Predictive smooth pursuit of complex two-dimensional trajectories in monkey: component interactions

Smooth pursuit eye movements were studied in monkeys tracking target spots that moved two-dimensionally. Complex target trajectories were created by applying either two or three sinusoids to horizontal and vertical axes in various combinations. The chance of observing predictable performance was increased by repeated training on each trajectory. Data analyses were based upon repeated presentations of each trajectory within sessions and on successive days. We wished to determine how accurately monkeys could pursue targets moving along these trajectories and to observe interactions among frequency components. At intermediate frequencies, tracking performance was smooth and consistent during repeated presentations with saccadic corrections that were well integrated with smooth pursuit. The mean gain for eight different sum-of-sines trajectories was 0.83 and the mean magnitude (absolute value) of the phase error was 6 degrees. In light of the long delays that have been associated with the processing of visual information, these values indicate that the monkeys were pursuing predictively. Five factors influenced predictive pursuit performance: (1) there was a decline in performance with increasing frequency; (2) horizontal pursuit was better than vertical pursuit; (3) high-frequency components were tracked with higher gains and phase lags, while lower-frequency components were tracked with lower gains and phase leads; (4) the gain of sinusoidal pursuit was always reduced when a second sinusoid was applied to the same axis or, to a lessor extent, when a second sinusoid of higher frequency was applied to the orthogonal axis; (5) the phase of sinusoidal pursuit shifted from a phase lag to a phase lead when combined with a second sinusoid of higher frequency, but was not affected by the addition of a lower-frequency sinusoid. Findings 1 and 2 confirm, in monkeys, results reported for humans, and 3 extends to monkeys and to two-dimensional pursuit results based upon human subjects. All of these findings demonstrate that complex predictive tracking is controlled by a nonlinear and nonhomogeneous system that uses predictive strategies in concert with feedback control to generate good pursuit.