Multiscale Patient-Specific Computational Fluid Dynamics to Assess Thoracic Aortic Hemodynamics

Thoracic aorta is the first portion of the main artery of the systemic circulation, i.e., the aorta, supplying oxygenated blood to main organs of our body. For this reason, it is evident that an impairment of its function can have dramatic impact on the overall circulation. Among the aortic diseases, arteriosclerotic (degenerative) disease represents the most common cause of thoracic aneurysms. A detailed comprehension of the local hemodynamic change and of the effects of vascular walls modification on the flow could be very useful in predicting the disease progression. The development of Computational Fluid Dynamics (CFD), also due to the increasing in the power of electronic computers and algorithms, has contributed to a significant improvement in vascular research. In this context, CFD simulations are less invasive than in vivo experiments and potentially more accurate and flexible than in vitro ones. CFD simulations can be performed by solving all the length scales of motion, i.e. Direct Numerical Simulation (DNS), or using alternative, but corroborated, approaches, like Reynolds Averaged Navier-Stokes (RANS) equations or Large-Eddy Simulation (LES). Due to the moderate/large Reynolds number and complex geometries, DNS could be significantly computationally expensive in aneurysmatic aortic simulations. Several studies demonstrated that LES models are promising candidates for hemodynamic problems, with high efficiency and accuracy. In three-dimensional (3D) CFD simulations the treatment of boundary conditions still represents a critical aspect. Recently, a widely used choice consists in the prescription of particular lumped parameter (or 0D) models, leading to the coupled 3D-0D models. These lumped parameter models allow to prescribe patient-specific boundary conditions, by tuning the parameter values according to the available measurements of patients. The enforcement of lumped parameters models as boundary conditions of 3D ones corresponds to the prescription of Neumann boundary conditions. However, it is known that Neumann boundary condition is more prone to numerical instabilities. In particular, Neumann outlet boundary conditions in presence of flow reversal at the outlets lead to the so called backflow instability. The goal of this work is to provide a set of tools and a clear workflow aiming at performing accurate and efficient CFD simulations with acceptable computational cost on both healthy and diseased patients. First, we derive, implement, and assess some particular lumped parameter models, useful for coupling to more sophisticated 3D models. Then, a patient-specific 3D-0D model is studied to investigate the impact of the transcatheter aortic root procedure on coronary perfusion. Moreover, a comparison between the coupled 3D-0D model and the full 0D model is addressed. Another prominent aim of this work consists in proving that a particular LES model, i.e. the Smagorinsky model, provides an accurate solution for patient-specific simulations, and controls the occurrence of backflow instability by a proper selection of the Smagorinsky coefficient. The application of CFD in other vascular regions is presented as well; we focus on a case study concerning the intra-stent thrombotic apposition that occurred in two patients undergoing endovascular treatment for popliteal arterial aneurysm.