Multiscale Approaches for Heart Perfusion

Microcirculation and perfusion exemplify the mesoscale in physiological systems, bridging larger and smaller scale phenomena. Multiscale mathematical models represent a valuable tool to investigate and understand such phenomena, where a brute force computational approach is not viable yet. For microcirculation accurate models must comprise both interstitial and vascular compartments, along with their complex morphology. Transport phenomena across the vascular wall couple these two main compartments. In addition, several nonlinear effects are required to properly model microvascular flow.

We apply this framework to human cardiac perfusion, developing a model that 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.