Characterization of pulse-step input for saccadic eye movements

The understanding of the neuronal firing input to the motor neurons innervating oculomotor muscles is vital in studying control of eye-movements. The firing rate of the motor neurons which causes rapid eye movements called saccades has been characterized here using a Gaussian function. Using experimental horizontal saccade data, the parameters of the Gaussian function are estimated by least square minimization. These parameters, peak firing rate and time-to-peak of the input firing rate were observed to be functions of the saccade amplitude. Their relationship is quantified using a least square curve fit. The peak firing rate is found to be linearly varying with saccade amplitude and time-to-peak varies as a quadratic function of saccade amplitude. The model can predict the input firing rate of motor neurons for all saccade amplitudes independent of the availability of data. This work provides a method that can be extended for predicting the neural firing rates to be generated by the motor neurons at the oculomotor muscles for producing different classes of eye movements.