Inter-scale information flow as a surrogate for downward causation that maintains spiral waves

A rotor, the rotation center of spiral waves, has been proposed as a causal mechanism to maintain atrial fibrillation (AF) in human. However, our current understanding of the causality between rotors and spiral waves remains incomplete. One approach to improving our understanding is to determine the relationship between rotors and downward causation from the macro-scale collective behavior of spiral waves to the micro-scale behavior of individual components in a cardiac system. This downward causation is quantifiable as inter-scale information flow that can be used as a surrogate for the mechanism that maintains spiral waves. We used a numerical model of a cardiac system and generated a renormalization group with system descriptions at multiple scales. We found that transfer entropy quantified the upward and downward inter-scale information flow between micro- and macro-scale descriptions of the cardiac system with spiral waves. In addition, because the spatial profile of transfer entropy and intrinsic transfer entropy was identical, there were no synergistic effects in the system. Furthermore, inter-scale information flow significantly decreased as the description of the system became more macro-scale. Finally, downward information flow was significantly correlated with the number of rotors, but the higher numbers of rotors were not necessarily associated with higher downward information flow. This finding contradicts the concept that the rotors are the causal mechanism that maintains spiral waves, and may account for the conflicting evidence from clinical studies targeting rotors to eliminate AF.