Effects of Uncertainty of Outlet Boundary Conditions in a Patient-Specific Case of Aortic Coarctation

Abstract

Computational Fluid Dynamics (CFD) simulations of blood flow are widely used to compute a variety of hemodynamic indicators such as velocity, time-varying wall shear stress, pressure drop, and energy losses. One of the major advances of this approach is that it is non-invasive. The accuracy of the cardiovascular simulations depends directly on the level of certainty on input parameters due to the modelling assumptions or computational settings. Physiologically suitable boundary conditions at the inlet and outlet of the computational domain are needed to perform a patient-specific CFD analysis. These conditions are often affected by uncertainties, whose impact can be quantified through a stochastic approach. A methodology based on a full propagation of the uncertainty from clinical data to model results is proposed here. It was possible to estimate the confidence associated with model predictions, differently than by deterministic simulations. We evaluated the effect of using three-element Windkessel models as the outflow boundary conditions of a patient-specific aortic coarctation model. A parameter was introduced to calibrate the resistances of the Windkessel model at the outlets. The generalized Polynomial Chaos method was adopted to perform the stochastic analysis, starting from a few deterministic simulations. Our results show that the uncertainty of the input parameter gave a remarkable variability on the volume flow rate waveform at the systolic peak simulating the conditions before the treatment. The same uncertain parameter had a slighter effect on other quantities of interest, such as the pressure gradient. Furthermore, the results highlight that the fine-tuning of Windkessel resistances is not necessary to simulate the post-stenting scenario.