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Derivation of cable equation by multiscale analysis for a model of myelinated axons
Universidad Adolfo Ibáñez Diagonal Las Torres, Peñalolén, Santiago, 2700, Chile.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
B. Verkin Institute for Low Temperature Physics and Engineering of NASU, 47 Nauky Ave., Kharkiv, 61103, Ukraine.
2020 (English)In: Discrete and continuous dynamical systems. Series B, ISSN 1531-3492, E-ISSN 1553-524X, Vol. 25, no 3, p. 815-839Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
American Institute of Mathematical Sciences , 2020. Vol. 25, no 3, p. 815-839
Keywords [en]
Cellular electrophysiology, Hodgkin-Huxley model, Homogenization, Multiscale modeling, Nonlinear cable equation
National Category
Neurosciences
Identifiers
URN: urn:nbn:se:hig:diva-31374DOI: 10.3934/dcdsb.2019191ISI: 000501609800001Scopus ID: 2-s2.0-85076437746OAI: oai:DiVA.org:hig-31374DiVA, id: diva2:1382912
Note

Funding:

Swedish Foundation for International Cooperation in Research and Higher Education STINT (IB 2017-7370)

Chile Fondecyt Regular (1171491)

Available from: 2020-01-07 Created: 2020-01-07 Last updated: 2020-01-07Bibliographically approved

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Pettersson, Irina

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