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.

Quantification and Visualization of CT Myocardial Perfusion Imaging to Detect Ischemia-Causing Coronary Arteries.

Coronary computed tomography angiography (cCTA) has poor specificity to identify coronary stenosis that limit blood flow to the myocardial tissue. Integration of dynamic CT myocardial perfusion imaging (CT-MPI) can potentially improve the diagnostic accuracy. We propose a method that integrates cCTA and CT-MPI to identify culprit coronary lesions that limit blood flow to the myocardium. Coronary arteries and left ventricle surfaces were segmented from cCTA and registered to CT-MPI. Myocardial blood flow (MBF) was derived from CT-MPI. A ray-casting approach was developed to project volumetric MBF onto the left ventricle surface. MBF volume were divided into coronary-specific territories based on proximity to the nearest coronary artery. MBF and normalized MBF were computed for the myocardium and each of the coronary artery. Projection of MBF onto cCTA allowed for direct visualization of perfusion defects. Normalized MBF had higher correlation with ischemic myocardial territory compared to MBF (MBF: R2=0.81 and Index MBF: R2=0.90). There were 18 vessels that showed angiographic disease (stenosis >50%); however, normalized MBF demonstrated only 5 coronary territories to be ischemic. These findings demonstrate that cCTA and CT-MPI can be integrated to visualize myocardial defects and detect culprit coronary arteries responsible for perfusion defects. These methods can allow for non-invasive detection of ischemia-causing coronary lesions and ultimately help guide clinicians to deliver more targeted coronary interventions.

Personalized coronary and myocardial blood flow models incorporating CT perfusion imaging and synthetic vascular trees.

Computational simulations of coronary artery blood flow, using anatomical models based on clinical imaging, are an emerging non-invasive tool for personalized treatment planning. However, current simulations contend with two related challenges - incomplete anatomies in image-based models due to the exclusion of arteries smaller than the imaging resolution, and the lack of personalized flow distributions informed by patient-specific imaging. We introduce a data-enabled, personalized and multi-scale flow simulation framework spanning large coronary arteries to myocardial microvasculature. It includes image-based coronary anatomies combined with synthetic vasculature for arteries below the imaging resolution, myocardial blood flow simulated using Darcy models, and systemic circulation represented as lumped-parameter networks. We propose an optimization-based method to personalize multiscale coronary flow simulations by assimilating clinical CT myocardial perfusion imaging and cardiac function measurements to yield patient-specific flow distributions and model parameters. Using this proof-of-concept study on a cohort of six patients, we reveal substantial differences in flow distributions and clinical diagnosis metrics between the proposed personalized framework and empirical methods based purely on anatomy; these errors cannot be predicted a priori. This suggests virtual treatment planning tools would benefit from increased personalization informed by emerging imaging methods.

A probabilistic neural twin for treatment planning in peripheral pulmonary artery stenosis.

The substantial computational cost of high-fidelity models in numerical hemodynamics has, so far, relegated their use mainly to offline treatment planning. New breakthroughs in data-driven architectures and optimization techniques for fast surrogate modeling provide an exciting opportunity to overcome these limitations, enabling the use of such technology for time-critical decisions. We discuss an application to the repair of multiple stenosis in peripheral pulmonary artery disease through either transcatheter pulmonary artery rehabilitation or surgery, where it is of interest to achieve desired pressures and flows at specific locations in the pulmonary artery tree, while minimizing the risk for the patient. Since different degrees of success can be achieved in practice during treatment, we formulate the problem in probability, and solve it through a sample-based approach. We propose a new offline-online pipeline for probabilistic real-time treatment planning which combines offline assimilation of boundary conditions, model reduction, and training dataset generation with online estimation of marginal probabilities, possibly conditioned on the degree of augmentation observed in already repaired lesions. Moreover, we propose a new approach for the parametrization of arbitrarily shaped vascular repairs through iterative corrections of a zero-dimensional approximant. We demonstrate this pipeline for a diseased model of the pulmonary artery tree available through the Vascular Model Repository.

Personalized coronary and myocardial blood flow models incorporating CT perfusion imaging and synthetic vascular trees.

Computational simulations of coronary artery blood flow, using anatomical models based on clinical imaging, are an emerging non-invasive tool for personalized treatment planning. However, current simulations contend with two related challenges - incomplete anatomies in image-based models due to the exclusion of arteries smaller than the imaging resolution, and the lack of personalized flow distributions informed by patient-specific imaging. We introduce a data-enabled, personalized and multi-scale flow simulation framework spanning large coronary arteries to myocardial microvasculature. It includes image-based coronary models combined with synthetic vasculature for arteries below the imaging resolution, myocardial blood flow simulated using Darcy models, and systemic circulation represented as lumped-parameter networks. Personalized flow distributions and model parameters are informed by clinical CT myocardial perfusion imaging and cardiac function using surrogate-based optimization. We reveal substantial differences in flow distributions and clinical diagnosis metrics between the proposed personalized framework and empirical methods based on anatomy; these errors cannot be predicted a priori. This suggests virtual treatment planning tools would benefit from increased personalization informed by emerging imaging methods.

Predictors of Myocardial Ischemia in Patients with Kawasaki Disease: Insights from Patient-Specific Simulations of Coronary Hemodynamics.

Current treatments for patients with coronary aneurysms caused by Kawasaki disease (KD) are based primarily on aneurysm size. This ignores hemodynamic factors influencing myocardial ischemic risk. We performed patient-specific computational hemodynamics simulations for 15 KD patients, with parameters tuned to patients' arterial pressure and cardiac function. Ischemic risk was evaluated in 153 coronary arteries from simulated fractional flow reserve (FFR), wall shear stress, and residence time. FFR correlated weakly with aneurysm [Formula: see text]-scores (correlation coefficient, [Formula: see text]) but correlated better with the ratio of maximum-to-minimum aneurysmal lumen diameter ([Formula: see text]). FFR dropped more rapidly distal to aneurysms, and this correlated more with the lumen diameter ratio ([Formula: see text]) than [Formula: see text]-score ([Formula: see text]). Wall shear stress correlated better with the diameter ratio ([Formula: see text]), while residence time correlated more with [Formula: see text]-score ([Formula: see text]). Overall, the maximum-to-minimum diameter ratio predicted ischemic risk better than [Formula: see text]-score. Although FFR immediately distal to aneurysms was nonsignificant, its rapid rate of decrease suggests elevated risk.

Phase separation and coexistence of hydrodynamically interacting microswimmers.

A striking feature of the collective behavior of spherical microswimmers is that for sufficiently strong self-propulsion they phase-separate into a dense cluster coexisting with a low-density disordered surrounding. Extending our previous work, we use the squirmer as a model swimmer and the particle-based simulation method of multi-particle collision dynamics to explore the influence of hydrodynamics on their phase behavior in a quasi-two-dimensional geometry. The coarsening dynamics towards the phase-separated state is diffusive in an intermediate time regime followed by a final ballistic compactification of the dense cluster. We determine the binodal lines in a phase diagram of Péclet number versus density. Interestingly, the gas binodals are shifted to smaller densities for increasing mean density or dense-cluster size, which we explain using a recently introduced pressure balance [S. C. Takatori, et al., Phys. Rev. Lett. 2014, 113, 028103] extended by a hydrodynamic contribution. Furthermore, we find that for pushers and pullers the binodal line is shifted to larger Péclet numbers compared to neutral squirmers. Finally, when lowering the Péclet number, the dense phase transforms from a hexagonal "solid" to a disordered "fluid" state.

Attraction-induced jamming in the flow of foam through a channel.

We study the flow of a pressure-driven foam through a straight channel using numerical simulations, and examine the effects of a tuneable attractive potential between bubbles. We show that the effect of an attractive potential is to introduce a regime of jamming and stick-slip flow in a channel, and report on the behaviour resulting from varying the strength of the attraction. We find that there is a force threshold below which the flow jams, and upon further increasing the driving force, a crossover from intermittent (stick-slip) to smooth flow is observed. This threshold force below which the foam jams increases linearly with the strength of the attractive potential. By examining the spectra of energy fluctuations, we show that stick-slip flow is characterized by low frequency rearrangements and strongly local behaviour, whereas steady flow shows a broad spectrum of energy drop events and collective behaviour. Our work suggests that the stick-slip and the jamming regimes occur due to the increased stabilization of contact networks by the attractive potential - as the strength of attraction is increased, bubbles are increasingly trapped within networks, and there is a decrease in the number of contact changes.