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   \section*{Materials and methods}
 
-  The previous implementation of Epileptor-2 \cite{Chizhov2018} didn't consider any spatial propagation. It's primary focus was a biophysical interpretation of its governing variables during the pathological states of brain activity \cite{Bazhenov2004, Kager2000, Cressman2009}. For that the implementation included ionic dynamics in a rate-based model for recurrently connected excitatory and inhibitory neuronal populations. Ionic dynamics were comprised of extracellular potassium and intracellular sodium. The firing rate was assumed to be proportional to that of the excitatory population while the inhibitory population has been accounted for implicitly. The firing rate has been described as a rectified sigmoid function of a membrane potential. The membrane potential has been described by Kirchoff’s current conservation law, which was written for a one-compartment neuron. The expressions for the excitatory and inhibitory synaptic currents, the input-output-function, the rate-based equations for the ionic dynamics, etc., are justified in \cite{Chizhov2018}. The short-term synaptic depression is described according to the Tsodyks-Markram model. An adaptive quadratic integrate-and-fire model was used as a model for a representative neuron.
+  The previous implementation of Epileptor-2 \cite{Chizhov2018} was restricted to consideration of a spatially homogeneous ativity, thus not considering any spatial propagation. A primary focus of that model was a biophysical interpretation of its governing variables describing the pathological states of brain activity. For that purpose, the ionic dynamics described in earlier studies \cite{Bazhenov2004, Kager2000, Cressman2009} was implemented into a rate-based model for recurrently connected excitatory and inhibitory neuronal populations. Ionic dynamics were comprised of extracellular potassium and intracellular sodium. The firing rate was assumed to be proportional to that of the excitatory population while the inhibitory population has been accounted for implicitly. The firing rate has been described as a rectified sigmoid function of a membrane potential. The membrane potential has been described by Kirchoff’s current conservation law, which was written for a one-compartment neuron. The expressions for the excitatory and inhibitory synaptic currents, the input-output-function, the rate-based equations for the ionic dynamics, etc., are justified in \cite{Chizhov2018}. The short-term synaptic depression is described according to the Tsodyks-Markram model. An adaptive quadratic integrate-and-fire model was used as a model for a representative neuron.
 
   To take into account spatial propagation the model has been expanded with the diffusion of potassium and the spike propagation along neuronal axons. The diffusion term was included into potassium ion dynamics with the diffusion coefficient of the same value as in \cite{Bazhenov2004}. And for the spike propagation a separation of the general population firing rate on soma's and presynaptic's firing rates was considered. In that concern presynaptic's firing rate depends on soma's one and represents its value after axial propagation.