Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart

  • Authors:

  • Aslak Tveito;Ola Skavhaug;Glenn T. Lines;Robert Artebrant

  • Affiliations:

  • Simula Research Laboratory, Center for Biomedical Computing, P.O. Box 134, Lysaker 1325, Norway and Department of Informatics, University of Oslo, P.O. Box 1072, 0316 Oslo, Norway;Simula Research Laboratory, Center for Biomedical Computing, P.O. Box 134, Lysaker 1325, Norway and Department of Informatics, University of Oslo, P.O. Box 1072, 0316 Oslo, Norway;Simula Research Laboratory, Center for Biomedical Computing, P.O. Box 134, Lysaker 1325, Norway and Department of Informatics, University of Oslo, P.O. Box 1072, 0316 Oslo, Norway;Simula Research Laboratory, Center for Biomedical Computing, P.O. Box 134, Lysaker 1325, Norway

  • Venue:
  • Computers in Biology and Medicine
  • Year:
  • 2011

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Abstract

Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model.