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.

Most direct volume renderings produced today employ one-dimensional transfer functions which assign color and opacity to the volume based solely on the single scalar quantity which comprises the data set. Though they have not received widespread attention, multidimensional transfer functions are a very effective way to extract materials and their boundaries for both scalar and multivariate data. However, identifying good transfer functions is difficult enough in one dimension, let alone two or three dimensions. This paper demonstrates an important class of three-dimensional transfer functions for scalar data, and describes the application of multidimensional transfer functions to multivariate data. We present a set of direct manipulation widgets that make specifying such transfer functions intuitive and convenient. We also describe how to use modern graphics hardware to both interactively render with multidimensional transfer functions and to provide interactive shadows for volumes. The transfer functions, widgets, and hardware combine to form a powerful system for interactive volume exploration.

This paper outlines the mathematical development and application of two analytically orthogonal tensor invariants sets. Diffusion tensors can be mathematically decomposed into shape and orientation information, determined by the eigenvalues and eigenvectors, respectively. The developments herein orthogonally decompose the tensor shape using a set of three orthogonal invariants that characterize the magnitude of isotropy, the magnitude of anisotropy, and the mode of anisotropy. The mode of anisotropy is useful for resolving whether a region of anisotropy is linear anisotropic, orthotropic, or planar anisotropic. Both tensor trace and fractional anisotropy are members of an orthogonal invariant set, but they do not belong to the same set. It is proven that tensor trace and fractional anisotropy are not mutually orthogonal measures of the diffusive process Key words: DT-MRI; tractography; tensor; invariant; anisotropyThe utility of magnetic resonance imaging (MRI) to characterize biologic tissue is amplified by analysis and visualization methods that help researchers to see and understand the structures within the data. Tensor-valued imaging is an increasingly important source of information about tissue structure and dynamics, such as with diffusion tensor MRI (DT-MRI), and strain tensors derived from displacement encoded MRI. An effective and established way of describing structure in tensor fields is through a function that maps tensors to more readily understood scalar metrics. The medical imaging literature provides a variety of such metrics (e.g., bulk mean diffusivity, fractional anisotropy).This paper uses a combination of mathematics and visualizations to generate a rigorous and intuitive exposition of tensor shape, characterized by sets of orthogonal tensor invariants. Each invariant set decomposes tensor shape with an orthogonal basis. When invariants have application-specific significance (as they do in DT-MRI imaging), orthogonality is a useful property of an invariant set, because it isolates the measurement of variation in one physiologic property from variations in another. These sets of orthogonal tensor invariants are then used to create informative visualizations of tensor field structure. The result is the establishment of two sets of orthogonal tensor invariants that incorporate the established use of fractional anisotropy (FA) and apparent diffusion coefficient (ADC).Diffusion tensors are symmetric and thus can be decomposed into an eigensystem of three real eigenvalues and three mutually orthogonal eigenvectors. We adopt the terminology that tensor "shape" refers to those degrees of freedom in tensor values (components of the matrix representation of a tensor) spanned by changes in the eigenvalues, while keeping eigenvectors fixed. "Orientation," on the other hand, refers to the complementary degrees of freedom associated with changes in the eigenvectors, while keeping the eigenvalues fixed. Defining shape and orientation in terms of the tensor eigensystem coincides with the standard visuali...

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.

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.helicity | fluid topology | vortex reconnections | superfluid vortices | topological fields