Noise-induced early afterdepolarizations in a three-dimensional cardiac action potential model

Abstract

Abstract We study the influence of noise on a mathematical model of the cardiac action potential described by a three-dimensional system of ordinary differential equations. The original deterministic system undergoes a cascade of period adding saddle-node bifurcations resulting in the appearance of small scale oscillations that correspond to early afterdepolarizations (EADs). We consider a parameter region where the deterministic system exhibits normal action potential behavior and show that a small additive noise in gating variable dynamics can induce EADs in this region. This stochastic phenomenon is confirmed by changes in the probability density distributions for phase trajectories and inter-event intervals. These qualitative changes in the system dynamics can be considered as a special stochastic P-bifurcation. The mechanism of noise-induced EADs is studied with a new semi-analytical approach based on the stochastic sensitivity function technique, the method of confidence domains and Mahalanobis metrics. Applying this approach, we give an explanation of the probabilistic mechanism of the observed stochastic phenomenon and provide the estimations of critical noise intensities for the onset of noise-induced EADs.