(539a) Finite Element & Finite Difference Methods for Cardiac Propagation

General computational models of cardiac impulse propagation are based on generic models solved on rectangular, isotropic domains. However, common intact ventricular myocardium differs from these models in complex biochemical events associated with the cell membrane that governs action potential, by means of variety of communication links among single cells or groups of cells and by the large scale geometric complexity. Sophisticated models of the membrane dynamics of the cardiac cell have been developed [1,2] , but the complexity of calculation of myocardial single cell membrane current requires that the system ordinary differential equations consisting of 20-30 variables be solved. Such complexity of single cell dynamics, which is incorporated in large tissue domains, where the effects of geometry, angle fiber orientation and inhomogeneous regions play significant role, remains to be explored from the standpoint of the best realizable and feasible computational methods that are capable of dealing with these complex issues.

Two powerful mathematical techniques for solving large scale parabolic PDE problems are finite difference method(FDM) and finite element method (FEM). Both methods are used in the current state-of-the-art simulation analysis of the cardiac action potential propagation [3,4]. Nevertheless, and for the purpose of comparison, the two methods may be evaluated with respect to their ability to accurately reproduce action potential propagation, speed of calculation, computer code implementation and realization.

In this note, we compare 2D and 3D homogeneous tissue numerical simulations of different models of cardiac propagation (Fitz Hugh-Nagumo, Beeler-Reuter, LR) with the use of multi processor supercomputer and parallelized code. We solve the large scale PDE problem using the well known operator splitting method. We use 32 dual-core processors Opteron 275 at 2.2GHz and parallel computing with message-passing interface (MPI) to resolve the large scale simulation. Comparative simulation studies demonstrate differences with respect to accuracy, speed and complexity of the code realization among the cardiac models and between FD and FEM methods.

[1] G. W. Beeler and H. Reuter, ?Reconstruction of the action potential of ventricular myocardial fibres,? Journal of Physiology, vol. 45, p. 11911202, 1977.

[2] C.-H. Luo and Y. Rudy, ?A model of the ventricular cardiac action potential:depolarization, repolarization, and their innteraction,? Circulation Research, vol. 68, p. 15011526, 1991.

[3] J. M. Rogers and A. McCulloch, ?A collocation-galerkin finite element model of cardiac action potential propagation,? IEEE Transaction on Biomedical Engineering, vol. 41, p. 743757, 1994.

[4] F. Xie, Z. Qu, J.Yang, A. Baher, J. N. Weiss, and A. Garfinkel, ?A simulation study of the effects of cardiac anatomy in ventricular fibrillation,? J. Clin. Invest., vol. 113, p. 686693, 2004.