Stochastic Models of the Slow/Fast Type of Atrioventricular Nodal Reentrant Tachycardia and Tachycardia with Conduction Aberration

Abstract

Models are proposed to describe the heart’s action potential. A system of stochastic differential equations is used to recreate pathological behaviour in the heart such as atrioventricular nodal reentrant tachycardia (AVNRT) and also AVNRT with conduction aberration. Part of the population has abnormal accessory pathways: fast and slow. An additional pathway is not always induced, since the deterministic model is not proper due to a stochasticity in this process. Introduction of a stochastic term allows modelling a pre-excitation perturbation (such as unexpected excitation by premature contractions in atrium (PAC)) which triggers the mechanism of AVNRT. Also, a system of AVNRT with additional conduction aberration, which is a rare type of arrhythmia, is considered. The aim of this work is to propose a mathematical model superior to the deterministic one that recreates this disease better and allows understanding its mechanism and physical dependencies, which may help to propose a new therapy of AVNRT. Results are illustrated with numerical solutions.

Keywords

• mathematical model
• stochastic differential equations
• action potential
• atrioventricular nodal reentrant tachycardia
• conduction aberration