Degeneracy-aware interpolation of 3D diffusion tensor fields

NeuroImage, 2006

To enhance the performance of diffusion tensor imaging (DTI)-based fiber tractography, this study proposes a unified framework for anisotropic interpolation and smoothing of DTI data. The critical component of this framework is an anisotropic sigmoid interpolation kernel which is adaptively modulated by the local image intensity gradient profile. The adaptive modulation of the sigmoid kernel permits image smoothing in homogeneous regions and meanwhile guarantees preservation of structural boundaries. The unified scheme thus allows piece-wise smooth, continuous and boundary preservation interpolation of DTI data, so that smooth fiber tracts can be tracked in a continuous manner and confined within the boundaries of the targeted structure. The new interpolation method is compared with conventional interpolation methods on the basis of fiber tracking from synthetic and in vivo DTI data, which demonstrates the effectiveness of this unified framework.

Medical Image Analysis, 2002

This paper presents processing and visualization techniques for Diffusion Tensor Magnetic Resonance Imaging (DT-MRI). In DT-MRI, each voxel is assigned a tensor that describes local water diffusion. The geometric nature of diffusion tensors enables us to quantitatively characterize the local structure in tissues such as bone, muscle, and white matter of the brain. This makes DT-MRI an interesting modality for image analysis. In this paper we present a novel analytical solution to the Stejskal-Tanner diffusion equation system whereby a dual tensor basis, derived from the diffusion sensitizing gradient configuration, eliminates the need to solve this equation for each voxel. We further describe decomposition of the diffusion tensor based on its symmetrical properties, which in turn describe the geometry of the diffusion ellipsoid. A simple anisotropy measure follows naturally from this analysis. We describe how the geometry or shape of the tensor can be visualized using a coloring scheme based on the derived shape measures. In addition, we demonstrate that human brain tensor data when filtered can effectively describe macrostructural diffusion, which is important in the assessment of fiber-tract organization. We also describe how white matter pathways can be monitored with the methods introduced in this paper. DT-MRI tractography is useful for demonstrating neural connectivity (in vivo) in healthy and diseased brain tissue.

Scientific …, 2010

Interpolation is an essential step in the visualization process. While most data from simulations or experiments are discrete many visualization methods are based on smooth, continuous data approximation or interpolation methods. We introduce a new interpolation method for symmetrical tensor fields given on a triangulated domain. Differently from standard tensor field interpolation, which is based on the tensor components, we use tensor invariants, eigenvectors and eigenvalues, for the interpolation. This interpolation minimizes the number of eigenvectors and eigenvalues computations by restricting it to mesh vertices and makes an exact integration of the tensor lines possible. The tensor field topology is qualitatively the same as for the component wise-interpolation. Since the interpolation decouples the "shape" and "direction" interpolation it is shape-preserving, what is especially important for tracing fibers in diffusion MRI data.

Medical Image Computing and Computer-Assisted Intervention, 1999

This paper describes work on the registration of diffusion tensor images of the human brain. An existing registration algorithm, the multi-resolution, elastic matching algorithm, [1-3], has been adapted for this purpose. One problem with the application of such a method to this new data type is that transformations of the image affect the DT values at each voxel, as the orientation can change with respect to the surrounding anatomical structures. Three methods for the estimation of an appropriate reorientation of the data from the local displacement field, which describes the image transformation, are presented and tested. Results indicate that the best matches are obtained from a reorientation strategy that takes into account the effects of local shearing on the data as well as the rigid rotational component of the displacement. The methods presented here may be useful for the computation of region based similarity measures of single valued intensity images, which also vary with local image orientation.

Journal of Magnetic Resonance Imaging, 2007

Purpose-To introduce a framework that automatically identifies regions of anatomical abnormality within anatomical MR images and uses those regions in hypothesis-driven selection of seed points for fiber tracking with diffusion tensor (DT) imaging (DTI).

SPIE Proceedings, 2001

Diffusion weighted magnetic resonance imaging (DW MRI) is a technique that measures the diffusion properties of water molecules to produce a tensor-valued volume dataset. Because water molecules can diffuse more easily along fiber tracts, for example in the brain, rather than across them, diffusion is anisotropic and can be used for segmentation. Segmentation requires the identification of regions with different diffusion properties. In this paper we propose a new set of rotationally invariant diffusion measures which may be used to map the tensor data into a scalar representation. Our invariants may be rapidly computed because they do not require the calculation of eigenvalues. We use these invariants to analyze a 3D DW MRI scan of a human head and build geometric models corresponding to isotropic and anisotropic regions. We then utilize the models to perform quantitative analysis of these regions, for example calculating their surface area and volume.

Proceedings of SPIE, 2001

Diffusion weighted magnetic resonance imaging (DW MRI) is a technique that measures the diffusion properties of water molecules to produce a tensor-valued volume dataset. Because water molecules can diffuse more easily along fiber tracts, for example in the brain, rather than across them, diffusion is anisotropic and can be used for segmentation. Segmentation requires the identification of regions with different diffusion properties. In this paper we propose a new set of rotationally invariant diffusion measures which may be used to map the tensor data into a scalar representation. Our invariants may be rapidly computed because they do not require the calculation of eigenvalues. We use these invariants to analyze a 3D DW MRI scan of a human head and build geometric models corresponding to isotropic and anisotropic regions. We then utilize the models to perform quantitative analysis of these regions, for example calculating their surface area and volume.

Magnetic resonance …, 2006

Tractography algorithms for diffusion tensor (DT) images consecutively connect directions of maximal diffusion across neighboring DTs in order to reconstruct the 3-dimensional trajectories of white matter tracts in vivo in the human brain. The performance of these algorithms, however, is strongly influenced by the amount of noise in the images and by the presence of degenerate tensors -i.e., tensors in which the direction of maximal diffusion is poorly defined. We propose a simple procedure for the classification of tensor morphologies that uses test statistics based on invariant measures of DTs, such as fractional anisotropy, while accounting for the effects of noise on tensor estimates. Examining DT images from seven human subjects, we demonstrate that this procedure validly classifies DTs at each voxel into standard types (nondegenerate DTs, as well as degenerate oblate, prolate or isotropic DTs), and we provide preliminary estimates for the prevalence and spatial distribution of degenerate tensors in these brains. We also show that the P values for test statistics are more sensitive tools for classifying tensor morphologies than are invariant measures of anisotropy alone.

IEEE journal of biomedical and health informatics, 2014

This paper studies and evaluates the feasibility and the performance of different level interpolations for improving spatial resolution of diffusion tensor magnetic resonance imaging (DT-MRI or DTI). In particular, the following techniques are investigated: anisotropic interpolation operating on scalar gray-level images, log-Euclidean interpolation method, and the quaternion interpolation method, which operate on diffusion tensor fields. The performance is evaluated both qualitatively and quantitatively using criteria such as tensor determinant, fractional anisotropy (FA), mean diffusivity (MD), fiber length, etc. We conclude that tensor field interpolations allow avoiding undesirable swelling effect in DTI, which is not the case with scalar gray-level interpolation, and that scalar gray-level image interpolation and log-Euclidean tensor field interpolation suffer from decrease in FA and MD, which may mislead the interpretation of the clinical parameters FA and MD. In contrast, the ...

Computerized Medical Imaging and Graphics, 2011

Tensor scale (t-scale) is a parametric representation of local structure morphology that simultaneously describes its orientation, shape and isotropic scale. At any image location, t-scale represents the largest ellipse (an ellipsoid in three dimensions) centered at that location and contained in the same homogeneous region. Here, we present an improved algorithm for t-scale computation and study its application to image interpolation. Specifically, the t-scale computation algorithm is improved by: (1) enhancing the accuracy of identifying local structure boundary and (2) combining both algebraic and geometric approaches in ellipse fitting. In the context of interpolation, a closed form solution is presented to determine the interpolation line at each image location in a gray level image using t-scale information of adjacent slices. At each location on an image slice, the method derives normal vector from its t-scale that yields trans-orientation of the local structure and points to the closest edge point. Normal vectors at the matching two-dimensional locations on two adjacent slices are used to compute the interpolation line using a closed form equation. The method has been applied to BrainWeb data sets and to several other images from clinical applications and its accuracy and response to noise and other image-degrading factors have been examined and compared with those of current state-of-the-art interpolation methods. Experimental results have established the superiority of the new t-scale based interpolation method as compared to existing interpolation algorithms. Also, a quantitative analysis based on the paired t-test of residual errors has ascertained that the improvements observed using the t-scale based interpolation are statistically significant.