Modeling Focal Epileptic Activity in the Wilson-Cowan Model with Depolarization Block

Hil Gaétan Ellart Meijer, Tahra L. Eissa, Bert Kiewiet, Jeremy F. Neuman, Catherine A. Schevon, Ronald G. Emerson, Robert R. Goodman, Guy M. McKhann Jr., Charles J. Marcuccilli, Andrew K. Tryba, Jack D. Cowan, Stephanus A. van Gils, Wim van Drongelen

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    Abstract

    Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an activity driven depolarization block, i.e. they saturate. We examined the effect of such a saturation in the Wilson–Cowan formalism by adapting the nonlinear activation function; we substituted the commonly applied sigmoid for a Gaussian function. We discuss experimental recordings during a seizure that support this substitution. Next we perform a bifurcation analysis on the Wilson–Cowan model with a Gaussian activation function. The main effect is an additional stable equilibrium with high excitatory and low inhibitory activity. Analysis of coupled local networks then shows that such high activity can stay localized or spread. Specifically, in a spatial continuum we show a wavefront with inhibition leading followed by excitatory activity. We relate our model simulations to observations of spreading activity during seizures.
    Original languageEnglish
    Pages (from-to)7
    Number of pages17
    JournalJournal of mathematical neuroscience
    Volume5
    Issue number1
    DOIs
    Publication statusPublished - 27 Mar 2015

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    Keywords

    • EWI-25880
    • IR-95515
    • Bifurcation analysis
    • METIS-312529
    • Focal epilepsy
    • Depolarization block
    • Activation function

    Cite this

    Meijer, H. G. E., Eissa, T. L., Kiewiet, B., Neuman, J. F., Schevon, C. A., Emerson, R. G., ... van Drongelen, W. (2015). Modeling Focal Epileptic Activity in the Wilson-Cowan Model with Depolarization Block. Journal of mathematical neuroscience, 5(1), 7. https://doi.org/10.1186/s13408-015-0019-4