Statistical properties of heartbeat intervals during atrial fibrillation

Atrial fibrillation is a common cardiac arrhythmia in which there is an irregular heartbeat. This paper develops a theoretical model for the intervals between successive heartbeats during atrial fibrillation based on the following ideas. There is an irregular pattern of activation of the upper chambers (atria) of the heart. Excitation travels from the atria through the specialized conducting tissue called the atrioventricular node to the lower chamber of the heart (ventricles). We model this situation by a stochastic map. If the map is linear, then it is possible to compute analytically the probability density for the timings between ventricular activations. Numerical simulations of nonlinear maps show correspondences with clinical data. Thus this work casts a clinical medical problem in the context of stochastic maps.