A simple 2-dimensional model of cardiac tissue conduction

Abstract

Objectives: The purpose of this study is to simulate cardiac tissue conduction using a 2-dimensional cellular automata (CA) model. Methods: Using a 2-dimensional CA model, we represented ventricular myocytes by cells arranged in a 33-by-33 grid to simulate a single ventricle. The neighborhood of each cell is a von Neumann neighborhood composed of 4 directly adjoining cells. The grid was composed in the shape of a torus to permit cells across the opposite face of the grid to interact. The design allows simulations of sustainable waves of electrical activity. The NetLogo 4.01 Beta software platform (Northwestern Illinois) was used to implement the CA model. Each tick of the simulation clock is equivalent to 1 millisecond. The simulations were run over millions of iterations. The pacemaker was set at 60 beats per minute. Results: Given normal physiologic parameters of heart rate, length of Na/Ca channel opening times, and QTc, the CA model simulates the normal conduction of the heart. The waves of depolarization and repolarization spread through the cardiac tissue without formation of pathologic dysrhythmias over hundreds of thousands of heartbeats. The virtual rhythm strip created by a virtual electrocardiogram lead shows a narrow complex rhythm at the rate set by the user-defined pacemaker parameter (Fig. 1A). Given the 2-dimensional nature of the model, the T wave is in the opposite direction to the QRS because there is no epicardium or endocardium. The plot of the electric potential at a time t + 1 vs time t shows a stable system that occupies a stable orbit (Fig. 1B). Once the system is perturbed by increasing the QTc, the CA model enters into an unstable tachycardia. The rate of ventricle depolarization ranges from 120 to 180 beats per minute depending on the exact setting of the QTc. The resultant rhythm strip (Fig. 1C) shows the tachyarrhythmia with a pacemaker spike occurring at regular intervals that is independent of the ventricular rhythm (ie, AV dissociation). The tachycardia is narrow complex because of the small number of cells in the virtual cardiac tissue. The state diagram shows the system trapped in a tachyarrhythmia from which it is unable to escape (Fig. 1D). Conclusions: The initial results of this article indicate that the cardiac conduction system can be readily simulated using CA. Cellular automata simulations offer a major advantage in their ability to monitor the electric potential of each myocyte as depolarization and repolarization proceeds. This implies that the effect of a large number of factors that influence conduction, for example, electrolyte concentrations, congenital and acquired alterations in voltage-gated channels, and ischemia-induced changes in conduction, can be readily simulated. These CA simulations are expected to provide information on the overall progress of both normal and abnormal electric activity as well as on individual myocyte function over time. Thus, CA modeling of cardiac tissue affords the novel possibility of creating simulations of the effect of antiarrhythmic medications and ischemia at the cardiac myocyte and tissue level.