The neurodynamics of epilepsy: a homotopy analysis between current-based and conductance-based synapses in a neural field model of epilepsy

Andre Dh Peterson,Anthony N Burkitt,Hamish Meffin,Mark J Cook,Iven My Mareels,David B Grayden

doi:10.1186/1471-2202-16-s1-p23

Abstract

Unlike Hodgkin-Huxley type spiking models, the overwhelming majority of neural field models use current-based synapses [1]. Although there exist neural field models that employ conductance-based synapses, it is not clear what their exact effects on the dynamics are, particularly with respect to epileptic dynamics. Neural field models of epilepsy typically describe the transition to seizure-like activity as a bifurcation [2]. This research examines the effects of conductance-based synapses on the transition from normal to seizure-like activity in neural field models.

Highlights

Introduction/Background Unlike Hodgkin-Huxley type spiking models, the overwhelming majority of neural field models use currentbased synapses [1]
In this research we construct a neural field model with a homotopy parameter, such that when = 0, the model has current-based synapses, and when = 1, it has conductance-based synapses. This enables us to compare and explain the key differences in dynamics caused by the different synaptic mechanisms
* Correspondence: peterson@unimelb.edu.au 1NeuroEngineering Lab, Dept. of Electrical & Electronic Engineering, University of Melbourne, Melbourne, Australia Full list of author information is available at the end of the article

Summary

Introduction

Introduction/Background Unlike Hodgkin-Huxley type spiking models, the overwhelming majority of neural field models use currentbased synapses [1]. Which makes conductance-based synapses nonlinear, considerably affects the dynamics. This is especially so in comparison with their linear current-based counterpart.

Results

Conclusion