title: Transitions to spike-wave oscillations and epileptic dynamics in a human cortico-thalamic mean-field model.
abstract: In this paper we present a detailed theoretical analysis of the onset of spike-wave activity in a model of human electroencephalogram (EEG) activity, relating this to clinical recordings from patients with absence seizures. We present a complete explanation of the transition from inter-ictal activity to spike and wave using a combination of bifurcation theory, numerical continuation and techniques for detecting the occurrence of inflection points in systems of delay differential equations (DDEs). We demonstrate that the initial transition to oscillatory behaviour occurs as a result of a Hopf bifurcation, whereas the addition of spikes arises as a result of an inflection point of the vector field. Strikingly these findings are consistent with EEG data recorded from patients with absence seizures and we present a discussion of the clinical significance of these results, suggesting potential new techniques for detection and anticipation of seizures.
authors.affiliation: Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1TR, UK.
authors.forename: Serafim
authors.initials: S
authors.lastname: Rodrigues
authors.forename: David
authors.initials: D
authors.lastname: Barton
authors.forename: Robert
authors.initials: R
authors.lastname: Szalai
authors.forename: Oscar
authors.initials: O
authors.lastname: Benjamin
authors.forename: Mark P
authors.initials: MP
authors.lastname: Richardson
authors.forename: John R
authors.initials: JR
authors.lastname: Terry
mesh_terms: D001683:Biological Clocks / Q000502:physiology*; D002540:Cerebral Cortex / Q000503:physiopathology*; D003198:Computer Simulation; D004569:Electroencephalography; D004832:Epilepsy, Absence / Q000473:pathology* / Q000503:physiopathology; D006801:Humans; D008954:Models, Biological; D016571:Neural Networks, Computer; D009434:Neural Pathways / Q000503:physiopathology; D017711:Nonlinear Dynamics; D011237:Predictive Value of Tests; D013788:Thalamus / Q000503:physiopathology*