Atrial fibrillation (AF) is the most common cardiac arrhytmia, characterised
by the chaotic motion of electrical wavefronts in the atria. In clinical
practice, AF is classified under two primary categories: paroxysmal AF, short
intermittent episodes separated by periods of normal electrical activity, and
persistent AF, longer uninterrupted episodes of chaotic electrical activity.
However, the precise reasons why AF in a given patient is paroxysmal or
persistent is poorly understood. Recently, we have introduced the percolation
based Christensen-Manani-Peters (CMP) model of AF which naturally exhibits both
paroxysmal and persistent AF, but precisely how these differences emerge in the
model is unclear. In this paper, we dissect the CMP model to identify the cause
of these different AF classifications. Starting from a mean-field model where
we describe AF as a simple birth-death process, we add layers of complexity to
the model and show that persistent AF arises from the formation of temporally
stable structural re-entrant circuits that form from the interaction of
wavefront collisions during paroxysmal AF. These results are compatible with
recent findings suggesting that the formation of re-entrant drivers in fibrotic
border zones perpetuates persistent AF.