Causal Scale Shift Associated with Phase Transition to Human Atrial Fibrillation

Abstract

An example of phase transition in natural complex systems is the qualitative and sudden change in the heart rhythm between sinus rhythm and atrial fibrillation (AF), the most common irregular heart rhythm in humans. While the system behavior is centrally controlled by the behavior of the sinoatrial node in sinus rhythm, the macro-scale collective behavior of the heart causes the micro-scale behavior in AF. To quantitatively analyze this causation shift associated with phase transition in human heart, we evaluated the causal architecture of the human cardiac system using the time series of multi-lead intracardiac unipolar electrograms in a series of spatiotemporal scales by generating a stochastic renormalization group. We found that the phase transition between sinus rhythm and AF is associated with a significant shift of the peak causation from macroscopic to microscopic scales. Causal architecture analysis provides a quantitative tool to improve our understanding of causality in phase transitions in other natural and social complex systems.Complex systems | Information theory | Renormalization group | Cardiac dynamics P hase transitions between ordered and disordered states often reveal critical features of the underlying natual and social complex systems comprised of large numbers of components (1). One example of phase transition in natural complex systems is the qualitative and sudden change in the heart rhythm between sinus rhythm and atrial fibrillation (AF) (2), the most common irregular heart rhythm in human beings (3). During sinus rhythm, the system behavior at the macroscopic scale is relatively simple, because it is centrally controlled by the behavior of the sinoatrial node. In contrast, as soon as the heart undergoes an order-disorder phase transition to AF, complex system behaviors emerge where the macro-scale collective behavior of the heart causes the micro-scale behavior ('supersedence'). The shift of causation from the centrally controlled sinus rhythm to AF, which controls the behaviors of individual cardiomyocytes to maintain itself, is clinically observable in the phenomenon called 'AF begets AF', where a longer duration of pacing-maintained AF results in a longer maintenance of AF after cessation of pacing (4). Although this causation shift associated with phase transition to human AF has been qualitatively described, it has never been documented in a quantitative fashion.The intra-and inter-scale interactions of multi-scale complex systems can be mathematically quantified by information theory (5). In the cardiac system, we have previously shown that information-theoretic metrics such as mutual information (6) and transfer entropy (7) can quantify the interactions between micro-scale components (8), and the interactions between microand macro-scale behaviors during fibrillation (9). We have also shown that those information-theoretic metrics can quantify how the interactions among micro-scale components alter the macro-scale collective behavior during fibrillation (10) or cause an order-d...