A mathematical model of ephaptic interactions in neuronal fiber pathways: Could there be more than transmission along the tracts?

While numerous studies of ephaptic interactions have focused on either axons of peripheral nerves or on cortical structures, no attention has been given to the possibility of ephaptic interactions in white matter tracts. Inspired by the highly organized, tightly packed geometry of axons in fiber pathways, we aim to investigate the potential effects of ephaptic interactions along these structures that are resilient to experimental probing. We use axonal cable theory to derive a minimal model of a sheet of N ephaptically coupled axons. Numerical solutions of the proposed model are explored as ephaptic coupling is varied. We demonstrate that ephaptic interactions can lead to local phase locking between adjacent traveling impulses and that, as coupling is increased, traveling impulses trigger new impulses along adjacent axons, resulting in finite size traveling fronts. For strong enough coupling, impulses propagate laterally and backwards, resulting in complex spatiotemporal patterns. While common large-scale brain network models often model fiber pathways as simple relays of signals between different brain regions, our work calls for a closer reexamination of the validity of such a view. The results suggest that in the presence of significant ephaptic interactions, the brain fiber tracts can act as a dynamic active medium.