Mathematical Model of the Oculomotor System

Mathematical modeling of eye movement contributes to the learning of the oculomotor system and the development of technologies for device control. We propose in the present article a representative model of the different movements and rotation of the eye (adduction, abduction, elevation and descent) taking into account the anatomical properties of the extraocular muscles, strength-elongation relationship, and the action of the agonist muscles and antagonists. An easy to understand model is presented that allows the analysis of applied forces in muscle contraction, the conversion of length of elongation (or shortening) of the muscle, which generates rotation of the eye, and the vector interpretation of the direction in the space of towards where the eye directs the sight. In addition, an interface was made that allows the user to vary the Force applied to the extraocular muscles and obtain the spatial movement of the eye, with the anatomical and physiological considerations of the oculomotor system. The proposed model allows a simplified understanding, compared to other models, of the physiology of the oculomotor system, and its implementation in computational simulation systems results in faster executions with lower computational cost. The implementation of the proposed model will serve in the future in the control of devices or development of technologies that depend on eye movements or that imitate these movements.