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Anton Chizhov edited untitled.tex
almost 8 years ago
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\end{equation}
where $\Bigl[ {d[K^+]_e \over dt} \Bigr]_{Glia}$ is the potassium concentration change due to glia; $k_G$ is a coefficient.
External potassium was modeled in \cite{Krishnan_2011}. Glial uptake was modeled in \cite{Kager_2006}. To simplify the consideration, we proposed the following phenomenological model. Potassium currents through neuronal membranes are most pronounced during the spiking activity. That is why, approximately these currents are just proportional to the firing rate of principal neurons, $\nu(t)$. $[K^+]_e$ is then buffered by glial cells. Concequently, the equation for the
rate of potassium concentration change due to glia should look like the refractory equation, as well as the associated extracellular potential $\varphi_G$:
\begin{equation} \label{e3}
\tau {\varphi_G(t) \over dt } = - \varphi_G(t) + c ~\nu(t),