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

Carlos Jerez-Hanckes, Irina Pettersson, Volodymyr Rybalko

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We derive a one-dimensional cable model for the electric potential propagation along an axon. Since the typical thickness of an axon is much smaller than its length, and the myelin sheath is distributed periodically along the neuron, we simplify the problem geometry to a thin cylinder with alternating myelinated and unmyelinated parts. Both the microstructure period and the cylinder thickness are assumed to be of order ε, a small positive parameter. Assuming a nonzero conductivity of the myelin sheath, we find a critical scaling with respect to ε which leads to the appearance of an additional potential in the homogenized nonlinear cable equation. This potential contains information about the geometry of the myelin sheath in the original three-dimensional model.

Original languageEnglish
Pages (from-to)815-839
Number of pages25
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number3
StatePublished - 2020
Externally publishedYes


  • Cellular electrophysiology
  • Hodgkin-Huxley model
  • Homogenization
  • Multiscale modeling
  • Nonlinear cable equation


Dive into the research topics of 'Derivation of cable equation by multiscale analysis for a model of myelinated axons'. Together they form a unique fingerprint.

Cite this