MODELING CONTROL OF EYE ORIENTATION IN 3 DIMENSIONS - I - ROLE OF MUSCLE PULLEYS IN DETERMINING SACCADIC TRAJECTORY

This study evaluates the effects of muscle axis shifts on the performa nce of a vector velocity-position integrator in the CNS. Earlier model s of the oculomotor plant assumed that the muscle axes remained fixed relative to the head as the eye rotated into secondary and tertiary ey e positions. Under this assumption, the vector integrator model genera tes torsional transients as the eye moves from secondary to tertiary p ositions of fixation. The torsional transient represents an eye moveme nt response to a spatial mismatch between the torque axes that remain fixed in the head and the displacement plane that changes by half the angle of the change in eye orientation. When muscle axis shifts were i ncorporated into the model, the torque axes were closer to the displac ement plane at each eye orientation throughout the trajectory, and tor sional transients were reduced dramatically. Their size and dynamics w ere close to reported data. It was also shown that when the muscle tor que axes were rotated by 50% of the eye rotation, there was no torsion al transient and Listing's law was perfectly obeyed. When muscle torqu e axes rotated >50%, torsional transients reversed direction compared with what occurred for muscle axis shifts of <50%. The model indicates that Listing's law is implemented by the oculomotor plant subject to a two-dimensional command signal that is confined to the pitch-yaw pla ne, having zero torsion. Saccades that bring the eye to orientations o utside Listing's plane could easily be corrected by a roll pulse that resets the roll state of the-velocity-position integrator to zero. Thi s would be a simple implementation of the corrective controller sugges ted by Van Opstal and colleagues. The model further indicates that mus cle axis shifts together with the torque orientation relationship for tissue surrounding the eye and Newton's laws of motion form a sufficie nt plant model to explain saccadic trajectories and periods of fixatio n when driven by a vector command confined to the pitch-yaw plane. Thi s implies that the velocity-position integrator is probably realized a s a subtractive feedback vector integrator and not as a quaternion-bas ed integrator that implements kinematic transformations to orient the eye.