Control Theoretic Model of the Cerebellum

这项研究的目的是建立一个人类小脑的数学模型，小脑是大脑中负责运动控制的部分。对小脑的全面了解是当今神经生物学的重大开放性问题之一。小脑的数学模型将为科学提供基础知识，它将使人们更好地了解共济失调、亨廷顿病和帕金森病等神经系统疾病。首先，我们将关注过去30年来认知心理学在运动适应方面的实验发现。适应视觉旋转是一项实验，其中人类受试者必须通过观察屏幕上的光标，用手快速到达水平屏幕上的目标圆盘。当光标位置为verdigal时，人类能够在第一次尝试中命中目标磁盘。相反，当光标角度从手的角度旋转了一个未知的量时，一个隐含的（潜意识的）适应过程就开始了，在这个过程中，人脑通过连续的试验来纠正观察到的错误。据信小脑负责内隐适应。有大量的研究集中在这个实验上，因为它揭示了一些适应的行为和原则。我们最近发现了一个线性时不变（LTI）的状态模型，解释适应在视觉旋转实验。我们的模型恢复了在实验中观察到的动态行为，而且，我们是第一个调和新报道的所谓的错误钳范例的结果。与以前的模型不同，我们的模型揭示了一个合理的架构的计算基础适应，它具有物理意义的状态。我们的模型是使用调节器理论推导出来的，这是第一次调节器理论被应用于推导出运动适应模型。** 我们的方法找到一个数学模型的小脑将对比所有其他方法心理学家今天。我们将自适应问题解释为控制综合问题：在存在未知干扰的情况下，综合控制律以实现跟踪。我们的方法论的力量来自于这样一个事实，就像牛顿定律告诉我们物体在引力场中运动的不可变极限一样，调节器理论也告诉我们控制系统的不可变极限：这就是内模原理。这种不可改变的限制缩小了寻找一个合理的数学模型的范围。因此，调节器理论似乎提供了一个新的证据，超越了实验，证明当运动任务中发生内隐适应时（在小脑中）发生的计算。我用了一年的休假来启动这项新的研究计划。我很高兴能为神经科学带来一个新的视角，并为更全面地了解人类小脑打开一扇大门。

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.