Neural bidomain model for multidimensional ephaptic coupling of neural spike propagation along myelinated fiber bundles with the nodes of Ranvier
A novel mathematical model is proposed to investigate the effects of ephaptic coupling between general neural fiber bundles in a multidimensional space with anisotropic neural fiber bundles. Ephaptic coupling corresponds to the spatiotemporal interaction between propagating fiber bundles through the extracellular space. Adapted from a well-known model in cardiac electrophysiology, the bidomain model comprises of the nonoverlapping intracellular and extracellular space except the common nodes of Ranvier. The proposed two-variable model, a neural bidomain model, is derived from the classic Frankenhaeuser-Huxley model for neural spike propagation along the general neural fiber bundles. The governing equation is mathematically and computationally validated against existing one-dimensional models of neural fiber bundle propagations with aligned nodes of Ranvier. A high-order continuous Galerkin scheme is employed for efficient two-dimensional computational simulation with moving frames, or orthonormal basis vectors, representing the intracellular and extracellular conductivity and nonoverlapping domains. The proposed model is simulated in various two-dimensional configurations of neural fiber bundles that are little known to the community, such as fiber bundles with misaligned nodes of Ranvier, opposite-traveling fiber bundles, and curved fiber bundles.