<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Models are proposed to describe the heart’s action potential. A system of stochastic differential equations is used to recreate pathological behaviour in the...

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

Published Online: Oct 08, 2022

Page range: 429 - 440

Received: Sep 29, 2021

Accepted: May 30, 2022

DOI: https://doi.org/10.34768/amcs-2022-0031

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

© 2022 Beata Jackowska-Zduniak, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Oct 08, 2022

Page range: 429 - 440

Received: Sep 29, 2021

Accepted: May 30, 2022

DOI: https://doi.org/10.34768/amcs-2022-0031

Keywordsmathematical model, stochastic differential equations, action potential, atrioventricular nodal reentrant tachycardia, conduction aberration

© 2022 Beata Jackowska-Zduniak, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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