Noise-sustained patterns in a model of volume-coupled neural tissue

Computational neuroscience operates on models based on several important paradigms. Among them is the assumption that coupling in neural ensembles is provided by chemical or electrical synapses. This assumption works well under normal conditions. However, there is a growing body of data that show the importance of other communication pathways caused by bi-directional transport of substances between the cells and the intercellular space. This type of interaction is called "volume transmission" and has not been rarely addressed in the model studies. The volume transmission pathway naturally appears in multidimensional quantitative models of cellular processes, but is not sufficiently represented at the level of lumped and computationally effective neural models. In this paper, we propose a simple model that allows one to study the features of volume transmission coupling at various spatial scales and taking into account various inhomogeneities. This model is obtained by the extension of the well-known FitzHugh-Nagumo system by the addition of the nonlinear terms and equations to describe, at a qualitative level, the release of potassium into the intercellular space, its diffusion, and the reverse effect on the neurons. The study of model dynamics in various spatial configurations has revealed a number of characteristic spatio-temporal types of behavior that include self-organizing bursting and phase-locked firing patterns, different scenarios of excitation spreading, noise-sustained target patterns, and long-living slow moving wave segments.