An unconditionally stable numerical method for the Luo-Rudy 1 model used in simulations of defibrillation

Mathematical Biosciences

Volumn 208, Issue 2, 2007, Pages 375-392

  Hanslien, Monica ^a   Sundnes, Joakim ^a   Tveito, Aslak ^a  

^a SIMULA RESEARCH LABORATORY   (Norway)

Author keywords

Defibrillation; Luo Rudy 1; Maximum principle; Stable scheme

Indexed keywords

CHEMICAL MODIFICATION; COMPUTER SIMULATION; ELECTRIC POTENTIAL; EULER EQUATIONS; MATHEMATICAL MODELS; NUMERICAL METHODS;

DEFIBRILLATION; LUO-RUDY 1; MAXIMUM PRINCIPLES; STABLE SCHEMES;

CELL MEMBRANES;

ELECTRODE; EULERIAN ANALYSIS; MEMBRANE; NUMERICAL MODEL; PHYSIOLOGY;

ARTICLE; DEFIBRILLATION; EXPERIMENTAL MODEL; MATHEMATICAL COMPUTING; MEMBRANE CONDUCTANCE; SIMULATION;

ELECTRIC COUNTERSHOCK; ELECTROPHYSIOLOGY; HUMANS; MATHEMATICS; MODELS, CARDIOVASCULAR; VENTRICULAR FIBRILLATION;

EID: 34547138465     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2006.09.006     Document Type: Article

References (24)

1. Mackenzie D. Making sense of a heart gone wild. Science 303 (2004) 786-787
2. Mintz E. Automated external defibrillators; understanding today's technology, preparing for wider use. J. Critical Illness (2000)
3. Tung L.A. Bi-domain model for describing ischemic myocardial D-C potentials (1978).
4. Keener J., and Sneyd J. Mathematical physiology Vol. 8 (1980), Springer
5. Xie F., Qu Z., Garfinkel A., and Weiss J.N. Electrophysiological heterogeneity and stability of reentry in simulated cardiac tissue. Am. J. Physiol. Heart. Circ. Physiol. 280 (2001) H535-H545
6. Trayanova N., and Skouibine K. Modeling defibrillation: effects of fiber curvature. J. Electrocardiol. 31 (1998) 23-29
7. Beeler G.W., and Reuter H. Reconstruction of the action potential of ventricular myocardial fibres. J. Phys. 268 (1977) 177-210
8. Luo C.H., and Rudy Y. A model of the ventricular cardiac action potential: depolarization, repolarization and their interaction. Circ. Res. 68 (1991) 1501-1526
9. Skouibine K., Trayanova N., and Moore P. A numerically efficient model for simulation of defibrillation in an active bidomain sheet of myocardium. Math. Biosc. 166 (2000) 85-100
10. J. Sundnes, G. Lines, X. Cai, B.F. Nielsen, A. Tveito. Computing the electrical activity in the human heart, Springer-Verlag (accepted for publication).
11. Keener J.P. The topology of defibrillation. J. Theor. Biol. 21 (2004) 459-473
12. FitzHugh R.A. Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1 (1961) 445
13. 2 +, and regulation of ion pumps in ventricular myocyte. Biophys. J. 81 (2001) 614-629
14. Winslow R.L., Rice J., Jafri S., Marban E., and O'Rourke B. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, ii, model studies. Circ. Res. 84 (1999) 571-586
15. Krassowska W., and DeBruin K.A. Modeling electroporation in a single cell ii: effects of ionic concentrations. Biophys. J. 77 (1999) 1225-1233
16. Nikolski V.P., Sambelashvili A.T., Krinsky V.I., and Efimov I.R. Effects of electroporation on optically recorded transmembrane potential responses to high-intensity electrical shocks. Am. J. Physiol. Heart. Circ. Physiol. 286 (2004) H412-H418
17. Cheek E.R., and Fast V.G. Nonlinear changes of transmembrane potential during electrical shocks; role of membrane electroporation. Circ. Res. 21 (2004) 208-214
18. Krassowska W. Effects of electroporation on transmembrane potential induced by defibrillation shocks. PACE 18 (1995) 1644-1660
19. Krassowska W., and DeBruin K.A. Modeling electroporation in a single cell. i. effects of field strength and rest potential. Biophys. J. 77 (1999) 1213-1224
20. Skouibine K., Trayanova N., and Moore P. Cathode/anode make and break phenomena during defibrillation. IEEE Trans. Biomed. Eng. 46 (1999) 769-777
21. J. Sundnes, G.T. Lines, A. Tveito. A second order scheme for solving the bidomain and forward problem. Biosciences, 2005 (accepted for publication).
22. Qu Z., and Garfinkel A. An advanced algorithm for solving partial differential equation in cardiac conduction. IEEE Trans. Biomed. Eng. 46 9 (1999) 1166-1168
23. Sundnes J., Lines G.T., Mardal K.A., and Tveito A. Multigrid block preconditioning for a coupled system of partial differential equations modeling the electrical activity in the heart. Comp. Meth. Biomech. Biomed. Eng. 5 6 (2002) 397-409
24. Shannon T.R., Wang F., Puglisi J., Weber C., and Bers D.M. A mathematical treatment of integrated ca dynamics within the ventricular myocyte. Biophys. J. 87 (2004) 3351-3371