International Journal of Neural Systems, Vol. 19, No. 5 (2009) 309–330 c  World Scientific Publishing Company AN UPDATED TIME-OPTIMAL 3RD-ORDER LINEAR SACCADIC EYE PLANT MODEL WEI ZHOU, XINNIAN CHEN and JOHN ENDERLE ∗ University of Connecticut, 260 Glenbrook Road Storrs, CT 06269-2247, USA ∗ jenderle@bme.uconn.edu A linear third-order model of the ocular motor plant for horizontal saccadic eye movements is presented consisting of a linear ocular motor plant and a time-optimal saccadic controller based on physiological considerations. The ocular motor plant consists of the eyeball and two extraocular muscles. All parame- ters and initial conditions are estimated or measured from physiological data. The neural inputs are described by pulse-slide-step waveforms with a post inhibitory rebound burst and based on a time-optimal controller. Model parameters are estimated using the system identification technique. The static and dynamic behaviors of the model are in excellent agreement with the experimental data. Keywords : Saccade; post-saccade phenomena; time-optimal; system identification. 0. Introduction Understanding how the brain controls eye move- ments has been studied for over one and one-half centuries. During the middle of 19th century, Donders, Listings, Helmholtz and many others pub- lished articles on the eye movement system that are still relevant today. 8,59 With the advent of the chronic single-unit recording method and precise his- tological slicing techniques, detailed anatomical and physiological descriptions of the ocular motor system became possible (see Ref. 45 for an earlier method and Scudder et al. for a modern method 49 ). A type of primate eye movement, called a saccade, has been studied extensively in the past 30 years due to its relative simplicity. A saccade is a fast eye move- ment that involves quickly moving the eyes from one target or image to another. Many of the studies have focused on identifying and modeling the brain circuitry involved in the generation of saccadic eye movements (for reviews, see Refs. 40, 20, 53 and 48). Apart from normal models, subsystem models have also been proposed while taking considerations of dysfunctional saccadic characteristics in situations such as nystagmus, 7,26,60 slow saccades, stuttering decelerated saccades, high-frequency saccade oscilla- tions, and macrosaccadic oscillations. 40,41 A number of studies have focused on modeling eye plant dynamics in response to saccade controllers. These studies began with the work of Westheimer in 1954 and have continued through today with ever more realistic ocular motor plants and saccade controllers. Some representative 1-D horizontal saccadic models include Robinson’s SQUINT model 44 with a velocity-position integra- tor, a nonlinear model, 43 Bahill’s linear homeo- morphic model, 4 and Enderle and coworkers linear homeomorphic eye plant model with a time-optimal controller. 9,10,12–15 Anderson and coworkers present a new oculomotor plant developed using simulation of the abducens nucleus with a brief of pulse trains of varying frequency. 2 The model includes four Voigt elements that represent the orbital tissue and a mus- cle model that consists of a spring and viscosity. The agonist eye muscle includes activation dynamics, but the antagonist does not have any input. This model is not homeomorphic as the model presented ∗ Corresponding author. 309