An effective mathematical model of cardiac electrical activities for Bundle Branch Blocks

Abstract

In this paper a mathematical model of cardiac induction system is developed. Sinoatrial node (SA), atrioventricular node (AV) and His Purkinje system (HP) are represented by modified Van der Pol-type oscillators (VDP) connected with time-delay coupling. Atrial and ventricular muscles are modeled using modified Aliev-Panfilov equations (AP), with stimulation current from the related pacemakers, to represent the P, QRS, Ta, and T waves. The main aim of this paper is to model bundle branch blocks (BBBs) for right (RBBB) and left (LBBB) branches. In fact, the right and left ventricles are directly affected by these blocks since the HP bundle is composed of right and left bundle branches that provide electrical signals, respectively, to the right and left ventricles. Four VDP oscillators are utilized, one for each of SA, AV, right HP, and left HP. The depolarization of the right and left ventricular muscles are represented by two systems of AP equations to produce right QRS and left QRS waves. The results of the simulation are compared with real normal and pathological electrocardiograms (ECGs) to show the effectiveness and the accuracy of the proposed model. The simulation proves that the model can reproduce the blocks in the HP bundle branches.