Simulation of heartbeat dynamics: A nonlinear model

The mathematical modeling of biological systems has proven to be a valuable tool by allowing experiments which would otherwise be unfeasible in a real situation. In this work we propose a system of nonlinear differential equations describing the macroscopic behavior of the cardiac conduction system. The model describes the interaction between the SinoAtrial and AtrioVentricular node. Its very simple structure consists of two nonlinear oscillators resistively coupled. The numerical analysis detects different kinds of bifurcations whose pathophysiological meanings are discussed. Moreover, the model is able to classify different pathologies, such as several classes of arrhythmic events, as well as to suggest hypothesis on the mechanisms that induce them. These results also show that the mechanisms generating the heartbeat obey complex laws. The model provides a quite complete description of different pathological phenomena and its simplicity can be exploited for further studies on the control of cardiac dynamics.