Multiscale analysis of myelinated axons

Carlos Jerez-Hanckes, Isabel A. Martínez, Irina Pettersson, Volodymyr Rybalko

Resultado de la investigación: Capítulo del libro/informe/acta de congresoCapítulorevisión exhaustiva

1 Cita (Scopus)

Resumen

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.

Idioma originalInglés
Título de la publicación alojadaSEMA SIMAI Springer Series
EditorialSpringer Science and Business Media Deutschland GmbH
Páginas17-35
Número de páginas19
DOI
EstadoPublicada - 2021
Publicado de forma externa

Serie de la publicación

NombreSEMA SIMAI Springer Series
Volumen10
ISSN (versión impresa)2199-3041
ISSN (versión digital)2199-305X

Huella

Profundice en los temas de investigación de 'Multiscale analysis of myelinated axons'. En conjunto forman una huella única.

Citar esto