Nonlinear Multidomain Model for Nerve Bundles with Random Structure
Journal article, 2025
We present a derivation of a multidomain model for the electric potential in bundles of randomly distributed axons with different radii. The FitzHugh-Nagumo dynamics is assumed on the axons' membrane, and the conductivity depends nonlinearly on the electric field. Under ergodicity conditions, we study the asymptotic behavior of the potential in the bundle when the number of axons in the bundle is sufficiently large and derive a macroscopic multidomain model describing the electrical activity of the bundle. Due to the randomness of geometry, the effective intracellular potential is not deterministic but is shown to be a stationary function with realizations that are constant on the axons' cross sections. The technique combines stochastic two-scale convergence and the method of monotone operators.
signals propagation in nerves
bidomain model
nonlinear conductivity
random media
stochastic homogenization
Author
Irina Pettersson
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
University of Gothenburg
Antonina Rybalko
Kharkiv National University of Radio Electronics
University of Gothenburg
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Volodymyr Rybalko
University of Gothenburg
Chalmers, Mathematical Sciences, Analysis and Probability Theory
Institute for Low Temperature Physics and Engineering
SIAM Journal on Mathematical Analysis
0036-1410 (ISSN) 10957154 (eISSN)
Vol. 57 4 3981-4015Levande cellers matematik
Swedish Foundation for Strategic Research (SSF) (UKR22-0004), 2022-04-08 -- 2024-10-08.
EINervio - Modeling of ephaptic coupling of myelinated neurons
The Swedish Foundation for International Cooperation in Research and Higher Education (STINT) (CS2018-7908), 2020-06-01 -- 2022-06-30.
Subject Categories (SSIF 2025)
Probability Theory and Statistics
Mathematical Analysis
DOI
10.1137/24M1688291