Mathematical Modeling of the Visual Cortex

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This project concerns a mathematical description of how mammals process some of the most elementary characteristics of the visual scene, such as orientation and spatial frequency. This processing takes place in the primary visual cortex (V1). In particular, experiments, which measure the response of neurons in V1 of a macaque monkey observing a screen with a drifting, standing, or randomly-flashed sinusoidal grating, will be described and analyzed with the aid of a coarse-grained neuronal model of V1. This model is a nonlinear integral equation, whose properties will be studied analytically as well as computationally. The coarse-grained model incorporates vital anatomical information, including the architecture of the orientation- and spatial-frequency-preference neuronal maps of V1, the sizes and strengths of the cortico-cortical neuronal connections, and the detailed layout of the neural input into V1. The orientation andspatial-frequency tuning of V1 neurons as functions of time will be computed and compared with the experimental data, with an eye on determining which cortical achitecture better describes the true biology:feed-forward (which assumes no importance of the cortico-cortical interactions), or feed-back (which assumes that cortico-cortical interactions contribute crucially to the spatio-temporal evolution of theneuronal tuning curves). The work will be performed in collaboration with neuroscientist Robert Shapley and applied mathematicians David McLaughlin and Michael Shelley at New York University's Center for Neural Science, in the framework of a year-long visit by the PI, Gregor Kovacic.This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).