A simple model of the right atrium of the human heart with the sinoatrial and atrioventricular nodes included

Abstract

Existing atrial models with detailed anatomical structure and multi-variable cardiac transmembrane current models are too complex to allow to combine an investigation of long time dycal properties of the heart rhythm with the ability to effectively simulate cardiac electrical activity during arrhythmia. Other ways of modeling need to be investigated. Moreover, many state-of-the-art models of the right atrium do not include an atrioventricular node (AVN) and only rarely—the sinoatrial node (SAN). A model of the heart tissue within the right atrium including the SAN and AVN nodes was developed. Looking for a minimal model, currently we are testing our approach on chosen well-known arrhythmias, which were until now obtained only using much more complicated models, or were only observed in a clinical setting. Ultimately, the goal is to obtain a model able to generate sequences of RR intervals specific for the arrhythmias involving the AV junction as well as for other phenomena occurring within the atrium. The model should be fast enough to allow the study of heart rate variability and arrhythmias at a time scale of thousands of heart beats in real-time. In the model of the right atrium proposed here, different kinds of cardiac tissues are described by sets of different equations, with most of them belonging to the class of Liénard nonlinear dynamical systems. We have developed a series of models of the right atrium with differing anatomical simplifications, in the form of a 2D mapping of the atrium or of an idealized cylindrical geometry, including only those anatomical details required to reproduce a given physiological phenomenon. The simulations allowed to reconstruct the phase relations between the sinus rhythm and the location and properties of a parasystolic source together with the effect of this source on the resultant heart rhythm. We model the action potential conduction time alternans through the atrioventricular AVN junction observed in cardiac tissue in electrophysiological studies during the ventricular-triggered atrial tachycardia. A simulation of the atrio-ventricular nodal reentry tachycardia was performed together with an entrainment procedure in which the arrhythmia circuit was located by measuring the post-pacing interval (PPI) at simulated mapping catheters. The generation and interpretation of RR times series is the ultimate goal of our research. However, to reach that goal we need first to (1) somehow verify the validity of the model of the atrium with the nodes included and (2) include in the model the effect of the sympathetic and vagal ANS. The current paper serves as a partial solution of the 1). In particular we show, that measuring the PPI–TCL entrainment response in proximal (possibly-the slow-conducting pathway), the distal and at a mid-distance from CS could help in rapid distinction of AVNRT from other atrial tachycardias. Our simulations support the hypothesis that the alternans of the conduction time between the atria and the ventricles in the AV orthodromic reciprocating tachycardia can occur within a single pathway. In the atrial parasystole simulation, we found a mathematical condition which allows for a rough estimation of the location of the parasystolic source within the atrium, both for simplified (planar) and the cylindrical geometry of the atrium. The planar and the cylindrical geometry yielded practically the same results of simulations.