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

• Published in: Revista española de cardiologia 2005, Vol.58 (1), p.41-47
• Main Authors: Alonso Atienza, Felipe, Requena Carrión, Jesús, García Alberola, Arcadi, Rojo Álvarez, José L., SÁnchez Muñoz, Juan J., Martínez SÁnchez, Juan, Valdés Chávarri, Mariano
• Format: Article
• Language: eng ; spa
• Subjects: Basic research; Computer model; Computer Simulation; Electrofisiología; Electrophysiology; Heart - physiology; Investigación bÁsica; Modelo matemático; Models, Biological; Models, Statistical
• ISSN: 1885-5857; 0300-8932; 1885-5857
• DOI: 10.1016/S1885-5857(06)60233-8

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. La utilización de modelos matemáticos de activación y propagación del impulso ha mejorado la comprensión de diversos mecanismos elec-trofisiológicos involucrados en la génesis de las arritmias. Las simulaciones mÁs realistas se basan en los modelos de reacción-difusión e implican una carga computacional muy elevada. El objetivo del estudio es desarrollar un modelo de activación eléctrica cardíaca por ordenador que permita simular fenómenos electrofisiológicos com-plejos y que no requiera la carga computacional necesa-ria en otros modelos habitualmente empleados. Se ha modelado el tejido cardíaco como un autómata celular, cada uno de cuyos elementos adopta estados discretos en función de su estado previo y del de las células vecinas siguiendo unas reglas senci-llas. La activación se contempla como un