Human Pupillary Light Reflex Model: research of dynamic in a Delay Differential Equation - Laureano, M.; Mendes, D. A. (Dynamics Days Europe, 2018)
It is presented a qualitative study of some features of the pupillary light reflex and a contribution to their clarification based on the nonlinear theory of dynamical systems. In order to introduce the necessary concepts, terminology, and relevant features of the pupillary light reflex, we start with an overview of the human eye anatomy and physiology with emphasis on the iris, pupil, retina and pupillary light reflex pathway. Then we consider the model developed by Longtin and Milton, which models the human pupillary light reflex, defined by a differential equation with nonlinear delay, and present the study carried out on the qualitative dynamic behavior of that neurophysiological control system. We show yet the chaotic behavior arising from the discrete model with associated delay. This study tends to illustrate how the understanding of neurophysiological models can be enhanced by the theory of nonlinear dynamical systems. We emphasize that the study of the pupillary light reflex is important from a medical point of view. Serious retinal diseases and optic nerve injuries may lead to relevant changes in the fotomotor reflex, responsible for pupillary contraction, since it is mediated by retinal photoreceptors and consists of four neurons (sensory, internuclear, preganglionic motor and postganglionic motor). Also, the pupillary dilation is mediated by the sympathetic innervation and includes three neurons (central,preganglionic and postganglionic) and, for many causes, this pathway can be affected leading to Horner syndrome.