Traveling fronts in a generalized neural field model that couples to the extracellular space

Extracellular ion concentrations directly influence neuronal excitability, synaptic transmission, and the generation of electrical signals. Capturing the ionic dynamics is essential for modeling both healthy and pathophysiological brain function. Here we explore how variations in ion concentration in the extracellular space affect the generation and propagation of traveling fronts of activity in cortical tissue. To this end, we develop a neural field model in which neuronal excitability is modulated by the local extracellular ionic concentration. Using an interface dynamics approach, we derive an analytic expression for the speed of propagating activity fronts. We demonstrate that increasing the ionic diffusion coefficient leads to a reduction in front speed. In addition, analysis of stationary bump solutions reveals that increases in the diffusion rate reduces the size of a region of high activity required to initiate a propagating front.