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Abstract Numerical simulations for computational hemodynamics in clinical settings require a combination of many ingredients, mathematical models, solvers and patient-specific data. The sensitivity of the solutions to these factors may be critical, particularly when we have a partial or noisy knowledge of data. Uncertainty quantification is crucial to assess the reliability of the results. We present here an extensive sensitivity analysis in aortic flow simulations, to quantify the dependence of clinically relevant quantities to the patient-specific geometry and the inflow boundary conditions. Geometry and inflow conditions are generally believed to have a major impact on numerical simulations. We resort to a global sensitivity analysis, (i.e., not restricted to a linearization around a working point), based on polynomial chaos expansion (PCE) and the associated Sobol' indices. We regard the geometry and the inflow conditions as the realization of a parametric stochastic process. To construct a physically consistent stochastic process for the geometry, we use a set of longitudinal-in-time images of a patient with an abdominal aortic aneurysm (AAA) to parametrize geometrical variations. Aortic flow is highly disturbed during systole. This leads to high computational costs, even amplified in a sensitivity analysis -when many simulations are needed. To mitigate this, we consider here a large Eddy simulation (LES) model. Our model depends in particular on a user-defined parameter called filter radius. We borrowed the tools of the global sensitivity analysis to assess the sensitivity of the solution to this parameter too. The targeted quantities of interest (QoI) include: the total kinetic energy (TKE), the time-average wall shear stress (TAWSS), and the oscillatory shear index (OSI). The results show that these indexes are mostly sensitive to the geometry. Also, we find that the sensitivity may be different during different instants of the heartbeat and in different regions of the domain of interest. This analysis helps to assess the reliability of in silico tools for clinical applications. 

Kidney dialysis is the most widespread treatment method for end-stage renal disease, a debilitating health condition common in industrialized societies. While ubiquitous, kidney dialysis suffers from an inability to remove larger toxins, resulting in a gradual buildup of these toxins in dialysis patients, ultimately leading to further health complications. To improve dialysis, hollow fibers incorporating a cell-monolayer with cultured kidney cells have been proposed; however, the design of such a fiber is nontrivial. In particular, the effects of fluid wall-shear stress have an important influence on the ability of the cell layer to transport toxins. In the present work, we introduce a model for cell-transport aided dialysis, incorporating the effects of the shear stress. We analyze the model mathematically and establish its well-posedness. We then present a series of numerical results, which suggest that a hollow-fiber design with a wavy profile may increase the efficiency of the dialysis treatment. We investigate numerically the shape of the wavy channel to maximize the toxin clearance. These results demonstrate the potential for the use of computational models in the study and advancement of renal therapies.

 

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.