Two-Dimensional Linear Homeomorphic Oculomotor Plant Mathematical Model

Abstract

This paper builds a two-dimensional linear homeomorphic oculomotor plant mathematical model and assesses its ability to simulate person-specific oblique saccades on a two-dimensional plane. The proposed model is driven by a simplified pulse-step neuronal control signal and accounts in a linear form for the unique characteristics of the eye globe and the extraocular muscles responsible for horizontal and vertical rotation (the lateral/medial recti and superior/inferior recti respectively). These characteristics include: series elasticity, length tension, passive elasticity, viscosity, eye globe inertial mass, and the force-velocity relationships of agonist/antagonist muscles. Results indicate that the model is capable of producing oblique saccade trajectories with properties resembling those of normal humans. The model can be simplified into two one-dimensional models for quicker signal simulation, making it applicable for time sensitive applications. Practical applications of the model might include: enhanced security in biometric identification systems; improved noise reduction and signal recovery facilities for eye tracking systems; and additional metrics from which to determine user effort during usability testing.