A Volterra approach to dynamic modeling of the visual cortex

The visual cortex of a freshwater turtle, when stimulated by a pattern of light, produces waves of activity that have been both recorded experimentally and simulated using a model cortex. The observed wave can be encoded using principal component analysis with respect to a set of spatial and temporal basis functions. The encoding process generates a vector time series of coefficients (temporal strands) in a suitable lower dimensional beta-space. The goal of this paper is to reproduce the temporal strands as an output of a non-linear, time-invariant, input-output dynamical system. The main result of this paper is to show that Volterra series can be used effectively for this purpose. We show this by conducting two separate simulations. In the first simulation, we stimulate the cortex with a flash of light that is spatially uniform but temporally varies cosinusoidally. In the second simulation, we consider input stimulations that are spatially restricted from the left, right, and center of the visual field. The simulations have been conducted by considering a single flash or a pair of flashes simultaneously applied to any of the above three locations of the visual field. Temporally, the flashes continue to vary cosinusoidally within a range of frequencies or frequency pairs.