Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

Abstract

Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an efficient uncertainty quantification framework utilizing a multilevel multifidelity Monte Carlo (MLMF) estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. We derive two low-fidelity models (zero-and one-dimensional) that we use to obtain different estimators. Our goal is to investigate and compare the efficiency of estimators built from these two low-fidelity model alternatives and our high-fidelity three-dimensional models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. Our goal is to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to single fidelity Monte Carlo estimators and to a multilevel Monte Carlo approach based only on three-dimensional simulations, but leveraging multiple spatial resolutions. We demonstrate significant, on the order of 10 to 100 times, reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, global quantities such as outlet pressure and flow show larger reductions than local quantities, such as those relating to wall shear stress, as the latter rely more heavily on the highest fidelity model evaluations. Similarly, healthy models show larger reductions than diseased models. In all cases, our workflow coupling Dakota's MLMF estimators with the SimVascular cardiovascular workflow make uncertainty quantification feasible for constrained computational budgets. range of diseases and anatomies. Coronary artery disease is the most prevalent cause of death in the United States [4], and has thus been the subject of many modeling studies. These include computing fractional flow reserve for patients with coronary stenoses [5] and assessing differences in the hemodynamic and mechanical response of arterial and venous grafts towards determining cause of vein graft failure [6]. Computational models have also been applied to congenital heart disease for prognosis and treatment planning, from testing designs for surgical interventions of single ventricle congenital heart disease [7-9] to thrombotic risk assessment for Kawasaki disease [10][11][12], and assessment of disease progression and mechanical stimuli in pulmonary hypertension [13,14]. Hemodynamic studies are also used for additional disease cases, such as analyzing bloo...

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