Linear Homeomorphic Models for Muscles in the Head–Neck Region

Static Characteristics of a New Three-Dimensional Linear Homeomorphic Saccade Model

A linear homeomorphic saccade model that produces 3D saccadic eye movements consistent with physiological and anatomical evidence is introduced. Central to the model is the implementation of a time-optimal controller with six linear muscles and pulleys that represent the saccade oculomotor plant. Each muscle is modeled as a parallel combination of viscosity [Formula: see text] and series elasticity [Formula: see text] connected to the parallel combination of active-state tension generator [Formula: see text], viscosity element [Formula: see text], and length tension elastic element [Formula: see text]. Additionally, passive tissues involving the eyeball include a viscosity element [Formula: see text], elastic element [Formula: see text], and moment of inertia [Formula: see text]. The neural input for each muscle is separately maintained, whereas the effective pulling direction is modulated by its respective mid-orbital constraint from the pulleys. Initial parameter values for the oculomotor plant are based on anatomical and physiological evidence. The oculomotor plant uses a time-optimal, 2D commutative neural controller, together with the pulley system that actively functions to implement Listing's law during both static and dynamic conditions. In a companion paper, the dynamic characteristics of the saccade model is analyzed using a time domain system identification technique to estimate the final parameter values and neural inputs from saccade data. An excellent match between the model estimates and the data is observed, whereby a total of 20 horizontal, 5 vertical, and 64 oblique saccades are analyzed.