A numerically efficient model for simulation of defibrillation in an active bidomain sheet of myocardium

Mathematical Biosciences

Volumn 166, Issue 1, 2000, Pages 85-100

  Skouibine, Kirill ^b   Trayanova, Natalia ^a   Moore, Peter ^a  

^a Tulane University   (United States)

^b NONE

Author keywords

Active membrane kinetics; Bidomain model; Defibrillation; Transmembrane potential

Indexed keywords

ALGORITHM; ARTICLE; DEFIBRILLATION; HEART MUSCLE EXCITABILITY; MATHEMATICAL MODEL; MEMBRANE MODEL; MEMBRANE POTENTIAL;

ALGORITHMS; COMPUTER SIMULATION; ELECTRIC COUNTERSHOCK; HUMANS; MODELS, CARDIOVASCULAR; MYOCARDIUM;

EID: 0033926678     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(00)00019-5     Document Type: Article

References (35)

1. Henriquez C.S. Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit. Rev. Biomed. Eng. 21:1993;1.
2. N. Trayanova, T.C. Pilkington, The use of spectral methods in bidomain studies, in: T.C. Pilkington et al. (Eds.), High-Performance Computing in Biomedical Research, CRC, Boca Raton, FL, 1993, p. 403.
3. Trayanova N., Roth B.J., Malden L.J. The response of a spherical heart to a uniform electric field: a bidomain analysis of cardiac stimulation. IEEE Trans. Bio-Med. Electron. 40:1993;899.
4. Trayanova N., Eason J.C. Shock-induced transmembrane potential distribution in the canine heart: effects of electrode location and polarity (abstract). PACE. 17:1995;331.
5. Entcheva E., Trayanova N., Claydon F. Patterns of and mechanisms for shock-induced polarization in the heart: a bidomain analysis. IEEE Trans. Bio-Med. Electron. 46:1999;260.
6. Roth B.J. A mathematical model of make and break electrical stimulation of cardiac tissue by a unipolar anode or cathode. IEEE Trans. Biomed. Eng. 42:1995;1174.
7. Saleheen H.I., Ng K.T A new three-dimensional finite-difference bidomain formulation for inhomogeneous anisotropic cardiac tissues. IEEE Trans. Bio-Med. Electron. 45:1998;15.
8. M. Fishler, Mechanisms of cardiac cell excitation and wave front termination via field stimulation, PhD thesis, Johns Hopkins University, Baltimore, MD, 1995.
9. Keener J., Bogar K. A numerical method for the solution of the bidomain equations in cardiac tissue. Chaos. 8:1998;57.
10. Beeler G.W., Reuter H. Reconstruction of the action potential of ventricular myocardial fibres. J. Physiol. 268:1977;177.
11. Drouhard J.P., Roberge F.A. Revised formulation of the Hodgkin-Huxley representation of the sodium current in cardiac cells. Comput. Biomed. Res. 20:1987;333.
12. Luo C.-H., Rudy Y. A model of the ventricular cardiac action potential. Circ. Res. 6:1991;1501.
13. Luo C.-H., Rudy Y. A dynamic model of the ventricular cardiac action potential. Circ. Res. 74:1994;1071.
14. Krassowska W. Effects of electroporation on transmembrane potential induced by defibrillation shocks. PACE. 18:1995;1644.
15. Skouibine K.B., Trayanova N.A., Moore P.K. Anode/cathode make and break phenomena in a model of defibrillation. IEEE Trans. Bio-Med. Electron. 46:1999;769.
16. Saad Y., Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7:1986;856.
17. Brenan K.E., Campbell S.L., Petzold L.R. Numerical Solution of Initial-Value Problems in Differential-Algebraic. 1985;North-Holland, Amsterdam.
18. Hairer E., Norsett S.P., Wanner G. Solving Ordinary Differential Equations. 1987;Springer, Berlin.
19. Saad Y. Practical use of some Krylov subspace methods for solving indefinite and non-symmetric linear systems. SIAM J. Sci. Statist. Comput. 5:1984;203.
20. Shampine L.F., Gordon M.K. Computer Solution of Ordinary Differential Equations. 1975;W.H. Freeman, New York.
21. Thomas J.W. Numerical Partial Differential Equations Finite Difference Methods. 1995;Springer, Berlin.
22. Knisley S.B., Hill B.C., Ideker R.E. Virtual electrode effects in myocardial fibers. Biophys. J. 66:1994;719.
23. Knisley S.B. Transmembrane voltage changes during unipolar stimulation of rabbit ventricle. Circ. Res. 77:1995;1229.
24. Wikswo J.P. Jr., Lin S.-F., Abbas R.A. Virtual electrodes in cardiac tissue: a common mechanism for anodal and cathodal stimulation. Biophys. J. 69:1995;2195.
25. Efimov I.R., Cheng Y.N., Biermann M., Van Wagoner D.R., Mazgalev T.N., Tchou P.J. Transmembrane voltage changes produced by real and virtual electrodes during monophasic defibrillation shock delivered by an implantable electrode. J. Cardiovasc. Electrophysiol. 8:1997;1031.
26. Efimov I.R., Cheng Y.N., Van Wagoner D.R., Mazgalev T.N., Tchou P.J. Virtual electrode-induced phase singularity: a basic mechanism of defibrillation failure. Circ. Res. 82:1998;918.
27. Fishler M.G., Sobie E.A., Tung L.et al. Cardiac responses to premature monophasic and biphasic field stimuli: results from cell and tissue modeling studies. J. Electrocardiol. 28(Suppl):1995;174.
28. Fishler M.G., Sobie E.A., Tung L.et al. Modeling the interaction between propagating cardiac waves and monophasic and biphasic field stimuli: the importance of the induced spatial excitatory response. J. Cardiovasc. Electrophysiol. 7:1996;1183.
29. Trayanova N., Bray M.-A. Membrane refractoriness and excitation induced in cardiac fibers by monophasic and biphasic shocks. J. Cardiovasc. Electrophysiol. 8:1997;745.
30. Trayanova N., Skouibine K., Aguel F. The role of cardiac tissue structure in defibrillation. Chaos. 8:1998;221.
31. K. Skouibine, N. Trayanova, P. Moore, Reorganization and termination of a spiral wave reentry following a defibrillation shock, in: Proceedings of the 19th Annual IEEE/EMBS Conf, 1997 (CD-ROM).
32. N. Trayanova, F. Aguel, K. Skouibine, Extension of refractoriness in a model of cardiac defibrillation, in: Altman, Dunker, Hunter, Klein, Lauderdale (Eds.), Proceedings of the Pacific Symposium on Biocomputing'99, World Scientific, Singapore, 1999, p. 240.
33. Trayanova N., Skouibine K. Modelling defibrillation: effects of fiber curvature. J. Cardiol. 31(Suppl):1998;23.
34. Roth B.J. Action potential propagation in a thick strand of cardiac muscle. Circ. Res. 68:1991;162.
35. Leon L.J., Roberge F.A., Vinet A. Simulation of two-dimensional anisotropic cardiac reentry: effects of wavelength on the reentry characteristics. Ann. Biomed. Eng. 22:1994;592.