| Beside the direct coupling between neurons via the chemical and electrical synapses, there are another communication pathways in the brain tissue, that deserve more attention from the modeling viewpoint. According to the conventional approach to model neural ensembles the extracellular environment has fixed ionic concentrations. However, in many cases the extracellular concentration of potassium ions can not be regarded as constant. That represents specific chemical pathway for neurons to interact and can influence strongly the behavior of a single neuron as well as large ensembles. We address this problem by studying simplified excitable units given by a extended FitzHugh-Nagumo dynamics. For a a single excitable unit embedded in the extracellular matter that leads to a number of noise-induced effects, like self-modulation of firing rate in an individual neuron. In the spatially extended situation various patterns appear ranging from spirals and traveling waves to oscillons and inverted structures depending on the parameters of the medium. Another important issue is related to neural-glial interactions. The confinement of the role of glial cells to only the metabolic support and uptake of K+ ions and neurotransmitters no longer agrees with data on glia participation in synaptic transmission, long-term potentiation, synaptic plasticity and the development of neuronal pathologies. As a result a new concept of "tripartite synapse" has arisen. It includes pre- and postsynaptic neurons and the astrocytic network covering a synapse. Under intensive synaptic activity the elevation of calcium waves in astrocyte can be significant enough to propagate long distances in the brain and to activate postsynaptic neurons at other synaptic terminals. We develop a functional model of a neuron-astrocyte network that can reproduce typical local and global dynamical patterns observed in biological experiments. The spatial structure of the model mimics the geometry of astrocytic networks in 2D approximation. Despite being qualitative and simplified, our model nevertheless reproduces the most typical glial responses and patterns of signal transmission. We believe that the proposed models can be useful in the investigation of nonlinear and biological mechanisms underlying the formation of dynamical and noise-induced patterns in brain tissue. |
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