A Multidimensional Neural Bidomain Model with Ephaptic Coupling via Moving Frames

Abstract. A novel mathematical model is proposed to provide a comprehensive framework for simulating ephaptic coupling arising from spatiotemporal interactions between propagating neural fiber bundles through the extracellular space. The resulting multidimensional macroscopic model, applicable to arbitrarily shaped fiber bundles, is derived from the Frankenhaeuser–Huxley formulation of neural spike propagation and extends the classic bidomain framework by explicitly accounting for complex fiber bundle geometries, in which intracellular and extracellular domains are nonoverlapping except at the nodes of Ranvier. To enable accurate simulation of such fiber geometries, a high-order continuous Galerkin method is introduced, incorporating anisotropic conductivities and domain discontinuities through orthonormal basis vectors, known as moving frames. The model is validated via two-dimensional simulations of neural spike propagation along both straight and curved fiber bundles.