Internal models of limb dynamics and the encoding of limb state

Studies of reaching suggest that humans adapt to novel arm dynamics by building internal models that transform planned sensory states of the limb, e.g., desired limb position and its derivatives, into motor commands, e.g., joint torques. Earlier work modeled this computation via a population of basis elements and used system identification techniques to estimate the tuning properties of the bases from the patterns of generalization. Here we hypothesized that the neural representation of planned sensory states in the internal model might resemble the signals from the peripheral sensors. These sensors normally encode the limb's actual sensory state in which movement errors occurred. We developed a set of equations based on properties of muscle spindles that estimated spindle discharge as a function of the limb's state during reaching and drawing of circles. We then implemented a simulation of a two-link arm that learned to move in various force fields using these spindle-like bases. The system produced a pattern of adaptation and generalization that accounted for a wide range of previously reported behavioral results. In particular, the bases showed gain-field interactions between encoding of limb position and velocity, very similar to the gain fields inferred from behavioral studies. The poor sensitivity of the bases to limb acceleration predicted behavioral results that were confirmed by experiment. We suggest that the internal model of limb dynamics is computed by the brain with neurons that encode the state of the limb in a manner similar to that expected of muscle spindle afferents.