Cellular Automata Models of Cardiac Conduction

Abstract

The application of cellular automata models of cardiac conduction (CAMCC) to cardiac arrhythmias is examined. We define the relation between simple two- and three-state CAMCC and contrast them with models of continuous variables. Of interest for the analysis of reentrant arrhythmias is the presence of stable vortex or spiral patterns of activity in CAMCC with uniform parameters of conduction. Such organizing patterns are also observed in other nonlinear, nonequilibrium systems; the cellular automata models preserve the large-scale features of these patterns while collapsing the core of the vortex to a line discontinuity whose length is a reflection of an intrinsic length constant, the conduction velocity multiplied by the refractory period. A discussion is made of the interpretation of the discrete spatial lattice used in CAMCC; the proper interpretation for scaling is that of spatially sampling activity at points, not averaging over local volumes. We also consider the interpretation of the assignment of spatial (dispersion vs. gradients) and temporal inhomogeneities in the parameters of conduction of a CAMCC.