Estimation of autonomic nervous activity using the inverse dynamic model of the pupil muscle plant

In order to elucidate the mechanism of the pupillary control system, the internal property of the pupillary muscle plant, as well as the autonomic nervous input to the muscle plant, must be analyzed. In this study, we approach the problem first by constructing a new homeomorphic biomechanical model for the human pupillary muscle plant (forward dynamic model). We showed that the model is able not only to reproduce various experimental results that exhibit various nonlinearities but also to explain how such nonlinear responses are generated in terms of the internal property of the model. Then, we contrive a possible method to estimate the autonomic nervous input to the muscle plant. This method utilizes the inverse dynamic model of the pupillary muscle plant so that the autonomic nervous input can be estimated from the pupillary response. We applied this method to the experimental step responses, and showed that the estimated neural input indicates characteristics quite similar to the results of the physiological experiment. Last, we discuss the origin of the pupillary escape and capture as well as the sustained and transient components of the pupillary response, based on the analysis of the forward and/or inverse dynamic model.

Modelling autonomous oscillations in the human pupil light reflex using non-linear delay-differential equations

Neurophysiological and anatomical observations are used to derive a non-linear delay-differential equation for the pupil light reflex with negative feedback. As the gain or the time delay in the reflex is increased, a supercritical Hopf bifurcation occurs from a stable fixed point to a stable limit cycle oscillation in pupil area. A Hopf bifurcation analysis is used to determine the conditions for instability and the period and amplitude of these oscillations. The more complex waveforms typical of the occurrence of higher order bifurcations were not seen in numerical simulations of the model. This model provides a general framework to study the different types of dynamical behaviors which can be produced by the pupil light reflex, e.g. edge-light pupil cycling.