Consistency of Listing's law and reciprocal innervation with pseudo-inverse control of eye position in 3-D.

Pseudo-inverse kinematics, under which small movements are produced by the least possible sum square changes in motor command, has been proposed as a unifying principle for the elimination of redundancy in general biological motor control systems (Pellionsz 1984) and in particular in the oculomotor system (Daunicht 1988, 1991). We have noted elsewhere (Dean et al, 1999) that this principle is incomplete without first specifying a parameterisation of motor command space and we proposed that the relevant motor-command parameter is summed motor unit firing rate. Under this assumption we were able to show that pseudo-inverse control of the horizontal extraocular muscles is consistent with available motor pool firing rate data. In this paper we extend this result to three dimensions and six extraocular muscles, showing that pseudo-inverse control is consistent with published firing rate date for a realistic model of oculomotor kinematics. We suggest that pseudo-inverse control may represent a common currency for modular control of many degree of freedom systems while its implementation may be a consequences of the minimisation of a more ecologically relevant parameter such as post-saccadic retinal slip.