  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 may improve our understanding of causality in phase
transitions in other natural and social complex systems.
