  During episodes of atrial fibrillation, the heart's electrical activity
becomes disorganized and shows fragmenting spiral waves. To systematically
address how this pattern terminates using spatially extended simulations
exceeds current computational resources. To circumvent this limitation, we
treat the number of spiral waves as a stochastic population with a
corresponding birth-death equation and use techniques from statistical physics
to determine the mean episode duration of atrial fibrillation. We show that
this duration can be computed for arbitrary geometries in minimal computational
time and that it depends exponentially on tissue size, consistent with the
critical mass hypothesis which states that fibrillation requires a minimal
organ size. Our approach can result in efficient and accurate predictions of
mean episode duration, thus creating a potentially important step towards
improved therapeutic interventions for atrial fibrillation.
