Search NASA⌕ Search

SEARCH · Search NASA

Results for “Multidimensional”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Statistical generic design of glass and optimization: Selective review on oxide glasses

Designing a single glass composition for a multidimensional property space is challenging, and the difficulty increases with the number of design criteria. Traditionally, the task is accomplished using multiple statistical models that describe the relationships between composition (C) and property (P) values, i.e., C-P models. Recently, the structure (S)-property (P) statistical modeling has emerged as a complementary approach. The S-P modeling approach has also been shown to be a preferred method for modeling glass properties, particularly when a small data set is available, such as in single-component studies, or when strong nonlinearities exist between composition and properties. The combined model package, C-S-P, implements the concept of generic glass design, i.e., designing glass for performance by first selecting a specific or optimized set of glass network structural groups using S-P models and then transferring the designed structures (genes) to a particular composition using C-S models. This article reviews a set of supporting cases from the previous C-S-P modeling studies of phosphate, silicate, and borosilicate glasses, which are relevant for many critical commercial applications. The methodology for developing the statistical C-S-P database is presented, enabling the application of P?S?C to achieve a generic glass design and optimization, targeting multiple design criteria for both performance and processing properties simultaneously.

Network structure↗
DOE OSTI2016

A cell wall reference profile for Miscanthus bioenergy crops highlights compositional and structural variations associated with development and organ origin

Summary Miscanthus spp. are promising lignocellulosic energy crops, but cell wall recalcitrance to deconstruction still hinders their widespread use as bioenergy and biomaterial feedstocks. Identification of cell wall characteristics desirable for biorefining applications is crucial for lignocellulosic biomass improvement. However, the task of scoring biomass quality is often complicated by the lack of a reference for a given feedstock. A multidimensional cell wall analysis was performed to generate a reference profile for leaf and stem biomass from several miscanthus genotypes harvested at three developmentally distinct time points. A comprehensive suite of 155 monoclonal antibodies was used to monitor changes in distribution, structure and extractability of noncellulosic cell wall matrix glycans. Glycan microarrays complemented with immunohistochemistry elucidated the nature of compositional variation, and in situ distribution of carbohydrate epitopes. Key observations demonstrated that there are crucial differences in miscanthus cell wall glycomes, which may impact biomass amenability to deconstruction. For the first time, variations in miscanthus cell wall glycan components were comprehensively characterized across different harvests, organs and genotypes, to generate a representative reference profile for miscanthus cell wall biomass. Ultimately, this portrait of the miscanthus cell wall will help to steer breeding and genetic engineering strategies for the development of superior energy crops.

Plant Sciences↗
DOE OSTI2021

An integrated framework of plant form and function: the belowground perspective

Summary Plant trait variation drives plant function, community composition and ecosystem processes. However, our current understanding of trait variation disproportionately relies on aboveground observations. Here we integrate root traits into the global framework of plant form and function. We developed and tested an overarching conceptual framework that integrates two recently identified root trait gradients with a well‐established aboveground plant trait framework. We confronted our novel framework with published relationships between above‐ and belowground trait analogues and with multivariate analyses of above‐ and belowground traits of 2510 species. Our traits represent the leaf and root conservation gradients (specific leaf area, leaf and root nitrogen concentration, and root tissue density), the root collaboration gradient (root diameter and specific root length) and the plant size gradient (plant height and rooting depth). We found that an integrated, whole‐plant trait space required as much as four axes. The two main axes represented the fast–slow ‘conservation’ gradient on which leaf and fine‐root traits were well aligned, and the ‘collaboration’ gradient in roots. The two additional axes were separate, orthogonal plant size axes for height and rooting depth. This perspective on the multidimensional nature of plant trait variation better encompasses plant function and influence on the surrounding environment.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Contrasting coordination of non‐structural carbohydrates with leaf and root economic strategies of alpine coniferous forests

Non-structural carbohydrates (NSCs), as the labile fraction and dominant carbon currency, are essential mediators of plant adaptation to environments. However, whether and how NSC coordinates with plant economic strategy frameworks, particularly the well-recognized leaf economics spectrums (LES) and root economics space (RES), remains unclear. We examined the relationships between NSC and key plant economics traits in leaves and fine roots across 90 alpine coniferous populations on the Tibetan Plateau, China. We observed contrasting coordination of NSC with economics traits in leaves and roots. Leaf total NSC and soluble sugar aligned with the leaf economic spectrum, conveying a trade-off between growth and storage in leaves. However, NSC in roots was independent of the root economic spectrum, but highly coordinated with root foraging, with more starch and less sugar in forage-efficient, thinner roots. Further, NSC-trait coordination in leaves and roots was, respectively, driven by local temperature and precipitation. These findings highlight distinct roles of NSC in shaping the above- and belowground multidimensional economics trait space, and NSC-based carbon economics provides a mechanistic understanding of how plants adapt to heterogeneous habitats and respond to environmental changes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Fast increased fidelity samplers for approximate Bayesian Gaussian process regression

Gaussian processes (GPs) are common components in Bayesian non-parametric models having a rich methodological literature and strong theoretical grounding. The use of exact GPs in Bayesian models is limited to problems containing several thousand observations due to their prohibitive computational demands. We develop a posterior sampling algorithm using H-matrix approximations that scales at O(n log 2 n). We show that this approximation’s Kullback-Leibler divergence to the true posterior can be made arbitrarily small. Though multidimensional GPs could be used with our algorithm, d-dimensional surfaces are modeled as tensor products of univariate GPs to minimize the cost of matrix construction and maximize computational efficiency. We illustrate the performance of this fast increased fidelity approximate GP, FIFA-GP, using both simulated and non-synthetic data sets

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A modern concept of Lagrangian hydrodynamics

Here, we offer a modern interpretation of Lagrangian hydrodynamics as employed in Lagrangian simulations of compressible fluid flow. Our main result is to show that artificial viscosity, traditionally viewed as a numerical artifice to control unphysical oscillations in flows with shocks, actually represents a physical process and is necessary to derive accurate simulations in any compressible flow. We begin by reviewing the origins of two numerical devices, artificial viscosity and finite-volume methods. We proceed to construct a mathematical (PDE) model that incorporates those numerics and in which a new length scale, the observer, arises representing the discretization. Associated with that length scale, there are new inviscid fluxes that are the artificial viscosity as first formulated by Richtmyer and an artificial heat flux postulated by Noh but typically not included in Lagrangian codes. We discuss the connection of our results to bivelocity hydrodynamics. We conclude with some speculation as to the direction of future developments in multidimensional Lagrangian codes as computers get faster and have larger memories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Multi-objective optimization of root phenotypes for nutrient capture using evolutionary algorithms

Root phenotypes are avenues to the development of crop cultivars with improved nutrient capture, which is an important goal for global agriculture. The fitness landscape of root phenotypes is highly complex and multidimensional. It is difficult to predict which combinations of traits (phene states) will create the best performing integrated phenotypes in various environments. Brute force methods to map the fitness landscape by simulating millions of phenotypes in multiple environments are computationally challenging. Evolutionary optimization algorithms may provide more efficient avenues to explore high dimensional domains such as the root phenotypic space. We coupled the three-dimensional functional–structural plant model, SimRoot, to the Borg Multi-Objective Evolutionary Algorithm (MOEA) and the evolutionary search over several generations facilitated the identification of optimal root phenotypes balancing trade-offs across nutrient uptake, biomass accumulation, and root carbon costs in environments varying in nutrient availability. Our results show that several combinations of root phenes generate optimal integrated phenotypes where performance in one objective comes at the cost of reduced performance in one or more of the remaining objectives, and such combinations differed for mobile and non-mobile nutrients and for maize (a monocot) and bean (a dicot). Functional–structural plant models can be used with multi-objective optimization to identify optimal root phenotypes under various environments, including future climate scenarios, which will be useful in developing the more resilient, efficient crops urgently needed in global agriculture.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

A Multicomponent Blend as a Diesel Fuel Surrogate for Compression Ignition Engine Applications

A mixture of n-dodecane and m-xylene is investigated as a diesel fuel surrogate for compression ignition engine applications. Compared to neat n-dodecane, this binary mixture is more representative of diesel fuel because it contains an alkyl-benzene which represents an important chemical class present in diesel fuels. A detailed multi-component mechanism for n-dodecane and m-xylene was developed by combining a previously developed n-dodecane mechanism with a recently developed mechanism for xylenes. The xylene mechanism is shown to reproduce experimental ignition data from a rapid compression machine and shock tube, speciation data from the jet stirred reactor and flame speed data. This combined mechanism was validated by comparing predictions from the model with experimental data for ignition in shock tubes and for reactivity in a flow reactor. The combined mechanism, consisting of 2885 species and 11754 reactions, was reduced to a skeletal mechanism consisting 163 species and 887 reactions for 3D diesel engine simulations. The mechanism reduction was performed using directed relation graph (DRG) with expert knowledge (DRG-X) and DRG-aided sensitivity analysis (DRGASA) at a fixed fuel composition of 77% of n-dodecane and 23% m-xylene by volume. The sample space for the reduction covered pressure of 1 – 80 bar, equivalence ratio of 0.5 – 2.0, and initial temperature of 700 – 1600 K for ignition. The skeletal mechanism was compared with the detailed mechanism for ignition and flow reactor predictions. Finally, the skeletal mechanism was validated against a spray flame dataset under diesel engine conditions documented on the Engine Combustion Network (ECN) website. These multidimensional simulations were performed using a Representative Interactive Flame (RIF) turbulent combustion model. In conclusion, encouraging results were obtained compared to the experiments with regards to the predictions of ignition delay and lift-off length at different ambient temperatures.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2016

Analytical Solution for Three-Dimensional, Unsteady Heat Conduction in a Multilayer Sphere

An analytical solution has been obtained for the transient problem of three-dimensional multilayer heat conduction in a sphere with layers in the radial direction. The solution procedure can be applied to a hollow sphere or a solid sphere composed of several layers of various materials. In general, the separation of variables applied to 3D spherical coordinates has unique characteristics due to the presence of associated Legendre functions as the eigenfunctions. Moreover, an eigenvalue problem in the azimuthal direction also requires solution; again, its properties are unique owing to periodicity in the azimuthal direction. Therefore, extending existing solutions in 2D spherical coordinates to 3D spherical coordinates is not straightforward. In a spherical coordinate system, one can solve a 3D transient multilayer heat conduction problem without the presence of imaginary eigenvalues. A 2D cylindrical polar coordinate system is the only other case in which such multidimensional problems can be solved without the use of imaginary eigenvalues. The absence of imaginary eigenvalues renders the solution methodology significantly more useful for practical applications. The methodology described can be used for all three types of boundary conditions in the outer and inner surface of the sphere. Lastly, the solution procedure is demonstrated on an illustrative problem for which results are obtained.

36 MATERIALS SCIENCE↗
DOE OSTI2018

High-Performance Computing and Analysis-Led Development of High Efficiency Dilute Opposed Piston Gasoline Engine

Pinnacle is developing a multicylinder 1.2 L gasoline engine for automotive applications using high-performance computing (HPC) and analysis methods. Pinnacle and Oak Ridge National Laboratory executed large-scale multidimensional combustion analyses at the Oak Ridge Leadership Computing Facility to thoroughly explore the design space. These HPC-led investigations show high fuel efficiency (~46% gross indicated efficiency) may be achieved by operating with extremely high charge dilution levels of exhaust gas recirculation (EGR) at a light load key drive cycle condition (2000 RPM, 3 bar brake mean effective pressure (BMEP)), while simultaneously attaining high levels of fuel conversion efficiency and low NO x emissions. In this extremely dilute environment, the flame propagation event is supported by turbulence and bulk in-cylinder charge motion brought about by modulation of inlet port flow. This arrangement produces a load and speed adjustable amalgamation of swirl and counter-rotating tumble which provides the turbulence required to support stable low-temperature combustion. At higher load conditions, the engine may operate at more traditional combustion modes to generate competitive power. In this work, the numerical results from these HPC simulations are presented. Finally, further HPC simulations and test validations are underway and will be reported in future publications.

42 ENGINEERING↗
DOE OSTI2022

Nondestructive Evaluation of Stress Corrosion Cracking in a Welded Steel Plate Using Guided Ultrasonic Waves

Stress corrosion cracking (SCC) had occurred in early-generation high-level nuclear waste tanks constructed by welding carbon steel. This paper describes an ultrasonic inspection system and its fundamental ability to detect and quantify the length of SCC on thick welded steel plates. The finite element method (FEM) was applied to simulate the welding process to estimate the welding residual stress field. Growth of stress corrosion cracks is driven by crack stress intensities exceeding the subcritical cracking threshold intensity. The subject plate was experimentally inspected with ultrasonic nondestructive evaluation (NDE) techniques to characterize the extent of SCC. The NDE system uses a piezoelectric transducer to generate guided waves in the thick steel plate, and a scanning laser Doppler vibrometer (SLDV) to measure multidimensional time–space wavefield data over a user-defined scanning area in the plate surface. The measured wavefield data can show wave interactions in a localized area in the plate due to the presence of the discontinuities of the SCC. To generate an inspection image that can precisely show the crack’s location and/or the dimension, the wavefield data are further processed to generate inspection image that maps the entire sample plate so the crack can be clearly identified in the plate while its length can be readily estimated. In conclusion, the ultrasonic test results for crack length agree well with the visually estimated length and are close to that predicted by the FEM for cracks in the weld residual stress field.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Toward Accelerating Discovery via Physics-Driven and Interactive Multifidelity Bayesian Optimization

Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and often nondifferentiable parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, processing spaces, and molecular embedding spaces. Often these systems are expensive or time consuming to evaluate a single instance, and hence classical approaches based on exhaustive grid or random search are too data intensive. This resulted in strong interest toward active learning methods such as Bayesian optimization (BO) where the adaptive exploration occurs based on human learning (discovery) objective. However, classical BO is based on a predefined optimization target, and policies balancing exploration and exploitation are purely data driven. In practical settings, the domain expert can pose prior knowledge of the system in the form of partially known physics laws and exploration policies often vary during the experiment. Here, we propose an interactive workflow building on multifidelity BO (MFBO), starting with classical (data-driven) MFBO, then expand to a proposed structured (physics-driven) structured MFBO (sMFBO), and finally extend it to allow human-in-the-loop interactive interactive MFBO (iMFBO) workflows for adaptive and domain expert aligned exploration. These approaches are demonstrated over highly nonsmooth multifidelity simulation data generated from an Ising model, considering spin–spin interaction as parameter space, lattice sizes as fidelity spaces, and the objective as maximizing heat capacity. Detailed analysis and comparison show the impact of physics knowledge injection and real-time human decisions for improved exploration with increased alignment to ground truth. Here, the associated notebooks allow to reproduce the reported analyses and apply them to other systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

NUMERICAL INVESTIGATION OF FUEL PROPERTY EFFECTS ON MIXED-MODE COMBUSTION IN A SPARK-IGNITION ENGINE

In the present study, mixed-mode combustion of an E30 fuel in a direct-injection spark-ignition engine is numerically investigated at a fuel-lean operating condition using multidimensional computational fluid dynamics (CFD). A fuel surrogate matching Research Octane Number (RON) and Motor Octane Number (MON) of E30 is first developed using neural network based non-linear regression model. To enable efficient 3D engine simulations, a 164-species skeletal reaction mechanism incorporating NO, chemistry is reducedfrom a detailed chemical kinetic model. A hybrid approach that incorporates the G-equation model for tracking turbulentflame front, and the multi-zone well-stirred reactor model for predicting auto-ignition in the end gas, is employed to account for turbulent combustion interactions in the engine cylinder. Predicted in-cylinder pressure and heat release rate traces agree well with experimental measurements. The proposed modelling approach also captures moderated cyclic variability. Two different types of combustion cycles, corresponding to purely deflagrative and mixed-mode combustion, are observed. In contrast to the purely deflagrative cycles, mixed-mode combustion cycles feature early flame propagation followed by end-gas auto-ignition, leading to two distinctive peaks in heat release rate traces. The positive correlation between mixed-mode combustion cycles and early flame propagation is well captured by simulations. With the validated numerical setup, effects of NOx chemistry on mixed-mode combustion predictions are investigated. NOx chemistry is found to promote auto-ignition through residual gas recirculation, while the deflagrative flame propagation phase remains largely unaffected. Local sensitivity analysis is then performed to understand effects of physical and chemical properties of the fuel, i.e., heat of evaporation (HoV) and laminar flame speed (S-L). An increased HoV tends to suppress end-gas auto-ignition due to increased vaporization cooling, while the impact of HoV on flame propagation is insignificant. In contrast, an increased SL is found to significantly promote both flame propagation and auto-ignition. The promoting effect of SL on auto-ignition is not a direct chemical effect; it is rather caused by an advancement of the combustion phasing, which increases compression heating of the end gas.

detailed chemical kinetics↗
DOE OSTI2017

2D/3D image charge for modeling field emission

Analytic image charge approximations exist for planar and spherical metal surfaces but approximations for more complex geometries, such as the conical and wirelike structures characteristic of field emitters, are lacking. Such models are the basis for the evaluation of Schottky lowering factors in equations for current density. The development of a multidimensional image charge approximation, useful for a general thermal-field emission equation used in space charge studies, is given and based on an analytical model using a prolate spheroidal geometry. A description of how the model may be adapted to be used with a line charge model appropriate for carbon nanotube and carbon fiber field emitters is discussed. [http://dx.doi.org/10.1116/1.4968007]

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Picometer sensitivity metrology for EUV absorber phase

With growing interest in EUV attenuated phase-shift masks due to their superior image quality for applications such as dense contact and pillar arrays, it is becoming critical to model, measure, and monitor the intensity and relative phase of multilayer and absorber reflections. We present a solution based on physical modeling of reflectometry data, which can achieve single picometer phase precision and sensitivity to changes in average film thickness below one atomic monolayer. We measure absorber and multilayer reflectivity to determine thin-film parameters with a multidimensional optimization and then acquire a new measurement of either multilayer or absorber to determine perturbations in surface contamination thickness. While it is difficult to assess the accuracy of the first step, the simplicity of the second step allows us to characterize our sensitivity to changes in contamination thickness. Thus, we apply this analysis using an initial set of measurements and repeated measurements after a period of storage. For the multilayer, the total contamination growth was 1068 pm, which occurred almost exclusively during storage (1085 pm) and decreased very slightly during repeated measurements (-17 pm). For the absorber, the behavior was quite different, with a total growth of 126 pm, which occurred much less during storage (28 pm) and primarily during repeated measurements (98 pm). Ultimately, the change in relative phase (absorber minus multilayer) was -0.86 deg for the multilayer and -1.12 deg for the absorber. We estimate the precision of the surface contamination measurement to be 3σ < 6 pm for measuring thickness and 3σ < 0.2 deg for measuring phase.

36 MATERIALS SCIENCE↗
DOE OSTI2014

A quality assurance framework for the fully automated and objective evaluation of image quality in cone-beam computed tomography

Purpose: Thousands of cone-beam computed tomography (CBCT) scanners for vascular, maxillofacial, neurological, and body imaging are in clinical use today, but there is no consensus on uniform acceptance and constancy testing for image quality (IQ) and dose yet. The authors developed a quality assurance (QA) framework for fully automated and time-efficient performance evaluation of these systems. In addition, the dependence of objective Fourier-based IQ metrics on direction and position in 3D volumes was investigated for CBCT. Methods: The authors designed a dedicated QA phantom 10 cm in length consisting of five compartments, each with a diameter of 10 cm, and an optional extension ring 16 cm in diameter. A homogeneous section of water-equivalent material allows measuring CT value accuracy, image noise and uniformity, and multidimensional global and local noise power spectra (NPS). For the quantitative determination of 3D high-contrast spatial resolution, the modulation transfer function (MTF) of centrally and peripherally positioned aluminum spheres was computed from edge profiles. Additional in-plane and axial resolution patterns were used to assess resolution qualitatively. The characterization of low-contrast detectability as well as CT value linearity and artifact behavior was tested by utilizing sections with soft-tissue-equivalent and metallic inserts. For an automated QA procedure, a phantom detection algorithm was implemented. All tests used in the dedicated QA program were initially verified in simulation studies and experimentally confirmed on a clinical dental CBCT system. Results: The automated IQ evaluation of volume data sets of the dental CBCT system was achieved with the proposed phantom requiring only one scan for the determination of all desired parameters. Typically, less than 5 min were needed for phantom set-up, scanning, and data analysis. Quantitative evaluation of system performance over time by comparison to previous examinations was also verified. The maximum percentage interscan variation of repeated measurements was less than 4% and 1.7% on average for all investigated quality criteria. The NPS-based image noise differed by less than 5% from the conventional standard deviation approach and spatially selective 10% MTF values were well comparable to subjective results obtained with 3D resolution pattern. Determining only transverse spatial resolution and global noise behavior in the central field of measurement turned out to be insufficient. Conclusions: The proposed framework transfers QA routines employed in conventional CT in an advanced version to CBCT for fully automated and time-efficient evaluation of technical equipment. With the modular phantom design, a routine as well as an expert version for assessing IQ is provided. The QA program can be used for arbitrary CT units to evaluate 3D imaging characteristics automatically.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

Analysis of perceived similarity between pairs of microcalcification clusters in mammograms

Purpose: Content-based image retrieval aims to assist radiologists by presenting example images with known pathology that are visually similar to the case being evaluated. In this work, the authors investigate several fundamental issues underlying the similarity ratings between pairs of microcalcification (MC) lesions on mammograms as judged by radiologists: the degree of variability in the similarity ratings, the impact of this variability on agreement between readers in retrieval of similar lesions, and the factors contributing to the readers’ similarity ratings. Methods: The authors conduct a reader study on a set of 1000 image pairs of MC lesions, in which a group of experienced breast radiologists rated the degree of similarity between each image pair. The image pairs are selected, from among possible pairings of 222 cases (110 malignant, 112 benign), based on quantitative image attributes (features) and the results of a preliminary reader study. Next, the authors apply analysis of variance (ANOVA) to quantify the level of variability in the readers’ similarity ratings, and study how the variability in individual reader ratings affects consistency between readers. The authors also measure the extent to which readers agree on images which are most similar to a given query, for which the Dice coefficient is used. To investigate how the similarity ratings potentially relate to the attributes underlying the cases, the authors study the fraction of perceptually similar images that also share the same benign or malignant pathology as the query image; moreover, the authors apply multidimensional scaling (MDS) to embed the cases according to their mutual perceptual similarity in a two-dimensional plot, which allows the authors to examine the manner in which similar lesions relate to one another in terms of benign or malignant pathology and clustered MCs. Results: The ANOVA results show that the coefficient of determination in the reader similarity ratings is 0.59. The variability level in the similarity ratings is proved to be a limiting factor, leading to only moderate correlation between the readers in their readings. The Dice coefficient, measuring agreement between readers in retrieval of similar images, can vary from 0.45 to 0.64 with different levels of similarity for individual readers, but is higher for average ratings from a group of readers (from 0.59 to 0.78). More importantly, the fraction of retrieved cases that match the benign or malignant pathology of the query image was found to increase with the degree of similarity among the retrieved images, reaching average value as high as 0.69 for the radiologists (p-value <10{sup −4} compared to random guessing). Moreover, MDS embedding of all the cases shows that cases having the same pathology tend to cluster together, and that neighboring cases in the plot tend to be similar in their clustered MCs. Conclusions: While individual readers exhibit substantial variability in their similarity ratings, similarity ratings averaged from a group of readers can achieve a high level of intergroup consistency and agreement in retrieval of similar images. More importantly, perceptually similar cases are also likely to be similar in their underlying benign or malignant pathology and image features of clustered MCs, which could be of diagnostic value in computer-aided diagnosis for lesions with clustered MCs.

62 RADIOLOGY AND NUCLEAR MEDICINE↗