Patient-specific cardiovascular models contain multiple sources of uncertainty which make deterministic simulations meaningless, motivating a transition to a stochastic framework that allows analysts to quantify uncertainty in simulation outputs. Despite many advancements in the computational tools to analyze numerical models subject to uncertain inputs, standard approaches are challenged by the large number of random inputs and high computational cost of realistic three-dimensional simulations. Multilevel multi-fidelity (MLMF) estimators were previously shown to effectively reduce the variability in model output expectations with a computational cost that is several orders of magnitude less expensive than traditional methods [1]. To achieve these improvements, we offload the computational cost to the solution of computationally inexpensive low-fidelity models. However, the MLMF framework relies on strong correlations between the model fidelities, as well as an identical parameterization of the random inputs. By leveraging the concept of active subspaces [2], we are able to improve accuracy for outputs such as wall shear stress which are captured only approximately in low fidelity models. Further, active subspaces allows us to construct multi-fidelity estimators between high- and low-fidelity models characterized by a dissimilar parameterizations. In this way, we can explore the uncertainties in three-dimensional parameters which are not present in our low-fidelity one- or zero-dimensional (lumped parameter) models. By combining active subspace sampling with UQ algorithms implemented in the Sandia National Laboratory‚Äôs DAKOTA toolkit, we can further reduce the variance in multilevel and multifidelity UQ approaches. Active subspaces have been shown to improve convergence in conjunction with multifidelity methods for patient-specific geometries of pulmonary and coronary arteries compared to their natural parameterization.

[1] Fleeter, C.M., Geraci, G., Schiavazzi, D.E., Kahn, A.M., and Marsden, A.L. Multilevel and multi-fidelity uncertainty quantification for cardiovascular hemodynamics. Comput Methods Appl Mech Eng, (2020)
[2] Geraci,G. and Eldred,M.S. Leveraging Intrinsic Principal Directions for Multifidelity Uncertainty
 Quantification. Sandia Report SAND2018-10817, (2018)

EMPLOYING ACTIVE SUBSPACES FOR CARDIOVASCULAR UNCERTAINTY QUANTIFICATION IN SIMILAR AND DISSIMILAR MODELS

The Virtual Technical Meeting of the Society of Engineering Science 2020 is the first fully virtual meeting of the SES community to envision and connect during the hiatus created by Covid-19, providing a platform for the exchange of ideas, and to showcase the latest research in the field of engineering science.

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