Time-Optimal Control of Saccadic Eye Movements

A new theory describing the time-optimal control of saccadic eye movements is proposed based on Pontryagin's minimum principle and physiological considerations. The lateral and medial rectus muscle of each eye is assumed to be a parallel combination of an active state tension generator with a viscosity and elastic element, connected to a series elastic element. The eyeball is modeled as a sphere connected to a viscosity and elastic element. Each of these elements is assumed to be ideal and linear. The neuronal control strategy is shown to be a first-order time-optimal control signal. Under this condition, the active state tension for each muscle is a low-pass filtered pulse-step waveform. The magnitude of the agonist pulse is a maximum for saccades of all sizes and only the duration of the agonist pulse affects the size of the saccade. The antagonist muscle is completely inhibited during the period of maximum stimulation for the agonist muscle. Horizontal saccadic eye movements were recorded from infrared signals reflected from the anterior surface of the cornea and then digitized. Parameter estimates for the model were calculated by using a conjugate gradient search program which minimizes the integral of the absolute value of the squared error between the model and the data. The predictions of the model under a time-optimal controller are in good agreement with the data.