Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-18T16:16:49.887Z Has data issue: false hasContentIssue false

Simulation of Electrophysiological Waveswithan Unstructured Finite Element Method

Published online by Cambridge University Press:  15 November 2003

Yves Bourgault
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, On, K1N 6N5 Canada. [email protected].
Marc Ethier
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, On, K1N 6N5 Canada. [email protected].
Victor G. LeBlanc
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, On, K1N 6N5 Canada. [email protected].
Get access

Abstract

Bidomain models are commonly used for studying and simulatingelectrophysiological waves in the cardiac tissue. Most of thetime, the associated PDEs are solved using explicit finitedifference methods on structured grids. We propose an implicitfinite element method using unstructured grids for an anisotropicbidomain model. The impact and numerical requirements ofunstructured grid methods is investigated using a test casewith re-entrant waves.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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