Abstract
Implicit methods are well known to have greater stability than explicit methods for stiff systems, but they often are not used in practice due to perceived computational complexity. This paper applies the backward Euler (BE) method and a second-order one-step two-stage composite backward differentiation formula (C-BDF2) for the monodomain equations arising from mathematically modeling the electrical activity of the heart. The C-BDF2 scheme is an L-stable implicit time integration method and easily implementable. It uses the simplest forward Euler and BE methods as fundamental building blocks. The nonlinear system resulting from application of the BE method for the monodomain equations is solved for the first time by a nonlinear elimination method, which eliminates local and nonsymmetric components by using a Jacobian-free Newton solver, called Newton--Krylov solver. Unlike other fully implicit methods proposed for the monodomain equations in the literature, the Jacobian of the global system after the nonlinear elimination has much smaller size, is symmetric and possibly positive definite, which can be solved efficiently by standard optimal solvers. Numerical results are presented demonstrating that the C-BDF2 scheme can yield a...Continue Reading
References
May 1, 1992·Medical & Biological Engineering & Computing·C Cabo, R C Barr
Jan 10, 1985·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·D DiFrancesco, D Noble
Sep 1, 1966·Biophysical Journal·J W Cooley, F A Dodge
Apr 1, 1994·Mathematical Biosciences·N HookeD Rose
Jul 1, 1997·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·D S Hochbaum, A Pathria
Jul 1, 1997·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·S Schbath
Oct 1, 1997·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·M G ReeseD Haussler
Oct 1, 1997·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·G Benson
Sep 24, 1999·IEEE Transactions on Bio-medical Engineering·Z Qu, A Garfinkel
Nov 27, 2002·IEEE Transactions on Bio-medical Engineering·Edward J VigmondNatalia A Trayanova
Jun 5, 2003·Chaos·J. P. Keener, K. Bogar
Aug 1, 1952·The Journal of Physiology·A L HODGKIN, A F HUXLEY
May 15, 2004·American Journal of Physiology. Heart and Circulatory Physiology·Vladimir E BondarenkoRandall L Rasmusson
Nov 13, 2004·IEEE Transactions on Bio-medical Engineering·Rodrigo Weber dos SantosEdward J Vigmond
Apr 28, 2005·Mathematical Biosciences·Joakim SundnesAslak Tveito
Citations
Jun 29, 2010·Annals of Biomedical Engineering·Raymond J Spiteri, Ryan C Dean
Nov 15, 2018·Frontiers in Physiology·Javiera Jilberto, Daniel E Hurtado
Jan 1, 2021·Frontiers in Physiology·Xindan GaoWenjun Ying