A model of two nonlinear coupled oscillators for the study of heartbeat dynamics

The cardiac conduction system may be assumed to be a network of self-excitatory pacemakers, with the SinoAtrial (SA) node having the highest intrinsic rate. Subsidiary pacemakers with slower firing frequencies are located in the AtrioVentricular (AV) node and the His-Purkinje system. Under physiological conditions, the SA node is the dominant pace-maker and impulses travel from this node to the ventricle through the AV junction, which is traditionally regarded as a passive conduit. We consider the AV node as an active pace-maker and develop a model of two nonlinear coupled oscillators in order to describe the interaction between the SA and the AV node. These two nonlinear oscillators are based on a modification of the van der Pol oscillator, so that the generated waveforms resemble the action potentials of cells in the SA and the AV node respectively. A bifurcation analysis of this model is performed and the pathophysiological meaning of each bifurcation is explained. We show how it is possible to simulate and classify different kinds of heartbeat pathologies (1 degrees, 2 degrees (both Wenckebach and non-Wenckebach) and 3 degrees AV blocks, sinus arrest, atrial bigeminy, etc.). This simple nonlinear model helps to improve the understanding of the complex phenomena involved in heart rhythm generation as well as of heart rate control and function.