Individual Research Project 06

Uncertainty Quantifications, using Polynomial Chaos Expansion, of CFD predictions for aneurysm studies

Christos Karliampas – ESR 06

Since it is important to identify hemodynamic variables which are of greatest importance in aneurysm stabilization or rupture, ESR06 will focus on useful sensitivity studies, after developing the necessary tools, which could be useful as part of the Digital Twin too; all studies will expand the CFD tools prepared by ESR04 and ESR05. The uncertainty quantification (UQ) for any quantity of interest (QoI; asymmetry metric, saccular index, deformation diameter rate, tortuosity index, etc.) will be based on the non-intrusive Polynomial Chaos Expansion (PCE) method, using the CFD software as a black-box. UQ computes the statistical moments (mean values and standard deviations usually suffice) of the output of a (CFD) simulation, for uncertainties to the problem inputs/data. By assuming a PDF for each uncertainty, according to the PCE theory, the QoI is expressed as a linear combination of orthogonal polynomials. Polynomial (or PCE) coefficients are computed by running the CFD tool at a number of data-sets and, then, integrating. The sought statistical moments are given by closed-form expressions of the PCE coefficients. Using UQ techniques, ESR6 will study uncertainties related to various parameters (see Results). Using clinical images of changes in wall position during the cardiac cycle, a wall motion model will be built and used in the CFD/FSI simulation. The sensitivity of the CFD model/results to small changes will be investigated. CAD-free techniques will be used to control the shape and simultaneously generate shape imperfections; next to this, a morphing/smoothing tool adapts the CFD mesh to any new shape. These CAD-free techniques (RBFs and volumetric NURBS) will be of the same type as those being used by the previous ESR for accounting for moving vessel walls and the ensuing mesh adaptation.

Expected Results

• Uncertainty Quantification of the results of CFD aneurysm modelling, on GPUs – Interaction with the Digital Twin.

• Know-how on the sensitivity of these models to input/output flow data.

• Know-how on the sensitivity of these models to working fluid properties (varying hemodynamics).