mathematics Article Impact of Arrhythmia on Myocardial Perfusion: A Computational Model-Based Study Xinyang Ge 1 , Sergey Simakov 2 , Youjun Liu 3 and Fuyou Liang 1,4, *   Citation: Ge, X.; Simakov, S.; Liu, Y.; Liang, F. Impact of Arrhythmia on Myocardial Perfusion: A Computational Model-Based Study. Mathematics 2021, 9, 2128. https:// doi.org/10.3390/math9172128 Academic Editor: Anatoliy Swishchuk Received: 6 August 2021 Accepted: 30 August 2021 Published: 2 September 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; gxy_sjtu_jiayou@sjtu.edu.cn 2 Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia; simakov.ss@mipt.ru 3 College of Life Science and Bioengineering, Beijing University of Technology, Beijing 100124, China; lyjlma@bjut.edu.cn 4 World-Class Research Center “Digital Biodesign and Personalized Healthcare”, Sechenov First Moscow State Medical University, 19991 Moscow, Russia * Correspondence: fuyouliang@sjtu.edu.cn; Tel.: +86-213-420-5120 Abstract: (1) Background: Arrhythmia, which is an umbrella term for various types of abnormal rhythms of heartbeat, has a high prevalence in both the general population and patients with coronary artery disease. So far, it remains unclear how different types of arrhythmia would affect myocardial perfusion and the risk/severity of myocardial ischemia. (2) Methods: A computational model of the coronary circulation coupled to the global cardiovascular system was employed to quantify the impacts of arrhythmia and its combination with coronary artery disease on myocardial perfusion. Furthermore, a myocardial supply–demand balance index (MSDBx) was proposed to quantitatively evaluate the severity of myocardial ischemia under various arrhythmic conditions. (3) Results: Tachycardia and severe irregularity of heart rates (HRs) depressed myocardial perfusion and increased the risk of subendocardial ischemia (evaluated by MSDBx), whereas lowering HR improved myocardial perfusion. The presence of a moderate to severe coronary artery stenosis considerably augmented the sensitivity of MSDBx to arrhythmia. Further data analyses revealed that arrhythmia induced myocardial ischemia mainly via reducing the amount of coronary artery blood flow in each individual cardiac cycle rather than increasing the metabolic demand of the myocardium (measured by the left ventricular pressure-volume area). (4) Conclusions: Both tachycardia and irregular heartbeat tend to increase the risk of myocardial ischemia, especially in the subendocardium, and the effects can be further enhanced by concomitant existence of coronary artery disease. In contrast, properly lowering HR using drugs like β-blockers may improve myocardial perfusion, thereby preventing or relieving myocardial ischemia in patients with coronary artery disease. Keywords: arrhythmia; myocardial perfusion; coronary artery disease; computational model 1. Introduction Arrhythmia is a common cardiovascular disease featured by abnormally low/high or irregular heartbeat. The prevalence of arrhythmia is high, especially in patients with basic cardiovascular disease [1–3]. Arrhythmia may cause various symptoms, such as palpitations, dyspnea, heart failure, and confusion, or even lead to sudden death [4–6]. Clinical studies have demonstrated that a physiologically low heart rate is associated with lower cardiovascular mortality [7–9], and that in patients with stable ischemic heart disease and left ventricular systolic dysfunction, reducing heart rate helps to improve prognosis [8]. On the other hand, tachycardia has been found to be an independent risk factor for poor outcome after coronary revascularization [9]. A theoretical study has demonstrated that reducing heart rate is beneficial to the distribution of blood toward the subendocardium, which is more susceptible than the subepicardium to ischemia in the presence of coronary artery disease [10]; this may partly explain the aforementioned clinical findings. However, Mathematics 2021, 9, 2128. https://doi.org/10.3390/math9172128 https://www.mdpi.com/journal/mathematics