A numerical scheme for modeling wavefront propagation on a monolayer of arbitrary geometry

IEEE Transactions on Biomedical Engineering

Volumn 50, Issue 4, 2003, Pages 412-420

  Zozor, Steeve ^a,b   Blanc, Olivier ^a   Jacquemet, Vincent ^a   Virag, Nathalie ^a,c   Vesin, Jean Marc ^a   Pruvot, Etienne ^d   Kappenberger, Lukas ^d   Henriquez, Craig ^d,e  

^a EPFL   (Switzerland)

^b Domaine Universitaire   (France)

^c Medtronic Europe SA   (Switzerland)

^d LAUSANNE UNIVERSITY HOSPITAL   (Switzerland)

^e Duke University   (United States)

Author keywords

Atrial modeling; Cardiac propagation; Finite difference methods; Triangular mesh

Indexed keywords

CARDIOLOGY; COMPUTER SIMULATION; FINITE VOLUME METHOD; WAVEFRONTS;

WAVEFRONT PROPAGATION;

TISSUE;

ANALYTIC METHOD; ARTICLE; ELECTRIC CURRENT; ELECTROGRAPHY; HEART ATRIUM; HEART ELECTROPHYSIOLOGY; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; SIMULATION; THREE DIMENSIONAL IMAGING; ALGORITHM; BIOLOGICAL MODEL; CELL MEMBRANE POTENTIAL; COMPUTER SIMULATION; ELECTROCARDIOGRAPHY; ELECTROMAGNETIC FIELD; EVALUATION; HEART; HEART MUSCLE CELL; HEART MUSCLE CONDUCTION SYSTEM; HUMAN; METHODOLOGY; PHYSIOLOGY;

ALGORITHMS; BODY SURFACE POTENTIAL MAPPING; COMPUTER SIMULATION; ELECTROCARDIOGRAPHY; ELECTROMAGNETIC FIELDS; HEART; HEART CONDUCTION SYSTEM; HUMANS; MEMBRANE POTENTIALS; MODELS, CARDIOVASCULAR; MYOCYTES, CARDIAC;

EID: 0037388961     PISSN: 00189294     EISSN: None     Source Type: Journal    
DOI: 10.1109/TBME.2003.809505     Document Type: Article

References (27)

1. D. M. Harrild and C. S. Henriquez, "A computer model of normal conduction in the human atria," Circ. Res., vol. 87, pp. 25e-36e, Sept. 2000.
2. O. Blanc, N. Virag, J.-M. Vesin, and L. Kappenberger, "A computer model of human atria with reasonable computation load and realistic anatomical properties," IEEE Trans. Biomed. Eng., vol. 48, pp. 1229-1237, Nov. 2001.
3. P. Levran, "Simulation de cellules cardiaques par automates cellulaires," Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, rapport de diplôme, département d'électricité, 2000.
4. D. M. Harrild and C. S. Henriquez, "A finite volume model of cardiac propagation," Ann. Biomed. Eng., vol. 28, no. 2, pp. 315-334, Mar.-Apr. 1997.
5. P. J. Hunter, B. H. Smail, P. M. F. Nielsen, and I. J. Le Grice, "A mathematical model of cardiac anatomy," in Computational Biology of the Heart, A. V. Panfilov and A. V. Holden, Eds. New York: Wiley, 1997, pp. 171-215.
6. J. M. Rogers and A. D. McCulloch, "A collocation - Galerkin finite element model of cardiac action potential propagation," IEEE Trans. Biomed. Eng., vol. 41, pp. 743-757, Aug. 1994.
7. F. B. Sachse, C. Werner, and G. Seeman, Simulation of Cardiac Electrophysiology and Electrocardiography, N. Virag, O. Blanc, and L. Kappenberger, Eds. New York: Futura, 2001.
8. C. W. Zemlin, H. Herzel, S. Y. Ho, and A. Panvilov, A Realistic and Efficient Model of Excitation Propagation in the Human Atria, N. Virag, O. Blanc, and L. Kappenberger, Eds. New York: Futura, 2001.
9. D. J. Rose, H. Shao, and C. S. Henriquez, "Discretization of anisotropic convection-diffusion equations, convective M-matrices and their iterative solution," VLSI Design, vol. 10, no. 4, pp. 485-529, 2000.
10. I. Ohnaka and T. Fukusako, "Finite element method and a matrix method in transient heat-conduction problems," in Proc. 6th Int. Heat Transfer Conf., vol. 3, 1988, p. 251.
11. M. Rappaz, M. Bellet, and M. Deville, Modélisation numérique en science et génie des matériaux. Lausanne, Switzerland: Presses Polytechniques et Universitaires Romandes, 1998.
12. C. S. Henriquez and A. A. Papazoglou, "Using computer models to understand the roles of tissue structure and membrane dynamics in arrhythmogenesis," Proc. IEEE, vol. 84, pp. 334-354, Mar. 1996.
13. G. W. Beeler and H. Reuter, "Reconstruction of the action potential of ventricular myocardial fibers," J. Physiol., vol. 268, pp. 177-210, 1977.
14. M. Courtemanche, R. J. Ramirez, and S. Nattel, "Ionic mechanism underlying human atrial action potential properties: Insights from a mathematical model," AJP - Heart Circulatory Physiol., vol. 44, no. 1, pp. H301-H321, July 1998.
15. D. DiFrancesco and D. Noble, "A model of cardiac electrical activity incorporating ionic pumps and concentration changes," Philosophical Trans. Roy. Soc. Lond. B, vol. 307, pp. 353-398, 1985.
16. R. A. FitzHugh, "Impulses and physiological states in theoretical models of nerve membrane," Biophys. J., vol. 1, pp. 445-466, 1961.
17. C. Luo and Y. Rudy, "A dynamic model of the cardiac ventricular action potential, I: Simulations of ionic currents and concentration changes," Circ. Res., vol. 74, pp. 1071-1096, June 1994.
18. A. Nygren, C. Fiset, L. Firek, J. W. Clark, D. S. Lindblad, R. B. Clark, and W. R. Giles, "Mathematical model of an adult human atrial cell. The role of K+ currents in repolarization," Circ. Res., vol. 82, pp. 63-81, January 1998.
19. D. B. Geselowitz, R. C. Barr, M. S. Spach, and W. T. Miller, 3rd, "The impact of adjacent isotropic fluids on electrograms from anisotropic cardiac muscle. A modeling study," Circ. Res., vol. 51, no. 5, pp. 605-613, Nov. 1982.
20. J. Garrigues, La méthode des éléments finis. Marseille, France: Cours de l'école supérieure de mécanique de Marseille, 2001.
21. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore: The John Hopkins University Press, 1987.
22. R. S. Varga, Matrix Iterative Analysis, 2nd ed. New York: Springer-Verlag, 2000.
23. R. Plonsey and R. C. Barr, Bioelectricity: A Quantitative Approach, 2nd ed. New York: Kluwer Academic/Plenum, 2000.
24. M. S. Spach and J. M. Kootsey, "Relating the sodium current and conductance to the shape of transmembrane and extracellular potentials by simulation: Effects of propagation boundaries," IEEE Trans. Biomed. Eng., vol. 32, pp. 743-755, Oct. 1985.
25. K. Gima and Y. Rudy, "Ionic current basis of electrocardiographic waveforms: A model study," Circ. Res., vol. 90, pp. 889-896, 2002.
26. F. X. Giraldo, "Lagrange-Galerkin methods on spherical geodesic grids," J. Computat. Phys., vol. 136, no. 1, pp. 197-217, Sept. 1997.
27. P. L. George and H. Borouchaki, Delaunay Triangulation and Meshing: Application to Finite Elements. Paris, France: Hermès, 1998.