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Mathematical modeling of electrophysiological activity in epilepsy
Mathematical modeling of electrophysiological activity in epilepsy is a computational method for simulating the key mechanism in the development of epileptic seizures, namely the transition from normal electrophysiological activity in the brain to abnormal hypersynchronization. A similar type of hypersynchronization occurs in delta waves during normal sleep. It is possible to estimate the rate of spread and migration of such regions of hypersynchronous neuronal activity in experimental and clinical settings using electroencephalography or electrocorticography for tracking electrophysiological activity of the brain.
== Modeling ==
Excessive, large-scale hypersynchronous neuronal activity in the brain is a hallmark of epilepsy.〔R. Fisher, W. van Emde Boas, W. Blume, C. Elger, P. Genton, P. Lee and J. Engel (2005). "Epileptic seizures and epilepsy: definitions proposed by the International League Against Epilepsy (ILAE) and the International Bureau for Epilepsy (IBE)". ''Epilepsia'' 46 (4): 470–2. doi:10.1111/j.0013-9580.2005.66104.x. PMID 15816939.〕 However, the analysis of large-scale electrophysiological activity during epileptic seizures is challenging, because simultaneous tracking of electrical activity in large numbers of neurons is technically difficult.〔Epilepsy as a Dynamic Disease, edited by J. Milton and P. Jung, Biological and Medical Physics series Springer, Berlin, 2003.〕 Moreover, electroencephalography (EEG), which is primarily used for monitoring electrophysiological activity of the brain during epileptic seizures, represents global (space-averaged) dynamical behavior of large neuronal populations. This global behavior involves millions of electrically connected, synchronized neuronal cells, and cannot be simply inferred from single-cell behavior.〔(Stefanescu RA, Shivakeshavan RG, Talathiemail SS. Computational models of epilepsy. Seizure: European Journal of Epilepsy, 2012; 21 (10):748-759. )〕 A number of models have been developed for studying electrophysiological activity in epilepsy, including those based on Hodgkin–Huxley-type equations, describing changes in the flow of ionic currents across the membrane of a single cell or small groups of cells.〔 The single-cell and small-group models are useful for studying ionic channels in the cell membrane, as well as other cellular, molecular and biochemical processes.〔 However, when the single-cell approach is applied to model behavior of the entire brain, both theoretical analysis and numerical simulations become difficult due to large numbers of interacting variables. Furthermore, it is difficult to validate such models' predictions based on EEG data, which represent global (space-averaged) dynamical behavior of neuronal populations.
To study the brain's behavior at the system level, Wilson and Cowan introduced a large-scale (coarse-grained mean field) approach, referred to as Wilson–Cowan model,〔(H.R. Wilson and J.D. Cowan. Excitatory and inhibitory interactions in localized populations of model neurons. ) Biophys. J., 12:1–24, 1972. PMID 4332108〕 which can be used for analyzing EEG patterns during epileptic seizures, as described below.
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