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Modeling focal epileptic activity in the Wilson-cowan model with depolarization block.

Meijer HG, Eissa TL, Kiewiet B, Neuman JF, Schevon CA, Emerson RG, Goodman RR, McKhann GM, Marcuccilli CJ, Tryba AK, Cowan JD, van Gils SA, van Drongelen W - J Math Neurosci (2015)

Bottom Line: 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.The main effect is an additional stable equilibrium with high excitatory and low inhibitory activity.The online version of this article (doi:10.1186/s13408-015-0019-4) contains supplementary material 1.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, MIRA Institute for Biomedical Engineering and Technical Medicine, University of Twente, Postbus 217, Enschede, 7500AE The Netherlands.

ABSTRACT

Unlabelled: 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.

Electronic supplementary material: The online version of this article (doi:10.1186/s13408-015-0019-4) contains supplementary material 1.

No MeSH data available.


Related in: MedlinePlus

Propagation. Top row: Excitatory (blue) and inhibitory (red) activity with sigmoidal population activation function. Activity is extinguished by 100 ms. No propagation is present. Middle row: Population activities with Gaussian firing rate function. Here, a traveling wave pulse forms and begins to propagate. Bottom row: same as middle but at later times. The traveling wave continues to propagate until it dies at the boundary. The wavespeed is approximately 1 mm/s. Parameters are the same in each plot
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Fig11: Propagation. Top row: Excitatory (blue) and inhibitory (red) activity with sigmoidal population activation function. Activity is extinguished by 100 ms. No propagation is present. Middle row: Population activities with Gaussian firing rate function. Here, a traveling wave pulse forms and begins to propagate. Bottom row: same as middle but at later times. The traveling wave continues to propagate until it dies at the boundary. The wavespeed is approximately 1 mm/s. Parameters are the same in each plot

Mentions: Finally, we simulate the spatially continuous model; see Fig. 11. On the top row, a sigmoid firing rate function produces transient behavior but no traveling pulse. The middle and bottom rows show a propagating wave associated with the introduction of a Gaussian activation function. Here, we can clearly see a wave originating in the middle and propagating to the edges. The excitatory activity provides sufficient input to the inhibitory neurons to drive them into depolarization block and the inhibitory activity is not strong enough to keep the activity localized. Thus, we may conclude that our formalism provides a mechanism for dynamic disinhibition arising from depolarization block which the sigmoid firing rate function has not been able to reproduce. One more thing to notice is that, while the input is only to the excitatory neurons, the excitatory pulse of excitation lags behind inhibition, a finding consistent with detailed recordings of epileptiform activity [8]. In [6] the speed of the wave was estimated around 0.8 mm/s. We varied the strength of the excitatory coupling to match the wave speed in the model with this experimental value. Fig. 11


Modeling focal epileptic activity in the Wilson-cowan model with depolarization block.

Meijer HG, Eissa TL, Kiewiet B, Neuman JF, Schevon CA, Emerson RG, Goodman RR, McKhann GM, Marcuccilli CJ, Tryba AK, Cowan JD, van Gils SA, van Drongelen W - J Math Neurosci (2015)

Propagation. Top row: Excitatory (blue) and inhibitory (red) activity with sigmoidal population activation function. Activity is extinguished by 100 ms. No propagation is present. Middle row: Population activities with Gaussian firing rate function. Here, a traveling wave pulse forms and begins to propagate. Bottom row: same as middle but at later times. The traveling wave continues to propagate until it dies at the boundary. The wavespeed is approximately 1 mm/s. Parameters are the same in each plot
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4385301&req=5

Fig11: Propagation. Top row: Excitatory (blue) and inhibitory (red) activity with sigmoidal population activation function. Activity is extinguished by 100 ms. No propagation is present. Middle row: Population activities with Gaussian firing rate function. Here, a traveling wave pulse forms and begins to propagate. Bottom row: same as middle but at later times. The traveling wave continues to propagate until it dies at the boundary. The wavespeed is approximately 1 mm/s. Parameters are the same in each plot
Mentions: Finally, we simulate the spatially continuous model; see Fig. 11. On the top row, a sigmoid firing rate function produces transient behavior but no traveling pulse. The middle and bottom rows show a propagating wave associated with the introduction of a Gaussian activation function. Here, we can clearly see a wave originating in the middle and propagating to the edges. The excitatory activity provides sufficient input to the inhibitory neurons to drive them into depolarization block and the inhibitory activity is not strong enough to keep the activity localized. Thus, we may conclude that our formalism provides a mechanism for dynamic disinhibition arising from depolarization block which the sigmoid firing rate function has not been able to reproduce. One more thing to notice is that, while the input is only to the excitatory neurons, the excitatory pulse of excitation lags behind inhibition, a finding consistent with detailed recordings of epileptiform activity [8]. In [6] the speed of the wave was estimated around 0.8 mm/s. We varied the strength of the excitatory coupling to match the wave speed in the model with this experimental value. Fig. 11

Bottom Line: 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.The main effect is an additional stable equilibrium with high excitatory and low inhibitory activity.The online version of this article (doi:10.1186/s13408-015-0019-4) contains supplementary material 1.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, MIRA Institute for Biomedical Engineering and Technical Medicine, University of Twente, Postbus 217, Enschede, 7500AE The Netherlands.

ABSTRACT

Unlabelled: 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.

Electronic supplementary material: The online version of this article (doi:10.1186/s13408-015-0019-4) contains supplementary material 1.

No MeSH data available.


Related in: MedlinePlus