Three-dimensional kinematics of saccadic and pursuit eye movements in humans: Relationship between Donders’ and Listing’s laws

For Listing's law to be obeyed during eye movements, the "half-angle rule" must be satisfied: the eye velocity axis must tilt away from Listing's plane by half the angle of eye position eccentricity from primary position. We aimed to determine if this rule is satisfied during horizontal and vertical pursuit compared with saccades. Three-dimensional (3-d) eye rotation data were acquired from five normal head-fixed humans using the search coil technique. Saccades were recorded in response to 40° horizontal or vertical steps in target position, at different elevations and azimuths. Pursuit was recorded while tracking a target moving horizontally or vertically at 20°/s, with peak-to-peak amplitude of 40°, at the same elevations and azimuths. First- and second-order surfaces were fitted to 3-d eye position data from periods of fixation. In all subjects, eye positions did not lie on a planar surface, but on a twisted surface in 3-d space. The tilt-angle coefficient (TAC) during saccades and pursuit was calculated as the ratio of the angle of eye velocity axis tilt to the angle of eye position eccentricity. During horizontal saccades and pursuit, mean TACs were 0.58 and 0.64, respectively. During vertical saccades and pursuit, mean TACs were 0.35 and 0.43, respectively, and lower than their horizontal counterparts (p<0.05). These findings suggest that Listing's law is not perfectly satisfied during saccades or pursuit. On the basis of model simulations, we propose that the discrepancy in horizontal and vertical TACs causes eye positions to lie on a twisted rather than a planar surface.