The mechanism that maintains atrial fibrillation (AF) remains elusive. One approach to understanding and controlling the mechanism (AF driver) is to quantify inter-scale information flow from macroscopic to microscopic behaviors of the cardiac system as a surrogate for the downward causation of the AF driver. We use a numerical model of a cardiac system with one of the potential AF drivers, a rotor, the rotation center of spiral waves, and generate a renormalization group with system descriptions at multiple scales. We find that transfer entropy accurately quantifies the upward and downward information flow between microscopic and macroscopic descriptions of the cardiac system with spiral waves. Because the spatial profile of transfer entropy and intrinsic transfer entropy is identical, there are no synergistic effects in the system. We also find that inter-scale information flow significantly decreases as the description of the system becomes more macroscopic. The downward information flow is significantly smaller than the upward information flow. Lastly, we find that downward information flow from macroscopic to microscopic descriptions of the cardiac system is significantly correlated with the number of rotors, but the higher number of rotors is not necessarily associated with a higher downward information flow. This result contradicts the concept that the rotors are the AF driver, and may account for the conflicting evidence from clinical studies targeting rotors as the AF driver.
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