Numerical simulation of aortic coarctations of different grades of severity: Flow features and importance of outlet boundary conditions

Numerical simulations of the blood flow inside a patient-specific thoracic aorta in presence of coarctation are considered. Different grades of severity of the coarctation are obtained by constructing parametric geometries in which the coarctation section is circular with varying diameter values. The impact of a fine-tuning of the Windkessel model resistances, at each outlet, is also investigated. A stochastic approach based on the generalized Polynomial Chaos (gPC) is used to carry out a systematic analysis. It allows obtaining continuous response surfaces of the quantities of interest in the parameter space from a limited number of simulations. Two parameters are selected: the vessel diameter, $D$, at the coarctation plane and a non-dimensional parameter, $\alpha$, through which it is possible to calibrate the resistance offered by organs and vessels downstream the thoracic aorta. The value of the coarctation diameter has the strongest impact on all the flow features, i.e., flow rate, pressure, velocity, and wall shear stresses. It is also shown that, as the value of $D$ increases, the dependence on $\alpha$ decreases. This means that the more the geometry of the thoracic aorta approaches a healthy shape, the less significant it is to perform a fine-tuning of the Windkessel model resistances to match the patient-specific pressure waveform, whereas it should be done in cases of severe coarctations.