Modeling electrocortical activity through improved local approximations of integral neural field equations

Coombes, Stephen and Venkov, Nikola and Shiau, LieJune and Bojak, Ingo and Liley, David and Laing, Carlo (2007) Modeling electrocortical activity through improved local approximations of integral neural field equations. Physical Review E, 76 . 051901-051908. (Submitted)

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Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular we are able to treat "patchy'" connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a "lattice-directed" traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

Article published and (c) American Physical Society 2007

Item Type: Article
Additional Information: Open Access Journal version at:
Uncontrolled Keywords: neural fields, brain wave equations, patchy connections
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Coombes, Prof Stephen
Date Deposited: 03 Oct 2007
Last Modified: 23 Jun 2011 07:07

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