Nonlinear Multidomain Model for Nerve Bundles with Random Structure
Artikel i vetenskaplig tidskrift, 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
Författare
Irina Pettersson
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Göteborgs universitet
Antonina Rybalko
Kharkiv National University of Radio Electronics
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Volodymyr Rybalko
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori
Institute for Low Temperature Physics and Engineering
SIAM Journal on Mathematical Analysis
0036-1410 (ISSN) 10957154 (eISSN)
Vol. 57 4 3981-4015Levande cellers matematik
Stiftelsen för Strategisk forskning (SSF) (UKR22-0004), 2022-04-08 -- 2024-10-08.
EINervio - Modeling of ephaptic coupling of myelinated neurons
STINT (CS2018-7908), 2020-06-01 -- 2022-06-30.
Ämneskategorier (SSIF 2025)
Sannolikhetsteori och statistik
Matematisk analys
DOI
10.1137/24M1688291