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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.
Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
B. Verkin Institute for Low Temperature Physics and Engineering of NASU, 47 Nauky Ave., Kharkiv, 61103, Ukraine.
2020 (Engelska)Ingår i: Discrete and continuous dynamical systems. Series B, ISSN 1531-3492, E-ISSN 1553-524X, Vol. 25, nr 3, s. 815-839Artikel i tidskrift (Refereegranskat) 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. 

Ort, förlag, år, upplaga, sidor
American Institute of Mathematical Sciences , 2020. Vol. 25, nr 3, s. 815-839
Nyckelord [en]
Cellular electrophysiology, Hodgkin-Huxley model, Homogenization, Multiscale modeling, Nonlinear cable equation
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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
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Funding:

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

Chile Fondecyt Regular (1171491)

Tillgänglig från: 2020-01-07 Skapad: 2020-01-07 Senast uppdaterad: 2021-03-03Bibliografiskt granskad

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Pettersson, Irina

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