Parametric Quantification Research Articles

Parametric Sensitivity Analysis of Stability Margins of Holos-Quad Microreactor

An analysis of the stability margins of the innovative Holos-Quad microreactor design is presented. This high-temeprature gas-cooled reactor (HTGR) system is designed to operate fully autonomously with passive safety mechanisms. Therefore, the inherent stability of the reactor is of great importance. Using a point-reactor model, which couples point kinetics to thermal-hydraulic heat balance equations and includes reactivity feedback effects of the fuel and moderator temperatures, the closed-loop transfer function of the reactor is derived. Applying the approach of linear systems and control theory, both the gain and phase margins of the Holos-Quad design are obtained. The analysis demonstrates that the design is stable, with an infinite gain margin and a finite phase margin. A parametric uncertainty quantification study is also performed using a total Monte Carlo approach. The stability of the reactor for different power levels, such as during reactor startup or load-following transients, is also explored. Finally, two sensitivity analysis methods are applied, namely, multiple regression (deriving standardized regression coefficients) and variance-based sensitivity analysis (known as the Sobol method), to study the contribution of each of the parameters to the stability margins’ uncertainty. This analysis improves our understanding of the role of each of the parameters in the stability of the reactor.

Parametric quantification of silicon-based heterojunctions via equivalent circuit and deep learning model

Parametric quantification of silicon-based heterojunctions via equivalent circuit and deep learning model

Population-based deep image prior for dynamic PET denoising: A data-driven approach to improve parametric quantification

The high noise level of dynamic Positron Emission Tomography (PET) images degrades the quality of parametric images. In this study, we aim to improve the quality and quantitative accuracy of Ki images by utilizing deep learning techniques to reduce the noise in dynamic PET images. We propose a novel denoising technique, Population-based Deep Image Prior (PDIP), which integrates population-based prior information into the optimization process of Deep Image Prior (DIP). Specifically, the population-based prior image is generated from a supervised denoising model that is trained on a prompts-matched static PET dataset comprising 100 clinical studies. The 3D U-Net architecture is employed for both the supervised model and the following DIP optimization process. We evaluated the efficacy of PDIP for noise reduction in 25%-count and 100%-count dynamic PET images from 23 patients by comparing with two other baseline techniques: the Prompts-matched Supervised model (PS) and a conditional DIP (CDIP) model that employs the mean static PET image as the prior. Both the PS and CDIP models show effective noise reduction but result in smoothing and removal of small lesions. In addition, the utilization of a single static image as the prior in the CDIP model also introduces a similar tracer distribution to the denoised dynamic frames, leading to lower Ki in general as well as incorrect Ki in the descending aorta. By contrast, as the proposed PDIP model utilizes intrinsic image features from the dynamic dataset and a large clinical static dataset, it not only achieves comparable noise reduction as the supervised and CDIP models but also improves lesion Ki predictions.

An in vitro experimental investigation of oscillatory flow in the cerebral aqueduct

This in vitro study aims at clarifying the relation between the oscillatory flow of cerebrospinal fluid (CSF) in the cerebral aqueduct, a narrow conduit connecting the third and fourth ventricles, and the corresponding interventricular pressure difference. Dimensional analysis is used in designing an anatomically correct scaled model of the aqueduct flow, with physical similarity maintained by adjusting the flow frequency and the properties of the working fluid. The time-varying pressure difference across the aqueduct corresponding to a given oscillatory flow rate is measured in parametric ranges covering the range of flow conditions commonly encountered in healthy subjects. Parametric dependences are delineated for the time-averaged pressure fluctuations and for the phase lag between the transaqueductal pressure difference and the flow rate, both having clinical relevance. The results are validated through comparisons with predictions obtained with a previously derived computational model. The parametric quantification in this study enables the derivation of a simple formula for the relation between the transaqueductal pressure and the stroke volume. This relationship can be useful in the quantification of transmantle pressure differences based on non-invasive magnetic-resonance-velocimetry measurements of aqueduct flow for investigation of CSF-related disorders.

Copula-based Bayesian uncertainty quantification framework of SST turbulence model for flow over a Gaussian bump

Quantitatively analyze the uncertainties in turbulence models is of great meaning for research and engineering. In this paper, we develop a Bayesian uncertainty analysis framework based on copulas. The proposed framework is applied to the parametric uncertainty quantification and calibration of the shear-stress transport turbulence model for the flow over a Gaussian bump. A copula function is used to establish the correlation between variables and construct the weight function, which enables greater consideration of Bayesian inference. Prior analysis is conducted based on Sobol indices with the nonintrusive polynomial chaos method, demonstrating the important effects of κ, a1, and β∗ on the flow, both for the wall force coefficients and the Reynolds shear stress. Next, the wall force coefficients and Reynolds shear stress are used as training sets to verify the effectiveness of the method. The results show that modeling the relationship based on copulas is necessary and effective, and that the weight function adaptively balances the influence of physical quantities at different inference locations. The proposed method effectively corrects the computational deviations of the corresponding physical quantities. In addition, the confidence interval for the posterior sample is increased, enhancing the likelihood of obtaining results close to the actual values.

Parametric quantification of sonochemical effect during the high frequency ultrasonic-assisted absorption of bulk CO2

Ultrasonic irradiation has been recently applied as a novel technique to the CO2 absorption process. The preliminary studies have proved the ultrasonic-assisted reactor could provide satisfactory performance, in terms of CO2 absorption rate, even by utilizing slow kinetic absorbents. In those studies, the main focus was on the physical effects of ultrasonic irradiation, ignoring the significance of the chemical effect. Elucidating the role of the sonochemical effect, which is linked with the hydroxyl radicals (OḢ), can be a crucial step in further developing this technique. Hence, this study aims to parametrically quantify the sonochemical effect during the CO2 absorption in the high-frequency ultrasonic-assisted reactor using promoter-free methyldiethanolamine (MDEA). The quantification is performed via scavenging of OḢ radicals using terephthalic acid (TA). Subsequently, the high-performance liquid chromatography (HPLC) analytical technique is implemented to analyze the scavenged OḢ radicals, and the findings are presented by calculating the radical scavenging activity (RSA) of TA. The results show that the RSA value increases from 0.14 −2.79 % as CO2 pressure rises from 3 to 11 bar, indicating a rise in the quantity of OḢ radicals formed at high pressure ranges that TA molecules can scavenge. In contrast to the CO2 pressure effect, increasing the temperature, ultrasonic power, and MDEA concentration can suppress the sonochemical effect under the fixed high-frequency condition of 1.7 MHz. Finally, along with the parametric analysis, the CO2 absorption rate is determined, and the significance of the sonochemical effect on the rate enhancement is discussed.

In-silico modelling of multi-strike insertion and torsional resistance of tapered revision hip stems: Insight into spline design philosophy.

Despite the clinical success of tapered splined titanium stems, a knowledge gap still exists between spline design and its primary mechanical stability, which is critical to the long-term success of revision hip arthroplasty. Additionally, almost all published pre-clinical studies relied on resource-intensive benchtop and cadaveric testing. Hence, the present study developed a novel computational model to investigate effects of spline geometry and configuration on axial and torsional stability of tapered stem. Dynamic explicit Finite Element Analysis coupled with a state-of-the-art adaptive meshing technique was used to simulate the highly non-linear contacts and large bony material deformations. Hybridising primary straight splines with secondary angled splines results in 41% and 10% increases of peak insertion force and post-seating moment than the predicate device for the same seating position. The primary straight splines cut at multiple circumferential bony locations, enhancing torsional stability; while the alternatively placed secondary angled splines form wedges with the bone, providing reliable seating and additional torsional resistance. To the best knowledge of the author, this is the first in-silico investigation of its kind to simulate multi-strike seating and torsional resistance of revision hip stems, offering an effective and efficient platform for future multi-factorial parametric study and uncertainty quantification.

Toward machine-assisted tuning avoiding the underestimation of uncertainty in climate change projections.

Documenting the uncertainty of climate change projections is a fundamental objective of the inter-comparison exercises organized to feed into the Intergovernmental Panel on Climate Change (IPCC) reports. Usually, each modeling center contributes to these exercises with one or two configurations of its climate model, corresponding to a particular choice of "free parameter" values, resulting from a long and often tedious "model tuning" phase. How much uncertainty is omitted by this selection and how might readers of IPCC reports and users of climate projections be misled by its omission? We show here how recent machine learning approaches can transform the way climate model tuning is approached, opening the way to a simultaneous acceleration of model improvement and parametric uncertainty quantification. We show how an automatic selection of model configurations defined by different values of free parameters can produce different "warming worlds," all consistent with present-day observations of the climate system.

Regional perception and multi-scale feature fusion network for cardiac segmentation

Objective. Cardiovascular disease (CVD) is a group of diseases affecting cardiac and blood vessels, and short-axis cardiac magnetic resonance (CMR) images are considered the gold standard for the diagnosis and assessment of CVD. In CMR images, accurate segmentation of cardiac structures (e.g. left ventricle) assists in the parametric quantification of cardiac function. However, the dynamic beating of the heart renders the location of the heart with respect to other tissues difficult to resolve, and the myocardium and its surrounding tissues are similar in grayscale. This makes it challenging to accurately segment the cardiac images. Our goal is to develop a more accurate CMR image segmentation approach. Approach. In this study, we propose a regional perception and multi-scale feature fusion network (RMFNet) for CMR image segmentation. We design two regional perception modules, a window selection transformer (WST) module and a grid extraction transformer (GET) module. The WST module introduces a window selection block to adaptively select the window of interest to perceive information, and a windowed transformer block to enhance global information extraction within each feature window. The WST module enhances the network performance by improving the window of interest. The GET module grids the feature maps to decrease the redundant information in the feature maps and enhances the extraction of latent feature information of the network. The RMFNet further introduces a novel multi-scale feature extraction module to improve the ability to retain detailed information. Main results. The RMFNet is validated with experiments on three cardiac data sets. The results show that the RMFNet outperforms other advanced methods in overall performance. The RMFNet is further validated for generalizability on a multi-organ data set. The results also show that the RMFNet surpasses other comparison methods. Significance. Accurate medical image segmentation can reduce the stress of radiologists and play an important role in image-guided clinical procedures.

Inter-pass motion correction for whole-body dynamic PET and parametric imaging.

Whole-body dynamic FDG-PET imaging through continuous-bed-motion (CBM) mode multi-pass acquisition protocol is a promising metabolism measurement. However, inter-pass misalignment originating from body movement could degrade parametric quantification. We aim to apply a non-rigid registration method for inter-pass motion correction in whole-body dynamic PET. 27 subjects underwent a 90-min whole-body FDG CBM PET scan on a Biograph mCT (Siemens Healthineers), acquiring 9 over-the-heart single-bed passes and subsequently 19 CBM passes (frames). The inter-pass motion correction was executed using non-rigid image registration with multi-resolution, B-spline free-form deformations. The parametric images were then generated by Patlak analysis. The overlaid Patlak slope Ki and y-intercept Vb images were visualized to qualitatively evaluate motion impact and correction effect. The normalized weighted mean squared Patlak fitting errors (NFE) were compared in the whole body, head, and hypermetabolic regions of interest (ROI). In Ki images, ROI statistics were collected and malignancy discrimination capacity was estimated by the area under the receiver operating characteristic curve (AUC). After the inter-pass motion correction was applied, the spatial misalignment appearance between Ki and Vb images was successfully reduced. Voxel-wise normalized fitting error maps showed global error reduction after motion correction. The NFE in the whole body (p = 0.0013), head (p = 0.0021), and ROIs (p = 0.0377) significantly decreased. The visual performance of each hypermetabolic ROI in Ki images was enhanced, while 3.59% and 3.67% average absolute percentage changes were observed in mean and maximum Ki values, respectively, across all evaluated ROIs. The estimated mean Ki values had substantial changes with motion correction (p = 0.0021). The AUC of both mean Ki and maximum Ki after motion correction increased, possibly suggesting the potential of enhancing oncological discrimination capacity through inter-pass motion correction.

Qilian Formula Inhibits Tumor Cell Growth in a Bone Metastasis Model of Lung Cancer.

Bone metastasis is frequently common in advanced lung cancer with the major issue of a pathological fracture. Previous studies suggested that Astragalus membranaceus (Qi) and Ampelopsis japonica (Lian), which are used as folk medicine in China, have potential effects on inhibiting tumor growth and protecting bones, respectively. In this study, an experiment on the inhibitory effect of the Qilian formula (AAF) in vivo was designed to examine tumor growth in bone and osteoclast formation. The bone metastasis xenograft models were established by implanting NCI-H460-luc2 lung cancer cells into the right tibiae bones of mice. After confirming the model's viability through optical imaging 7 days post-implantation, 2 groups, namely the AAF group and the control group, were administered 0.3 mL of AAF extract (9 g/kg/day) or normal saline via intragastric delivery for a duration of 4 weeks. Throughout the study, we longitudinally assessed tumor burden, bone destruction, and weight-bearing capacity in vivo using reporter gene bioluminescence imaging (BLI), micro-CT, and dynamic weight-bearing (DWB) tests. Mechanistic insights were gained through Hematoxylin-eosin (H&E) staining, immunohistochemical (IHC) analysis, western blotting, and flow cytometry. Qilian formula produced significant inhibition to the progress of bone destruction and tumor burden in the right tibiae bone in the treatment group. It was further evidenced by molecular imaging in vivo via small animal micro-CT and BLI with parametric quantification, characterizing significantly lower uptake of BLI signal in the treated tumor lesions and improving the pathological changes in the microstructure of bone. Furthermore, DWB tests revealed that Qilian formula treatment significantly maintained the weight-bearing capacity. According to immunohistochemical analysis, the effect of the Qilian formula appeared to involve the suppression of osteoclast formation by lower expression of the tartrate-resistant acid phosphatase. Cell apoptosis and death induction were evidenced by a higher percentage of Bal2、BAX and caspase 3 expressions of Qilian formula-treated tumor tissues. Our study demonstrated a significant inhibitory effect of the Qilian formula on the progression of osteolytic invasion in vivo by suppressing osteoclastogenesis and promoting apoptotic cell death.

TAI-GAN: Temporally and Anatomically Informed GAN for Early-to-Late Frame Conversion in Dynamic Cardiac PET Motion Correction.

The rapid tracer kinetics of rubidium-82 (82Rb) and high variation of cross-frame distribution in dynamic cardiac positron emission tomography (PET) raise significant challenges for inter-frame motion correction, particularly for the early frames where conventional intensity-based image registration techniques are not applicable. Alternatively, a promising approach utilizes generative methods to handle the tracer distribution changes to assist existing registration methods. To improve frame-wise registration and parametric quantification, we propose a Temporally and Anatomically Informed Generative Adversarial Network (TAI-GAN) to transform the early frames into the late reference frame using an all-to-one mapping. Specifically, a feature-wise linear modulation layer encodes channel-wise parameters generated from temporal tracer kinetics information, and rough cardiac segmentations with local shifts serve as the anatomical information. We validated our proposed method on a clinical 82Rb PET dataset and found that our TAI-GAN can produce converted early frames with high image quality, comparable to the real reference frames. After TAI-GAN conversion, motion estimation accuracy and clinical myocardial blood flow (MBF) quantification were improved compared to using the original frames. Our code is published at https://github.com/gxq1998/TAI-GAN.

Low-Cost and Highly Accurate Behavioral Modeling of Antenna Structures by Means of Knowledge-Based Domain-Constrained Deep Learning Surrogates

The awareness and practical benefits of behavioral modeling methods have been steadily growing in the antenna engineering community over the last decade or so. Undoubtedly, the most important advantage thereof is a possibility of a dramatic reduction of computational expenses associated with computer-aided design procedures, especially those relying on full-wave electromagnetic (EM) simulations. In particular, the employment of fast replacement models (surrogates) allows for repetitive evaluations of the antenna structure at negligible cost, thereby accelerating processes such as parametric optimization, multi-criterial design, or uncertainty quantification. Notwithstanding, a construction of reliable data-driven surrogates is seriously hindered by the curse of dimensionality and the need for covering broad ranges of geometry/material parameters, which is imperative from the perspective of design utility. A recently proposed constrained modeling approach with knowledge-based stochastic determination of the model domain addresses this issue to a large extent and has been demonstrated to enable quasi-global modeling capability while maintaining a low setup cost. This work introduces a novel technique that capitalizes on the domain confinement paradigm and incorporates deep-learning-based regression modeling to facilitate handling of highly-nonlinear antenna characteristics. The presented framework is demonstrated using three microstrip antennas and favorably compared to several state-of-the-art techniques. The predictive power of our models reaches remarkable 2% of a relative rms error (averaged over the considered antenna structures), which is a significant improvement over all benchmark methods.

Expedited Variable-Resolution Surrogate Modeling of Miniaturized Microwave Passives in Confined Domains

The design of miniaturized microwave components is largely based on computational models, primarily, full-wave electromagnetic (EM) simulations. The EM analysis is capable of giving an accurate account for cross-coupling effects, substrate and radiation losses, or interactions with environmental components (e.g., connectors). Unfortunately, direct execution of EM-based design tasks, such as parametric optimization or uncertainty quantification (UQ), may turn prohibitively expensive in computational terms. A workaround has been offered by surrogate-assisted procedures that capitalize on replacing expensive EM simulations by fast metamodels, notably data-driven ones. However, the construction of general-purpose metamodels is impeded by the curse of dimensionality as well as a limited capability of approximation techniques to represent highly nonlinear responses of microwave devices. This article proposes a novel technique that integrates the performance-driven modeling paradigm as well as variable-resolution EM simulations. The former focuses on the construction of the surrogate in the parameter space subset encompassing high-quality designs, which effectively addresses the dimensionality issues. The latter—realized through co-kriging—contributes to further computational savings by executing the majority of circuit evaluations at the level of coarse-discretization EM analysis. Verification experiments conducted for three microstrip components demonstrate the superiority of the proposed approach over existing performance-driven techniques, let alone conventional modeling procedures, both with respect to accuracy and computational cost of the surrogate construction.

Sensitivity Analysis and Parametric Uncertainty Quantification of a Modular Multilevel Converter

Abstract This paper presents the numerical approaches for sensitivity analysis (SA) and its application in the modeling effort of a modular multilevel converter (MMC). A review of the state-of-the-art techniques in the sensitivity analysis is provided, with a special focus on the numerical approaches, followed by the sensitivity analysis of an MMC. To further reduce the computational cost per model evaluation in parametric uncertainty quantification (P-UQ) of the MMC, this paper also proposes a simplified model with a minimum number of power modules for P-UQ analysis without introducing any further uncertainties in the modeling and simulation.

Bayesian, frequentist, and information geometric approaches to parametric uncertainty quantification of classical empirical interatomic potentials

In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these tools with the Open Knowledgebase of Interatomic Models and study three models based on the Lennard-Jones, Morse, and Stillinger-Weber potentials. We confirm that IPs are typically sloppy, i.e., insensitive to coordinated changes in some parameter combinations. Because the inverse problem in such models is ill-conditioned, parameters are unidentifiable. This presents challenges for traditional statistical methods, as we demonstrate and interpret within both Bayesian and frequentist frameworks. We use information geometry to illuminate the underlying cause of this phenomenon and show that IPs have global properties similar to those of sloppy models from fields, such as systems biology, power systems, and critical phenomena. IPs correspond to bounded manifolds with a hierarchy of widths, leading to low effective dimensionality in the model. We show how information geometry can motivate new, natural parameterizations that improve the stability and interpretation of uncertainty quantification analysis and further suggest simplified, less-sloppy models.

P46 THREE–DIMENSIONAL ECHOCARDIOGRAPHY EVALUATION OF MITRAL VALVE ANATOMY AFTER PERCUTANEOUS EDGE TO EDGE REPAIR

Abstract Background Transcatheter edge–to–edge repair (TEER) is a safe strategy for high–risk patients with significant mitral regurgitation (MR). We aimed to characterize by three–dimensional echocardiography (3D–E) acute reshaping of mitral valve apparatus, with specific reference to the underlying MR mechanism (functional (FMR)and degenerative (DMR)) Methods We prospectively enrolled 15 patients(November 2020 to September 2021),(median age 81 y.o, range 79–84, 50% male, 1 urgent procedure) with severe mitral valve regurgitation who underwent intra–procedural 3D–E before and after device deployment. Using a dedicated semiautomatic software, we obtain parametric quantification of mitral valve anatomy to describe acute changes in FMR and DMR. Results Eight patients (53%) were affected by FMR of whom one case was performed as bridge to heart transplantation candidacy. In the remaining 7 DMR cases, P2 prolapse was present in 5 (71%), commissural flail and A2 flail in 2 cases. Procedural success (MR < 2) was achieved in 14 cases (93%). 30–day survival was 100% in elective cases. A second clip was necessary in 8 patients (53%). After TEER, the FMR group experienced an immediate annular reshaping, with reduction of antero–posterior diameter (p 0.05), next to a recovery of physiological saddle–shape, defined by lower non–planar angle (p = 0.001) and higher annulus height (p ≤ 0.001). The DMR group showed a trend of decrease of maximum annular velocity, addressing a stabilizing effect of the device.The deployment of a second clip has no significant effect of the annular reshaping in both groups. Conclusions TEER causes multiple effects on mitral valve geometry which variesaccording to MR mechanism. Three–D parametric quantification of MV anatomy identifiedspecific parameters of acute annular remodeling. FMR exhibited pronounced modification. This “annuloplasty–like” effect may play a role in the late freedom from MR.

Parametric uncertainty quantification of SST turbulence model for a shock train and pseudo-shock phenomenon

Computational fluid dynamics simulations are performed to identify the inadequacy of the Menter shear-stress transport (SST) turbulence model for the prediction of the shock train and pseudo-shock phenomenon in a square duct (Mr = 1.61, Re = 3 × 107 m−1), and the uncertainty of the SST model coefficients is quantified. Due to the underprediction of Reynolds stress and failures in predicting corner flow in a square duct, both two-dimensional and three-dimensional SST simulations tended to predict weaker first shock, more secondary shocks, and larger spacing between shocks. The static pressure of the wall fluctuates in the shock train region and suffers a greater loss after the shocks. Based on the two-dimensional simulations, parametric sensitivity analysis using Sobol indices is performed, and the SST model coefficients are classified into three groups according to their sensitivity and influence regions (before and within the shock train). Bayesian inference is conducted on three-dimensional simulations to quantify the uncertainty and calibrate the coefficients that mainly influence the shock train structure. After calibration using maximum a posteriori estimates, the eddy viscosity is greatly increased, and the prediction of the shock structures and the static pressure of the wall is significantly improved, while the prediction of the friction deteriorates.

Adaptive Model Refinement Approach for Bayesian Uncertainty Quantification in Turbulence Model

The Bayesian uncertainty quantification technique has become well-established in turbulence modeling over the past few years. However, it is computationally expensive to construct a globally accurate surrogate model for Bayesian inference in a high-dimensional design space, which limits uncertainty quantification for complex flow configurations. Borrowing ideas from stratified sampling and inherited sampling, an adaptive model refinement approach is proposed in this work, which concentrates on asymptotically improving the local accuracy of the surrogate model in the high-posterior-density region by adaptively appending model evaluation points. To achieve this goal, a modification of inherited Latin hypercube sampling is proposed and then integrated into the Bayesian framework. The effectiveness and efficiency of the proposed approach are demonstrated through a two-dimensional heat source inversion problem and its extension to a high-dimensional design space. Compared with the prior-based method, the adaptive model refinement approach has the ability to obtain more reliable inference results using fewer evaluation points. Finally, the approach is applied to parametric uncertainty quantification of the Menter shear-stress transport turbulence model for an axisymmetric transonic bump flow and provides convincing numerical results.

A fast computational model for the electrophysiology of the whole human heart

In this study we present a novel computational model for unprecedented simulations of the whole cardiac electrophysiology. According to the heterogeneous electrophysiologic properties of the heart, the whole cardiac geometry is decomposed into a set of coupled conductive media having different topology and electrical conductivities: (i) a network of slender bundles comprising a fast conduction atrial network, the AV–node and the ventricular bundles; (ii) the Purkinje network; and (iii) the atrial and ventricular myocardium. The propagation of the action potential in these conductive media is governed by the bidomain/monodomain equations, which are discretized in space using an in–house finite volume method and coupled to three different cell models, the Courtemanche model [1] for the atrial myocytes, the Stewart model [2] for the Purkinje Network and the ten Tusscher–Panfilov model [3] for the ventricular myocytes. The developed numerical model correctly reproduces the cardiac electrophysiology of the whole human heart in healthy and pathologic conditions and it can be tailored to study and optimize resynchronization therapies or invasive surgical procedures. Importantly, the whole solver is GPU–accelerated using CUDA Fortran providing an unprecedented speedup, thus opening the way for systematic parametric studies and uncertainty quantification analyses.