Vol. 4, No. 1, 2009

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A numerical method for cellular electrophysiology based on the electrodiffusion equations with internal boundary conditions at membranes

Yoichiro Mori and Charles S. Peskin

Vol. 4 (2009), No. 1, 85–134
Abstract

We present a numerical method for solving the system of equations of a model of cellular electrical activity that takes into account both geometrical effects and ionic concentration dynamics. A challenge in constructing a numerical scheme for this model is that its equations are stiff: There is a time scale associated with “diffusion” of the membrane potential that is much faster than the time scale associated with the physical diffusion of ions. We use an implicit discretization in time and a finite volume discretization in space. We present convergence studies of the numerical method for cylindrical and two-dimensional geometries for several cases of physiological interest.

Keywords
three-dimensional cellular electrophysiology, electrodiffusion, ephaptic transmission, finite volume method
Mathematical Subject Classification 2000
Primary: 65M12, 92C30, 92C50
Milestones
Received: 20 June 2007
Revised: 22 June 2009
Accepted: 24 June 2009
Published: 2 October 2009
Authors
Yoichiro Mori
School of Mathematics
University of Minnesota
206 Church St. SE
Minneapolis, MN 55455-0487
United States
http://www.math.umn.edu/~ymori
Charles S. Peskin
Courant Institute of Mathematical Sciences
New York University
251 Mercer St.
New York, NY 10012-1110
United States