Title: Memory effects, transient growth, and wave breakup in a model of paced atrium,
Abstract: The mechanisms underlying cardiac fibrillation have been investigated for
over a century, but we are still finding surprising results that change our
view of this phenomenon. The present study focuses on the transition from
normal rhythm to atrial fibrillation associated with a gradual increase in the
pacing rate. While some of our findings are consistent with existing
experimental, numerical, and theoretical studies of this problem, one result
appears to contradict the accepted picture. Specifically we show that, in a
two-dimensional model of paced homogeneous atrial tissue, transition from
discordant alternans to conduction block, wave breakup, reentry, and spiral
wave chaos is associated with transient growth of finite amplitude disturbances
rather than a conventional instability. It is mathematically very similar to
subcritical, or bypass, transition from laminar fluid flow to turbulence, which
allows many of the tools developed in the context of fluid turbulence to be
used for improving our understanding of cardiac arrhythmias.