Patient‐specific CFD modelling in the thoracic aorta with PC‐MRI–based boundary conditions: A least‐square three‐element Windkessel approach

The increasing use of computational fluid dynamics for simulating blood flow in clinics demands the identification of appropriate patient‐specific boundary conditions for the customization of the mathematical models. These conditions should ideally be retrieved from measurements. However, finite resolution of devices as well as other practical/ethical reasons prevent the construction of complete data sets necessary to make the mathematical problems well posed. Available data need to be completed by modelling assumptions, whose impact on the final solution has to be carefully addressed. Focusing on aortic vascular districts and related pathologies, we present here a method for efficiently and robustly prescribing phase contrast MRI–based patient‐specific data as boundary conditions at the domain of interest. In particular, for the outlets, the basic idea is to obtain pressure conditions from an appropriate elaboration of available flow rates on the basis of a 3D/0D dimensionally heterogeneous modelling. The key point is that the parameters are obtained by a constrained optimization procedure. The rationale is that pressure conditions have a reduced impact on the numerical solution compared with velocity conditions, yielding a simulation framework less exposed to noise and inconsistency of the data, as well as to the arbitrariness of the underlying modelling assumptions. Numerical results confirm the reliability of the approach in comparison with other patient‐specific approaches adopted in the literature. Computational fluid dynamics simulations within the thoracic aorta need an accurate prescription of boundary conditions in patient‐specific analyses. Measurements in clinics are not always available, and modelling assumptions are to be made when using big data sets. Here we propose a constrained optimization procedure to calibrate a three‐element Windkessel lumped model in a cohort of patients. We focus on how to incorporate missing data and show that our method performs better than other options present in literature.