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A finite volume method solution for the bidomain equations and their application to modelling cardiac ischaemia

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  • Peter R. Johnston

Abstract

This paper presents an implementation of the finite volume method with the aim of studying subendocardial ischaemia during the ST segment. In this implementation, based on hexahedral finite volumes, each quadrilateral sub-face is split into two triangles to improve the accuracy of the numerical integration in complex geometries and when fibre rotation is included. The numerical method is validated against previously published solutions obtained from slab and cylindrical models of the left ventricle with subendocardial ischaemia and no fibre rotation. Epicardial potential distributions are then obtained for a half-ellipsoid model of the left ventricle. In this case it is shown that for isotropic cardiac tissue the degree of subendocardial ischaemia does not affect the epicardial potential distribution, which is consistent with previous findings from analytical studies in simpler geometries. The paper also considers the behaviour of various preconditioners for solving numerically the resulting system of algebraic equations resulting from the implementation of the finite volume method. It is observed that each geometry considered has its own optimal preconditioner.

Suggested Citation

  • Peter R. Johnston, 2010. "A finite volume method solution for the bidomain equations and their application to modelling cardiac ischaemia," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 13(2), pages 157-170.
    • Handle: RePEc:taf:gcmbxx:v:13:y:2010:i:2:p:157-170
    DOI: 10.1080/10255840903067072
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    Cited by:

    1. Daniel E. Hurtado & Ellen Kuhl, 2014. "Computational modelling of electrocardiograms: repolarisation and T-wave polarity in the human heart," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 17(9), pages 986-996, July.
    2. Michael Chen & Jonathan Wong & Ellen Kuhl & Laurent Giovangrandi & Gregory Kovacs, 2013. "Characterisation of electrophysiological conduction in cardiomyocyte co-cultures using co-occurrence analysis," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 16(2), pages 185-197.
    3. Josef P. Barnes & Peter R. Johnston, 2017. "The effect of boundary conditions on epicardial potential distributions," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 20(10), pages 1031-1037, July.

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