Emergence of Complex Behavior: An Interactive Model of Cardiac Excitation Provides a Powerful Tool for Understanding Electric Propagation

We have developed a straightforward, physiologically based mathematical in silico model of cardiac electric activity to facilitate understanding of the fundamental principles that determine how excitation propagates through the heart. Despite its simplicity, the model provides a very powerful teaching tool. In fact, its simplicity is integral to the model's utility. The contrast between the minimal set of rules that govern the model's function and the widely varied complex behaviors it can manifest offers insight into the nature of emergent behavior in wave propagation. Emergence in this context refers to the richness of the tissue activation patterns that arise from the aggregate behavior of the simple cells that comprise the tissue. Each cell can be active, inactive, or refractory and interacts only with its immediate neighbors. From these simple building blocks, very elaborate global behaviors emerge. From the perspective of the electrophysiology student, the notion of emergent properties can act as a Rosetta stone for deciphering electrophysiological behavior. The spread of electric excitation through the intricate 3D structure of the heart can take widely varied forms, ranging from the orderly propagation seen during sinus rhythm to the marked disorganization seen during ventricular fibrillation. Observation of the diverse and sometimes complex patterns of conduction (eg, unidirectional block, reentry, spiral waves) as well as the responses to pacing maneuvers (eg, entrainment) suggests to the electrophysiology student a nearly infinite array of possibilities, the mastery of which can be daunting. However, with study, it becomes apparent that one need not memorize every possible cardiac behavior. Instead, there are overarching principles of cardiac excitation and propagation1 from which these varied phenomena emerge and through which one can understand and predict rather than memorize electrophysiological behavior. Understanding these fundamental principles is integral to mastering electrophysiology. A framework for interpreting clinical observations predicated on these …