Abstract
Purpose: :
In order to better understand the physiological mechanisms of the human pupillary light reflex (PLR), we tested a computational model [1] for the PLR elicited by brief flashes of light.
Methods: :
After dark adaptation, six subjects with healthy vision were shown a series of 640nm red Ganzfeld stimuli (Espion, Diagnosys, LLC) of 10, 100, 1000ms duration [2]. For each duration, the intensities ranged from -3 to 2.6 log cd/m2, and the inter-stimulus intervals were long enough for baseline recovery. The PLRs were recorded using an infrared camera (Arrington Research) [3]. Based on the model of Fan & Yao [1], a second-order differential equation was fitted to the PLR waveforms of the 100ms data; ten parameters were optimized with a nested Nelder-Mead algorithm [4]. To a first approximation, six parameters (the resting sizes, spring constants, a damping constant, and the difference in baseline forces of the constrictor and dilator muscles) were stimulus-independent (SI); they were approximately constant with intensity. The SI parameters were held constant, while four stimulus-dependent (SD) parameters (the forces and latencies of the constrictor and dilator) were optimized for each intensity. Sigmoidal functions of intensity were fitted to each SD parameter. For the final model, all parameters were either constant or a function of intensity, and the model became fully computational by setting flash intensity.
Results: :
For the 100ms data, the fully computational model did nearly as well as the model optimized for all parameters. With increasing intensity, the force of the constrictor and the latency of the dilator increased, while the force of the dilator and the latency of the constrictor decreased. By adjusting the intensity by a log unit to compensate for the decrease in energy, the model predicted the PLRs for the 10ms intensity series. However, the model failed to predict the 1000ms data even with an adjustment for energy.
Conclusions: :
The parameters of the Fan & Yao model [1] can be specified as either constant values or sigmoidal functions of intensity. Originally developed for a stimulus duration of 100ms, the model fits the 10ms data with an adjustment for energy. However, the failure of the model to predict the 1000ms data indicates it must be modified for longer lights. A time-dependent model for the input (ganglion cell response) and/or for pupil mechanics may be needed. 1. Fan & Yao, IEEE Trans, 2011; 2. Park et al, IOVS, 2011; 3. Kardon et al, Ophthalmol, 2009; 4. Lagarias et al, SIAM J Optim, 1998.
Keywords: pupillary reflex • computational modeling • ganglion cells