title: Modeling focal epileptic activity in the Wilson-cowan model with depolarization block.
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.
  
  
  BACKGROUND
  The online version of this article (doi:10.1186/s13408-015-0019-4) contains supplementary material 1.
authors: Department of Applied Mathematics, MIRA Institute for Biomedical Engineering and Technical Medicine, University of Twente, Postbus 217, Enschede, 7500AE The Netherlands.
authors: Hil G E
authors: HG
authors: Meijer
authors: Department of Pediatrics, University of Chicago, KCBD 900 East 57th Street, Chicago, IL 60637 USA.
authors: Tahra L
authors: TL
authors: Eissa
authors: Department of Applied Mathematics, MIRA Institute for Biomedical Engineering and Technical Medicine, University of Twente, Postbus 217, Enschede, 7500AE The Netherlands.
authors: Bert
authors: B
authors: Kiewiet
authors: Department of Physics, University of Chicago, 5720 South Ellis Avenue, Chicago, IL 60637 USA.
authors: Jeremy F
authors: JF
authors: Neuman
authors: Department of Neurology, Columbia University, 710 West 168th Street, New York, NY 10032 USA.
authors: Catherine A
authors: CA
authors: Schevon
authors: Department of Neurology, Columbia University, 710 West 168th Street, New York, NY 10032 USA ; Department of Neurological Surgery, Columbia University, 710 West 168th Street, New York, NY 10032 USA.
authors: Ronald G
authors: RG
authors: Emerson
authors: Department of Neurological Surgery, Columbia University, 710 West 168th Street, New York, NY 10032 USA.
authors: Robert R
authors: RR
authors: Goodman
authors: Department of Neurological Surgery, Columbia University, 710 West 168th Street, New York, NY 10032 USA.
authors: Guy M
authors: GM
authors: McKhann
authors: Department of Pediatrics, University of Chicago, KCBD 900 East 57th Street, Chicago, IL 60637 USA.
authors: Charles J
authors: CJ
authors: Marcuccilli
authors: Department of Pediatrics, University of Chicago, KCBD 900 East 57th Street, Chicago, IL 60637 USA.
authors: Andrew K
authors: AK
authors: Tryba
authors: Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, IL 60637 USA.
authors: Jack D
authors: JD
authors: Cowan
authors: Department of Applied Mathematics, MIRA Institute for Biomedical Engineering and Technical Medicine, University of Twente, Postbus 217, Enschede, 7500AE The Netherlands.
authors: Stephan A
authors: SA
authors: van Gils
authors: Department of Pediatrics, University of Chicago, KCBD 900 East 57th Street, Chicago, IL 60637 USA.
authors: Wim
authors: W
authors: van Drongelen
keywords: Activation function; Bifurcation analysis; Depolarization block; Focal epilepsy