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Simulation of Electrophysiological Waves withan Unstructured Finite Element Method

Published online by Cambridge University Press:  15 November 2003

Yves Bourgault ,
Marc Ethier  and
Victor G. LeBlanc
Yves Bourgault
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, On, K1N 6N5 Canada. ybourg@mathstat.uottawa.ca.
Marc Ethier
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, On, K1N 6N5 Canada. ybourg@mathstat.uottawa.ca.
Victor G. LeBlanc
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, On, K1N 6N5 Canada. ybourg@mathstat.uottawa.ca.
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Abstract

Bidomain models are commonly used for studying and simulating electrophysiological waves in the cardiac tissue. Most of the time, the associated PDEs are solved using explicit finite difference methods on structured grids. We propose an implicit finite element method using unstructured grids for an anisotropic bidomain model. The impact and numerical requirements of unstructured grid methods is investigated using a test case with re-entrant waves.

Keywords

Anisotropic bidomain modelspiral wavesFEM.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 4: Special issue on Biological and Biomedical Applications , July 2003 , pp. 649 - 661
Copyright
© EDP Sciences, SMAI, 2003

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References

Barkley, D., Euclidean symmetry and the dynamics of spiral waves. Phys. Rev. Lett. 72 (1994) 165-167. CrossRef
P. Brown and Y. Saad, Hybrid Krylov methods for nonlinear systems of equations. Technical Report UCRL-97645, Lawrence Livermore National Laboratory (November 1987).
Golubitsky, M., LeBlanc, V.G. and Melbourne, I., Meandering of the spiral tip: An alternative approach. J. Nonlinear Sci. 7 (1997) 557-586. CrossRef
Gomatam, J. and Amdjadi, F., Reaction-diffusion equations on a sphere: Mendering of spiral waves. Phys. Rev. E 56 (1997) 3913-3919. CrossRef
Harrild, D.M. and Henriquez, C.S., A finite volume model of cardiac propagation. Ann. Biomed. Eng. 25 (1997) 315-334. CrossRef
Keener, J.P. and Bogar, K., A numerical method for the solution of the bidomain equations in cardiac tissue. Chaos 8 (1998) 234-241. CrossRef
J.P. Keener and A.V. Panfilov, The effect of geometry and fibre orientation on propagation and extracellular potentials in myocardium, in Computational Biology of the Heart, A.V. Panfilov and A.V. Holden Eds., John Wiley & Sons (1997) 235-258.
J. Keener and J. Sneyd, Mathematical Physiology, Springer-Verlag (1998).
LeBlanc, V.G., Rotational symmetry-breaking for spiral waves. Nonlinearity 15 (2002) 1179-1203. CrossRef
V.G. LeBlanc and B.J. Roth, Meandering of spiral waves in anisotropic tissue. Dynam. Contin. Discrete Impuls. Systems B 10 (2003) 29-41.
Murillo, M. and Cai, X.C., Parallel Newton-Krylov-Schwarz method for solving the anisotropic bidomain equations from the excitation of the heart model. Lecture Notes in Comput. Sci. 2329 (2002) 533-542. CrossRef
Otani, N.F., Computer modeling in cardiac electrophysiology. J. Comput. Phys. 161 (2000) 21-34. CrossRef
A.V. Panfilov and A.V. Holden, editors, Computational Biology of the Heart. John Wiley & Sons (1997).
J. Rogers, M. Courtemanche and A. McCulloch, Finite element methods for modelling impulse propagation in the heart, in Computational Biology of the Heart, A.V. Panfilov and A.V. Holden Eds., John Wiley & Sons (1997) 217-233.
Roth, B.J., Approximate analytical solutions to the bidomain equations with unequal anisotropy ratio. Phys. Rev. E 55 (1997) 1819-1826. CrossRef
Roth, B.J., Mendering of spiral waves in anisotropic cardiac tissue. Phys. D 150 (2001) 127-136. CrossRef
Zykov, V.S. and Müller, S.C., Spiral waves on circular and spherical domains of excitable medium. Phys. D 97 (1996) 322-332. CrossRef