Multiscale analysis of myelinated axons

Carlos Jerez-Hanckes, Isabel A. Martínez, Irina Pettersson, Volodymyr Rybalko

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations


We consider a three-dimensional model for a myelinated neuron, which includes Hodgkin–Huxley ordinary differential equations to represent membrane dynamics at Ranvier nodes (unmyelinated areas). Assuming a periodic microstructure with alternating myelinated and unmyelinated parts, we use homogenization methods to derive a one-dimensional nonlinear cable equation describing the potential propagation along the neuron. Since the resistivity of intracellular and extracellular domains is much smaller than the myelin resistivity, we assume this last one to be a perfect insulator and impose homogeneous Neumann boundary conditions on the myelin boundary. In contrast to the case when the conductivity of the myelin is nonzero, no additional terms appear in the one-dimensional limit equation, and the model geometry affects the limit solution implicitly through an auxiliary cell problem used to compute the effective coefficient. We present numerical examples revealing the forecasted dependence of the effective coefficient on the size of the Ranvier node.

Original languageEnglish
Title of host publicationSEMA SIMAI Springer Series
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages19
StatePublished - 2021
Externally publishedYes

Publication series

NameSEMA SIMAI Springer Series
ISSN (Print)2199-3041
ISSN (Electronic)2199-305X


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