A computational model applied to myocardial perfusion in the human heart: From large coronaries to microvasculature

In this paper we present a mathematical and numerical model for human cardiac perfusion which accounts for the different length scales of the vessels in the coronary tree. Epicardial vessels are represented with fully three-dimensional (3D) fluid-dynamics, whereas intramural vessels are modeled as a multi-compartment porous medium. The coupling of these models takes place through interface conditions based on the continuity of mass and momentum. Instead, is neglected in this first preliminary model the myocardium deformation. To estimate the physical parameters of the multi-compartment model, a virtual intramural vascular network is generated using a novel algorithm which works in non-convex domains. Modeling epicardial vessels with a 3D model and intramural ones with a porous medium approach makes it possible to apply the proposed strategy to patient-specific heart geometries reconstructed from clinical imaging data. We also address the derivation of numerical solvers for the coupled problem. In particular, we propose a splitting algorithm for the monolithic problem, with the corresponding convergence analysis performed in a simplified linearized case, and a suitable preconditioner for the multi-compartment porous sub-model. Finally, we test the computational framework in a realistic human heart, obtaining results that fall in the physiological range for both pressures and local myocardial flows.