The geometric evolution of aortic dissections: Predicting surgical success using fluctuations in integrated Gaussian curvature.

Clinical imaging modalities are a mainstay of modern disease management, but the full utilization of imaging-based data remains elusive. Aortic disease is defined by anatomic scalars quantifying aortic size, even though aortic disease progression initiates complex shape changes. We present an imaging-based geometric descriptor, inspired by fundamental ideas from topology and soft-matter physics that captures dynamic shape evolution. The aorta is reduced to a two-dimensional mathematical surface in space whose geometry is fully characterized by the local principal curvatures. Disease causes deviation from the smooth bent cylindrical shape of normal aortas, leading to a family of highly heterogeneous surfaces of varying shapes and sizes. To deconvolute changes in shape from size, the shape is characterized using integrated Gaussian curvature or total curvature. The fluctuation in total curvature (δK) across aortic surfaces captures heterogeneous morphologic evolution by characterizing local shape changes. We discover that aortic morphology evolves with a power-law defined behavior with rapidly increasing δK forming the hallmark of aortic disease. Divergent δK is seen for highly diseased aortas indicative of impending topologic catastrophe or aortic rupture. We also show that aortic size (surface area or enclosed aortic volume) scales as a generalized cylinder for all shapes. Classification accuracy for predicting aortic disease state (normal, diseased with successful surgery, and diseased with failed surgical outcomes) is 92.8±1.7%. The analysis of δK can be applied on any three-dimensional geometric structure and thus may be extended to other clinical problems of characterizing disease through captured anatomic changes.

SlicerDMRI: Diffusion MRI and Tractography Research Software for Brain Cancer Surgery Planning and Visualization.

PURPOSE: We present SlicerDMRI, an open-source software suite that enables research using diffusion magnetic resonance imaging (dMRI), the only modality that can map the white matter connections of the living human brain. SlicerDMRI enables analysis and visualization of dMRI data and is aimed at the needs of clinical research users. SlicerDMRI is built upon and deeply integrated with 3D Slicer, a National Institutes of Health-supported open-source platform for medical image informatics, image processing, and three-dimensional visualization. Integration with 3D Slicer provides many features of interest to cancer researchers, such as real-time integration with neuronavigation equipment, intraoperative imaging modalities, and multimodal data fusion. One key application of SlicerDMRI is in neurosurgery research, where brain mapping using dMRI can provide patient-specific maps of critical brain connections as well as insight into the tissue microstructure that surrounds brain tumors. PATIENTS AND METHODS: In this article, we focus on a demonstration of SlicerDMRI as an informatics tool to enable end-to-end dMRI analyses in two retrospective imaging data sets from patients with high-grade glioma. Analyses demonstrated here include conventional diffusion tensor analysis, advanced multifiber tractography, automated identification of critical fiber tracts, and integration of multimodal imagery with dMRI. RESULTS: We illustrate the ability of SlicerDMRI to perform both conventional and advanced dMRI analyses as well as to enable multimodal image analysis and visualization. We provide an overview of the clinical rationale for each analysis along with pointers to the SlicerDMRI tools used in each. CONCLUSION: SlicerDMRI provides open-source and clinician-accessible research software tools for dMRI analysis. SlicerDMRI is available for easy automated installation through the 3D Slicer Extension Manager.

Looks Good To Me: Visualizations As Sanity Checks.

Famous examples such as Anscombe's Quartet highlight that one of the core benefits of visualizations is allowing people to discover visual patterns that might otherwise be hidden by summary statistics. This visual inspection is particularly important in exploratory data analysis, where analysts can use visualizations such as histograms and dot plots to identify data quality issues. Yet, these visualizations are driven by parameters such as histogram bin size or mark opacity that have a great deal of impact on the final visual appearance of the chart, but are rarely optimized to make important features visible. In this paper, we show that data flaws have varying impact on the visual features of visualizations, and that the adversarial or merely uncritical setting of design parameters of visualizations can obscure the visual signatures of these flaws. Drawing on the framework of Algebraic Visualization Design, we present the results of a crowdsourced study showing that common visualization types can appear to reasonably summarize distributional data while hiding large and important flaws such as missing data and extraneous modes. We make use of these results to propose additional best practices for visualizations of distributions for data quality tasks.

SlicerDMRI: Open Source Diffusion MRI Software for Brain Cancer Research.

Diffusion MRI (dMRI) is the only noninvasive method for mapping white matter connections in the brain. We describe SlicerDMRI, a software suite that enables visualization and analysis of dMRI for neuroscientific studies and patient-specific anatomic assessment. SlicerDMRI has been successfully applied in multiple studies of the human brain in health and disease, and here, we especially focus on its cancer research applications. As an extension module of the 3D Slicer medical image computing platform, the SlicerDMRI suite enables dMRI analysis in a clinically relevant multimodal imaging workflow. Core SlicerDMRI functionality includes diffusion tensor estimation, white matter tractography with single and multi-fiber models, and dMRI quantification. SlicerDMRI supports clinical DICOM and research file formats, is open-source and cross-platform, and can be installed as an extension to 3D Slicer (www.slicer.org). More information, videos, tutorials, and sample data are available at dmri.slicer.org Cancer Res; 77(21); e101-3. ©2017 AACR.

Diderot: a Domain-Specific Language for Portable Parallel Scientific Visualization and Image Analysis.

Many algorithms for scientific visualization and image analysis are rooted in the world of continuous scalar, vector, and tensor fields, but are programmed in low-level languages and libraries that obscure their mathematical foundations. Diderot is a parallel domain-specific language that is designed to bridge this semantic gap by providing the programmer with a high-level, mathematical programming notation that allows direct expression of mathematical concepts in code. Furthermore, Diderot provides parallel performance that takes advantage of modern multicore processors and GPUs. The high-level notation allows a concise and natural expression of the algorithms and the parallelism allows efficient execution on real-world datasets.

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.

The effects of noise over the complete space of diffusion tensor shape.

Diffusion tensor magnetic resonance imaging (DT-MRI) is a technique used to quantify the microstructural organization of biological tissues. Multiple images are necessary to reconstruct the tensor data and each acquisition is subject to complex thermal noise. As such, measures of tensor invariants, which characterize components of tensor shape, derived from the tensor data will be biased from their true values. Previous work has examined this bias, but over a narrow range of tensor shape. Herein, we define the mathematics for constructing a tensor from tensor invariants, which permits an intuitive and principled means for building tensors with a complete range of tensor shape and salient microstructural properties. Thereafter, we use this development to evaluate by simulation the effects of noise on characterizing tensor shape over the complete space of tensor shape for three encoding schemes with different SNR and gradient directions. We also define a new framework for determining the distribution of the true values of tensor invariants given their measures, which provides guidance about the confidence the observer should have in the measures. Finally, we present the statistics of tensor invariant estimates over the complete space of tensor shape to demonstrate how the noise sensitivity of tensor invariants varies across the space of tensor shape as well as how the imaging protocol impacts measures of tensor invariants.

An Algebraic Process for Visualization Design.

We present a model of visualization design based on algebraic considerations of the visualization process. The model helps characterize visual encodings, guide their design, evaluate their effectiveness, and highlight their shortcomings. The model has three components: the underlying mathematical structure of the data or object being visualized, the concrete representation of the data in a computer, and (to the extent possible) a mathematical description of how humans perceive the visualization. Because we believe the value of our model lies in its practical application, we propose three general principles for good visualization design. We work through a collection of examples where our model helps explain the known properties of existing visualizations methods, both good and not-so-good, as well as suggesting some novel methods. We describe how to use the model alongside experimental user studies, since it can help frame experiment outcomes in an actionable manner. Exploring the implications and applications of our model and its design principles should provide many directions for future visualization research.

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.

Linear invariant tensor interpolation applied to cardiac diffusion tensor MRI.

PURPOSE: Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. METHODS: Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. RESULTS: EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. CONCLUSION: GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost.

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.

Interactive diffusion tensor tractography visualization for neurosurgical planning.

BACKGROUND: Diffusion tensor imaging (DTI) infers the trajectory and location of large white matter tracts by measuring the anisotropic diffusion of water. DTI data may then be analyzed and presented as tractography for visualization of the tracts in 3 dimensions. Despite the important information contained in tractography images, usefulness for neurosurgical planning has been limited by the inability to define which are critical structures within the mass of demonstrated fibers and to clarify their relationship to the tumor. OBJECTIVE: To develop a method to allow the interactive querying of tractography data sets for surgical planning and to provide a working software package for the research community. METHODS: The tool was implemented within an open source software project. Echo-planar DTI at 3 T was performed on 5 patients, followed by tensor calculation. Software was developed that allowed the placement of a dynamic seed point for local selection of fibers and for fiber display around a segmented structure, both with tunable parameters. A neurosurgeon was trained in the use of software in < 1 hour and used it to review cases. RESULTS: Tracts near tumor and critical structures were interactively visualized in 3 dimensions to determine spatial relationships to lesion. Tracts were selected using 3 methods: anatomical and functional magnetic resonance imaging-defined regions of interest, distance from the segmented tumor volume, and dynamic seed-point spheres. CONCLUSION: Interactive tractography successfully enabled inspection of white matter structures that were in proximity to lesions, critical structures, and functional cortical areas, allowing the surgeon to explore the relationships between them.

DTI measures in crossing-fibre areas: increased diffusion anisotropy reveals early white matter alteration in MCI and mild Alzheimer's disease.

Though mild cognitive impairment is an intermediate clinical state between healthy aging and Alzheimer's disease (AD), there are very few whole-brain voxel-wise diffusion MRI studies directly comparing changes in healthy control, mild cognitive impairment (MCI) and AD subjects. Here we report whole-brain findings from a comprehensive study of diffusion tensor indices and probabilistic tractography obtained in a very large population of healthy controls, MCI and probable AD subjects. As expected from the literature, all diffusion indices converged to show that the cingulum bundle, the uncinate fasciculus, the entire corpus callosum and the superior longitudinal fasciculus are the most affected white matter tracts in AD. Significant differences between MCI and AD were essentially confined to the corpus callosum. More importantly, we introduce for the first time in a degenerative disorder an application of a recently developed tensor index, the "mode" of anisotropy, as well as probabilistic crossing-fibre tractography. The mode of anisotropy specifies the type of anisotropy as a continuous measure reflecting differences in shape of the diffusion tensor ranging from planar (e.g., in regions of crossing fibres from two fibre populations of similar density or regions of "kissing" fibres) to linear (e.g., in regions where one fibre population orientation predominates), while probabilistic crossing-fibre tractography allows to accurately trace pathways from a crossing-fibre region. Remarkably, when looking for whole-brain diffusion differences between MCI patients and healthy subjects, the only region with significant abnormalities was a region of crossing fibres in the centrum semiovale, showing an increased mode of anisotropy. The only white matter region demonstrating a significant difference in correlations between neuropsychological scores and a diffusion measure (mode of anisotropy) across the three groups was the same region of crossing fibres. Further examination using probabilistic tractography established explicitly and quantitatively that this previously unreported increase of mode and co-localised increase of fractional anisotropy was explained by a relative preservation of motor-related projection fibres (at this early stage of the disease) crossing the association fibres of the superior longitudinal fasciculus. These findings emphasise the benefit of looking at the more complex regions in which spared and affected pathways are crossing to detect very early alterations of the white matter that could not be detected in regions consisting of one fibre population only. Finally, the methods used in this study may have general applicability for other degenerative disorders and, beyond the clinical sphere, they could contribute to a better quantification and understanding of subtle effects generated by normal processes such as visuospatial attention or motor learning.

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.

Multi-diffusion-tensor fitting via spherical deconvolution: a unifying framework.

In analyzing diffusion magnetic resonance imaging, multi-tensor models address the limitations of the single diffusion tensor in situations of partial voluming and fiber crossings. However, selection of a suitable number of fibers and numerical difficulties in model fitting have limited their practical use. This paper addresses both problems by making spherical deconvolution part of the fitting process: We demonstrate that with an appropriate kernel, the deconvolution provides a reliable approximative fit that is efficiently refined by a subsequent descent-type optimization. Moreover, deciding on the number of fibers based on the orientation distribution function produces favorable results when compared to the traditional F-Test. Our work demonstrates the benefits of unifying previously divergent lines of work in diffusion image analysis.

Automatic lung lobe segmentation using particles, thin plate splines, and maximum a posteriori estimation.

We present a fully automatic lung lobe segmentation algorithm that is effective in high resolution computed tomography (CT) datasets in the presence of confounding factors such as incomplete fissures (anatomical structures indicating lobe boundaries), advanced disease states, high body mass index (BMI), and low-dose scanning protocols. In contrast to other algorithms that leverage segmentations of auxiliary structures (esp. vessels and airways), we rely only upon image features indicating fissure locations. We employ a particle system that samples the image domain and provides a set of candidate fissure locations. We follow this stage with maximum a posteriori (MAP) estimation to eliminate poor candidates and then perform a post-processing operation to remove remaining noise particles. We then fit a thin plate spline (TPS) interpolating surface to the fissure particles to form the final lung lobe segmentation. Results indicate that our algorithm performs comparably to pulmonologist-generated lung lobe segmentations on a set of challenging cases.