Epileptic Seizure Propagation Across Cortical Tissue: Simple Model Based on Potassium Diffusion
Mechanisms of epileptic discharge generation and spread are not well known. Interictal and ictal discharges (IIDs and IDs) are determined by neuronal interactions and ionic dynamics. In order to reproduce the discharges in a simplest way, we have recently proposed a minimal mathematical model that is alternative to the known model Epileptor. Our model is of similar complexity, but in contrast to the Epileptor formulated in terms of abstract variables, it attributes physical meaning to the main variables. The model is expressed in ordinary differential equations for four principal variables, extracellular potassium and intracellular sodium concentrations, a mean membrane potential and a short-term depressing synaptic resource. Our model reproduces IIDs as bursts of spikes, and IDs as clusters of spike bursts. Potassium accumulation governs the transition to IDs. Here we generalize the model to the case of spatial propagation. Diffusion of the extracellular potassium concentration is assumed to govern the spatial spread of spiking activity across cortical tissue. Simulations are consistent with experimental registrations of waves in pro-epileptic conditions, propagating at a speed of about 0.5 mm/s.
KeywordsEpilepsy Biophysical model Potassium diffusion
This work was supported by the Russian Science Foundation (project 16-15-10201).
- 10.Chizhov, A.V., Zefirov, A.V., Amakhin, D.V., Smirnova, EYu., Zaitsev, A.V.: Minimal model of interictal and ictal discharges “Epileptor-2”. PLoS CB 14(5), e1006186 (2018)Google Scholar