Cardiac perfusion coupled with a structured coronary network tree

Sufficient myocardial perfusion plays a pivotal role in maintaining normal pump function. However the development of a comprehensive myocardial perfusion model remains particularly challenging as it requires the incorporation of complex interactions across different spatial scales and physical domains. In this study, we couple a coronary blood flow model to our previous work on a poroelastic immersed finite element framework for myocardial perfusion in a left ventricle (LV) heart. The coronary flow in the epicardial vessels is described by a 1-D flow model, and the intramural vessels are modelled as a structural tree-based vascular bed. The intramyocardial pressure resulting from myocardial contraction is further imposed on the coronary vessel wall. We first benchmark this coupled myocardial perfusion and coronary flow in a healthy heart. The systolic impediment phenomenon of the coronary flow can be reproduced with this coupled model, and the wall volume change is around 13 mL, which is consistent with literature-reported values. We further study cardiac perfusion under coronary network rarefaction, arterial wall stiffening and ventricular wall stiffening. Our results suggest that both vessel rarefaction and a stiffer arterial wall can directly impede flow through the coronaries leading to perfusion deficiency, and LV wall stiffening will impair heart pump function significantly but with a minor drop in coronary flow rate. It is expected that such a coupled myocardial perfusion and coronary flow model will have the potential to deepen our understanding of myocardial dysfunction due to perfusion deficiency.