A great deal is known about the cardiac cell, particularly about the fundamental mechanisms of voltage and ion regulation. When mathematical expressions for these mechanisms are collected together into differential equations and simulated, the resulting behavior looks exactly like that of the real cell. Unfortunately, the most important cardiac arrhythmias, ventricular tachycardia and ventricular fibrillation (the leading cause of sudden cardiac death), cannot be understood from the point of view of the single cell. They are disorders of tissue conduction caused directly by distortion of cell electrical couplings in tissue and indirectly by disorders in cells function.
Therefore, these cardiac rhythm distortions must be understood by assembling cell models and conduction model together. Such a model is not difficult to state. One simply takes a grid of cardiac cell models, each cell connected to nearest neighbors by resistive coupling. Such a model would contain in it the ability to answer some very basic questions, especially the question of what conditions predispose tachycardia (a single spiral wave of excitation rotating through the tissue) to degenerate into lethal fibrillation (multiple, uncoordinated wavefronts). The problem is that such a model is computationally intractable.
As an order of magnitude estimate, the simplest second order FitzHugh-Nagumo cell model.compiled in C and running on a Pentium 60 PC, runs approximately in real time (that is,about one bit per second) The minimum model necessary to simulate tachycardia and fibrillation would be 128x128 such cells which would be about 16,000 times slower without parallelization.We have gained about 1.5 order of magnitude by simulating such a model on the CM-2 Connection Machine [Kogan et. al.1990]. This allows us to study the effect of APD restitution properties on 2D wave propagation in isotropic model of cardiac tissue. Particularly we showed that depending on APD restitution characteristics it is possible to observe the changes of speed and length of propagated waves, non-stationary propagation of spiral waves, and site-specific induction of spiral waves with premature stimulation [B. Kogan et.al.]. Simulation on Connection Machine an excitation propagation along the narrow pathways created by scars after myocardial infarction proved that geometry and boundary properties play a crucial role in the possibility of reentry appearance [Kogan et.al.1992].
The comparative analysis of the existing second order simplified cell model [Karpoukhin et.al 1995] showed that all these models are the simplification of the old Noble model [Noble 1962] and did not took into consideration the restitution in a maximum speed of depolarization processes in a cell. The latter were introduced in improved physiological models [Beeller, Reuter 1977 and Loo and Rudy 1991]. We proposed an approach to reduce these physiological models to a third order models retaining almost all propagation properties [Kogan et.al. i995]. On the basis of this cell model the computer simulation on CM-2 of 2D propagation in 128x128 grid allowed to find the conditions of spontaneous break up of the spiral wave front [Karpoukhin 1996].
The limited memory and and speed of processing per node of that CM machine ultimately limits our work. Moreover the progress achieved in development of serial machine (Dec-alpha workstation) made the further simulation on CM-machine not reasonable. Recently a new cardiac cell sophisticated physiological model was introduced [Luo and Rudy 1994]. That model includes the effect of Ca currents very important for correct simulation of wave propagation. Inadequate computer resources for simulation with this model,especially for the case of 3-dimensional tissue is the major factor standing now between cardiology and understanding of tissue arrhythmias. We consider that one of alternative is to implement the problem on parallel supercomputer (T3E) with adequate optimization of the numerical algorithms. The first steps in this direction are now undertaking by our group.