Cerebral Cortex Advance Access originally published online on November 9, 2005
Cerebral Cortex 2006 16(9):1296-1313; doi:10.1093/cercor/bhj072
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A Unifying Explanation of Primary Generalized Seizures Through Nonlinear Brain Modeling and Bifurcation Analysis
1 School of Physics, University of Sydney, NSW 2006, Australia, 2 Brain Dynamics Centre, Westmead Hospital and University of Sydney, Westmead, NSW 2145, Australia, 3 School of Psychiatry, University of New South Wales, Randwick, NSW 2031, Australia, 4 Department of Mathematical Sciences, Loughborough University, Loughborough, LE 113TU UK, 5 Department of Neurology, Westmead Hospital, Westmead, NSW 2145, Australia, and 6 The Black Dog Institute, Hospital Road, Randwick, NSW 2031, Australia
Address correspondence to email: mbreak{at}unsw.edu.au.
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. Hence, we argue that the core electrophysiological and cognitive differences between tonic–clonic and absence seizures are predicted and interrelated 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.
Key Words: bifurcation • neural modeling • nonlinear dynamics • primary generalized epilepsy • time series analysis
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