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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

Experimental data supporting the use of a Gaussian population response function during human seizure activity. A: Recording setup depicting the multi-electrode array situated in between the standard electrocorticography electrodes numbered 22, 23, 30, and 31. B: Example recordings of the low-frequency component of the local field potential (2–50 Hz, L-LFP, upper trace), the rectified signal filtered for spikes (300–3000 Hz, middle trace), and the integrated version thereof, using a leaky integrator with a 50 ms time constant (bottom trace) generating a firing rate index (FRI) for the multi-unit spike activity. The relationship between L-LFP and FRI is plotted in panel C; the error bars indicate SEM values
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Fig1: Experimental data supporting the use of a Gaussian population response function during human seizure activity. A: Recording setup depicting the multi-electrode array situated in between the standard electrocorticography electrodes numbered 22, 23, 30, and 31. B: Example recordings of the low-frequency component of the local field potential (2–50 Hz, L-LFP, upper trace), the rectified signal filtered for spikes (300–3000 Hz, middle trace), and the integrated version thereof, using a leaky integrator with a 50 ms time constant (bottom trace) generating a firing rate index (FRI) for the multi-unit spike activity. The relationship between L-LFP and FRI is plotted in panel C; the error bars indicate SEM values

Mentions: A technique, recently approved for use in humans, allows application of micro-electrode recordings, during seizure activity [6]. Study participants consisted of adults with pharmaco-resistant focal epilepsy who underwent chronic invasive EEG studies to help identify the epileptogenic zone for subsequent removal. A 96, 4 mm × 4 mm, micro-electrode array (also known as Utah array) was implanted along with subdural electrodes with the goal of recording from seizure onset sites; see Fig. 1A. The study was approved by the Institutional Review Board of the Columbia University Medical Center, and informed consent was obtained from each patient prior to implantation. Signals from the micro-electrode array were acquired continuously at 30 kHz per channel (0.3 Hz–7.5 kHz bandpass, 16-bit precision, range ±8 mV). The reference was either subdural or epidural, chosen dynamically based on recording quality. See also [6] for details of study enrollment, surgical procedures and signal recording. Fig. 1


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)

Experimental data supporting the use of a Gaussian population response function during human seizure activity. A: Recording setup depicting the multi-electrode array situated in between the standard electrocorticography electrodes numbered 22, 23, 30, and 31. B: Example recordings of the low-frequency component of the local field potential (2–50 Hz, L-LFP, upper trace), the rectified signal filtered for spikes (300–3000 Hz, middle trace), and the integrated version thereof, using a leaky integrator with a 50 ms time constant (bottom trace) generating a firing rate index (FRI) for the multi-unit spike activity. The relationship between L-LFP and FRI is plotted in panel C; the error bars indicate SEM values
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4385301&req=5

Fig1: Experimental data supporting the use of a Gaussian population response function during human seizure activity. A: Recording setup depicting the multi-electrode array situated in between the standard electrocorticography electrodes numbered 22, 23, 30, and 31. B: Example recordings of the low-frequency component of the local field potential (2–50 Hz, L-LFP, upper trace), the rectified signal filtered for spikes (300–3000 Hz, middle trace), and the integrated version thereof, using a leaky integrator with a 50 ms time constant (bottom trace) generating a firing rate index (FRI) for the multi-unit spike activity. The relationship between L-LFP and FRI is plotted in panel C; the error bars indicate SEM values
Mentions: A technique, recently approved for use in humans, allows application of micro-electrode recordings, during seizure activity [6]. Study participants consisted of adults with pharmaco-resistant focal epilepsy who underwent chronic invasive EEG studies to help identify the epileptogenic zone for subsequent removal. A 96, 4 mm × 4 mm, micro-electrode array (also known as Utah array) was implanted along with subdural electrodes with the goal of recording from seizure onset sites; see Fig. 1A. The study was approved by the Institutional Review Board of the Columbia University Medical Center, and informed consent was obtained from each patient prior to implantation. Signals from the micro-electrode array were acquired continuously at 30 kHz per channel (0.3 Hz–7.5 kHz bandpass, 16-bit precision, range ±8 mV). The reference was either subdural or epidural, chosen dynamically based on recording quality. See also [6] for details of study enrollment, surgical procedures and signal recording. Fig. 1

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