  Mathematical models for excitable cells are commonly based on cable theory,
which considers a homogenized domain and spatially constant ionic
concentrations. Although such models provide valuable insight, the effect of
altered ion concentrations or detailed cell morphology on the electrical
potentials cannot be captured. In this paper, we discuss an alternative
approach to detailed modelling of electrodiffusion in neural tissue. The
mathematical model describes the distribution and evolution of ion
concentrations in a geometrically-explicit representation of the intra- and
extracellular domains. As a combination of the electroneutral
Kirchhoff-Nernst-Planck (KNP) model and the
Extracellular-Membrane-Intracellular (EMI) framework, we refer to this model as
the KNP-EMI model. Here, we introduce and numerically evaluate a new, finite
element-based numerical scheme for the KNP-EMI model, capable of efficiently
and flexibly handling geometries of arbitrary dimension and arbitrary
polynomial degree. Moreover, we compare the electrical potentials predicted by
the KNP-EMI and EMI models. Finally, we study ephaptic coupling induced in an
unmyelinated axon bundle and demonstrate how the KNP-EMI framework can give new
insights in this setting.
