Helicity conservation by flow across scales in reconnecting vortex links and knots.

The conjecture that helicity (or knottedness) is a fundamental conserved quantity has a rich history in fluid mechanics, but the nature of this conservation in the presence of dissipation has proven difficult to resolve. Making use of recent advances, we create vortex knots and links in viscous fluids and simulated superfluids and track their geometry through topology-changing reconnections. We find that the reassociation of vortex lines through a reconnection enables the transfer of helicity from links and knots to helical coils. This process is remarkably efficient, owing to the antiparallel orientation spontaneously adopted by the reconnecting vortices. Using a new method for quantifying the spatial helicity spectrum, we find that the reconnection process can be viewed as transferring helicity between scales, rather than dissipating it. We also infer the presence of geometric deformations that convert helical coils into even smaller scale twist, where it may ultimately be dissipated. Our results suggest that helicity conservation plays an important role in fluids and related fields, even in the presence of dissipation.

Visual embedding: a model for visualization.

The authors propose visual embedding as a model for automatically generating and evaluating visualizations. A visual embedding is a function from data points to a space of visual primitives that measurably preserves structures in the data (domain) within the mapped perceptual space (range). The authors demonstrate its use with three examples: coloring of neural tracts, scatterplots with icons, and evaluation of alternative diffusion tensor glyphs. They discuss several techniques for generating visual-embedding functions, including probabilistic graphical models for embedding in discrete visual spaces. They also describe two complementary approaches--crowdsourcing and visual product spaces--for building visual spaces with associated perceptual--distance measures. In addition, they recommend several research directions for further developing the visual-embedding model.

Pulmonary lobe segmentation based on ridge surface sampling and shape model fitting.

PURPOSE: Performing lobe-based quantitative analysis of the lung in computed tomography (CT) scans can assist in efforts to better characterize complex diseases such as chronic obstructive pulmonary disease (COPD). While airways and vessels can help to indicate the location of lobe boundaries, segmentations of these structures are not always available, so methods to define the lobes in the absence of these structures are desirable. METHODS: The authors present a fully automatic lung lobe segmentation algorithm that is effective in volumetric inspiratory and expiratory computed tomography (CT) datasets. The authors rely on ridge surface image features indicating fissure locations and a novel approach to modeling shape variation in the surfaces defining the lobe boundaries. The authors employ a particle system that efficiently samples ridge surfaces in the image domain and provides a set of candidate fissure locations based on the Hessian matrix. Following this, lobe boundary shape models generated from principal component analysis (PCA) are fit to the particles data to discriminate between fissure and nonfissure candidates. The resulting set of particle points are used to fit thin plate spline (TPS) interpolating surfaces to form the final boundaries between the lung lobes. RESULTS: The authors tested algorithm performance on 50 inspiratory and 50 expiratory CT scans taken from the COPDGene study. Results indicate that the authors' algorithm performs comparably to pulmonologist-generated lung lobe segmentations and can produce good results in cases with accessory fissures, incomplete fissures, advanced emphysema, and low dose acquisition protocols. Dice scores indicate that only 29 out of 500 (5.85%) lobes showed Dice scores lower than 0.9. Two different approaches for evaluating lobe boundary surface discrepancies were applied and indicate that algorithm boundary identification is most accurate in the vicinity of fissures detectable on CT. CONCLUSIONS: The proposed algorithm is effective for lung lobe segmentation in absence of auxiliary structures such as vessels and airways. The most challenging cases are those with mostly incomplete, absent, or near-absent fissures and in cases with poorly revealed fissures due to high image noise. However, the authors observe good performance even in the majority of these cases.

Open-box spectral clustering: applications to medical image analysis.

Spectral clustering is a powerful and versatile technique, whose broad range of applications includes 3D image analysis. However, its practical use often involves a tedious and time-consuming process of tuning parameters and making application-specific choices. In the absence of training data with labeled clusters, help from a human analyst is required to decide the number of clusters, to determine whether hierarchical clustering is needed, and to define the appropriate distance measures, parameters of the underlying graph, and type of graph Laplacian. We propose to simplify this process via an open-box approach, in which an interactive system visualizes the involved mathematical quantities, suggests parameter values, and provides immediate feedback to support the required decisions. Our framework focuses on applications in 3D image analysis, and links the abstract high-dimensional feature space used in spectral clustering to the three-dimensional data space. This provides a better understanding of the technique, and helps the analyst predict how well specific parameter settings will generalize to similar tasks. In addition, our system supports filtering outliers and labeling the final clusters in such a way that user actions can be recorded and transferred to different data in which the same structures are to be found. Our system supports a wide range of inputs, including triangular meshes, regular grids, and point clouds. We use our system to develop segmentation protocols in chest CT and brain MRI that are then successfully applied to other datasets in an automated manner.

Computed tomographic measures of pulmonary vascular morphology in smokers and their clinical implications.

RATIONALE: Angiographic investigation suggests that pulmonary vascular remodeling in smokers is characterized by distal pruning of the blood vessels. OBJECTIVES: Using volumetric computed tomography scans of the chest we sought to quantitatively evaluate this process and assess its clinical associations. METHODS: Pulmonary vessels were automatically identified, segmented, and measured. Total blood vessel volume (TBV) and the aggregate vessel volume for vessels less than 5 mm(2) (BV5) were calculated for all lobes. The lobe-specific BV5 measures were normalized to the TBV of that lobe and the nonvascular tissue volume (BV5/T(issue)V) to calculate lobe-specific BV5/TBV and BV5/T(issue)V ratios. Densitometric measures of emphysema were obtained using a Hounsfield unit threshold of -950 (%LAA-950). Measures of chronic obstructive pulmonary disease severity included single breath measures of diffusing capacity of carbon monoxide, oxygen saturation, the 6-minute-walk distance, St George's Respiratory Questionnaire total score (SGRQ), and the body mass index, airflow obstruction, dyspnea, and exercise capacity (BODE) index. MEASUREMENTS AND MAIN RESULTS: The %LAA-950 was inversely related to all calculated vascular ratios. In multivariate models including age, sex, and %LAA-950, lobe-specific measurements of BV5/TBV were directly related to resting oxygen saturation and inversely associated with both the SGRQ and BODE scores. In similar multivariate adjustment lobe-specific BV5/T(issue)V ratios were inversely related to resting oxygen saturation, diffusing capacity of carbon monoxide, 6-minute-walk distance, and directly related to the SGRQ and BODE. CONCLUSIONS: Smoking-related chronic obstructive pulmonary disease is characterized by distal pruning of the small blood vessels (<5 mm(2)) and loss of tissue in excess of the vasculature. The magnitude of these changes predicts the clinical severity of disease.

COMPUTATIONAL VASCULAR MORPHOMETRY FOR THE ASSESSMENT OF PULMONARY VASCULAR DISEASE BASED ON SCALE-SPACE PARTICLES.

We present a fully automatic computational vascular morphometry (CVM) approach for the clinical assessment of pulmonary vascular disease (PVD). The approach is based on the automatic extraction of the lung intraparenchymal vasculature using scale-space particles. Based on the detected features, we developed a set of image-based biomarkers for the assessment of the disease using the vessel radii estimation provided by the particle's scale. The biomarkers are based on the interrelation between vessel cross-section area and blood volume. We validate our vascular extraction method using simulated data with different complexity and we present results in 2,500 CT scans with different degrees of chronic obstructive pulmonary disease (COPD) severity. Results indicate that our CVM pipeline may track vascular remodeling present in COPD and it can be used in further clinical studies to assess the involvement of PVD in patient populations.

AUTOMATIC AIRWAY ANALYSIS FOR GENOME-WIDE ASSOCIATION STUDIES IN COPD.

We present an image pipeline for airway phenotype extraction suitable for large-scale genetic and epidemiological studies including genome-wide association studies (GWAS) in Chronic Obstructive Pulmonary Disease (COPD). We use scale-space particles to densely sample intraparenchymal airway locations in a large cohort of high-resolution CT scans. The particle methodology is based on a constrained energy minimization problem that results in a set of candidate airway points situated in both physical space and scale. Those points are further clustered using connected components filtering to increase their specificity. Finally, we use the particle locations to perform airway wall detection using an edge detector based on the zero-crossing of the second order derivative. Given the airway wall locations, we compute three phenotypes for airway disease: wall thickening (Pi10,WA%) and luminal remodeling (P%). We validate the airway extraction technique and present results in 2,500 scans for the association of the extracted phenotypes with clinical outcomes that will be deployed as part of the COPDGene study GWAS analysis.

Superquadric glyphs for symmetric second-order tensors.

Symmetric second-order tensor fields play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods. The utility of displaying tensor field samples has driven the development of visualization techniques that encode the tensor shape and orientation into the geometry of a tensor glyph. With some exceptions, these methods work only for positive-definite tensors (i.e. having positive eigenvalues, such as diffusion tensors). We expand the scope of tensor glyphs to all symmetric second-order tensors in two and three dimensions, gracefully and unambiguously depicting any combination of positive and negative eigenvalues. We generalize a previous method of superquadric glyphs for positive-definite tensors by drawing upon a larger portion of the superquadric shape space, supplemented with a coloring that indicates the quadratic form (including eigenvalue sign). We show that encoding arbitrary eigenvalue magnitudes requires design choices that differ fundamentally from those in previous work on traceless tensors that arise in the study of liquid crystals. Our method starts with a design of 2-D tensor glyphs guided by principles of scale-preservation and symmetry, and creates 3-D glyphs that include the 2-D glyphs in their axis-aligned cross-sections. A key ingredient of our method is a novel way of mapping from the shape space of three-dimensional symmetric second-order tensors to the unit square. We apply our new glyphs to stress tensors from mechanics, geometry tensors and Hessians from image analysis, and rate-of-deformation tensors in computational fluid dynamics.

Local white matter geometry from diffusion tensor gradients.

We introduce a mathematical framework for computing geometrical properties of white matter fibers directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it possible to define scalar indices (or measures) that describe the local white matter geometry directly from the diffusion tensor field and its gradient, without requiring prior tractography. We derive new scalar indices of (1) fiber dispersion and (2) fiber curving, and we demonstrate them on synthetic and in vivo data. Finally, we illustrate their applicability to a group study on schizophrenia.

Sampling and visualizing creases with scale-space particles.

Particle systems have gained importance as a methodology for sampling implicit surfaces and segmented objects to improve mesh generation and shape analysis. We propose that particle systems have a significantly more general role in sampling structure from unsegmented data. We describe a particle system that computes samplings of crease features (i.e. ridges and valleys, as lines or surfaces) that effectively represent many anatomical structures in scanned medical data. Because structure naturally exists at a range of sizes relative to the image resolution, computer vision has developed the theory of scale-space, which considers an n-D image as an (n+1)-D stack of images at different blurring levels. Our scale-space particles move through continuous four-dimensional scale-space according to spatial constraints imposed by the crease features, a particle-image energy that draws particles towards scales of maximal feature strength, and an inter-particle energy that controls sampling density in space and scale. To make scale-space practical for large three-dimensional data, we present a spline-based interpolation across scale from a small number of pre-computed blurrings at optimally selected scales. The configuration of the particle system is visualized with tensor glyphs that display information about the local Hessian of the image, and the scale of the particle. We use scale-space particles to sample the complex three-dimensional branching structure of airways in lung CT, and the major white matter structures in brain DTI.

Optimization of volumetric computed tomography for skeletal analysis of model genetic organisms.

Forward and reverse genetics now allow researchers to understand embryonic and postnatal gene function in a broad range of species. Although some genetic mutations cause obvious morphological change, other mutations can be more subtle and, without adequate observation and quantification, might be overlooked. For the increasing number of genetic model organisms examined by the growing field of phenomics, standardized but sensitive methods for quantitative analysis need to be incorporated into routine practice to effectively acquire and analyze ever-increasing quantities of phenotypic data. In this study, we present platform-independent parameters for the use of microscopic x-ray computed tomography (microCT) for phenotyping species-specific skeletal morphology of a variety of different genetic model organisms. We show that microCT is suitable for phenotypic characterization for prenatal and postnatal specimens across multiple species.

Practical vessel imaging by computed tomography in live transgenic mouse models for human tumors.

Contrast-enhanced small-animal computed tomography is an economical and highly quantitative tool for serially examining tumor development in situ, for analyzing the network of blood vessels that nourish them, and for following the response of tumors to preclinical therapeutic intervention(s). We present practical considerations for visualizing the vascular network of transgenic mouse tumors. Using a long-acting iodinated triglyceride blood-pool contrast agent, we present optimized scanner acquisition parameters and volume-rendering techniques for examining the intermediate and large vessels of complex spontaneous tumors (e.g., alveolar rhabdomyosarcomas) in transgenic mice. Our findings indicate that multiple-frame, 360-720 view acquisitions were mandatory for clarifying bone and soft tissue from vessel contrast. This finding was consistent in visualizations using a one-dimensional transfer function where voxel color and opacity was assigned in proportion to CT value and a two-dimensional transfer function where voxel color and opacity was assigned in proportion to CT value and gradient magnitude. This study lays a groundwork for the qualitative and quantitative assessment of anti-angiogenesis preclinical studies using transgenic mice.