The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT...

Diffusion tensor magnetic resonance imaging (DT-MRI) is a non-invasive imaging method for assessing the characteristics and organization of tissue microstructure. The diffusion tensor provides information about the magnitude, anisotropy, and orientation of water diffusion in biological tissues. In brain white matter, the direction of greatest diffusivity is typically assumed to be parallel to t...

This paper explains how radio frequency (RF) background noise produces uncertainty in measured diffusion tensor MRI (DT-MRI) data, how this noise can be modeled, and how its effects can be mitigated. DT-MRI data are derived from a series of magnitude diffusion-weighted images (DWI) in which RF noise is rectified. A new Gaussian distribution is proposed that describes the variability of the esti...

This article treats the theoretical underpinnings of diffusion-tensor magnetic resonance imaging (DT-MRI), as well as experimental design and data analysis issues. We review the mathematical model underlying DT-MRI, discuss the quantitative parameters that are derived from the measured effective diffusion tensor, and describe artifacts that arise in typical DT-MRI acquisitions. We also discuss ...

Diffusion tensor imaging (DT-MRI) is very sensitive to corrupting noise due to the non linear relationship between the diffusion-weighted image intensities (DW-MRI) and the resulting diffusion tensor. Denoising is a crucial step to increase the quality of the estimated tensor field. This enhanced quality allows for a better quantification and a better image interpretation. The methods proposed ...

A somewhat recent extension to traditional MRI imaging techniques, Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) measures the self-diffusion of water in biological tissue. Neural fiber tracts contain bundles of parallel axons whose membranes restrict diffusion, so the self-diffusion of water occurs preferentially along the tracts. Thus in DT-MRI imagery of the brain, each diffusion tenso...

Diffusion tensor magnetic resonance imaging (DT-MRI) is the first noninvasive in vivo imaging modality with the potential to generate fiber tract trajectories in soft fibrous tissues, such as the brain white matter. Several newly developed fiber reconstruction and tractography techniques based on DT-MRI are reviewed in this article, including streamline fiber tracking techniques, diffusion tens...

In this paper, we present an affine image coregistration technique for Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data sets based on mutual information. The technique is based on a multichannel approach where the diffusion weighted images are aligned according to the corresponding acquisition gradient directions. Also, in addition to the coregistration of the DT-MRI data sets, an appr...

Fractional anisotropy (FA), defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assess...

Diffusion Tensor MRI (DT-MRI) measurements are a discrete noisy sample of an underlying macroscopic effective diffusion tensor field, D(x), of water. This field is presumed to be piecewise continuous/smooth at a gross anatomical length scale. Here we describe a mathematical framework for obtaining an estimate of this tensor field from the measured DT-MRI data using a spline-based continuous app...