Control Theoretic Model of the Cerebellum

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The aim of this research is to develop a mathematical model of the human cerebellum, the part of the brain responsible for motor control. A complete understanding of the cerebellum is one of the great open problems of neurobiology today. A mathematical model of the cerebellum would contribute fundamental knowledge to science, and it would enable better understanding of neurological disorders such as ataxia, Huntington's disease, and Parkinson's disease. Initially, we will focus on experimental findings from cognitive psychology over the last 30 years on motor adaptation. Adaptation to visuomotor rotations is an experiment in which a human subject must make a fast reach with the hand to a target disk on a horizontal screen, by observing a cursor on the screen. When the cursor position is verdigal, humans are able to hit the target disk within the first attempt. Instead, when the cursor angle is rotated from the hand angle by an unknown amount, an implicit (subconscious) process of adaptation is initiated in which the human brain corrects for the observed error through consecutive trials. It is believed that the cerebellum is responsible for implicit adaptation. There has been an outpouring of research focusing on this experiment because it exposes a number of behaviours and principles of adaptation.******We have recently discovered a linear time-invariant (LTI) state model that explains adaptation in the visuomotor rotation experiment. Our model recovers the dynamic behaviours observed in experiments, and moreover, we are the first to reconcile newly reported results on the so-called error clamp paradigm. Unlike previous models, our model reveals a plausible architecture for the computations underlying adaptation, and it has states with a physical meaning. Our model was derived using regulator theory; this is the first time regulator theory has been applied to derive a model of motor adaptation. ******Our methodology to find a mathematical model of the cerebellum will contrast with all other approaches taken by psychologists today. We interpret the problem of adaptation as a problem of control synthesis: to synthesize a control law to achieve tracking in the presence of an unknown disturbance. The power of our methodology derives from the fact that, like Newton's laws that tell us about immutable limits on the motion of bodies in a gravitational field, so too regulator theory informs us on immutable limits of a control system: this is the internal model principle. Such immutable limits narrow the search for a plausible mathematical model. As such, regulator theory appears to provide a new body of evidence beyond experimentation about the computations occurring (in the cerebellum) when implicit adaptation in a motor task occurs.******I have dedicated my sabbatical year to launch this new research initiative. I am excited to bring a new perspective to neuroscience and to open a door to a fuller understanding of the human cerebellum.