A Cell-Based Model for Ionic Electrodiffusion in Excitable Tissue

This chapter presents the KNP-EMI model describing ion concentrations and electrodiffusion in excitable tissue. The KNP-EMI model extends on the EMI model by removing the assumption that ion concentrations are constant in time and space, and may as such be more appropriate in connection with modelling e.g. spreading depression, stroke and epilepsy. The KNP-EMI model defines a system of time-dependent, nonlinear, mixed dimensional partial differential equations. We here detail the derivation of the system and present a numerical example illustrating how ion concentrations evolve during neuronal activity.