Di Gregorio, S.; Fedele, M.; Pontone, G.; Corno, A.F.; Zunino, P.; Vergara, C.; Quarteroni, A.

MOX Report 48/2019

Open Access: https://mox.polimi.it/publication-results/?id=828&tipo=add_qmox


In this paper we present a multiscale 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. 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, and a suitable preconditioner for the multi-compartment porous sub-model. Finally, we test the computational framework in a realistic human heart, and we obtain results that fall in the physiological range for both pressures and local myocardial flows.