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

Abstract

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.

4-D Flow MRI-Based Computational Analysis of Blood Flow in Patient-Specific Aortic Dissection

“…Mesh sensitivity tests were performed, and the differences in mean and maximum WSS between the chosen mesh and a finer one were less than 1.5% and 3%, respectively. The size of the final adopted mesh was consistent with similar studies of TBAD in the literature [10,23].…”

“…These BCs have recently been replaced by physiologically more realistic 3element Windkessel models (3-EWM) [3, 4, 9, 22] which account for the behavior of the distal vascular bed at each outlet. Since Windkessel models do not directly impose flow rate at the specified boundary, they are particularly suited for use with phase-contrast MRI (PC-MRI) data when the conservation of mass is not satisfied due to either wall compliance or image noise [23]. However, parameter estimation for 3-EWM remains an issue, owing to the lack of complete patient-specific pressure and flow data.…”

“…However, parameter estimation for 3-EWM remains an issue, owing to the lack of complete patient-specific pressure and flow data. This has been addressed in several recent papers [9,19,22,23], particularly Romarowski et al [23] proposed a new least-square approach to calibrate the 3-EWM parameters for hemodynamic studies of the aorta.…”

Computational prediction of hemodynamical and biomechanical alterations induced by aneurysm dilatation in patient‐specific ascending thoracic aortas

“…In order to use it in clinical practice these methods need to be validated. Combining 4D MRI and CFD represents an efficient method to predict the hemodynamical factors of ATAAs . Parameters such as WSS, oscillatory shear index (OSI), relative residence time (RRT), and viscosity may be useful to predict the state of cardiovascular diseases in individual patients.…”

Patient-specific haemodynamic simulations of complex aortic dissections informed by commonly available clinical datasets

“…However, the calibration of the Windkessel models is not an easy exercise, and different strategies are proposed in the literature. Some strategies adopt only haemodynamic data taken from the literature [8], others make use of patient-specific flow waves integrated with literaturebased pressure waves [7], while more advanced approaches use sophisticated techniques such as Kalman filters to assimilate boundary flow waves acquired with PC-MRI [9].…”