Derivation of cable equation by multiscale analysis for a model of myelinated axons

Abstract

The paper concerns the multiscale modeling of a myelinated axon. Taking into account the microstructure with alternating myelinated parts and nodes Ranvier, we derive a nonlinear cable equation describing the potential propagation along the axon. We assume that the myelin is not a perfect insulator, and assign a low (asymptotically vanishing) conductivity in the myelin. Compared with the case when myelin is assumed to have zero conductivity, an additional potential arises in the limit equation. The coefficient in front of the effective potential contains information about the geometry of the myelinated parts.