A Mathematical Model for Pupillary Light Response with Regard to Special Morphology of Pupillary Smooth Muscles

Abstract

This study used an optimization algorithm to mathematically investigate the light-regulation mechanism of the pupil. Regulation criteria were derived from consideration of the autonomic nervous system and the morphology of pupillary smooth muscles. An objective function was defined as follows : square of the rate of change of acceleration multiplied by an exponential function of time integrated over the entire movement. Variational calculus was used to obtain the equations expressing the pupil behavior. To evaluate the model, infrared pupillography was used to measure pupillary constriction and dilatation in response to step changes of light. The observed data was in good agreement with the model output, supporting our idea that the pupillary light response is regulated to maximize rapidity as well as smoothness.