Computational and analytical modeling of the early mammalian visual pathway: Distribution function approach

Neurons of the visual cortex are organized in functional regions, such as orientation or ocularity columns, spatial proximity ensuring functional similarity. For theoretical and computational modeling, this property suggests the possibility to simplify description by considering relatively large subpopulations of spatially close neurons, rather than individual neurons, as elemental entities. Such a subpopulation can be characterized by the distribution function (or probability density) P(U), where U is the membrane potential (or in the general case, F(U), where U = {U_i} is a vector in the configuration space of an individual neuron). We construct a "kinetic equation" which governs the temporal evolution of the distribution function (and determines the mean firing rate) and investigate its properties. The results are compared with time-dependent distribution functions obtained from a numerical model of mammalian early visual pathway, and from a simplified network of leaky integrators. The statistical properties of firing patterns are also studied.