Stochastic Aspects of Cardiac Arrhythmias

Abnormal cardiac rhythms (cardiac arrhythmias) often display complex changes over time that can have a random or haphazard appearance. Mathematically, these changes can on occasion be identified with bifurcations in difference or differential equation models of the arrhythmias. One source for the variability of these rhythms is the fluctuating environment. However, in the neighborhood of bifurcation points, the fluctuations induced by the stochastic opening and closing of individual ion channels in the cell membrane, which results in membrane noise, may lead to randomness in the observed dynamics. To illustrate this, we consider the effects of stochastic properties of ion channels on the resetting of pacemaker oscillations and on the generation of early afterdepolarizations. The comparison of the statistical properties of long records showing arrhythmias with the predictions from theoretical models should help in the identification of different mechanisms underlying cardiac arrhythmias.