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Pulsating fronts in periodically modulated neural field models.

S Coombes¹, C R Laing

¹School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom. stephen.coombes@nottingham.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 17, 2011

Summary

We developed new analysis techniques for neural field models with periodic microstructures. These methods accurately predict wave propagation, including pulsating fronts and wave failure, in cortical tissue.

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Area of Science:

Computational neuroscience
Mathematical biology
Biophysics

Background:

Neural field models simulate synaptic activity in cortical tissue.
Periodicity in microstructure can significantly impact wave propagation dynamics.
Existing models may not fully capture complex wave behaviors like pulsating fronts.

Purpose of the Study:

To develop novel analytical techniques for coarse-grained neural field models.
To investigate the effects of periodic microstructural modulation on wave propagation.
To accurately predict phenomena such as pulsating fronts and wave-propagation failure.

Main Methods:

Utilized a coarse-grained neural field model described by an integrodifferential equation.
Employed two complementary analytical techniques: linearized wave edge analysis and nonlinear interface description.
Performed direct numerical simulations for validation.

Main Results:

Developed methods for estimating wave speeds of pulsating fronts.
Established an interface description for wave dynamics in the nonlinear model.
Achieved excellent agreement between analytical predictions and numerical simulations for weak modulation.

Conclusions:

The new analysis provides accurate predictions for wave propagation in periodically modulated neural fields.
The interface dynamics description offers improvements over standard homogenization techniques.
These findings enhance our understanding of wave phenomena in complex neural tissues.