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A predictive method allowing the use of a single ionic model innumerical cardiac electrophysiology

Published online by Cambridge University Press:  07 June 2013

M. Rioux  and
Y. Bourgault
M. Rioux
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Canada. ybourg@uottawa.ca
Y. Bourgault
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Canada. ybourg@uottawa.ca
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Abstract

One of the current debate about simulating the electrical activity in the heart is thefollowing: Using a realistic anatomical setting, i.e. realisticgeometries, fibres orientations, etc., is it enough to use a simplified 2-variablephenomenological model to reproduce the main characteristics of the cardiac actionpotential propagation, and in what sense is it sufficient? Using a combination ofdimensional and asymptotic analysis, together with the well-known Mitchell − Schaeffermodel, it is shown that it is possible to accurately control (at least locally) thesolution while spatial propagation is involved. In particular, we reduce the set ofparameters by writing the bidomain model in a new nondimensional form. The parameters ofthe bidomain model with Mitchell − Schaeffer ion kinetics are then set and shown to be inone-to-one relation with the main characteristics of the four phases of a propagatedaction potential. Explicit relations are derived using a combination of asymptotic methodsand ansatz. These relations are tested against numerical results. We illustrate how theserelations can be used to recover the time/space scales and speed of the action potentialin various regions of the heart.

Keywords

Asymptotic analysiscardiac electrophysiologyMitchell−Schaeffer model
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 4: Direct and inverse modeling of the cardiovascular and respiratory systems , July 2013 , pp. 987 - 1016
Copyright
© EDP Sciences, SMAI, 2013

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