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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Seizures
Sigmoid Colon
Human Activities
Theoretical Models
Neurons

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
Meijer, Hil Gaétan Ellart ; Eissa, Tahra L. ; Kiewiet, Bert ; Neuman, Jeremy F. ; Schevon, Catherine A. ; Emerson, Ronald G. ; Goodman, Robert R. ; McKhann Jr., Guy M. ; Marcuccilli, Charles J. ; Tryba, Andrew K. ; Cowan, Jack D. ; van Gils, Stephanus A. ; van Drongelen, Wim. / Modeling Focal Epileptic Activity in the Wilson-Cowan Model with Depolarization Block. In: Journal of mathematical neuroscience. 2015 ; Vol. 5, No. 1. pp. 7.
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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.",
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Meijer, HGE, Eissa, TL, Kiewiet, B, Neuman, JF, Schevon, CA, Emerson, RG, Goodman, RR, McKhann Jr., GM, Marcuccilli, CJ, Tryba, AK, Cowan, JD, van Gils, SA & van Drongelen, W 2015, 'Modeling Focal Epileptic Activity in the Wilson-Cowan Model with Depolarization Block' Journal of mathematical neuroscience, vol. 5, no. 1, pp. 7. https://doi.org/10.1186/s13408-015-0019-4

Modeling Focal Epileptic Activity in the Wilson-Cowan Model with Depolarization Block. / Meijer, Hil Gaétan Ellart; Eissa, Tahra L.; Kiewiet, Bert; Neuman, Jeremy F.; Schevon, Catherine A.; Emerson, Ronald G.; Goodman, Robert R.; McKhann Jr., Guy M.; Marcuccilli, Charles J.; Tryba, Andrew K.; Cowan, Jack D.; van Gils, Stephanus A.; van Drongelen, Wim.

In: Journal of mathematical neuroscience, Vol. 5, No. 1, 27.03.2015, p. 7.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Modeling Focal Epileptic Activity in the Wilson-Cowan Model with Depolarization Block

AU - Meijer, Hil Gaétan Ellart

AU - Eissa, Tahra L.

AU - Kiewiet, Bert

AU - Neuman, Jeremy F.

AU - Schevon, Catherine A.

AU - Emerson, Ronald G.

AU - Goodman, Robert R.

AU - McKhann Jr., Guy M.

AU - Marcuccilli, Charles J.

AU - Tryba, Andrew K.

AU - Cowan, Jack D.

AU - van Gils, Stephanus A.

AU - van Drongelen, Wim

N1 - eemcs-eprint-25880

PY - 2015/3/27

Y1 - 2015/3/27

N2 - 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.

AB - 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.

KW - EWI-25880

KW - IR-95515

KW - Bifurcation analysis

KW - METIS-312529

KW - Focal epilepsy

KW - Depolarization block

KW - Activation function

U2 - 10.1186/s13408-015-0019-4

DO - 10.1186/s13408-015-0019-4

M3 - Article

VL - 5

SP - 7

JO - Journal of mathematical neuroscience

JF - Journal of mathematical neuroscience

SN - 2190-8567

IS - 1

ER -