Patterns in Potassium-driven Neuronal Media

According to the conventional approach neural ensembles
are modeled with fixed ionic concentrations in the extracellular
environment. However, recent studies on the patho-physiology of tissue
from epileptic human patients revealed aberrations in potassium
regulation. These findings can be interpreted as neuronal interaction
via specific chemical pathways, that influence strongly the behavior of
single neurons and large ensembles. Released chemical agents, which
diffuse in the extracellular medium is able to lower thresholds of
individual excitable units.
We address this problem by studying a modified stochastic
FitzHugh-Nagumo dynamics. In our model the neurons interact only
chemically via the released and diffusing potassium in the surrounding
non-active medium. The dynamics of a single neuron as well as neurons
embedded in a heterogeneous medium is investigated.
We find coexistent excitable and oscillatory states for the local neuron
and patterns ranging from spirals and traveling waves to oscillons and
wandering spots in the spatially extended situation. Also a poisoned
state appears in which a high level potassium concentration leads to
a frozen depolarized state corresponding to cell death.