# Mathematical modelling of myocardial perfusion: coronary flow and myocardial mechanics

Wang, Yingjie (2023) Mathematical modelling of myocardial perfusion: coronary flow and myocardial mechanics. PhD thesis, University of Glasgow.

Full text available as:

## Abstract

Coronary artery disease (CAD) is a condition characterised by the narrowing or blockage of the major blood vessels that supply blood to the heart muscle. This can cause insufficient myocardial perfusion to the heart and deficient cardiac outputs, leading to the possibility of heart failure. CAD is one of the leading causes of morbidity and mortality worldwide. Early and accurate diagnosis and treatment of CAD are essential to minimise the risk of complications, including heart attack or heart failure. In cardiovascular research, computational modelling of coronary circulation is proving to be a valuable tool for gaining insights and information. It enables researchers to isolate the effects of various physiological and pathological conditions on the coronary circulation. Thus, this thesis aimed to develop computational models of one dimensional (1D) coronary flow and three-dimensional (3D) heart. Both models included detailed geometric information tosimulate and predict physiologically realistic results. A one- way coupling of the coronary flow model and the heart model was achieved and produced physiologically accurate myocardial perfusion.

Specifically, we first investigated the effect of intramyocardial pressure (IMP) on coronary flow and developed a 1D finite difference coronary flow model. A coronary network based on experimental data was constructed to simulate coronary flow along the complete path of the coronary vasculature. Utilising an assumed aortic pressure, right atrial pressure, and IMP, our simulated coronary pressure and flow rates were in good agreement with published
experimental data. It was observed that the majority of the coronary arterial flow on the left side occurs during diastole, while the flow slows down or even reverses during systole. Secondly, we developed a 3D finite element model of the left ventricle (LV) to obtain a more
realistic IMP. The LV model was constructed from a patient-specific geometry. The simulated pressure and volume of the LV cavity in repeated cardiac cycles, as well as the ejection fraction, were all within published physiological ranges. We further analysed the stress distributions within the LV wall. Thirdly, a brief review of experimental IMP, as well as calculations of IMP from lumped parameter models and 3D heart models, were presented. Through analysis, we determined a formula for calculating IMP from our 3D LV model. Additionally, we proposed an assignment scheme of the epicardial coronary arteries to the 17 segments of the LV wall recommended by the American Heart Association. Based on the assignment, we devised the one-way coupling framework between the coronary flow model and the LV model to investigate myocardial perfusion.

We further developed a bi-ventricular model to investigate the effect of pulmonary regurgitation (PR) on cardiac function. The model provided a computational approach for exploring the influence of PR on right ventricle (RV) dilation and the interaction between
LV and RV. Our simulated RV end-diastolic volumes under varying degrees ofPR were comparable with published magnetic resonance imaging data. Moreover, from the long-axis and short-axis views of the bi-ventricular geometry, we observed clearly the motion of the interventricular septum from the baseline case to the severe PR case. This bi-ventricular model was intended to further couple with the coronary flow model to investigate the interaction of right coronary arterial flow and left coronary arterial flow. However, due to time constraints, this has not yet been undertaken.

The computational models of the coronary flow and heart developed in this thesis exhibit promising capabilities for providing physiologically accurate predictions of coronary flow and myocardial mechanics. Further application of these models has the potential to deepen our understanding of the underlying mechanisms in physiological coronary flow and various CAD.

Item Type: Thesis (PhD) Doctoral Supported by funding from China Scholarship Council (CSC). Q Science > QA MathematicsR Medicine > RC Internal medicineT Technology > T Technology (General) College of Science and Engineering > School of Mathematics and Statistics > Mathematics China Scholarship Council Luo, Professor Xiaoyu and Gao, Dr. Hao 2023 Theses Team glathesis:2023-83789 Copyright of this thesis is held by the author. 31 Aug 2023 10:52 10 Apr 2024 14:09 10.5525/gla.thesis.83789 https://theses.gla.ac.uk/id/eprint/83789