On a finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity

International Journal of Numerical Analysis and Modeling

Volumn 3, Issue 4, 2006, Pages 395-412

  Hanslien, Monica ^a   Karlsen, Kenneth H ^a,b   Tveito, Aslak ^a   Tai, Xue Cheng ^c  

^a SIMULA RESEARCH LABORATORY   (Norway)

^b UNIVERSITY OF OSLO   (Norway)

^c NONE

Author keywords

Cardiac electric field; Convergence; Excitable cells; Finite difference scheme; Maximum principle; Monodomain model; Reaction diffusion system of Beeler Reuter type

Indexed keywords

EID: 34547553080     PISSN: 17055105     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

1. G. W. Beeler and H. Reuter, Reconstruction of the action potential of ventricular myocardial fibres. J Physiol, 268: 177-210, 1977.
2. D. DiFrancesco and D. Noble, A model of the cardiac electrical activity incorporating ionic pumps and concentration changes. Philos Trans R Soc Lond Biol, 307: 353-398, 1985.
3. L. C. Evans, Partial differential equations, V. 19. American Mathematical Society, Providence, R.I., 1998.
4. R. Eymard, T. Gallouët, and R. Herbin, Finite volume methods. In Handbook of numerical analysis, 7: 713-1020. North-Holland, Amsterdam, 2000.
5. P. Colli Franzone and G. Savaré, Degenerate evolution systems modeling the cardiac electric field at micro-and macroscopic level. In Evolution equations, semigroups and functional analysis (Milano, 2000), V. 50 of Progr Nonlin Diff Eq Appl, 49-78. Birkhäuser, Basel, 2002.
6. M. Hanslien, K. H. Karlsen and A. Tveito, A maximum principle for an explicit finite difference scheme approximating the hodgkin-huxley model. To appear in BIT.
7. J. Keener and J. Sneyd, Mathematical physiology, V. 8. Springer, 1980.
8. C. H. Luo and Y. Rudy, A model of the ventricular cardiac action potential: depolarization, repolarization and their interaction. Circ Res, 68: 1501-1526, 1991.
9. S. Sanfelici, Numerical and analytic study of a parabolic-ordinary system modelling cardiac activation under equal anisotropy conditions. Riv Mat Univ Parma (5), 5: 143-157 (1997), 1996.
10. R. L. Winslow, J. Rice, S. Jafri, E. Marban, and B. O’Rourke, Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, ii, model studies. Circ Res, 84: 571-586, 1999.