Personalized and uncertainty-aware coronary hemodynamics simulations: From Bayesian estimation to improved multi-fidelity uncertainty quantification

Abstract

Background: Non-invasive simulations of coronary hemodynamics have improved clinical risk stratification and treatment outcomes for coronary artery disease, compared to relying on anatomical imaging alone. However, simulations typically use empirical approaches to distribute total coronary flow amongst the arteries in the coronary tree, which ignores patient variability, the presence of disease, and other clinical factors. Further, uncertainty in the clinical data often remains unaccounted for in the modeling pipeline.

Objective: We present an end-to-end uncertainty-aware pipeline to (1) personalize coronary flow simulations by incorporating vessel-specific coronary flows as well as cardiac function; and (2) predict clinical and biomechanical quantities of interest with improved precision, while accounting for uncertainty in the clinical data.

Methods: We assimilate patient-specific measurements of myocardial blood flow from clinical CT myocardial perfusion imaging to estimate branch-specific coronary artery flows. Simulated noise in the clinical data is used to estimate the joint posterior distributions of the model parameters using adaptive Markov Chain Monte Carlo sampling. Additionally, the posterior predictive distribution for the relevant quantities of interest is determined using a new approach combining multi-fidelity Monte Carlo estimation with non-linear, data-driven dimensionality reduction. This leads to improved correlations between high- and low-fidelity model outputs.

Results: Our framework accurately recapitulates clinically measured cardiac function as well as branch-specific coronary flows under measurement noise uncertainty. We observe substantial reductions in confidence intervals for estimated quantities of interest compared to single-fidelity Monte Carlo estimation and state-of-the-art multi-fidelity Monte Carlo methods. This holds especially true for quantities of interest that showed limited correlation between the low- and high-fidelity model predictions. In addition, the proposed multi-fidelity Monte Carlo estimators are significantly cheaper to compute than traditional estimators, under a specified confidence level or variance.

Conclusions: The proposed pipeline for personalized and uncertainty-aware predictions of coronary hemodynamics is based on routine clinical measurements and recently developed techniques for CT myocardial perfusion imaging. The proposed pipeline offers significant improvements in precision and reduction in computational cost.

Figure B.1:

Comparison of measured versus simulated metrics of cardiac function after model personalization. Dia. BP: Diastolic blood pressure. Sys. BP: Systolic blood pressure. Stroke Vol.: Stroke volume. EF: Ejection fraction.

Figure B.2:

Distributions of simulated (scatter) versus measured (dashed ellipse) covariance between branch-specific coronary flows resulting from Bayesian parameters estimation.

Figure 1:

An overview of the pipeline developed in this work, from clinical image analysis, to Bayesian parameter estimation, and, finally, the computation of posterior predictive quantities of interest.

Figure 2:

(a) Slices of the estimated posterior distributions of the distal resistance for all 14 coronary outlets. (b) Distributions of predicted coronary flows compared with clinically measured targets (vertical line) and noise distribution for each coronary artery.

Figure 3:

Correlation between maximum OSI from 3D simulations and mean outlet flow from 0D simulations. Data is shown for the standard and MFMC-AE-reparameterized 0D models. The three panels show the correlations for the LAD, LCx and RCA branches.

Figure 4:

Maximum OSI in (a)-(c) and minimum TAWSS in (d)-(f) for LAD, LCx and RCA branches estimated using one realization of MC, MFMC and MFMC-AE estimators. Solid and dashed lines show 95% and 99% confidence intervals, respectively.

Figure 5:

FFR estimated with 0D FFR in (a)-(c), and 0D mean flow in (d)-(f), using one realization of MC, MFMC and MFMC-AE. The three panels show data for the LAD, LCx and RCA branches. Solid and dashed lines show 95% and 99% confidence intervals.

Figure 6:

Convergence of MFMC-AE with respect to N_3D using maximum OSI as the QoI. Top panel shows original and modified correlations between 3D and 0D outputs. Bottom panel shows the Monte Carlo mean. Each marker is an independent trial.

Figure 7:

Computational budget analysis using maximum OSI as an example QoI. (a) Optimal variance reduction versus computational cost. (b) Additional computational budget required to reduce current (non-optimal) estimator variance.