Reduced model and simulation of myelinated axon using eigenfunction expansion and singular perturbation

In a myelinated axon, there exist many nodes of Ranvier where myelin sheaths are absent and action potentials are actively regenerated. Hence, a myelinated axon is a nonuniform cable where myelinated parts and unmyelinated nodes of Ranvier are described by different cable equations. For the modelling of a myelinated axon, the compartment model based on finite volume or finite difference discretization was dominantly used. In this paper, we propose a hybrid approach where an eigenfunction expansion combined with singular perturbation is employed for myelinated parts, and demonstrate that the proposed scheme can achieve an order of magnitude accuracy improvement for low order models. Moreover, it is also shown that the proposed scheme converges faster to attain a given accuracy. Hence, for simulation of myelinated axons, the proposed scheme can be an attractive alternative to the compartment model, that leads to a low order model with much higher accuracy or that converges faster for a given accuracy.