Integrating Uncertainty Quantification into Computational Fluid Dynamics Models of Coronary Arteries Under Steady Flow

Computational models are continuously integrated in the clinical space, where they support clinicians in disease diagnosis, prognosis, and prevention strategies. While assisting in clinical space, these computational models frequently use deterministic approaches, where the inherent (aleatoric) variability of input parameters is ignored. This questions the credibility and often hinders the clinical adoption of these computational models. Therefore, in this study, we introduced uncertainty quantification in the computational fluid dynamics models of the left main coronary artery to analyze the influence of input hemodynamics parameters on wall shear stress (WSS). UncertainSCI was used, where an emulator was built using polynomial chaos expansion between the input parameters and the output quantity of interest, and the output sensitivities and statistics were directly extracted from the emulator. The uncertainty-informed framework was first applied to an analytical solution of the Navier-Stokes equation (Poiseuille flow) and then to a patient-specific model of the left main coronary artery. Different input hemodynamics parameters are considered, such as pressure, viscosity, density, velocity, and radius, whereas wall shear stress was considered as our output quantity of interest. The results suggest that velocity dominated the variability in WSS in the analytical model (~79%), whereas viscosity dominated in the patient-specific model (~59%). The results further suggest that out of all the Sobol indices interactions, unary interactions were the most dominant ones, contributing ~93.2% and ~99% for the analytical and patient-specific model, respectively. This study will enhance confidence in computational models, facilitating their adoption in the clinical space to improve decision-making for coronary artery disease diagnosis, prognosis, and therapeutic strategies.

💡 Research Summary

This paper presents a comprehensive framework for integrating Uncertainty Quantification (UQ) into Computational Fluid Dynamics (CFD) models of coronary arteries, specifically targeting the left main coronary artery under steady flow conditions. The primary motivation is to address a critical shortcoming in current clinical CFD applications: the widespread use of deterministic models that ignore inherent variability in input parameters, which undermines model credibility and hinders clinical adoption.

The study employs a non-intrusive UQ approach using the UncertainSCI software suite. The core methodology involves constructing an emulator via Polynomial Chaos Expansion (PCE) that maps variable input hemodynamic parameters—including viscosity, velocity, radius, density, and pressure—to the output Quantity of Interest (QoI), which is Wall Shear Stress (WSS). This emulator acts as a surrogate model, enabling efficient statistical analysis and global sensitivity analysis without requiring thousands of computationally expensive full-order CFD simulations. The framework is rigorously tested on two models: first, an analytical solution for Poiseuille flow in a rigid cylinder (serving as a verification case), and second, a patient-specific 3D finite element model of a left main coronary artery reconstructed from intravascular ultrasound and angiography data, simulated using the FEBio solver.

Key findings reveal significant differences in uncertainty propagation between the simplified and complex models. In the analytical Poiseuille model, uncertainty in inlet velocity dominated the variance in WSS, contributing approximately 79%. In stark contrast, for the patient-specific coronary model, uncertainty in blood viscosity was the dominant source, accounting for about 59% of the WSS variance. This shift highlights how geometric complexity and boundary conditions in realistic anatomies alter sensitivity profiles, underscoring the necessity of performing UQ directly on patient-specific models rather than relying on insights from simplified analogs. Furthermore, global sensitivity analysis via Sobol indices indicated that unary (first-order) effects were overwhelmingly dominant, explaining over 93% and 99% of the total variance in the analytical and patient-specific models, respectively. This suggests that higher-order interactions between parameters are minimal for this specific hemodynamic system under the considered conditions.

The study also demonstrates the computational efficiency of the PCE-based UQ approach. Convergence for the patient-specific model was achieved with only 45 high-fidelity CFD runs (for polynomial order 3), from which the constructed emulator could instantly predict outputs for any parameter combination within the defined ranges. This represents a substantial efficiency gain over traditional Monte Carlo methods.

In conclusion, the research successfully establishes an efficient and practical UQ pipeline for coronary artery CFD models. By quantifying the impact of input variability on clinically relevant outputs like WSS, this framework enhances the reliability and interpretability of simulation results. It provides clinicians with crucial information about the confidence bounds of model predictions, thereby facilitating more informed decision-making in the diagnosis, prognosis, and treatment planning of coronary artery disease and accelerating the translation of computational modeling into routine clinical practice.