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.
@article{M2AN_2003__37_4_649_0,
author = {Bourgault, Yves and Ethier, Marc and LeBlanc, Victor G.},
title = {Simulation of electrophysiological waves with an unstructured finite element method},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {37},
year = {2003},
pages = {649-661},
doi = {10.1051/m2an:2003051},
mrnumber = {2018435},
zbl = {1065.92004},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2003__37_4_649_0}
}
Bourgault, Yves; Ethier, Marc; LeBlanc, Victor G. Simulation of electrophysiological waves with an unstructured finite element method. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 37 (2003) pp. 649-661. doi : 10.1051/m2an:2003051. http://gdmltest.u-ga.fr/item/M2AN_2003__37_4_649_0/
[1] , Euclidean symmetry and the dynamics of spiral waves. Phys. Rev. Lett. 72 (1994) 165-167.
[2] and, Hybrid Krylov methods for nonlinear systems of equations. Technical Report UCRL-97645, Lawrence Livermore National Laboratory (November 1987). | Zbl 0708.65049
[3] , and, Meandering of the spiral tip: An alternative approach. J. Nonlinear Sci. 7 (1997) 557-586. | Zbl 0902.58025
[4] and, Reaction-diffusion equations on a sphere: Mendering of spiral waves. Phys. Rev. E 56 (1997) 3913-3919.
[5] and, A finite volume model of cardiac propagation. Ann. Biomed. Eng. 25 (1997) 315-334.
[6] and, A numerical method for the solution of the bidomain equations in cardiac tissue. Chaos 8 (1998) 234-241. | Zbl 1069.92507
[7] and, 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. | Zbl 0953.92009
[8] and, Mathematical Physiology, Springer-Verlag (1998). | MR 1673204 | Zbl 0913.92009
[9] , Rotational symmetry-breaking for spiral waves. Nonlinearity 15 (2002) 1179-1203. | Zbl 1017.34036
[10] and, Meandering of spiral waves in anisotropic tissue. Dynam. Contin. Discrete Impuls. Systems B 10 (2003) 29-41. | Zbl 1021.92006
[11] and, 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. | Zbl 1048.92011
[12] , Computer modeling in cardiac electrophysiology. J. Comput. Phys. 161 (2000) 21-34. | Zbl 0943.92014
[13] and, editors, Computational Biology of the Heart. John Wiley & Sons (1997). | Zbl 0867.92011
[14] , and, 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. | Zbl 0879.92007
[15] , Approximate analytical solutions to the bidomain equations with unequal anisotropy ratio. Phys. Rev. E 55 (1997) 1819-1826.
[16] , Mendering of spiral waves in anisotropic cardiac tissue. Phys. D 150 (2001) 127-136. | Zbl 0974.92005
[17] and, Spiral waves on circular and spherical domains of excitable medium. Phys. D 97 (1996) 322-332.