Multi-scale modeling of blood flows in large scale coronary arteries

The study of blood dynamics requires the inclusion of several levels of description, ranging from the nanoscopic level in proximity of the endothelium to fully resolved flow patterns in large scale circulatory system. All these levels play simultaneous and crucial roles in the context of plaque formation and atherosclerosis. In fact, the non-Newtonian nature of blood, the corpuscular nature of blood and the effects of micro-rheology close to the vessel walls play significant roles in the uptake of lipidic material by the endothelium. In our work we focus on the multi-scale modeling of blood mechanics and endothelial structure in order to gain substantial understanding on the plaque formation process. In order to attain this goal, we have devised a computational strategy to simultaneously include three physical components, the glylcocalyx, the red blood cells and the blood plasma. Our modeling of the glycocalyx reproduces the ordered layer of fibers that covers the endothelium. In this way, the porous medium and its intrinsic flexibility are reproduced at high accuracy. Red blood cells are modelled as suspended bodies that have the capacity to sustain solid-like tumbling as much as tank-treading motion. This dual behavior allows for the subtle interplay of hydrodynamic forces that induce lateral migration, with the ensuing Fahraeus-Lindqvist and skimming effects. Finally, our handling of the plasma is done via the Lattice Boltzmann method, a numerical approach that presents numerical advantages in including suspended bodies and overall stability of the multi-scale methodology. Our computational framework has the merit of being particularly light-weight, allowing to simulate large scale arterial systems (~ 1 billion voxels) by using commodity hardware. In this respect, we make large use of parallel graphical processing units (GPU) to study coronary systems with computational resources performing at 10-100 TFlops. We have next undertaken a systematic study of extended coronary arteries, with clinical data collected with 320-rows CT angiography for the detailed reconstruction of multi-branched coronary systems. It is well-known that plaque formation is highly correlated to regions of low endothelial shear stress, often localized in correspondence of bifurcations and in presence of strong centrifugal effects. We have applied both single-scale and multi-scale simulations to identify the hot spots of the circulatory system. Our simulations show the role of the corpuscular nature of red blood cells in altering the shear pattern and reveal the rich phenomenology induced by the multi-level description of blood