A developmental model of ocular dominance column formation on a growing cortex
Mathematical Biosciences Institute (MBI), The Ohio State University
(September 7, 2006 10:30 AM - 11:30 AM)
A brief overview of the the visual system, focusing on the primary visual cortex. In particular, we will derive an activity-based developmental model of ocular dominance column formation in primary visual cortex that takes into account cortical growth. The resulting evolution equation for the densities of feedforward afferents from the two eyes exhibits a sequence of pattern forming instabilities as the size of the cortex increases. We use linear stability analysis to investigate the nature of the transitions between successive patterns in the sequence. We show that these transitions involve the splitting of existing ocular dominance columns, such that the mean width of an OD column is approximately preserved during the course of development. This is consistent with recent experimental observations of postnatal growth in cat. Additionally, I will briefly discuss the joint development of cytochrome oxidase blobs with ocular dominance columns, another problem I have worked on.
Joint work with Paul Bressloff (Dept. of Mathematics, University of Utah).