Modeling of Heartbeat Dynamics with a System of Coupled Nonlinear Oscillators

Abstract

We model electrical activity of cardiac electric system including atrial and ventricular muscles solving a set of coupled nonlinear oscillator equations. In the proposed mathematical model the heart pacemakers are considered as a network of self-excitatory elements represented by strongly asymmetric van der Pol-type oscillators, whereas cardiac muscles are modeled by driven non-oscillatory FitzHugh-Nagumo-type equations. The oscillators of the system are connected with unidirectional time delay couplings. The resulting total response of the system is obtained as a composition of calculated signals in the form of synthetic electrocardiogram. The proposed model allows to reproduce several well-known electrocardiological phenomena, such as tachycardia, complete heart block, atrial flutter, and ventricular fibrillation. © Springer-Verlag Berlin Heidelberg 2014.