Geometric Uncertainty of Patient-Specific Blood Vessels and its Impact on Aortic Hemodynamics

TL;DR

This study develops a stochastic modeling approach to quantify how local geometric uncertainties in patient-specific blood vessels affect aortic blood flow simulations, revealing moderate perturbations cause manageable errors in key hemodynamic measures.

Contribution

It introduces a methodology to systematically model local geometric uncertainties in patient-specific aortas and assesses their impact through extensive blood flow simulations.

Findings

Moderate geometric perturbations lead to single-digit percentage errors in flow quantities.

Flow measures are more sensitive to boundary perturbations than to interior mesh variations.

The methodology enables statistically relevant analysis of uncertainty impacts in vascular simulations.

Abstract

In the context of numerical simulations of the vascular system, local geometric uncertainties have not yet been examined in sufficient detail due to model complexity and the associated large numerical effort. Such uncertainties are related to geometric modeling errors resulting from computed tomography imaging, segmentation and meshing. This work presents a methodology to systematically induce local modifications and perform a sufficient number of blood flow simulations to draw statistically relevant conclusions on the most commonly employed quantities of interest, such as flow rates or wall shear stress. The surface of a structured hexahedral mesh of a patient-specific aorta is perturbed by displacement maps defined via Gaussian random fields to stochastically model the local uncertainty of the boundary. Three different cases are studied, with the mean perturbation magnitude of $0.25$, $0.5$ and $1.0~$mm. Valid, locally perturbed meshes are constructed via an elasticity operator that extends surface perturbations into the interior. Otherwise, identical incompressible flow problems are solved on these meshes, taking physiological boundary conditions and Carreau fluid parameters into account. Roughly $300\,000$ three-dimensional non-stationary blood flow simulations are performed for the three different perturbation cases to estimate the probability distributions of the quantities of interest. Convergence studies justify the spatial resolution of the employed meshes. Overall, the results suggest that moderate geometric perturbations result in reasonable engineering accuracy (relative errors in single-digit percentage range) of the quantities of interest, with higher sensitivity for gradient-related measures, noting that the observed errors are not negligible.