  The heart exhibits complex systems behaviors during atrial fibrillation (AF),
where the macroscopic collective behavior of the heart causes the microscopic
behavior. However, the relationship between the downward causation and scale is
nonlinear. We describe rotors in multiple spatiotemporal scales by generating a
renormalization group from a numerical model of cardiac excitation, and
evaluate the causal architecture of the system by quantifying causal emergence.
Causal emergence is an information-theoretic metric that quantifies emergence
or reduction between microscopic and macroscopic behaviors of a system by
evaluating effective information at each spatiotemporal scale. We find that
there is a spatiotemporal scale at which effective information peaks in the
cardiac system with rotors. There is a positive correlation between the number
of rotors and causal emergence up to the scale of peak causation. In
conclusion, one can coarse-grain the cardiac system with rotors to identify a
macroscopic scale at which the causal power reaches the maximum. This scale of
peak causation should correspond to that of the AF driver, where networks of
cardiomyocytes serve as the causal units. Those causal units, if identified,
can be reasonable therapeutic targets of clinical intervention to cure AF.
