Derivation and analysis of an ordinary differential equation mean-field model for studying clinically recorded epilepsy dynamics

Frank Marten, Serafim Rodrigues, Piotr Suffczynski, Mark P. Richardson, and John R. Terry
Phys. Rev. E 79, 021911 – Published 11 February 2009

Abstract

In this paper we describe how an ordinary differential equation model of corticothalamic interactions may be obtained from a more general system of delay differential equations. We demonstrate that transitions to epileptic dynamics via changes in system parameters are qualitatively the same as in the original model with delay, as well as demonstrating that the onset of epileptic activity may arise due to regions of bistability. Hence, the model presents in one unique framework, two competing theories for the genesis of epileptiform activity. Similarities between model transitions and clinical data are presented and we argue that statistics obtained from, and a parameter estimation of this model may be a potential means of classifying and predicting the onset and offset of seizure activity.

    • Received 30 October 2008

    DOI:https://doi.org/10.1103/PhysRevE.79.021911

    ©2009 American Physical Society

    Authors & Affiliations

    Frank Marten1, Serafim Rodrigues1, Piotr Suffczynski2, Mark P. Richardson3, and John R. Terry1,*

    • 1Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1TR, United Kingdom†
    • 2Department of Biomedical Physics, Warsaw University, Poland
    • 3Institute of Psychiatry, King’s College London, Camberwell, SE5 8AF, United Kingdom

    • *J.R.Terry@bristol.ac.uk
    • The study was approved by the local research ethics committee of King's College Hospital. This approval included the sharing of anonymized data with nonclinical collaborators.

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    Issue

    Vol. 79, Iss. 2 — February 2009

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