For positive semi-definite tensors like diffusion tensors in the plane it is possible to calculate several different means or p-averages. These are related to p-norms for functions, but produce mappings rather than numbers as means. We compare these means for various values of the real parameter p. One important future application is the filtering and interpolation of tensor fields in Diffusion...

We describe a virtual reality application for visualizing tensorvalued volume data acquired with diffusion tensor magnetic resonance imaging (DT-MRI). We have prototyped a virtual environment that displays geometric representations of the volumetric 2nd-order diffusion tensor data and are developing interaction and visualization techniques for two application areas: studying changes in white-ma...

Segmentation of anatomical regions of the brain is one of the fundamental problems in medical image analysis. It is traditionally solved by iso-surfacing or through the use of active contours/ deformable models on a gray-scale magnetic resonance imaging (MRI) data. We develop a technique that uses anisotropic diffusion properties of brain tissue available from diffusion tensor (DT)-MRI to segme...

Diffusion Tensor MRI (DT-MRI) provides a statistical estimate of a symmetric 2 nd -order diffusion tensor, D, for each voxel within an imaging volume. We propose a new normal distribution, p(D) ~ exp(1/2 D:A:D), for a tensor random variable, D. The scalar invariant, D:A:D, is the contraction of a positive definite symmetric 4 th -order precision tensor, A , and D. A formal correspondence is est...

OBJECTIVE We wanted to evaluate the effect of the number of diffusion-sensitizing gradient directions on the image quality for evaluating myocardial anisotropy and fiber tracking by using in vitro diffusion tensor MR imaging (DT-MRI). MATERIALS AND METHODS The DT-MR images, using a SENSE-based echoplanar imaging technique, were acquired from ten excised porcine hearts by using a 3T MR scanner...

Recent advancement of MRI techniques and development of new methods of image analysis have allowed us to study large neural tracts within the human brain. This is based on the principle of diffusion tensor MRI that is similar to that of diffusion-weighted imaging but takes magnitude and direction of the diffusion of water into account. Using this technique we have been able to define large neur...

G. K. Rohde1,2, S. Pajevic3, C. Pierpaoli1 STBB/LIMB/NICHD, National Institutes of Health, Bethesda, Maryland, United States, Dept. of Mathematics, University of Maryland, College Park, Maryland, United States, MSCL/CIT, National Institutes of Health, Bethesda, Maryland, United States Introduction In Diffusion Tensor (DT) MRI [1], local diffusion properties are described via a 3x3 symmetric dif...

Recent advancement of MRI techniques and development of new methods of image analysis have allowed us to study large neural tracts within the human brain. This is based on the principle of diffusion tensor MRI that is similar to that of diffusion-weighted imaging but takes magnitude and direction of the diffusion of water into account. Using this technique we have been able to define large neur...

There are conflicting opinions in the literature as to whether it is more beneficial to use a large number of gradient sampling orientations in diffusion tensor MRI (DT-MRI) experiments than to use a smaller number of carefully chosen orientations. In this study, Monte Carlo simulations were used to study the effect of using different gradient sampling schemes on estimates of tensor-derived qua...

In diffusion tensor magnetic resonance imaging (DT-MRI), limitations concerning complex fiber architecture (when an image voxel contains fiber populations with more than one dominant orientation) are well-known. Fractional anisotropy (FA) values are lower in such areas because of a lower directionality of diffusion on the voxel-scale, which makes the interpretation of FA less straightforward. M...