This talk summarizes two modeling studies on the motor cortex and the cerebellum.
The motor cortex is the final cortical pathway to motor circuits in the spinal cord, but its functional role has long been debated, particularly whether the motor cortex represents movement kinematics or dynamics. To resolve this issue, I modeled the visuomotor transformation using Newton-Euler equations of motion that has been used in robotics, and proposed that neural activities in the motor cortex represent vector cross products in the equations. This model explains a wide variety of the characteristics reported in the motor cortex in a unified manner.
The cerebellum is hypothesized to predict a future state of the body from a current state and a corollary discharge, the computation known as an internal forward model. Although this hypothesis has been supported from a number of clinical, psychophysical and neuroimaging studies, a direct neurophysiological evidence is missing. I analyzed firing rates of mossy fibers (cerebellar inputs), Purkinje cells (outputs from cerebellar cortex), and dentate cells (cerebellar outputs) recorded from a behaving monkey. I found that the cerebellar outputs provided predictive information about future inputs to the cerebellum, providing direct neurophysiological evidence for the forward-model hypothesis of the cerebellum.
 Tanaka, H., & Sejnowski, T. J. (2013). Computing reaching dynamics in motor cortex with Cartesian spatial coordinates. Journal of Neurophysiology, 109(4), 1182-1201.
 Tanaka, H., & Sejnowski, T. J. (2015). Motor adaptation and generalization of reaching movements using motor primitives based on spatial coordinates. Journal of Neurophysiology, 113(4), 1217-1233.
 Tanaka, H., Ishikawa, T., & Kakei, S. (2019). Neural Evidence of the Cerebellum as a State Predictor. The Cerebellum, 1-23.