A time-dependent adaptive remeshing for electrical waves of the heart

IEEE Transactions on Biomedical Engineering

Volumn 55, Issue 2, 2008, Pages 443-452

  Belhamadia, Youssef ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Action potential; Anisotropic mesh adaptation; Bidomain model; Finite element method; Spiral waves

Indexed keywords

ANISOTROPY; COMPUTER SIMULATION; DEPOLARIZATION; FINITE ELEMENT METHOD; NUMERICAL METHODS; TISSUE;

ACTION POTENTIAL; ANISOTROPIC MESH ADAPTATION; BIDOMAIN MODEL; ELECTRICAL ACTIVITY; ELECTRICAL WAVES; SPIRAL WAVES; TIME-DEPENDENT REMESHING;

BIOMEDICAL ENGINEERING;

ACTION POTENTIAL; ANISOTROPY; ARTICLE; ELECTRIC ACTIVITY; FINITE ELEMENT ANALYSIS; HEART DEPOLARIZATION; HEART ELECTROPHYSIOLOGY; HEART FUNCTION; HEART MUSCLE; HEART REPOLARIZATION; MATHEMATICAL MODEL; SIMULATION; TIME;

ACTION POTENTIALS; ANIMALS; BODY SURFACE POTENTIAL MAPPING; COMPUTER SIMULATION; DIAGNOSIS, COMPUTER-ASSISTED; HEART CONDUCTION SYSTEM; HUMANS; MODELS, CARDIOVASCULAR; VENTRICULAR FIBRILLATION;

EID: 38349002708     PISSN: 00189294     EISSN: None     Source Type: Journal    
DOI: 10.1109/TBME.2007.905415     Document Type: Article

References (37)

1. R. R. Aliev and A. V. Panfilov, "A simple two-variable model of cardiac excitation," Chaos, Sol., Fract., vol. 7, no. 3, pp. 293-301, 1996.
2. S. Balay, K. Buschelman, V. Eijkhout, W. Gropp, D. Kaushik, M. Knepley, L. C. McInnes, B. Smith, and H. Zhang, PETSc Users Manual, Argonne National Laboratory, Argonne, IL, Tech. Rep. ANL-95/11-Revision 2.1.6, 2003 [Online]. Available: http://www.mcs.anl.gov/petsc
3. R. E. Bank, "A simple analysis of a posteriori error estimates," Appl. Numer. Math., vol. 26, pp. 153-164, 1998.
4. R. E. Bank and R. K. Smith, "A posteriori error estimates based on hierarchical bases," SIAM J. Numer. Anal., vol. 30, pp. 921-935, 1993.
5. Y. Belhamadia, A. Fortin, and É. Chamberland, "Anisotropic mesh adaptation for the solution of the stefan problem," J. Comput. Phys., vol. 194, no. 1, pp. 233-255, 2004.
6. V. N. Biktashev, A. V. Holden, S. F. Mironov, A. M. Pertsov, and A. V. Zaitsev, "Three dimensional aspects of re-entry in experimental and numerical models of ventricular fibrillation," Int. J. Bifur. Chaos, vol. 9, no. 4, pp. 694-704, 1999.
7. Y. Bourgault, M. Ethier, and V. G. LeBlanc, "Simulation of electrophysiological waves with an unstructured finite element method," Math. Model. Numer. Anal., vol. 37, no. 4, pp. 649-662, 2003.
8. E. M. Cherry, H. S. Greenside, and C. S. Henriquez, "Efficient simulation of three-dimensional anisotropic cardiac tissue using an adaptive mesh refinement method," Chaos: Interdisciplinary J. Nonlin. Sci., vol. 13, no. 3, pp. 853-865, 2003.
9. P. C. Franzone, P. Deufhard, B. Erdmann, J. Lang, and L. F. Pavarino, "Adaptivity in space and time for reaction-diffusion systems in electrocardiology," SIAM J. Sci. Comput., vol. 28, no. 3, pp. 942-962, 2006.
10. P. C. Franzone and L. F. Pavarino, "A parallel solver for reaction-diffusion systems in computational electrocardiology," Math. Models Meth. Appl. Sci., vol. 14, no. 6, pp. 883-911, 2004.
11. R. A. FitzHugh, "Impulses and physiological states in theoretical models of nerve membrane," Biophys. J., vol. 1, pp. 445-466, 1961.
12. A. Fortin and Y. Belhamadia, "Numerical prediction of freezing fronts in cryosurgery: Comparison with experimental results," Comput. Meth. Biomech. Biomed. Eng., vol. 8, no. 4, pp. 241-249, 2005.
13. P. J. Frey and P. L. George, Mesh Generation. Application to Finite Elements. Oxford, U.K.: Hermes, 2000.
14. P. L. George, H. Borouchaki, P. J. Frey, P. Laug, and E. Saltel, , E. Stein, R. de Borst, and T. J. R. Hughes, Eds., "Encyclopedia of computational mechanics," in Mesh Generation and Mesh Adaptivity: Theory and Techniques. New York: Wiley, 2004.
15. Y. Gong and D. J. Christini, "Functional reentrant waves propagate outwardly in cardiac tissue," Phys. Lett. A, vol. 331, pp. 209-216, 2004.
16. F. Hecht and B. Mohammadi, "Mesh adaptation by metric control for multi-scale phenomena and turbulence," AIAA, pp. 97-0859, 1997.
17. A. L. Hodgkin and A. F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve," J. Physiol., vol. 117, pp. 500-544, 1952.
18. J. Jalife, "Ventricular fibrillation: Mechanisms of initiation and maintenance," Ann. Rev. Physiol., vol. 60, pp. 25-50, 2000.
19. X. Jiang, R. H. Nochetto, and C. Verdi, "A P1-P1 finite element method for a phase relaxation model. Part ii : Adaptively refined meshes," SIAM J. Numer. Anal., vol. 36, no. 3, pp. 974-999, 1999.
20. M. G. Karpoukhin, B. Y. Kogan, and J. W. Karplus, "The application of a massively parallel computer to the simulation of electrical wave propagation phenomena in the heart muscle using simplified models," HICSS, vol. 5, pp. 112-122, 1995.
21. J. Keener and J. Sneyd, Mathematical Physiology. New York: Springer-Verlag, 1998.
22. J. P. Keener and K. Bogar, "A numerical method for the solution of the bidomain equations in cardiac tissue," Chaos: An Interdisciplinary J. Nonlin. Sci., vol. 8, no. 1, pp. 234-241, 1998.
23. S. C. Muller, T. Plesser, and B. Hess, "Two-dimensional spectrophotometry and pseudo-color representation of chemical reaction patterns," Naturwissenschaften, vol. 73, no. 4, pp. 165-179, 1986.
24. J. D. Murray, Mathematical Biology. New York: Springer-Verlag, 2002.
25. J. S. Nagumo, S. Arimoto, and S. Yoshizawa, "An active pulse transmission line simulating nerve axon," Proc IRE, vol. 50, pp. 2061-71, 1962.
26. A. V. Panfilov, "Spiral breakup as a model of ventricular fibrillation," Chaos: An Interdisciplinary J. Nonlin. Sci., vol. 8, no. 1, pp. 75-64, 1998.
27. A. V. Panfilov and P. L. M. Kerkhof, "Quantifying ventricular fibrillation: In silico research and clinical implications," IEEE Trans. Biomed. Eng., vol. 51, no. 1, pp. 195-196, Jan. 2004.
28. É. Pichelin, M. Fortin, and S. Boivin, "Étude numérique d'estimations d'erreurs a posteriori," REÉR, vol. 9, no. 4, pp. 467-486, 2000.
29. B. J. Roth, "Approximate analytical solutions to the bidomain equations with unequal anisotropy ration," Phys. Rev. E, vol. 55, pp. 1819-1826, 1997.
30. H. Saleheen and Kwong, "A new three-dimensional finite-difference bidomain formulation for inhomogeneous anisotropic cardiac tissues," IEEE Trans. Biomed. Eng., vol. 45, no. 1, pp. 15-25, Jan. 1998.
31. J. Sundnes, G. Lines, and A. Tveito, "An operator splitting method for solving the bidomain equations coupled to a volume conductor model for the torso," Math. Biosci., vol. 194, no. 2, pp. 233-248, 2005.
32. K. H. Ten Tusscher and A. V. Panfilov, "Influence of nonexcitable cells on spiral breakup in two-dimensional and three-dimensional excitable media," Phys. Rev. E, vol. 68, 2003, 062902.
33. J. A. Trangenstein and C. Kim, "Operator splitting and adaptive mesh refinement for the Luo-Rudy I model," J. Computat. Phys., vol. 196, no. 2, pp. 645-679, 2004.
34. E. J. Vigmond, F. Aguel, and N. A. Trayanova, "Computational techniques for solving the bidomain equations in three dimensions," IEEE Trans. Biomed. Eng., vol. 49, no. 11, pp. 1260-9, Nov. 2002.
35. R. Weber dos Santos, G. Plank, S. Bauer, and E. J. Vigmond, "Parallel multigrid preconditioner for the cardiac bidomain model," IEEE Trans. Biomed. Eng., vol. 51, no. 11, pp. 1960-1968, Nov. 2004.
36. Y. Saad, Iterative Methods for Sparse Linear Systems. Boston, MA: PWS, 1996.
37. C. Zhang, H. Zhang, Q. Ouyang, B. Hu, and G. H. Gunaratne, "Transition from spiral waves to defect-mediated turbulence induced by gradient effects in a reaction-diffusion system," Phys. Rev. E, vol. 68, 2003, 036202.