Multifidelity methods for uncertainty quantification in cardiovascular hemodynamics

Computational models of the cardiovascular system are increasingly adopted due to the hemodynamic insights they provide, which can be beneficial in diagnosis, assessment of disease progression risk, and treatment planning for cardiovascular disease. Unfortunately, all models of the cardiovascular system, as well as biological and biomedical systems more generally, are intrinsically affected by model and data uncertainty. Therefore, relying on a solely deterministic framework lacking statistical distributions or confidence intervals hinders their application to a clinical setting. Standard approaches for uncertainty quantification pose challenges due to the large number of uncertain inputs, large number of function evaluations required, and the significant computational cost of realistic three-dimensional cardiovascular simulations. In this dissertation, I will discuss multifidelity approaches to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. The first portion of this dissertation will focus on the development and implementation of an efficient uncertainty quantification framework utilizing multilevel multifidelity Monte Carlo (MLMF) estimators. This is achieved by leveraging three cardiovascular model fidelities to investigate and compare the efficiency of estimators built from combinations of low-fidelity model alternatives and our high-fidelity three-dimensional models. I demonstrate significant reduction in total computational cost with the MLMF estimators as compared to other Monte Carlo-based estimators. Additionally, my approach coupling Sandia National Laboratories' Dakota software with my research group's SimVascular cardiovascular modeling framework makes uncertainty quantification automated and feasible for constrained computational budgets. The second portion of the dissertation aims to combine ideas from active subspace research with multifidelity uncertainty quantification approaches. By sampling a shared active subspace between the high and low fidelity models, I demonstrate enhanced correlations between the fidelities, which in turn improves our uncertainty quantification. As the estimators rely on correlations between the models to converge the estimator, increasing correlations results in convergence at a lower computational cost, both due to shifting simulation burden tot the inexpensive low-fidelity models and necessitating a smaller number of total simulations. Additionally, active subspaces allow for the inclusion of low fidelity models with dissimilar parameterizations to their corresponding high fidelity model, expanding our options for model fidelities and use of data libraries. The dissertation concludes with discussion of the broader application of my uncertainty quantification approaches. We demonstrate success of the estimators in coronary anatomy models of interest, with uncertainties assimilated from clinical data. The integration of uncertainty quantification with geometric uncertainties extracted from our automated machine learning framework for model generation demonstrates the impact of model construction to our overall confidence in modeling results. Finally, future directions are proposed, such as work utilizing low fidelity models to explore uncertain treatment outcomes in balloon angioplasty for Peripheral Pulmonary Artery Stenosis (PPAS) patients

Advisor: Marsden Alison (Alison Leslie)
Gorle Catherine
Schiavazzi Daniele