Uncertainty quantification of simulated biomechanical stimuli in coronary artery bypass grafts

Abstract

Coronary artery bypass graft surgery (CABG) is performed on more than 400,000 patients annually in the U.S. However, saphenous vein grafts (SVGs) implanted during CABG exhibit poor patency compared to arterial grafts, with failure rates up to 40% within 10 years after surgery. Differences in mechanical stimuli are known to play a role in driving maladaptation and have been correlated with endothelial damage and thrombus formation. As these quantities are difficult to measure in vivo, multi-scale coronary models offer a way to quantify them, while accounting for complex coronary physiology. However, prior studies have primarily focused on deterministic evaluations, without reporting variability in the model parameters due to uncertainty. This study aims to assess confidence in multi-scale predictions of wall shear stress and wall strain while accounting for uncertainty in peripheral hemodynamics and material properties. Boundary condition distributions are computed by assimilating uncertain clinical data, while spatial variations of vessel wall stiffness are obtained through approximation by a random field. We developed a stochastic submodeling approach to mitigate the computational burden of repeated multi-scale model evaluations to focus exclusively on the bypass grafts. This produces a two-level decomposition of quantities of interest into submodel contributions and full model/submodel discrepancies. We leverage these two levels in the context of forward uncertainty propagation using a previously proposed multi-resolution approach. The time-and space-averaged wall shear stress is well estimated with a coefficient of variation of <35%, but ignorance about the spatial distribution on the wall elastic modulus and thickness lead to large variations in an objective measure of wall strain, with coefficients of variation up to 100%. Sensitivity analysis reveals how the interactions between the flow and material parameters contribute to output variability.

The effects of clinically‐derived parametric data uncertainty in patient‐specific coronary simulations with deformable walls

“…and confirmed to reproduce physiologically admissible responses. 20 To minimize computational effort while still providing accurate coronary response, our study focuses on a left coronary sub-model, where appropriate boundary conditions are applied to match the simulation outcomes of the complete model (eg, a similar approach in 30 ). This reduces the total volume of the region of interest to approximately 1/15 of the full aorto-coronary model.…”

“…61 Similar approaches have been previously demonstrated in the literature. For example, a spectral decomposition is proposed in Brault et al 22 to model the random distribution of aortic stiffness in a one-dimensional cardiovascular model, while the Expansion Optimal Linear Estimation (EOLE) approach is used in Tran et al 30 to model the spatial distribution of material properties in a coronary bypass graft. In this study, we assume an exponential covariance function, K(t, t…”

“…The MW approach has been shown to perform better than MC, QMC, and SC in various benchmarks, and applied to coronary artery bypass graft modeling. 26,30 Many studies in the literature have focused on rigid wall models, due to the large computational cost of deformable wall models and the complexity of accounting for the interaction between fluid and structure. However, wall deformation is critical for capturing vascular wave propagation, and for characterizing mechanical forces acting on the vessel wall such as wall shear stress, which are crucial to mechanobiology.…”

“…32,34 The effect of material property uncertainty on onedimensional hemodynamics was considered in, [21][22][23] and Biehler et al 35,36 studied the effects of such uncertainties in the biomechanics of an aortic abdominal aneurysm using a multi-fidelity approach. To date, Tran et al 30 was among the first studies to consider material property uncertainty in a three-dimensional patient-specific model incorporating fluidstructure interaction. In this work, fluid-structure interaction was enabled using a lightweight shell formulation via the coupled-momentum method (CMM).…”

Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

“…By adopting a stochastic framework, model parameters are sampled from appropriate probability distributions which are either assumed, relying on existing literature and clinical data, or assimilated from available patient-specific data.Recently, UQ has gained traction in the field of cardiovascular modeling, primarily utilizing UQ techniques centered around a single model complexity, primarily three-dimensional computational fluid dynamics (CFD) simulations or lower complexity one-dimensional models. Recent studies have investigated the impact of geometry and boundary condition parameters on coronary fractional flow reserve [28], demonstrated a multi-resolution approach to quantify boundary condition uncertainties [29] and in conjugation with random fields [30] for coronary artery bypass grafts, and performed stochastic collocation in a one-dimensional arterial network [31], along with others [32][33][34][35][36][37][38][39].Several challenges arise when quantifying uncertainty in cardiovascular simulations. First, there are typically multiple sources of uncertainty to account for and propagate through the model.…”