Modeling Inter-trial Variability of Saccade Trajectories: Effects of Lesions of the Oculomotor Part of the Fastigial Nucleus

This study investigates the inter-trial variability of saccade trajectories observed in five rhesus macaques (Macaca mulatta). For each time point during a saccade, the inter-trial variance of eye position and its covariance with eye end position were evaluated. Data were modeled by a superposition of three noise components due to 1) planning noise, 2) signal-dependent motor noise, and 3) signal-dependent premotor noise entering within an internal feedback loop. Both planning noise and signal-dependent motor noise (together called accumulating noise) predict a simple S-shaped variance increase during saccades, which was not sufficient to explain the data. Adding noise within an internal feedback loop enabled the model to mimic variance/covariance structure in each monkey, and to estimate the noise amplitudes and the feedback gain. Feedback noise had little effect on end point noise, which was dominated by accumulating noise. This analysis was further extended to saccades executed during inactivation of the caudal fastigial nucleus (cFN) on one side of the cerebellum. Saccades ipsiversive to an inactivated cFN showed more end point variance than did normal saccades. During cFN inactivation, eye position during saccades was statistically more strongly coupled to eye position at saccade end. The proposed model could fit the variance/covariance structure of ipsiversive and contraversive saccades. Inactivation effects on saccade noise are explained by a decrease of the feedback gain and an increase of planning and/or signal-dependent motor noise. The decrease of the fitted feedback gain is consistent with previous studies suggesting a role for the cerebellum in an internal feedback mechanism. Increased end point variance did not result from impaired feedback but from the increase of accumulating noise. The effects of cFN inactivation on saccade noise indicate that the effects of cFN inactivation cannot be explained entirely with the cFN’s direct connections to the saccade-related premotor centers in the brainstem.Author Summary: In movement control, online feedback compensation of internal noise directly affects the statistics of the movement trajectory, namely the development of the variance during the movement and the correlation of the effectors position during the movement and its end position. We used here the statistics of the movement trajectory to gain inference about features of the underlying noise sources and of the actual feedback mechanism. We developed a method to analytically determine the statistics of movement trajectories resulting from noise entered inside and outside of an internal feedback loop and obtained a general model of noise in the output of feedback controlled motor systems. In detail we consider here the special case of saccade control and show that the number of free model parameters is small enough to identify the contribution of the noise components inside and outside of the loop, and the strength of the feedback. The model was fitted to the inter-trial saccade variability observed in five rhesus monkeys (Macaca mulatta). By comparing our parameter estimates for saccades under control conditions to saccades executed during inactivation of the fastigial nucleus (the main cerebellar output to the brainstem saccade generator) we quantify the role of the cerebellum in feedback motor control.