calibration EVS and post-visual calibration EVS conditions. The recalibration phenomenon was previously reported by Héroux et al. (2015). Here, we descriptively show these previously observed balance behaviours to show similar changes were achieved with our low-cost wearable system. 7.4. Results 7.4.1. Hardware validation and performance We first evaluated our hardware’s performance in providing real-time vestibular feedback. Based on the sampling clock from our National Instruments data acquisition board, the estimated sampling rate of the microcontroller was 199.997 ± 0.005Hz (Mean ± SD) which was less than 0.1% off from the target sampling rate. When leaving the IMU stationary on a table for 100s, we noted that the net output driving the linear current stimulator exhibited a mean value of -22.90 ± 0.23mV (corresponding to -22.90µA assuming a 1V:1mA stimulator ratio) after amplification and filtering of the microcontroller output (Figure 7-4A, left). When correcting for this offset, the VRMS was 7.70 ± 0.06mV (i.e., 7.70µA) and its VPP was 64.79 ± 3.07mV (i.e., 64.79µA). The noise components estimated from the stationary IMU showed a relatively uniform power across frequencies from 0.01 to 70Hz (Figure 7-4A, right). The attenuation in power above 70Hz was present due to the low-pass filter component in our circuit (fc = 72Hz). 166 7.4.2. Comparison of the real-time to the expected EVS model output The analog voltage output signal sent to the stimulator was consistent with the programmed digital (Simulink) output in our 20 min standing data (r = 0.997; Figure 7-4B). Furthermore, when comparing the relationship between analog output and head angular velocity input, segment-averaged gain and phase followed closely to the idealized model response (Figure 7-5). Gain gradually increased from 0.01 to 0.1Hz and a relatively flat gain was present between 0.1Hz and 10Hz. Within the low frequency bandwidth for natural head motion (0-2Hz), the difference between the model and actual phase lag between the analog output voltage and head angular velocity was greatest between 0.01 to 0.15Hz (from 35° to 10°) but the signals were nearly in-phase (<10°) between 0.15 to 5Hz. At higher frequencies (5-25Hz), we observed a progressive increase in the difference between the model and actual input-output phase lag up to 50°. Figure 7-4: Hardware validation & model output comparison. (A) Background command voltage noise from a stationary IMU over 20 min (left). The corresponding offset removed frequency-domain representation averaged over twelve 100s segments (right). Background noise resembles uniform white noise with relatively constant power at frequencies below 70Hz; however, power decreased beyond 70Hz due to our low-pass RC filter. (B) Digital and analog 167 command voltage data during 20 min of standing balance. Command voltage was derived by passing measured head angular velocity (from an IMU) about the net-evoked EVS rotational axis measured through our linear motion-to-current model in our Arduino microcontroller. The model’s command voltage output is sent to a digital-to-analog converter from the Arduino as a Digital Command Signal with 12-bit resolution (left, top). The actual Analog Voltage Command Signal from the converter (left, bottom) was simultaneous recorded. The box denotes a zoomed window between the two signals in the inset (middle). Correlation plot (right) between the Digital Command (what is sent to the converter) and Analog Command (what is delivered from the converter to the current stimulator) showed a strong correlation (r = 0.997). Figure 7-5: Bode plot of model and recorded data. Gain (top) and phase (bottom) plots for current output relative to the head angular velocity input about the net EVS rotational vector. The current amplitude was assumed from the command voltage using a 1mA:1V ratio. The predicted frequency response of our implemented motion-to-current EVS conversion model (solid-line) and the estimated frequency response (dots) from the 20 min of head motion data during standing. Predicted frequency response of the conversion model implemented by Héroux et al. 168 (2015) plotted for comparison (dashed-line) shows the overestimation in applied current gain at frequencies above 1 Hz by their model. 7.4.3. Recalibration of vestibular signals We used our real-time head-coupled EVS modulatory system to replicate partly the findings from Héroux et al. (2015). Initially, all participants maintained their upright stance and exhibited sway in the medio-lateral direction with a mean-removed RMS of 11.0 ± 2.1mm (Figure 7-6A). Participants became immediately unstable when exposed to head-coupled EVS that amplified vestibular afferent response; the mean removed RMS sway in the mediolateral direction increased nearly four-fold (41.6 ± 17.7mm). Participants were visibly oscillating in the mediolateral direction and external support was provided when participants were about to fall to help them regain balance. After visual recalibration to the new vestibular signal, participants were able to maintain balance for the 60s period without external support. Their mean removed RMS sway in the medio-lateral direction returned to near baseline values (18.1 ± 0.5mm). Participants reported non-painful skin sensations. Figure 7-6: Sway data for the standing balance adaptation experiment. (A) Representative participant whole-body sway (birds’ eye view) during baseline quiet standing (no EVS), before (pre-calibration), and after (post-calibration) visual recalibration with head-coupled EVS. 169 Small baseline sway increased when participants were initially exposed to head-coupled EVS. After a 240s period of visual recalibration, whole-body sway returned near baseline level. (B) Individual participants (n=3) RMS-removed sway amplitude (dots) during baseline, pre-calibration, and post-calibration periods. 7.5. Discussion In the present study, we described a portable and cost-effective solution to implement a real-time closed-loop modulation of the vestibular sense with EVS. We used a miniature IMU to measure head angular velocity and an Arduino microcontroller programmed through Simulink to deliver physiologically-accordant head motion signals using current stimuli. This was achieved by incorporating the embedded motion-to-current transfer functions, described by Schneider et al., (2015) and Kwan et al., (2019), consequently matching the vestibular afferent responses to mechanical and current stimuli. Our portable system operates in real-time (~10ms delay) with minimal background noise (<0.2% of full ±10V range) thereby allowing us to deliver the desired electrical stimuli. We further demonstrated that our portable system, using the transfer functions based on vestibular physiology, can elicit vestibular recalibration in a balance task by partially replicating the experimental protocol established by Héroux et al. (2015). To modulate vestibular feedback in a task-relevant manner, we ensured that the instantaneous current sent to participants: (1) exhibited low background noise and (2) replicated the expected EVS output from linear models of vestibular function. Time-domain analysis from our stationary test to estimate background noise revealed that voltage(current) root mean square and peak-to-peak were, respectively, ~5 and 20% of the amplitude thought to induce vestibular stochastic resonance effects (0.35mA; see Wuehr et al. 2016) or afferent detection thresholds (~0.4–0.6mA; see Kwan et al. 2019). Spectral analysis for the same stationary data showed uniform power across frequencies resembling white noise which decreased above 70Hz due to our chosen RC filter (fc = 170 72Hz). Moreover, the gain and phase between input head angular velocity and output voltage/current from our 20-min standing data showed good agreement between our model’s prediction and our measured response up to 25Hz. We focused on responses up to 25Hz as the bandwidth of natural head rotation is predominately at these lower frequencies (Carriot et al. 2014) and signal power above 20Hz recorded from an immobile IMU is generally below our IMU noise floor. This feature of our system response would only become a limitation if attempting to modulate transient, high frequency (up to 400Hz) head motions during head impacts (Forbes et al. 2020; Kuo et al. 2017; Wu et al. 2017). Our findings demonstrate that our modulatory system can adequately deliver accurate electrical currents to participants that correspond to the expected model behavior within the bandwidth of naturalistic head motion. Two important differences exist between our portable system and the one used by Héroux et al. (2015). First, our system’s time-delay (~10ms) was 10 times larger than theirs. These delays mainly stem from the maximum sampling rate (200Hz, 5ms), digital lowpass filter on the IMU (3ms), and hardware lowpass filter (2ms). This consequently leads to a temporal delay between the head motion encoded by the vestibular afferents and the superimposed activity induced by our current stimulus. Nonetheless, evidence shows that humans are unaffected by sensorimotor delays of 50ms when maintaining standing balance while they only perceive the consequences of delays when they reach >100ms (Rasman et al. 2021) or upwards of 250ms for visual-inertial heading estimation (Rodriguez and Crane 2021). In our experiment, the ~10ms delay of our portable system was small enough to enable participants to adapt to head-coupled EVS as shown previously by Héroux et al., (2015). A second main difference was that we used two sets of transfer functions estimated from primary afferent responses to motion (Ramachandran and Lisberger, 2006; Sadeghi et al., 2007; Schneider et al., 2015) and transmastoidal electrical stimulation (Kwan et al. 2019) in non-human primates. This 171 was performed to better represent the natural dynamics of vestibular activation to actual motion and electrical stimuli. Critically, the motion-to-afferent transfer functions used by Héroux et al (2015) exhibited a higher gain than ours past 1Hz (see Figure 7-5). This was due to two factors: (1) our model characterized the afferent responses to motion in the upper frequency bandwidth (>2Hz) as opposed to assuming a constant gain (Fernandez and Goldberg, 1971; Goldberg and Fernandez, 1971) and (2) we included the dynamics of the current-to-afferent responses that also show larger gain at frequencies past 1Hz (Kwan et al. 2019) which has been previously overemphasized at high frequency components (cf. Figure 5-5, dashed and solid lines; Héroux et al., 2015). Therefore, our portable system with affordable hardware components more accurately reproduced the dynamics of the electrical current needed to physiologically mimic expected afferent activity based on actual head motion. This system produced similar balance adaptation results despite methodological differences between our study and the one from Héroux et al. (2015) and from this, we argue that our brain has flexibility in adapting to new vestibular-motor relationships. We also recognize that future work is require to test this possibility as we only tested a small number (n=3) of participants because our main goal was to replicate the findings reported by Héroux et al., (2015) using our new portable system. To our knowledge, only a handful of studies have coupled EVS to recorded head movement in a feedback manner (Day and Reynolds 2005; Moore et al. 2006). The most prevalent use of EVS, however, is to apply a standardized, experimentally ‘hard-coded’ stimulus waveforms (e.g., sine, square, stochastic, etc.) to induce externally applied perturbations (Dakin et al. 2010; Forbes et al. 2017; Lenggenhager et al. 2007; Mackenzie and Reynolds 2018a; Toth et al. 2019; Wuehr et al. 2018) or to provide supplemental vestibular feedback in periods of visual-vestibular mismatch such as those during controlled virtual reality experiences (e.g., rollercoasters) (Aoyama et al. 2017; Sra et al. 2019). These stimuli, depending on the setup, may be tentatively coupled to a predetermined event, be it an 172 occurrence or movement but are ultimately nonetheless external to the generation of active self-motion. Conversely, head-coupled EVS manipulation alters the brain’s expectation of the ongoing vestibular sense, thus changing movement-related sensory prediction errors not dissimilar to altered active arm trajectories using force fields in reaching tasks (Shadmehr 2017). However, unlike these motor control tasks, our portable system uniquely focuses on the vestibular sense to investigate the brain’s ability to distinguish and reattribute vestibular afference in humans. As previously demonstrated by Héroux et al., (2015), head-coupled EVS is a prerequisite for recalibration of the vestibular sense because non-coherent EVS signals unrelated to self-generated motor commands but with identical amplitude and frequency characteristics to head-coupled EVS failed to induce any adaptation or downregulation of vestibular signals. Given that the cerebellum is involved in the processing and recalibration of vestibular information during active, self-generated head movements (Brooks et al., 2015; Cullen et al., 2011; reviewed in Cullen, 2019) our portable system may be used to assess neural adaptation in persons with cerebellar degeneration (Bertolini et al., 2012; Dahlem et al., 2016). Simulink and its Arduino support package allows users to control an Arduino microcontroller with a low barrier to entry when programming. Simple data acquisition and processing tasks can be readily achieved through block diagrams or calling MATLAB functions. We have made our system readily available to use by providing our Simulink code. Users would only need to make minor alterations based on their application for modulating vestibular sensation during natural motions. In our example, we applied EVS to amplify standing balance vestibular sensations, but our system could be easily modified for other scenarios, such as attenuating vestibular sensation by inverting the transfer function gain (Peterka 2012), separately modulating bilateral vestibular sensation, or simply applying pre-defined waveforms (e.g., multi-sine, stochastic, square, etc.) by adding software controls 173 to our application. Furthermore, modifications depending on user needs: when powered by a 12V rechargeable battery (for both the analog circuit and stimulator [STMISOLA]), we can create a mobile EVS system inside a backpack. Although a host PC running Simulink is required for data visualization and logging, compiled code uploaded onto the Arduino is sufficient to apply head-coupled EVS and hardware switches may be used to turn on/off EVS for headless operation. Altogether, we believe through eliminating the need to write Arduino code and our system’s portability, we will encourage adoption of our vestibular recalibration method/system to be used in novel experimental questions, designs, and circumstances. This may include recalibrating the vestibular sense in naturalistic settings outside the lab, vestibular evaluations for Parkinson’s disease (Galea et al. 2012), or concussion (Banman et al. 2021; Qiao et al. 2021) or aging (Peters et al. 2016), wearable vestibular prosthesis, or even probing long-term vestibular habituation with prolonged EVS exposure (Dilda et al. 2014; Kitazaki and Kimura 2010). Despite its potential and multiple applications, some considerations should be made when using our system. First, if one chose to run additional serial peripherals, such as different IMUs or higher resolution digital to analog converters via I2C, SPI, or RS232, considerations must be made as to how to best integrate them. This is because the code for peripheral interfacing is limited by whether dedicated blocks are present in the Simulink library. An example of this was the ease of using the MPU-6050 IMU with I2C protocol because a function exists in the Simulink library. However, the MCP-4725 D/A, which also uses I2C, required a solution using C++ code with Simulink’s S-Function Builder to build the function. Second, the computational capabilities are limited by the overhead required when interfacing the Arduino microcontroller with Simulink. Particularly, this connection is needed for data logging and visualization which, for our setup, cannot be executed above 200Hz. For our application, we elected to use a fitted mouthguard to anchor our IMU as this couples to the 174 participant’s head as directly as possible to minimize soft-tissue motion artifacts (Wu et al. 2016). This is not always necessary as direct attachment to the skin over the skull or face may be sufficient for slower everyday movement activities encompassing naturalistic head motion (Carriot et al. 2014). However, if any dynamic motions occur (such as in sports activities), users should be aware that impact can cause significant extraneous ~20-25Hz oscillations of sensors mounted on soft-tissue. The direction and gain of our head-coupled current stimulus was estimated under the assumption that all (regular and irregular) vestibular afferent were activated leading to a net rotational response vector based on the anatomy of the semicircular canals (Fitzpatrick and Day 2004). As such, our stimulus was limited to a net motion about this vector that did not account for potential asymmetries between left and right afferent activation or mechanisms underlying how the brain combines afferent activation from the left and right vestibular end organs to generate this net signal of motion. Given that the contribution of regular and irregular vestibular afferents likely differs for vestibulo-ocular, vestibulo-spinal or perceptual responses (Cullen 2019), future considerations should include task-specific modifications of the overall gain provided here. Perception and motor responses to EVS also show between-participants variability (Goel et al. 2015, 2019; MacDougall et al. 2002; Mackenzie and Reynolds 2018b) and differ in persons with certain pathologies (Sprenger et al. 2020) that are not accounted for in the average gain provided here. Future work is needed to account for these individual and task-dependent differences. To account for between-participant variability in gain, one must record a common output (eye or perception) to both electrical and mechanical inputs, similar to Chen et al. (2020). A possible protocol is to manually induce rotation, record the input, and replay the input using EVS after passing it through the EVS model. Comparing the responses evoked by the mechanical rotation and derived EVS would allow for a personalized gain. Lastly, another challenge would include potential integration with alternative configurations of vestibular electrical stimulation (i.e., binaural-monopolar, three-pole, and four-pole) in our portable system (Aoyama et al. 2015; Cauquil et al. 1998). 175 7.6. Conclusion We leveraged the portability of an open-source Arduino microcontroller with the familiarity of MATLAB and Simulink to develop a configurable and accessible tool to modulate and recalibrate vestibular feedback in real-time using electrical vestibular stimulation. This was achieved by delivering electrical current based on instantaneous head motion that is transformed in accordance with the anatomical and physiological principles of the vestibular system. We envision our portable design will make such closed-loop manipulations more accessible for the community-at-large and, in turn, to encourage novel investigations and biomedical applications using EVS to probe vestibular contributions to human sensorimotor control. 176 Chapter 8. General discussion and conclusion 8.1. Summary of thesis goals and discussion The overall goal of this dissertation was to understand the physiological computations underlying vestibular processing and to enhance current methodology for probing the vestibular system. We built (Chapter 3) a novel computational model of vestibular integration constructed from available physiological and anatomical data. Critically, this model used a probabilistic sampling framework for the integration of distributed vestibular signals. In the first experiment (Chapter 4), we characterized perceptual self-motion during and following prolonged constant angular accelerations and contextualized how these percepts arise from the integration of differently adapting primary vestibular afferents using our sampling model. In the next experiment (Chapter 5), we considered how vestibular integration changes when head motion is encoded by different vestibular end-organs leading to dissimilar self-motion percepts. The goals of the next two experiments (Chapters 6 and 7) were to evaluate electrical vestibular stimulation as a technique for probing the vestibular system in humans. More specifically, we assessed the equivalence in central processing between real head motion and those electrically produced. Using this equivalence, we subsequently implemented a real-time solution for human-in-the-loop vestibular sense modulation using electrical vestibular stimulation during active head movements. The following sections will summarize the main results and conclusion from each of the four experiments. The implications of our findings as a whole and how they may impact future research and clinical approaches will also be discussed. 8.1.1. Central expectation may modulate vestibular sensory integration In Experiment 1 of this dissertation (Chapter 4), we established that the time course of self-motion perception during and following constant angular acceleration were similar between males 177 and females. Specifically, during constant acceleration regardless of rotational direction, an initial detection was felt, but perception adapted towards a state of motionlessness given enough time (~30-100s). This contrasts with the underlying neural information encoded by primary vestibular afferents which show a range in adaptation behaviour (Goldberg and Fernandez 1971a; Rabbitt et al. 2005); some adapting to constant angular accelerations, and some not . As such, this brings into question as to how the integration of differently adapting afferents lead to a motionless percept. We explained this apparent incongruity through a top-down influence exerted by the brain which more favourably weighs sensory information that conforms to an expectation of being motionless. This assumption aligns well with previous reports (Freeman et al. 2010; Hürlimann et al. 2002; Laurens and Droulez 2007; Stocker and Simoncelli 2006) giving support that humans have sensory preference for neural signals encoding rest or low speeds. In our sampling model, this central expectation takes the form of a prior weighting (using a zero-amplitude, Gaussian distribution) on sensory particles. We compared simulation results given a large and small Gaussian variance and found that a larger variance increases the time constant of adaptation in our internal (perception) representation. Conversely, a smaller variance does drive adaptation of the internal representation towards no-motion. Predictions from our model break away from previous linear time-invariant models of dynamical vestibular inference. Altogether, this sampling framework generates new mechanistic intuition about the interaction between the brain’s expectation and the variability of the underlying neural code. As such, potential differences observed between healthy individual and those suffering from vestibular ailments may be interrogated using our approach. 8.1.2. Vestibular self-motion depends on encoding vestibular end-organ Experiment 2 of this dissertation (Chapter 5) evaluated why the time course of self-motion perception differs during constant angular velocity stimuli when encoded by different vestibular end- 178 organs. We first hypothesized that discrepancies were due to contrasting canal types and in the number of encoding canals. Indeed, we found that perceptual adaptation to an identical constant velocity stimulus was more prolonged when encoded by two horizontal canals as opposed to the vertical canal counterparts. This was not surprising as it echoed results from indirect comparisons in previous studies (Bertolini et al. 2011, 2012). Contrary to our second hypothesis, we found that head motion encoding from four vertical canals prolonged perceptual adaptation greater than encoding from two vertical canals. In a follow-up comparison, we observed that perceptual prolongation depended on whether the otoliths were aligned to the axis of rotation when controlling for the activation of both canal type and number of canals. This suggests that the otoliths may provide additional rotational information to the brain encoded from linear tangential acceleration experienced during angular acceleration. Importantly, our finding implicates that the otoliths can detect angular motion without gravity through tangential acceleration. This departs from the more general role of the otoliths as encoding head orientation with respect to gravity (Angelaki and Hess 1996). Additional evidence have also been found showing angular VOR compensation from translational otolith signal after labyrinthectomy in mice (Khan et al. 2019). Taken together, our result advances the idea about the functional role of the otoliths. 8.1.3. Equivalence between virtual and mechanical vestibular stimuli through matching primary vestibular afferent dynamics In Experiment 3 of this dissertation (Chapter 6), we assessed the physiological-equivalence in the integration of primary vestibular afferents between mechanical motion and electrically induced ‘virtual’ motion. Importantly, we used a novel physiological EVS model of primary vestibular afferent dynamics estimated from non-human primate data (Kwan et al. 2019) to compute the dynamics of our motion-equivalent electrical current input. In the first experiment, response decay in torsional 179 vestibulo-ocular reflex and self-motion perception were statistically equivalent between a constant angular velocity input and its EVS model counterpart. We similarly found equivalent ocular responses following mechanical and model-derived electrical stimulation when using a multi-sine stimulus. These results suggest that a physiological approach matching afferent dynamics to mechanical and electrical stimuli can produce equivalent behaviours in humans. Using this method, we can thereby establish the necessary electrical current amplitude and profile needed to replicate angular motion to uniquely probe vestibular influence on eye movement, postural control, and perception. 8.1.4. Using physiologically-equivalent EVS to modulate vestibular sensory feedback in a real-time human-in-the-loop system In the final Experiment 4 (Chapter 7), we extended upon our previously validated physiological motion to EVS model by creating an accessible research tool for real-time modulation of the vestibular sense. We were chiefly motivated by a general perspective shift towards out-of-laboratory evaluation of vestibular function. Prior research employed cumbersome and costly instrumentation (Day and Reynolds 2005; Héroux et al. 2015) which limited applicability to only a laboratory context. In our approach, we leveraged the accessibility of open-source hardware to build an affordable and compact real-time electrical stimulation controller. Our controller, programmed within the MATLAB-Simulink environment, used a small inertial measurement unit to record head motion and then calculate the equivalent electrical current using the validated physiological EVS model from Experiment 3. Our portable controller was able to run at 200Hz, and the system’s actual response dynamics (gain, phase) were well-matched to the simulated theoretical dynamics. We also conducted a partial replication of an experiment by Héroux et al. (2015) modulating vestibular reafference during a standing balance task. Here, we showed that standing balance with eyes closed was initially destabilized by our electrical vestibular modulation; however, after a period of visual availability, balance was restored near 180 baseline level. These results supported the technical and experimental viability of using physiologically-equivalent EVS for real-time modulation of the vestibular sense in real-world environments. 8.2. Implications for vestibular processing The brain is a network of distributed neurons and together, the integration of these neurons lead to changes in firing patterns that eventually generate behaviours like perception. The exact computational steps the brain uses, however, remains unresolved. The experimental results and vestibular sampling model presented in this thesis provide several insights as to how vestibular (and possibly other) sensory signals may be processed. We took a first principles approach in our projects and started by looking at the sensory signals making up vestibular self-motion. We considered how the encoded signals from primary vestibular afferents are transmitted (variability and origin) to the brain. Distinct sources of variabilities start at the anatomical level. The vestibular apparatus itself is composed of discrete end-organ elements transducing linear and rotational head acceleration separately but with unique directional preferences. Primary vestibular afferents innervating each end-organ also vary in their response dynamics and resting firing rate characteristics (Goldberg et al. 2012; Jamali et al. 2013; Sadeghi et al. 2007a). Recognizing how these afferent populations integrate is essential towards making further progress in vestibular modeling. A drawback of classic dynamical linear time-invariant vestibular models is their representation of variability which is constrain to normal distributions (Glasauer 1992; Merfeld et al. 1993; Zupan et al. 2002). While this approximation does replicate observed behaviours, this approach may not accurately capture physiological variability like afferent response dynamics or the origin of encoding afferents. This was accounted for in our sampling model because each sensory particle may be 181 uniquely conditioned. For instance, we considered individual afferent variability based on their unique dynamical responses (gain and phase). As a result, sensory particles do not necessarily encode head motion with identical dynamics between (irregular and regular) and within afferent types. This generates sensory particle distributions that are not necessarily Gaussian, and through sampling allows us to integrate these distributions in what would otherwise may be analytically intractable. The end-organ origin of encoded information likewise presents additional considerations as to how the brain may integrate them. By considering the geometry of the vestibular end-organs in space with respect to the head’s orientation, we controlled for the activation of certain end-organs. We surprisingly found evidence for a role of the otoliths in influencing/encoding our perception of angular head motion. Mechanistically, we propose that this additional information may be mediated by their encoding of tangential acceleration during changes in angular velocity. From an evolutionary standpoint, as the otolith system predates the semicircular canals by 235 million years, it can be reasoned that the otoliths subserve angular motion in some capacity (Ramos de Miguel et al. 2020). An important extension when considering the geometry of the vestibular end-organs is that we can further predict more complex self-motions such as eccentric rotations or curvilinear trajectories (MacNeilage et al. 2010b; Soyka et al. 2015). Both scenarios involve encoding from the canals and otoliths. Logically, our sampling model can be used to integrate both sensory channels to interrogate the inference that give rise to self-motion perception. Another vestibular processing implication relates to how “top down” modulation may influence sensory integration. In our study, we questioned how vestibular afferent signals, some adapting to a constant angular acceleration stimulus and some not, are integrated to bring perceived self-motion to rest during constant stimulation. We modelled this in the form of a prior belief – an expectation of being stationary (Freeman et al. 2010; Laurens and Droulez 2007). Such expectation 182 can be a method used by the brain to direct inference or perception. Of course, the idea of a prior/expectation has been known (Freeman et al. 2010; Hürlimann et al. 2002; Laurens and Droulez 2007; Stocker and Simoncelli 2006). However, it remains an open question as to how the brain actually incorporates expectations. This gives pause as to the prevalence/impact of our expectations, in either subconscious or conscious, on neural processing as a whole. An interesting question is whether expectation in sensory processing is independent of functional tasks. For instance, given deviations between our internal representation of perception and balance control, expectation of motion may be applied differently. Further study on expectations in sensory processing using our approach can provide novel insights as to how the brain operates. 8.3. Adapting a physiology-based sampling model for other sensory systems? We took initial steps in making a physiology-based sampling model for the vestibular processing. A logical extension could be to use the same approach to model other sensory systems. However, incorporating other sensory systems using a similar physiology-based approach would be more challenging. For example, encoding in the visual sense is multifaceted (e.g., optic flow, contrast, exposure, depth). Encoding for the proprioceptive system also presents unique challenges as the information is distributed across the body and presents non-linear activation dynamics (Blum et al. 2020; Goodwin et al. 1975; Poppele 1981). Importantly, known proprioceptive muscle spindle behaviour in functional tasks, like balance or locomotion, are limited (Day et al. 2017; Peters et al. 2017) despite existing characterization of response dynamics in isolation (Houk et al. 1981; Poppele and Bowman 1970; Prochazka 1996). Additional complexity exists given fusimotor modulation of spindle dynamics (Lan and He 2012; Matthews 1981). First steps would likely involve identifying 183 functional specific responses and use that information to begin modeling a simpler muscle-joint system such as the ankle-soleus. 8.4. Implications for novel vestibular research using EVS A major goal of this dissertation was to enhance current methodology for probing vestibular processing. We took steps towards achieving this goal in experiments performed in Chapters 6 and 7 where a physiologically-guided model was used to generate head motion equivalent with electrical vestibular stimuli. We embedded this EVS model into a portable real-time control system allowing for head motion coupled vestibular modulation using EVS. Traditional EVS methods employ predefined (and often static) waveforms, like pulse-trains or sine waves, to evoke vestibular-evoked ocular, muscle, or perceptual response (Banman et al. 2021; Dakin et al. 2007; Mackenzie and Reynolds 2018a; Reynolds 2011b; Welgampola et al. 2013). However, such behaviours are inherently external to one’s movement (ex-afference) and do not address how we learn to expect the sensory consequences of our movements (re-afference). Applying electrical vestibular stimuli coupled to head motion addresses this concern and may be fruitful for research and clinical endeavors. A clear example would be targeting vestibulo-cerebellar processing, an area thought to be involved in distinguishing re-afference from ex-afference. Here, we can alter the brain’s expectation vestibular afference which changes movement-related sensory prediction errors. One potential use case could be in concussed individuals where vestibular dysfunction was observed (Banman et al. 2021; Hwang et al. 2017). In fact, Banman and colleagues (2021) used EVS-based assessments as a clinical tool for evaluating concussion using a stochastic stimulus to measure vestibular-evoked muscle responses. We propose that head-coupled EVS may enable the evaluation of potential disruptions within the vestibulo-cerebellar pathways. Where 184 healthy individuals may recalibrate to novel vestibular signals of head motion (Héroux et al. 2015 and Chapter 7), this may not be true in those with concussion. Thus, head-coupled vestibular modulation using EVS may be used as an objective indicator for concussion or head trauma. Alternatively, head-coupled EVS may be used as a methodological tool for studying vestibular imbalance. By altering vestibular modulation between left and right sides, we may also (to a degree) generate bilateral vestibular asymmetries. This has potential in evaluating balance control following vestibular asymmetry to gain mechanistic insights on compensatory mechanisms following vestibular hypofunction. A fundamental question in movement control is to understand the cost determinants of movements. For example, studies on locomotion established that human gait tends towards optimizing (minimizing) energetic expenditure (Selinger et al. 2015); however, other cost functions driving human gait optimization may exists such as head stability (Veerkamp et al. 2021). Tackling these questions, however, is often not trivial as we need a method to modulate the sensory consequence to one’s movement. Critically, efforts made in Experiment 4 (Chapters 6) provides a solution to implement sensory modulation based on movement. This allows us to modify the existing ‘cost’ landscape for a given function. In this case, we could use a head-movement coupled EVS to modulate sensory prediction error (or head stability) in addition to energy expenditure to reveal the two-dimensional cost landscape during locomotion. 8.5. Limitations and future works Several limitations are present in this dissertation. We focused on self-motion perception as a measure of vestibular output in Chapters 4 and 5. As with any perceptual measure, a degree of uncertainty is present due to cognitive processes involving attention, stimulus interpretation, and 185 subsequent decision making (D’Amour et al. 2021). To robustly evaluate vestibular processing, additional work must be done looking at other vestibular pathways such as the vestibulo-ocular reflex (predominately encoded by regular afferents) and vestibulo-spinal (predominately encoded by irregular afferents) responses. Our sampling model represents a first attempt at combining different sources of afferent information, including variability in afferent dynamics from the same and distinct vestibular end-organs. Although we used physiological data where applicable (mainly for primary vestibular afferent characteristics), major assumptions were made regarding several model parameters. First, the representation of the internal state was an abstraction of central encoding. We can point to several instances of neural correlates of probabilistic inference; however, the exact processing as to how the brain computes them from neural impulses remains an open question (Sohn and Narain 2021). In our abstraction, we represented the internal state as a single distribution, and an arbitrary particle ratio between internal state and afferent was chosen. Although this abstraction did not detract from our conclusions on central expectation nor role of the otoliths, it is known that higher-order processing, such as frequency-specific non-linear gain modulation, exists (Carriot et al. 2022). That was not considered in our implementation here. It should be noted that we assumed signals from each end-organs are vectorially combined in a linear manner. This, for example, allowed us to predict canal afferent activation for different head orientations. Likewise, this assumption predicted the net rotational response vector based on the directionality of the semicircular canals (Fitzpatrick and Day 2004) for EVS. We also used this assumption to estimate the differential amplification of left/right tangential acceleration signals from the otoliths. The exact steps the brain takes to combine different signals are not understood. Recent evidence, however, suggests that neural responses are non-linear which can produce directional bias in the resultant net internal representation of motion (Forbes et al. 2023). Future work is needed to provide empirical evidence for the predicted responses proposed by Forbes et al. (2023). 186 Technical limitations made it difficult to capture accurate eye movements in our set up. The relatively small angular acceleration stimuli (±1.10 deg⋅s-2) used in Chapter 4 produced ocular responses with low signal-to-noise ratio in our recorded video-oculographic data. This, combined with potential fatigue/blinking leading to data loss over a prolonged period (8 min), dissuaded us from measuring ocular responses in this study. Participants in Chapter 5 were asked to sit while maintaining different head orientations which, given our setup, was not able to practically record ocular responses. Additionally, horizontal, vertical and torsional vestibulo-ocular reflex all have distinct dynamics (Tweed et al. 1994). Limitations specific to Chapter 6 and 7 pertain to our head-coupled EVS system. Firstly, our EVS model assumed a static regular-to-irregular afferent ratio and motion-to-current gain. We also assumed that EVS activated all (regular and irregular) vestibular afferents based on linear model predictions. It may also be possible to use alternative electrode configurations of electrical vestibular stimulation to elicit response about other directions (Aoyama et al. 2015; Cauquil et al. 1998); however, such responses are relatively weaker and not as well characterized. Future work should aim to check our existing assumptions used for EVS and to develop methods to induce motion in other head motion axes. 8.6. Conclusion The experiments presented here collectively advance the existing knowledge of how the brain processes sensory cues of motion. Our studies were predicated on current understanding of vestibular encoding at the level of the primary vestibular afferents. As such, physiological data guided the development of our computational sampling model and study hypotheses. Findings from this thesis highlights several intriguing aspects of vestibular processing. First, we provide evidence that the brain may be an active mediator of vestibular information through pre-existing expectation or beliefs. Second, we showed that the otoliths can provide an additional cue about rotational self- 187 motion, a notion often unconsidered. We lastly showed that by matching primary afferent response using electrical stimulation can produce equivalent responses to those during actual head motion. This allows us to produce physiologically consistent vestibular feedback in humans. Critically, this will facilitate future studies on identifying mechanistic insights into how the brain deals with changes in consequence to one’s action. 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An Arduino Due reads angular velocity and linear acceleration data captured from the MPU-6050 inertial measurement unit. Digital command output is transformed into an analog signal using the MCP-4725 D/A converter (0-5V). A voltage divider, unity gain amplifier, and differential amplifier were used to convert the 0-5V signal into a ±10V range. Lastly, this voltage signal was passed through a resistor-capacitor lowpass filter (cut-off = 72Hz) before being sent to the constant current stimulator. Table A-1: Simulink sensor parameters Sensor Settings Value Description Lowpass Filter Bandwidth 96Hz Accelerometer 98Hz Gyroscope Frequency cut-off of the lowpass filter. This setting induces a 3ms delay. Accelerometer range ± 16g Range of acceleration measured by accelerometer Gyroscope range ± 1000dps Range of angular velocity measured by accelerometer 219 Table A-2: Simulink Model Configuration Parameters Heading Parameter Input Solver Solver selection Type Fixed-step Solver selection Solver discrete (no continuous states) Solver detail: Fixed-step size 1/200 Hardware Implementation Hardware Board Arduino Due Hardware board settings: Host-board connection: Automatically or manually I2C properties: Bus speed (Hz) 400000 External mode: Communication interface XCP on Serial External mode: Logging buffer size (in bytes) 24576 – adjustable
Thesis/Dissertation
eng
Kinesiology
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Blouin, Jean-Sébastien
Boushel, Robert
Physiological computations underlying our internal representation of vestibular self-motion
Text