We present a framework for the estimation of the Fractional Flow Reserve index based on blood ow simulations that incorporate clinical imaging and patient-specic characteristics. The process of model design implies making choices in order to build a suitable mathematical model, e.g. simulating a 3D domain versus a 1D domain, modeling of peripheral resistances, determining the regions of interest, etc. Here we thoroughly evaluate the impact of such choices on FFR prediction accuracy by reduced-order models with respect to more complete models by means of uncertainty quantication and sensitivity analysis. Moreover, we assess the uncertainty of FFR predictions based on our framework with respect to input data, and further determine the most inuential inputs with sensitivity analysis, aiming at increasing the clinical usability of predictions by providing information on the reliability of model output on a per case basis. Analysis is carried out for a population of 13 patients for which 24 invasive FFR measurements are available. Our analysis conrms previously observed sources of uncertainty and provides insight into aspects to be improved in any model-based non-invasive FFR estimation method.

Uncertainty propagation is used to quantify the uncertainty in model predictions in the presence of uncertain input variables. In this study, we analyze a steady-state point-model for two-phase gas-liquid flow. We present prediction intervals for holdup and pressure drop that are obtained from knowledge of the measurement error in the variables provided to the model. The analysis also uncovers which variables the predictions are most sensitive to. Sensitivity indices and prediction intervals are calculated by two different methods, Monte Carlo and polynomial chaos. The methods give similar prediction intervals, and they agree that the predictions are most sensitive to the pipe diameter and the liquid viscosity. However, the Monte Carlo simulations require fewer model evaluations and less computational time. The model predictions are also compared to experiments while accounting for uncertainty, and the holdup predictions are accurate, but there is bias in the pressure drop estimates.Algorithms 2020, 13, 53 2 of 22 in Holm et al. [3,4], where they demonstrated how uncertainty propagation may be used for flow assurance on the Shtokman gas and condensate field. Their analysis included pressure drop and liquid holdup predictions using a one-dimensional model in the software OLGA. They determined probability distributions for a selection of input variables and closure laws and they propagated these uncertainties through the multiflow model using a Monte Carlo method. The result is the 10th, 50th, and 90th output percentiles for pressure drop and liquid holdup predictions and measures of sensitivity to the input variables. Hoyer et al. [5] used Monte Carlo simulations with OLGA in order to identify influential variables and closure laws in several groups of data with different flow conditions. They are only able to construct satisfactory probability distributions for each closure law when using a group of data where the closure law is significant.Klavetter et al.[6] modeled liquid holdup and pressure drop in two-phase pipe flow using the TUFFP Unified Model for two-phase flow. They assumed an uncertainty range for each input variable and compared perturbation, Taylor series approximations and Monte Carlo methods for uncertainty propagation. They concluded that Taylor series approximations overestimate the output uncertainty while the other methods perform well. Keinath et al. [7] also demonstrated the importance of selecting an appropriate framework when handling uncertainty in multiphase modeling and highlighted the value of quantitative information about the input uncertainty distributions for decision making. Just recently, in Liu et al. [8], a Gaussian process and principal component analysis were applied to a complex two-phase flow model in order to explore the uncertainty and reduce the complexity of the model. Picchi and Poesio [9] considered a one-dimensional model for two-phase pipe flow. Known distributions for input variables are propagated through the model using Monte Carlo methods to obtain first-order a...

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The prediction uncertainty in simulators for industrial processes is due to uncertainties in the input variables and uncertainties in specification of the models, in particular the closure laws. In this work, the uncertainty in each closure law was modeled as a random variable and the parameters of its distribution were optimized to correctly quantify the uncertainty in predictions. We have developed two methods for optimization, based on the integrated quadratic distance and the energy score. The proposed methods were applied to the commercial multiphase flow simulator LedaFlow with the liquid volume fraction and pressure gradient as output variables. Two datasets were analyzed. Both describe two-phase gas-liquid flow, but are otherwise fundamentally different. One is gas-dominated stratified/annular flow and the other is liquiddominated slug flow. The closure law for the gas-wall friction factor is decisive for the gas-dominated predictions, and the estimated relative standard deviation is 4.5 % or 8.0 % depending on method. The liquid-dominated study showed that the liquid-wall friction factor and the slug bubble velocity are the closure laws with the greatest impact. Moreover, the estimated relative standard deviation in the liquid-wall friction factor is 5 %, and the deviation in the slug bubble velocity is 4 %. We used direct measurements of the slug bubble velocity to validate the estimated uncertainty.