Simulation of Electrophysiological Waves with an Unstructured Finite Element Method

Yves Bourgault; Marc Ethier; Victor G. LeBlanc

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 4, page 649-661
  • ISSN: 0764-583X

Abstract

top
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.

How to cite

top

Bourgault, Yves, Ethier, Marc, and LeBlanc, Victor G.. "Simulation of Electrophysiological Waves with an Unstructured Finite Element Method." ESAIM: Mathematical Modelling and Numerical Analysis 37.4 (2010): 649-661. <http://eudml.org/doc/194183>.

@article{Bourgault2010,
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. },
author = {Bourgault, Yves, Ethier, Marc, LeBlanc, Victor G.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Anisotropic bidomain model; spiral waves; FEM.; FEM},
language = {eng},
month = {3},
number = {4},
pages = {649-661},
publisher = {EDP Sciences},
title = {Simulation of Electrophysiological Waves with an Unstructured Finite Element Method},
url = {http://eudml.org/doc/194183},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Bourgault, Yves
AU - Ethier, Marc
AU - LeBlanc, Victor G.
TI - Simulation of Electrophysiological Waves with an Unstructured Finite Element Method
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 4
SP - 649
EP - 661
AB - 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.
LA - eng
KW - Anisotropic bidomain model; spiral waves; FEM.; FEM
UR - http://eudml.org/doc/194183
ER -

References

top
  1. D. Barkley, Euclidean symmetry and the dynamics of spiral waves. Phys. Rev. Lett.72 (1994) 165-167.  
  2. P. Brown and Y. Saad, Hybrid Krylov methods for nonlinear systems of equations. Technical Report UCRL-97645, Lawrence Livermore National Laboratory (November 1987).  
  3. M. Golubitsky, V.G. LeBlanc and I. Melbourne, Meandering of the spiral tip: An alternative approach. J. Nonlinear Sci.7 (1997) 557-586.  
  4. J. Gomatam and F. Amdjadi, Reaction-diffusion equations on a sphere: Mendering of spiral waves. Phys. Rev. E56 (1997) 3913-3919.  
  5. D.M. Harrild and C.S. Henriquez, A finite volume model of cardiac propagation. Ann. Biomed. Eng.25 (1997) 315-334.  
  6. J.P. Keener and K. Bogar, A numerical method for the solution of the bidomain equations in cardiac tissue. Chaos8 (1998) 234-241.  
  7. 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.  
  8. J. Keener and J. Sneyd, Mathematical Physiology, Springer-Verlag (1998).  
  9. V.G. LeBlanc, Rotational symmetry-breaking for spiral waves. Nonlinearity15 (2002) 1179-1203.  
  10. V.G. LeBlanc and B.J. Roth, Meandering of spiral waves in anisotropic tissue. Dynam. Contin. Discrete Impuls. SystemsB10 (2003) 29-41.  
  11. M. Murillo and X.C. Cai, 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.  
  12. N.F. Otani, Computer modeling in cardiac electrophysiology. J. Comput. Phys.161 (2000) 21-34.  
  13. A.V. Panfilov and A.V. Holden, editors, Computational Biology of the Heart. John Wiley & Sons (1997).  
  14. 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.  
  15. B.J. Roth, Approximate analytical solutions to the bidomain equations with unequal anisotropy ratio. Phys. Rev. E55 (1997) 1819-1826.  
  16. B.J. Roth, Mendering of spiral waves in anisotropic cardiac tissue. Phys. D150 (2001) 127-136.  
  17. V.S. Zykov and S.C. Müller, Spiral waves on circular and spherical domains of excitable medium. Phys. D97 (1996) 322-332.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.