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Author (up) Jerez-Hanckes, C.; Pettersson, I.; Rybalko, V. pdf  doi
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  Title Derivation Of Cable Equation By Multiscale Analysis For A Model Of Myelinated Axons Type
  Year 2020 Publication Discrete And Continuous Dynamical Systems-Series B Abbreviated Journal Discrete Contin. Dyn. Syst.-Ser. B  
  Volume 25 Issue 3 Pages 815-839  
  Keywords Hodgkin-Huxley model; nonlinear cable equation; cellular electrophysiology; multiscale modeling; homogenization  
  Abstract 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 epsilon, a small positive parameter. Assuming a nonzero conductivity of the myelin sheath, we find a critical scaling with respect to epsilon 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.  
  Address [Jerez-Hanckes, Carlos] Univ Adolfo Ibanez, Fac Engn & Sci, Diagonal Torres 2700, Santiago, Chile, Email: carlos.jerez@uai.cl;  
  Corporate Author Thesis  
  Publisher Amer Inst Mathematical Sciences-Aims Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1531-3492 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000501609800001 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1069  
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