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Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells.

Authors
Type
Published Article
Journal
Mathematical Biosciences
0025-5564
Publisher
Elsevier
Publication Date
Volume
172
Issue
2
Pages
55–72
Identifiers
PMID: 11520499
Source
Medline

Abstract

The contraction of the heart is preceded and caused by a cellular electro-chemical reaction, causing an electrical field to be generated. Performing realistic computer simulations of this process involves solving a set of partial differential equations, as well as a large number of ordinary differential equations (ODEs) characterizing the reactive behavior of the cardiac tissue. Experiments have shown that the solution of the ODEs contribute significantly to the total work of a simulation, and there is thus a strong need to utilize efficient solution methods for this part of the problem. This paper presents how an efficient implicit Runge-Kutta method may be adapted to solve a complicated cardiac cell model consisting of 31 ODEs, and how this solver may be coupled to a set of PDE solvers to provide complete simulations of the electrical activity.

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