# Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

## TL;DR

This paper introduces a multilevel multifidelity Monte Carlo framework that significantly reduces computational costs in uncertainty quantification for cardiovascular hemodynamics by leveraging models of varying fidelities.

## Contribution

It develops and demonstrates a novel MLMF approach combining multiple model fidelities to efficiently quantify uncertainty in cardiovascular simulations.

## Key findings

- MLMF estimators outperform traditional Monte Carlo methods in cost efficiency.
- Significant cost reduction achieved in uncertainty quantification for cardiovascular models.
- Global quantities benefit more from MLMF than local quantities, especially in healthy models.

## 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 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 employ two low-fidelity models to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these low-fidelity and high-fidelity models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. We seek 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 Monte Carlo and multilevel Monte Carlo estimators based only on three-dimensional simulations. We demonstrate significant 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 and healthy models show larger reductions than local quantities and diseased model, as the latter rely more heavily on the highest fidelity model evaluations. In all cases, our workflow coupling Dakota's MLMF estimators with the SimVascular cardiovascular modeling framework makes uncertainty quantification feasible for constrained computational budgets.