An explanation of the distribution of inter-seizure intervals

TL;DR

This paper explains the power-law distribution of inter-seizure intervals using a branching process model approximated by a random walk, supported by numerical simulations.

Contribution

It provides a theoretical explanation for the observed power-law distribution of seizure intervals based on a branching process model.

Findings

Distribution follows a power law with exponent 1.5

Model accurately reproduces empirical distribution

Numerical simulations confirm theoretical predictions

Abstract

Recently Osorio et al (Eur. J. Neurosci., 30 (2009) 1554) reported that probability distribution of intervals between successive epileptic seizures follows a power law with exponent 1.5. We theoretically explain this finding by modeling epileptic activity as a branching process, which we in turn approximate by a random walk. We confirm the theoretical conclusion by numerical simulation.