Derivation Of Cable Equation By Multiscale Analysis For A Model Of Myelinated Axons
Jerez-Hanckes
C
author
Pettersson
I
author
Rybalko
V
author
2020
English
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 epsilon, a small positive parameter. Assuming a nonzero conductivity of the myelin sheath, we find a critical scaling with respect to epsilon 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.
Hodgkin-Huxley model
nonlinear cable equation
cellular electrophysiology
multiscale modeling
homogenization
WOS:000501609800001
exported from refbase (show.php?record=1069), last updated on Fri, 03 Jan 2020 13:17:26 -0300
text
files/1069_Jerez-Hanckes_etal2020.pdf
10.3934/dcdsb.2019191
Jerez-Hanckes_etal2020
Discrete And Continuous Dynamical Systems-Series B
Discrete Contin. Dyn. Syst.-Ser. B
2020
Amer Inst Mathematical Sciences-Aims
continuing
periodical
academic journal
25
3
815
839
1531-3492