A Probabilistic Model of Cardiac Electrical Activity Based on a Cellular Automata System

Abstract

Mathematical models of cardiac electrical activity may help to elucidate the electrophysiological mechanisms involved in the genesis of arrhythmias. The most realistic simulations are based on reaction-diffusion models and involve a considerable computational burden. The aim of this study was to develop a computer model of cardiac electrical activity able to simulate complex electrophysiological phenomena but free of the large computational demands required by other commonly used models. A cellular automata system was used to model the cardiac tissue. Each individual unit had several discrete states that changed according to simple rules as a function of the previous state and the state of the neighboring cells. Activation was considered as a probabilistic process and was adjusted using restitution curves. In contrast, repolarization was modeled as a deterministic phenomenon. Cell currents in the model were calculated with a prototypical action potential that allowed virtual monopolar and bipolar electrograms to be simulated at any point in space. Reproducible flat activation fronts, propagation from a focal stimulus, and reentry processes that were stable and unstable in two dimensions (with their corresponding electrograms) were obtained. The model was particularly suitable for the simulation of the effects observed in curvilinear activation fronts. Fibrillatory conduction and stable rotors in two- and three-dimensional substrates were also obtained. The probabilistic cellular automata model was simple to implement and was not associated with a high computational burden. It provided a realistic simulation of complex phenomena of interest in electrophysiology.