Behaviour space of a stretch reflex model and its implications for the neural control of voluntary movement

A nonlinear model for the stretch reflex has recently been used to study the interactions between voluntary and reflex controls during fast, targeted movements. The present study explores the topography of a 'behaviour space' generated by computer simulations of this model under various combinations of values for the gain parameters and time constants in the model's feedback loops. In general, we define a behaviour space to be any set of behavioural characteristics of the simulated movement, such as movement time, peak acceleration or peak velocity. The mathematical model can therefore be viewed as an M x N dimensional map from its parameter space N to a behaviour space M. Here, a one-dimensional behaviour space is explored. This provides a method for quantitatively comparing the different control strategies that might be employed by the nervous system for integrating reflex and descending signals during fast, voluntary movements. The results indicate that an optimal strategy will employ proprioceptive feedback as a means of fine-tuning the braking and clamping activities of fast, goal-directed movements and that descending signals are primarily important for initiating the movement and for controlling reciprocal patterns of muscle activity during the end phase of the movement.