In this letter we describe how an ordinary differential equation (ODE) model of cortico-thalamic interactions may be obtained from a more general system of delay differential equations (DDEs). 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. We demonstrate similarities between model transitions and clinical data and argue that statistics obtained from and parameter estimation of this new model may be a potential means of classifying and predicting the onset and offset of seizure activity.
|Publication status||Published - 30 Oct 2008|
Bibliographical noteSponsorship: EPSRC Grant EP/D068436/01
- bifurcation theory
- dynamical systems
- mean-field model