primary generalized epilepsy neural modeling nonlinear dyanamics bifurcation time series analysis
The aim of this paper is to explain critical features of the human primary generalized
epilepsies by investigating the dynamical bifurcations of a nonlinear model of the
brain’s mean field dynamics. The model treats the cortex as a medium for the
propagation of waves of electrical activity, incorporating key physiological processes
such as propagation delays, membrane physiology and corticothalamic feedback.
Previous analyses have demonstrated its descriptive validity in a wide range of
healthy states and yielded specific predictions with regards to seizure phenomena. We
show that mapping the structure of the nonlinear bifurcation set predicts a number of
crucial dynamic processes, including the onset of periodic and chaotic dynamics as
well as multistability. Quantitative study of electrophysiological data supports the
validity of these predictions and reveals processes unique to the global bifurcation set.
Specifically, we argue that the core electrophysiological and cognitive differences
between tonic-clonic and absence seizures are predicted by the global bifurcation
diagram of the model’s dynamics. The present study is the first to present a unifying
explanation of these generalized seizures using the bifurcation analysis of a dynamical
model of the brain.