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A numerical method
for cellular electrophysiology based on the electrodiffusion
equations with internal boundary conditions at membranes
Yoichiro Mori and Charles S. Peskin |
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Vol. 4 (2009), No. 1, 85–134
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Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 65M12, 92C30, 92C50
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Milestones
Received: 20 June 2007
Revised: 22 June 2009
Accepted: 24 June 2009
Published: 2 October 2009
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Authors |
| Yoichiro Mori | |
| School of Mathematics University of Minnesota 206 Church St. SE Minneapolis, MN 55455-0487 United States |
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| 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 |
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