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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 Journal Article
  Year 2019 Publication Discrete And Continous Dynamical Systems Series B Abbreviated Journal Discrete And Continous Dynamical Systems Series B  
  Volume to appear Issue Pages  
  Keywords  
  Abstract Abstract. We derive a one-dimensional cable model for the electrical poten- tial 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 alternat- ing 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 informa- tion about the geometry of the myelin sheath in the original three-dimensional model.  
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  ISSN 1531-3492 ISBN Medium  
  Area Expedition Conference  
  Notes Approved no  
  Call Number UAI @ eduardo.moreno @ Serial 1043  
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