Control Theoretic Model of the Cerebellum

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My research concerns the development of a control theoretic model of the cerebellum. A complete understanding of the cerebellum is one of the great open problems of neuroscience today, not very different from Kepler's problem on the motion of the planets, in its day. The cerebellum has remarkable features. It contains about half the neurons of the brain (more than the cerebral cortex), it has a purely feedforward neural architecture (in contrast with the recurrent architecture of the cerebral cortex), it operates on a timescale of milliseconds, 1-2 orders of magnitude faster than the cerebral cortex. Most importantly, despite the many regulatory functions it performs and independently of the particular function it is regulating (e.g. motor control, locomotion, eye movement, speech timing, emotion regulation), the computations are identical. What are those computations? Since the 1960's, control theory and robotics have offered plausible explanations. Yet no complete model has been found, to date. I initiated research on modeling the cerebellum during my sabbatical in 2017. I began with an experiment in cognitive psychology on adaptation to visuomotor rotations. A human subject is presented with a task to make a fast reach with the hand to a target disk on a horizontal screen. When the cursor angle is rotated from the hand angle by an amount unknown to the subject, an implicit (subconscious) process of adaptation takes place. This process is believed to reside in the cerebellum. We developed a model that predicts the dynamic phenomena observed in the experiments. The cerebellum is also involved in eye movement. Behaviours of the oculomotor system include the vestibuloocular reflex, smooth pursuit, saccades, and the optokinetic reflex. The computations (in the cerebellum) are the same for both the visuomotor experiment and the oculomotor system. We developed a second generation model that both recovers the behaviours of the oculomotor system and reveals the computations of the cerebellum. Rather than deriving a mathematical model based on analysis of experimental data, I approach the cerebellum modeling problem as one of synthesis: to synthesize a control law using tools from control theory. An advantage of applying control theory in this way is that, like Newton's laws that tell us about immutable limits on the motion of bodies in a gravitational field, so too control theory explains the immutable limits of a control system to achieve tracking in the presence of unknown disturbances. In essence, control theory narrows the search for a plausible mathematical model. The first phase of our research to develop a control-theoretic model of the cerebellum is well underway. The second phase is to relate the model to the neurophysiology of the cerebellum. We hope our work can contribute to basic science as well as to understanding neurological disorders such as ataxia, Huntington's disease, and Parkinson's disease.