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Multiscale Analysis of Myelinated Axons
Universidad Adolfo Ibáñez, Santiago, Chile.
Pontificia Universidad Católica de Chile, Santiago, Chile.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
Institute for Low Temperature Physics and Engineering, Kharkiv, Ukraine.
2021 (English)In: SEMA SIMAI Springer Series, Springer , 2021, p. 17-35Chapter in book (Refereed)
Abstract [en]

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

Place, publisher, year, edition, pages
Springer , 2021. p. 17-35
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Other Natural Sciences
Identifiers
URN: urn:nbn:se:hig:diva-39972DOI: 10.1007/978-3-030-62030-1_2Scopus ID: 2-s2.0-85100969030OAI: oai:DiVA.org:hig-39972DiVA, id: diva2:1698087
Available from: 2022-09-22 Created: 2022-09-22 Last updated: 2022-09-22Bibliographically approved

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Pettersson, Irina

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