Shadmehr R, Donchin O, Hwang EJ, Hemminger SE, Rao A (2005) Learning dynamics of reaching.  In: Motor Cortex in Voluntary Movements: A distributed system for distributed functions, A. Riehle and E. Vaadia (eds), CRC Press, pp. 297-328.

Abstract  When one moves their hand from one point to another, the brain guides the arm by relying on neural structures that estimate physical dynamics of the task.  For example, if one is about to lift a bottle of milk that appears full rather than empty, the brain takes into account the subtle changes in the dynamics of the task and this is reflected in the altered motor commands.  The neural structures that compute the task’s dynamics are “internal models” that transform the desired motion into motor commands.  Internal models are learned with practice and are a fundamental part of voluntary motor control.  What do internal models compute, and which neural structures perform that computation?  We approach these problems by considering a task where physical dynamics of reaching movements are altered by force fields that act on the hand.  Experiments by a number of laboratories on this paradigm suggest that internal models are sensorimotor transformations that map a desired sensory state of the arm into an estimate of forces, i.e., a model of the inverse dynamics of the task.  If this computation is represented as a population code via a flexible combination of basis functions, then one can infer activity fields of the bases from the patterns of generalization.  We provide a mathematical technique that facilitates this inference by analyzing trial-to-trial changes in performance.  Results suggest that internal models are computed with bases that are directionally tuned to limb motion in intrinsic coordinates of joints and muscles, and this tuning is modulated multiplicatively as a function of static position of the limb.  That is, limb position acts as a gain field on directional tuning.  Some of these properties are consistent with activity fields of neurons in the motor cortex and the cerebellum.  We suggest that activity fields of these cells are reflected in human behavior in the way that we learn and generalize patterns of dynamics in reaching movements.