On the heart rhythm analysis using a nonlinear dynamics perspective: analytical study and electronic simulation

Abstract

Biological systems are highly complex, so understanding them requires extensive analysis. Cardiac rhythms are one such analysis. These rhythms are linked to a complex dynamic system defined on the basis of the electrical activity of cardiac cells. This electrical activity is essential to human physiology, defining numerous behaviours that include normal or pathological rhythms, generally measured by the electrocardiogram (ECG). This article presents a mathematical model to describe the electrical activity of the heart, using a nonlinear dynamics perspective. The stability analysis of this model in its autonomous state, uni-directionally coupled, shows a very rich dynamical behaviour characterized by periodical regions of stability and unstability. The model studied makes it possible to construct synthetic ECGs. These ECGs demonstrate a variety of responses, including normal and pathological rhythms: ventricular flutter, ventricular fibrillation, ventricular tachycardia and ventricular extrasystole. A quantitative analysis of the model is also carried out using bifurcation diagrams and the corresponding maximum Lyapunov exponents. In addition, variations in sinus rhythm are described by a time-dependent frequency (a dynamic variable varying in a disordered manner or following a given law), representing transient disturbances. This type of situation can represent transitions between different pathological behaviours or between normal and pathological physiologies. In this respect, the perspective of nonlinear dynamics is used to describe cardiac rhythms, which makes it possible to represent normal or pathological behaviours. An electronic simulation performed with the OrCAD-Pspice software for a real implementation of the cardiac system is carried out. The results obtained are in agreement with those obtained numerically.