Effects of synaptic connectivity inhomogeneities on dynamics of wave propagation in neural tissue
Mathematics and Statistics, Georgia State University
(May 1, 2014 10:20 AM - 11:15 AM)
The study of traveling waves of activity in neural tissue can provide deep insights into the functions of the brain during sensory processing or during abnormal states such as epilepsy, migraines or hallucinations. Computational models of these systems usually describe the tissue as a vast interconnected network of excitatory neurons comprised of large number of units with similar properties, for example integrate and fire neurons. It is also widely assumed that while the strength of the connections between neurons changes as a function of distance that separates them, this interaction does not depend on other local parameters. These assumptions allow for formulation of a set of integro-differential equations describing the propagation of the traveling wave fronts in a one-dimensional integrate-and-fire network of synaptically coupled neurons, allowing for investigation of the network dynamics during wave initiation and during the transition toward constant-speed propagation. We further explore how the presence of periodic inhomogeneities affects the propagation dynamics, aiming to derive more precise estimates for the conditions when propagation failure occurs.