Frontiers in Mathematical Biology

Mathematical models of abnormal network dynamics in the epileptic brain

Catherine Stamoulis

Harvard Medical School/ Children's Hospital Boston

Dynamic interactions between neuronal ensembles at multiple spatio-temporal scales constitute a fundamental mechanism of normal brain function. In response to external stimuli and/or cognitive demands, neuronal networks are differentially modulated and coordinated in order for information to be transmitted between brain regions. The neurodynamic mechanisms underlying resting and functional network interactions are not fully understood. It is thought that one such mechanism may involve propagating waves with distinct characteristic frequencies that facilitate local and long-range network interactions. Furthermore, in neurological disorders that are associated with abnormal coordination of neuronal networks, e.g., epilepsy and several neuropsychiatric disorders, wave propagation may also constitute a fundamental mechanism of neural synchronization. In the absence of invasive measurements, travelling waves are difficult to measure in non-invasive recordings from healthy humans. In contrast, they may be easier to measure and correlate with (abnormal) neuronal coordination in patients with epilepsy, both from non-invasive (scalp) and invasive (intracranial) recordings. In this talk I will present recent results on seizure dynamics from the analysis of scalp and intracranial recordings from pediatric epilepsy patients and will discuss data-inspired models of macroscale wave propagation in the epileptic brain. These models may provide novel insights not only into the neurodynamics of seizure evolution, but also into the mechanisms of functional network interactions in the healthy brain.