Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques.

We study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

In Vitro Assessment of Right Ventricular Outflow Tract Anatomy and Valve Orientation Effects on Bioprosthetic Pulmonary Valve Hemodynamics.

PURPOSE: The congenital heart defect Tetralogy of Fallot (ToF) affects 1 in 2500 newborns annually in the US and typically requires surgical repair of the right ventricular outflow tract (RVOT) early in life, with variations in surgical technique leading to large disparities in RVOT anatomy among patients. Subsequently, often in adolescence or early adulthood, patients usually require surgical placement of a xenograft or allograft pulmonary valve prosthesis. Valve longevity is highly variable for reasons that remain poorly understood. METHODS: This work aims to assess the performance of bioprosthetic pulmonary valves in vitro using two 3D printed geometries: an idealized case based on healthy subjects aged 11 to 13 years and a diseased case with a 150% dilation in vessel diameter downstream of the valve. Each geometry was studied with two valve orientations: one with a valve leaflet opening posterior, which is the native pulmonary valve position, and one with a valve leaflet opening anterior. RESULTS: Full three-dimensional, three-component, phase-averaged velocity fields were obtained in the physiological models using 4D flow MRI. Flow features, particularly vortex formation and reversed flow regions, differed significantly between the RVOT geometries and valve orientations. Pronounced asymmetry in streamwise velocity was present in all cases, while the diseased geometry produced additional asymmetry in radial flows. Quantitative integral metrics demonstrated increased secondary flow strength and recirculation in the rotated orientation for the diseased geometry. CONCLUSIONS: The compound effects of geometry and orientation on bioprosthetic valve hemodynamics illustrated in this study could have a crucial impact on long-term valve performance.

Validation of Wall Shear Stress Assessment in Non-invasive Coronary CTA versus Invasive Imaging: A Patient-Specific Computational Study.

Endothelial shear stress (ESS) identifies coronary plaques at high risk for progression and/or rupture leading to a future acute coronary syndrome. In this study an optimized methodology was developed to derive ESS, pressure drop and oscillatory shear index using computational fluid dynamics (CFD) in 3D models of coronary arteries derived from non-invasive coronary computed tomography angiography (CTA). These CTA-based ESS calculations were compared to the ESS calculations using the gold standard with fusion of invasive imaging and CTA. In 14 patients paired patient-specific CFD models based on invasive and non-invasive imaging of the left anterior descending (LAD) coronary arteries were created. Ten patients were used to optimize the methodology, and four patients to test this methodology. Time-averaged ESS (TAESS) was calculated for both coronary models applying patient-specific physiological data available at the time of imaging. For data analysis, each 3D reconstructed coronary artery was divided into 2 mm segments and each segment was subdivided into 8 arcs (45°).TAESS and other hemodynamic parameters were averaged per segment as well as per arc. Furthermore, the paired segment- and arc-averaged TAESS were categorized into patient-specific tertiles (low, medium and high). In the ten LADs, used for optimization of the methodology, we found high correlations between invasively-derived and non-invasively-derived TAESS averaged over segments (n = 263, r = 0.86) as well as arcs (n = 2104, r = 0.85, p < 0.001). The correlation was also strong in the four testing-patients with r = 0.95 (n = 117 segments, p = 0.001) and r = 0.93 (n = 936 arcs, p = 0.001).There was an overall high concordance of 78% of the three TAESS categories comparing both methodologies using the segment- and 76% for the arc-averages in the first ten patients. This concordance was lower in the four testing patients (64 and 64% in segment- and arc-averaged TAESS). Although the correlation and concordance were high for both patient groups, the absolute TAESS values averaged per segment and arc were overestimated using non-invasive vs. invasive imaging [testing patients: TAESS segment: 30.1(17.1-83.8) vs. 15.8(8.8-63.4) and TAESS arc: 29.4(16.2-74.7) vs 15.0(8.9-57.4) p < 0.001]. We showed that our methodology can accurately assess the TAESS distribution non-invasively from CTA and demonstrated a good correlation with TAESS calculated using IVUS/OCT 3D reconstructed models.

Assessment of Coronary Artery Aneurysms Caused by Kawasaki Disease Using Transluminal Attenuation Gradient Analysis of Computerized Tomography Angiograms.

Patients with coronary artery aneurysms (CAAs) resulting from Kawasaki disease (KD) are at risk for thrombosis and myocardial infarction. Current guidelines recommend CAA diameter ≥8 mm as the criterion for initiating systemic anticoagulation. Transluminal attenuation gradient (TAG) analysis has been proposed as a noninvasive method for evaluating functional significance of coronary stenoses using computerized tomography angiography (CTA), but has not previously been used in CAA. We hypothesized that abnormal hemodynamics in CAA caused by KD could be quantified using TAG analysis. We studied 23 patients with a history of KD who had undergone clinically indicated CTA. We quantified TAG in the major coronary arteries and aneurysm geometry was characterized using maximum diameter, aneurysm shape index, and sphericity index. A total of 55 coronary arteries were analyzed, 25 of which had at least 1 aneurysmal region. TAG in aneurysmal arteries was significantly lower than in normal arteries (-23.5 ± 10.7 vs -10.5 ± 9.0, p = 0.00002). Aneurysm diameter, aneurysm shape index, and sphericity index were weakly correlated with TAG (r2 = 0.01, p = 0.6; r2 = 0.15, p = 0.06; r2 = 0.16, p = 0.04). This is the first application of TAG analysis to CAA caused by KD, and demonstrates significantly different TAG values in aneurysmal versus normal arteries. Lack of correlation between TAG and CAA geometry suggests that TAG may provide hemodynamic information not available from anatomy alone. TAG represents a possible extension to standard CTA for KD patients who may improve thrombotic risk stratification and aid in clinical decision making.

In Vitro Assessment of the Assisted Bidirectional Glenn Procedure for Stage One Single Ventricle Repair.

This in vitro study compares the hemodynamic performance of the Norwood and the Glenn circulations to assess the performance of a novel assisted bidirectional Glenn (ABG) procedure for stage one single ventricle surgery. In the ABG, the flow in a bidirectional Glenn procedure is assisted by injection of a high-energy flow stream from the systemic circulation using an aorta-caval shunt with nozzle. The aim is to explore experimentally the potential of the ABG as a surgical alternative to current surgical practice. The experiments are directly compared against previously published numerical simulations. A multiscale mock circulatory system was used to measure the hemodynamic performance of the three circulations. For each circulation, the system was tested using both low and high values of pulmonary vascular resistance. Resulting parameters measured were: pressure and flow rate at left/right pulmonary artery and superior vena cava (SVC). Systemic oxygen delivery (OD) was calculated. A parametric study of the ratio of ABG nozzle to shunt diameter was done. We report time-based comparisons with numerical simulations for the three surgical variants tested. The ABG circulation demonstrated an increase of 30-38% in pulmonary flow with a 2-3.7 mmHg increase in SVC pressure compared to the Glenn and a 4-14% higher systemic OD than either the Norwood or the Glenn. The nozzle/shunt diameter ratio affected the local hemodynamics. These experimental results agreed with those of the numerical model: mean flow values were not significantly different (p > 0.05) while mean pressures were comparable within 1.2 mmHg. The results verify the approaches providing two tools to study this complicated circulation. Using a realistic experimental model we demonstrate the performance of a novel surgical procedure with potential to improve patient hemodynamics in early palliation of the univentricular circulation.

A new multiparameter approach to computational simulation for Fontan assessment and redesign.

INTRODUCTION: Despite an abundance of prior Fontan simulation articles, there have been relatively few clinical advances that are a direct result of computational methods. We address a few key limitations of previous Fontan simulations as a step towards increasing clinical relevance. Previous simulations have been limited in scope because they have primarily focused on a single energy loss parameter. We present a multi-parameter approach to Fontan modeling that establishes a platform for clinical decision making and comprehensive evaluation of proposed interventions. METHODS: Time-dependent, 3-D blood flow simulations were performed on six patient-specific Fontan models. Key modeling advances include detailed pulmonary anatomy, catheterization-derived pressures, and MRI-derived flow with respiration. The following performance parameters were used to rank patients at rest and simulated exercise from best to worst performing: energy efficiency, inferior and superior vena cava (IVC, SVC) pressures, wall shear stress, and IVC flow distribution. RESULTS: Simulated pressures were well matched to catheterization data, but low Fontan pressure did not correlate with high efficiency. Efficiency varied from 74% to 96% at rest, and from 63% to 91% with exercise. Distribution of IVC flow ranged from 88%/12% (LPA/RPA) to 53%/47%. A "transcatheter" virtual intervention demonstrates the utility of computation in evaluating interventional strategies, and is shown to result in increased energy efficiency. CONCLUSIONS: A multiparameter approach demonstrates that each parameter results in a different ranking of Fontan performance. Ranking patients using energy efficiency does not correlate with the ranking using other parameters of presumed clinical importance. As such, current simulation methods that evaluate energy dissipation alone are not sufficient for a comprehensive evaluation of new Fontan designs.