Inferring the Type of Phase Transitions Undergone in Epileptic Seizures Using Random Graph Hidden Markov Models for Percolation in Noisy Dynamic Networks

TL;DR

This paper introduces a novel statistical framework using random graph hidden Markov models to analyze phase transitions in noisy, dynamic brain networks during epileptic seizures, aiding in understanding seizure mechanisms and informing treatment.

Contribution

It develops a new class of RG-HMMs for modeling percolation in noisy, evolving networks and provides a hypothesis testing framework for inferring percolation regimes in epilepsy.

Findings

Different percolation types can occur in human seizures.

The method can distinguish between percolation regimes.

Inferred percolation types may inform treatment strategies.

Abstract

In clinical neuroscience, epileptic seizures have been associated with the sudden emergence of coupled activity across the brain. The resulting functional networks - in which edges indicate strong enough coupling between brain regions - are consistent with the notion of percolation, which is a phenomenon in complex networks corresponding to the sudden emergence of a giant connected component. Traditionally, work has concentrated on noise-free percolation with a monotonic process of network growth, but real-world networks are more complex. We develop a class of random graph hidden Markov models (RG-HMMs) for characterizing percolation regimes in noisy, dynamically evolving networks in the presence of edge birth and edge death, as well as noise. This class is used to understand the type of phase transitions undergone in a seizure, and in particular, distinguishing between different percolation regimes in epileptic seizures. We develop a hypothesis testing framework for inferring putative percolation mechanisms. As a necessary precursor, we present an EM algorithm for estimating parameters from a sequence of noisy networks only observed at a longitudinal subsampling of time points. Our results suggest that different types of percolation can occur in human seizures. The type inferred may suggest tailored treatment strategies and provide new insights into the fundamental science of epilepsy.