PMID: 21405718Mar 17, 2011

Pulsating fronts in periodically modulated neural field models

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Stephen Coombes, Carlo R Laing

Abstract

We consider a coarse-grained neural field model for synaptic activity in spatially extended cortical tissue that possesses an underlying periodicity in its microstructure. The model is written as an integrodifferential equation with periodic modulation of a translationally invariant spatial kernel. This modulation can have a strong effect on wave propagation through the tissue, including the creation of pulsating fronts with widely varying speeds and wave-propagation failure. Here we develop a new analysis for the study of such phenomena, using two complementary techniques. The first uses linearized information from the leading edge of a traveling periodic wave to obtain wave speed estimates for pulsating fronts, and the second develops an interface description for waves in the full nonlinear model. For weak modulation and a Heaviside firing rate function the interface dynamics can be analyzed exactly and gives predictions that are in excellent agreement with direct numerical simulations. Importantly, the interface dynamics description improves on the standard homogenization calculation, which is restricted to modulation that is both fast and weak.

Citations

May 17, 2012·Journal of Mathematical Biology·Paul C Bressloff
Dec 9, 2010·Biological cybernetics·Thomas M WasylenkoIoannis G Kevrekidis
Nov 23, 2011·Biological cybernetics·Julie Goulet, G Bard Ermentrout
Jan 9, 2013·Biological cybernetics·Mauricio Cerda, Bernard Girau
Jun 5, 2012·Journal of Mathematical Neuroscience·Paul C Bressloff
Mar 5, 2016·Journal of Mathematical Neuroscience·Rüdiger ThulCarlo R Laing
Jan 20, 2018·Physical Review. E·Zachary P Kilpatrick, Daniel B Poll
Apr 3, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Zachary P Kilpatrick, Bard Ermentrout
Jan 13, 2016·Journal of Computational Neuroscience·Daniel B PollZachary P Kilpatrick
Mar 17, 2018·Journal of Computational Neuroscience·Nikhil KrishnanZachary P Kilpatrick
May 17, 2017·Physical Review. E·D AvitabileE Knobloch
Apr 3, 2020·Chaos·Helmut Schmidt, Daniele Avitabile

Related Concepts

Brain
Periodicity
Cerebral Cortex
Spatial Distribution
Modulated
Description
Structure
Simulation
Analysis
Synaptic Junction Pathway

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