Diffusion Tensor MRI Data Research Articles

Altered white matter diffusion anisotropy in normal and preterm infants at term‐equivalent age

To investigate white matter (WM) development, voxelwise analyses of diffusion tensor MRI (DTMRI) data, acquired from 12 very preterm and 11 preterm infants with gestational ages (GA) ranging from 25 to 29 and 29 to 32 weeks, respectively, and 10 newborn normal term infants were performed. T(2) relaxation measures were also generated to assess brain water content. Compared with newborn term infants, very preterm infants were found to possess reduced fractional anisotropy (FA) within the frontal lobe, and a number of anterior and posterior commissural pathways. Preterm infants possessed reduced FA mainly within the posterior regions of the corpus callosum. Unexpectedly, we observed significantly reduced FA and increased T(2) within a number of corticospinal projections in the newborn term infants compared to the preterm groups. This finding may reflect increased water concentration and/or a lowering of FA due to the presence of crossing interhemispheric WM projections. These findings indicate that care should be taken when interpreting FA indices without knowledge of the possible effects of water concentration in the newborn infant brain.

Gray matter density and white matter integrity in pianists’ brain: A combined structural and diffusion tensor MRI study

The current study combined structural magnetic resonance imaging (sMRI) and diffusion tensor MRI (DT-MRI) to investigate both gray matter density (GMD) and white matter integrity (WMI) in 18 pianists and 21 age-matched non-musicians. The pianists began their piano training at a mean age of 12. Voxel-based morphometry of the sMRI data showed that the pianists had higher GMD in the left primary sensorimotor cortex and right cerebellum. Voxel-based analysis of the DT-MRI data showed that pianists had higher fractional anisotropy (FA) (indicating higher WMI) in the right posterior limb of the internal capsule. The sMRI and DT-MRI results indicate that both the GMD and WMI of pianists may exhibit movement-related increases during adolescence or even early adulthood compared with non-musicians.

Shape-Adaptive DCT for Denoising of 3D Scalar and Tensor Valued Images

During the last ten years or so, diffusion tensor imaging has been used in both research and clinical medical applications. To construct the diffusion tensor images, a large set of direction sensitive magnetic resonance image (MRI) acquisitions are required. These acquisitions in general have a lower signal-to-noise ratio than conventional MRI acquisitions. In this paper, we discuss computationally effective algorithms for noise removal for diffusion tensor magnetic resonance imaging (DTI) using the framework of 3-dimensional shape-adaptive discrete cosine transform. We use local polynomial approximations for the selection of homogeneous regions in the DTI data. These regions are transformed to the frequency domain by a modified discrete cosine transform. In the frequency domain, the noise is removed by thresholding. We perform numerical experiments on 3D synthetical MRI and DTI data and real 3D DTI brain data from a healthy volunteer. The experiments indicate good performance compared to current state-of-the-art methods. The proposed method is well suited for parallelization and could thus dramatically improve the computation speed of denoising schemes for large scale 3D MRI and DTI.

Whole brain voxel-wise analysis of single-subject serial DTI by permutation testing

Diffusion tensor MRI (DTI) has been widely used to investigate brain microstructural changes in pathological conditions as well as for normal development and aging. In particular, longitudinal changes are vital to the understanding of progression but these studies are typically designed for specific regions of interest. To analyze changes in these regions traditional statistical methods are often employed to elucidate group differences which are measured against the variability found in a control cohort. However, in some cases, rather than collecting multiple subjects into two groups, it is necessary and more informative to analyze the data for individual subjects. There is also a need for understanding changes in a single subject without prior information regarding the spatial distribution of the pathology, but no formal statistical framework exists for these voxel-wise analyses of DTI. In this study, we present PERVADE (permutation voxel-wise analysis of diffusion estimates), a whole brain analysis method for detecting localized FA changes between two separate points in time of any given subject, without any prior hypothesis about where changes might occur. Exploiting the nature of DTI that it is calculated from multiple diffusion-weighted images of each region, permutation testing, a non-parametric hypothesis testing technique, was modified for the analysis of serial DTI data and implemented for voxel-wise hypothesis tests of diffusion metric changes, as well as for suprathreshold cluster analysis to correct for multiple comparisons. We describe PERVADE in detail and present results from Monte Carlo simulation supporting the validity of the technique as well as illustrative examples from a healthy subject and patients in the early stages of multiple sclerosis.

Assessing atrophy of the major white matter fiber bundles of the brain from diffusion tensor MRI data

Brain atrophy is a typical feature of many neurological conditions. Therefore, quantitative evaluation and spatial characterization of atrophy are potentially useful for monitoring the evolution of central nervous system (CNS) disorders. In this study, a method for measuring atrophy of the major white matter (WM) fiber bundles in the brain using diffusion tensor (DT) MRI data is developed. To this end, an atlas was created from sets of diffusion anisotropy images from normal subjects, and the deformations necessary to match single subject anisotropy images to this atlas were then computed. Because diffusion anisotropy images were used, this approach should be sensitive to fiber bundle volume changes in the same way that using T1-weighted images allows gray matter volume changes to be measured. The Jacobian determinant of the deformation field for each subject was then used as a measure of contraction or expansion of the tissue at each image voxel. An overview of the nonlinear registration problem is given; then an optimization of the parameters for the chosen algorithm is performed and the method for producing the atlas is described. The effectiveness of the method was then tested on data from five patients with multiple sclerosis (MS) and two patients with amyotrophic lateral sclerosis (ALS).

Quantitative diffusion tensor MRI-based fiber tracking of human skeletal muscle

Diffusion-tensor magnetic resonance imaging (DT-MRI) offers great potential for understanding structure-function relationships in human skeletal muscles. The purposes of this study were to demonstrate the feasibility of using in vivo human DT-MRI fiber tracking data for making pennation angle measurements and to test the hypothesis that heterogeneity in the orientation of the tibialis anterior (TA) muscle's aponeurosis would lead to heterogeneity in pennation angle. Eight healthy subjects (5 male) were studied. T(1)-weighted anatomical MRI and DT-MRI data were acquired of the TA muscle. Fibers were tracked from the TA's aponeurosis by following the principal eigenvector. The orientations of the aponeurosis and muscle fiber tracts in the laboratory frame of reference and the orientation of the fiber tracts with respect to the aponeurosis [i.e., the pennation angle (theta)] were determined. The muscle fiber orientations, when expressed relative to the laboratory frame of reference, did not change as functions of superior-to-inferior position. The sagittal and coronal orientations of the aponeurosis did not change in practically significant manners either, but the aponeurosis' axial orientation changed by approximately 40 degrees . As a result, the mean value for theta decreased from 16.3 (SD 6.9) to 11.4 degrees (SD 5.0) along the muscle's superior-to-inferior direction. The mean value of theta was greater in the deep than in the superficial compartment. We conclude that pennation angle measurements of human muscle made using DT-MRI muscle fiber tracking are feasible and reveal that in the foot-head direction, there is heterogeneity in the pennation properties of the human TA muscle.

Astrocytic hypertrophy in dysmyelination influences the diffusion anisotropy of white matter

The effect of a proteolipid protein (PLP) mutation on the developing white matter anisotropy was examined by diffusion tensor magnetic resonance imaging (DT-MRI) in a noninvasive study of a mouse model of Pelizaeus-Merzbacher disease (PMD). The jimpy PLP mutation in mice produces an irreversible dysmyelination in jimpy males, whereas heterozygous females exhibit a transient hypomyelination, as assessed by a longitudinal study of the same mice during development. Modifications of the different individual DT-MRI parameters were highlighted by specific changes in tissue structures caused by the mutation that includes the hypomyelination, axonal abnormalities, and recovery. Astrocytic hypertrophy is a striking cellular event in dysmyelinated jimpy brain, where most axons or bundles of fibers are entirely wrapped by astrocyte cytoplasmic processes, so its influences on DT-MRI parameters in dysmyelination were examined for the first time. DT-MRI data of the jimpy brain were compared with those obtained from dysmyelination of (oligo-TTK) transgenic mice, induced by oligodendrocyte killing, which have a mild astrocyte hypertrophy (Jalabi et al., 2005), and from recovering jimpy females, which have reduced astrocyte hypertrophy. The unique morphological feature of astrocytes in jimpy males coupled with an increase in the water channel protein aquaporin 4 (AQP4) was found to facilitate the directional water diffusion in the white matter. In addition to the major changes of DT-MRI parameters in the two dysmyelinated mice caused by the myelin loss and axonal modifications, the amplified magnitude of radial and axial diffusions in jimpy males was attributed principally to the strongly pronounced astrocyte hypertrophy.

A longitudinal study of diffusion tensor MRI in ALS

In this study, we investigated whether diffusion tensor MRI (DTI) could detect progressive corticospinal tract degeneration in amyotrophic lateral sclerosis (ALS) and whether changes in diffusion variables reflected clinical deterioration. Twenty-three ALS patients and 25 healthy volunteers underwent whole brain DTI. Patients and a subset (n = 12) of controls returned for a second scan. Clinical measures of disease severity were assessed in the ALS group. Changes in fractional anisotropy (FA) and mean diffusivity (MD) were measured along the corticospinal tract using a region of interest approach. Adequate DTI data were available in 11 ALS patients and 11 controls at two time points. FA and MD differed significantly between ALS patients and controls at both time points, but neither changed significantly over time, while global measures of disease severity in patients increased with time. Although we confirmed that DTI detects corticospinal tract damage in ALS, there were no significant changes in diffusion measures over time. The sensitivity of DTI may be improved by advanced data analysis techniques, although the high dropout rate suggests that use of MRI as a biomarker in ALS may be restricted to earlier stages of disease.

A quantitative comparison of two methods to correct eddy current-induced distortions in DT-MRI

Eddy current-induced geometric distortions of single-shot, diffusion-weighted, echo-planar (DW-EP) images are a major confounding factor to the accurate determination of water diffusion parameters in diffusion tensor MRI (DT-MRI). Previously, it has been suggested that these geometric distortions can be removed from brain DW-EP images using affine transformations determined from phantom calibration experiments using iterative cross-correlation (ICC). Since this approach was first described, a number of image-based registration methods have become available that can also correct eddy current-induced distortions in DW-EP images. However, as yet no study has investigated whether separate eddy current calibration or image-based registration provides the most accurate way of removing these artefacts from DT-MRI data. Here we compare how ICC phantom calibration and affine FLIRT (http://www.fmrib.ox.ac.uk), a popular image-based multi-modal registration method that can correct both eddy current-induced distortions and bulk subject motion, perform when registering DW-EP images acquired with different slice thicknesses (2.8 and 5 mm) and b-values (1000 and 3000 s/mm(2)). With the use of consistency testing, it was found that ICC was a more robust algorithm for correcting eddy current-induced distortions than affine FLIRT, especially at high b-value and small slice thickness. In addition, principal component analysis demonstrated that the combination of ICC phantom calibration (to remove eddy current-induced distortions) with rigid body FLIRT (to remove bulk subject motion) provided a more accurate registration of DT-MRI data than that achieved by affine FLIRT.

Quantifying Human Brain Connectivity from Diffusion Tensor MRI

A new approach for quantifying the degree of connectivity between human brain regions from Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data is presented. To this aim, a functional is proposed and its theoretical properties are shown. The connectivity between pairs of white matter points is quantified by minimizing the weighted length of the curves within white matter connecting the points to each other. The weighting factor is a decreasing function of the diffusion coefficient along the curve tangent. This coefficient is a linear function of the diffusion tensor components, which are estimated from DT-MRI data. As a by-product of the analysis, the minimizing curves connecting the two points are provided. The solution of the minimization problem is obtained numerically by approximating the functional on a lattice and then solving a shortest path problem on an undirected weighted graph. The presented method is global and therefore not affected by problems due to fiber branching and crossing. It is also automatic and fast. Some results obtained from the implementation of this method on real data in physiological and simulated pathological conditions are illustrated.

Robust Tensor Splines for Approximation of Diffusion Tensor MRI Data.

In this paper, we present a novel and robust spline approximation algorithm given a noisy symmetric positive definite (SPD) tensor field. Such tensor fields commonly arise in the field of Medical Imaging in the form of Diffusion Tensor (DT) MRI data sets. We develop a statistically robust algorithm for constructing a tensor product of B-splines - for approximating and interpolating these data - using the Riemannian metric of the manifold of SPD tensors. Our method involves a two step procedure wherein the first step uses Riemannian distances in order to evaluate a tensor spline by computing a weighted intrinsic average of diffusion tensors and the second step involves minimization of the Riemannian distance between the evaluated spline curve and the given data. These two steps are alternated to achieve the desired tensor spline approximation to the given tensor field. We present comparisons of our algorithm with four existing methods of tensor interpolation applied to DT-MRI data from fixed heart slices of a rabbit, and show significantly improved results in the presence of noise and outliers. We also present validation results for our algorithm using synthetically generated noisy tensor field data with outliers. This interpolation work has many applications e.g., in DT-MRI registration, in DT-MRI Atlas construction etc. This research was in part funded by the NIH ROI NS42075 and the Department of Radiology, University of Florida.

A Riemannian approach to anisotropic filtering of tensor fields

Tensors are nowadays an increasing research domain in different areas, especially in image processing, motivated for example by diffusion tensor magnetic resonance imaging (DT-MRI). Up to now, algorithms and tools developed to deal with tensors were founded on the assumption of a matrix vector space with the constraint of remaining symmetric positive definite matrices. On the contrary, our approach is grounded on the theoretically well-founded differential geometrical properties of the space of multivariate normal distributions, where it is possible to define an affine-invariant Riemannian metric and express statistics on the manifold of symmetric positive definite matrices. In this paper, we focus on the contribution of these tools to the anisotropic filtering and regularization of tensor fields. To validate our approach we present promising results on both synthetic and real DT-MRI data.

Curvature-Driven PDE Methods for Matrix-Valued Images

Matrix-valued data sets arise in a number of applications including diffusion tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour. Consequently, there arises the need to filter and segment such tensor fields. In order to detect edge-like structures in tensor fields, we first generalise Di Zenzo's concept of a structure tensor for vector-valued images to tensor-valued data. This structure tensor allows us to extend scalar-valued mean curvature motion and self-snakes to the tensor setting. We present both two-dimensional and three-dimensional formulations, and we prove that these filters maintain positive semidefiniteness if the initial matrix data are positive semidefinite. We give an interpretation of tensorial mean curvature motion as a process for which the corresponding curve evolution of each generalised level line is the gradient descent of its total length. Moreover, we propose a geodesic active contour model for segmenting tensor fields and interpret it as a minimiser of a suitable energy functional with a metric induced by the tensor image. Since tensorial active contours incorporate information from all channels, they give a contour representation that is highly robust under noise. Experiments on three-dimensional DT-MRI data and an indefinite tensor field from fluid dynamics show that the proposed methods inherit the essential properties of their scalar-valued counterparts.

Optimization of white matter tractography for pre-surgical planning and image-guided surgery

Accurate localization of white matter fiber tracts in relation to brain tumors is a goal of critical importance to the neurosurgical community. White matter fiber tractography by means of diffusion tensor magnetic resonance imaging (DTI) is the only non-invasive method that can provide estimates of brain connectivity. However, conventional tractography methods are based on data acquisition techniques that suffer from image distortions and artifacts. Thus, a large percentage of white matter fiber bundles are distorted, and/or terminated early, while others are completely undetected. This severely limits the potential of fiber tractography in pre-surgical planning and image-guided surgery. In contrast, Turboprop-DTI is a technique that provides images with significantly fewer distortions and artifacts than conventional DTI data acquisition methods. The purpose of this study was to evaluate fiber tracking results obtained from Turboprop-DTI data. It was demonstrated that Turboprop may be a more appropriate DTI data acquisition technique for tracing white matter fibers than conventional DTI methods, especially in applications such as pre-surgical planning and image-guided surgery.

Tractography to Depict Three Layers of Visual Field Trajectories to the Calcarine Gyri

Fiber-tracking by diffusion tensor magnetic resonance imaging (DT-MRI) is currently the only noninvasive in vivo method for white matter fiber-tracking in the human brain. We used this method in attempts to visualize the optic radiation and to examine the clinical applicability of this technique. Observational case series. DT-MRI scans for fiber-tracking were obtained in five healthy volunteers by use of a whole-body, 1.5 Tesla imager. DT-MRI data were transferred to an off-line workstation; PRIDE software was used for image analysis. We constructed 3 diopters fiber trajectories by tracking the direction of the fastest diffusion from the lateral geniculate nucleus, and then selected tracts on the basis of anatomical knowledge of the optic radiation. Our method successfully reconstructed the macroscopic 3 diopters architecture of the three major groups of optic radiation in all subjects. Meyer's loop depicted by tractography was located more posterior than the known anatomical locations, although our results on the central and posterior bundles were in good agreement with them. DT-MRI scanning required 7 minutes; preliminary images of the optic radiation could be obtained in approximately 20 minutes. Fiber-tracking enabled us to obtain information quickly on the 3 diopters course of the optic radiation in vivo. The finding that the fiber-tracking method underestimates the anterior extent of the optic radiations could prove to be an important limitation in the utility of this technique for preoperative planning. The time required for data acquisition and processing makes this method acceptable for routine clinical use.

White matter fiber tractography via anisotropic diffusion simulation in the human brain

A novel approach to noninvasively tracing brain white matter fiber tracts is presented using diffusion tensor magnetic resonance imaging (DT-MRI). This technique is based on successive anisotropic diffusion simulations over the human brain, which are utilized to construct three dimensional diffusion fronts. The fiber pathways are determined by evaluating the distance and orientation from the fronts to their corresponding diffusion seeds. Synthetic and real DT-MRI data are employed to demonstrate the tracking scheme. It is shown that the synthetic tracts are accurately replicated, and several major white matter fiber pathways can be reproduced noninvasively, with the tract branching being allowed. Since simulating the diffusion process, which is truly a physical phenomenon reflecting the underlying architecture of cerebral tissues, makes full use of the diffusion tensor data, including both the magnitude and orientation information, the proposed approach is expected to enhance robustness and reliability in white matter fiber reconstruction.

White matter fiber tract modeling based on reconstruction of fiber orientation vector field in DT-MRI

The human brain undergoes rapid and dynamic development early in life. Assessment of brain growth patterns relevant to neurological disorders and disease requires a normative population model of growth and variability in order to evaluate deviation from typical development. In this paper, we focus on maturation of brain white matter as shown in diffusion tensor MRI (DT-MRI), measured by fractional anisotropy (FA), mean diffusivity (MD), as well as axial and radial diffusivities (AD, RD). We present a novel methodology to model temporal changes of white matter diffusion from longitudinal DT-MRI data taken at discrete time points. Our proposed framework combines nonlinear modeling of trajectories of individual subjects, population analysis, and testing for regional differences in growth pattern. We first perform deformable mapping of longitudinal DT-MRI of healthy infants imaged at birth, 1 year, and 2 years of age, into a common unbiased atlas. An existing template of labeled white matter regions is registered to this atlas to define anatomical regions of interest. Diffusivity properties of these regions, presented over time, serve as input to the longitudinal characterization of changes. We use non-linear mixed effect (NLME) modeling where temporal change is described by the Gompertz function. The Gompertz growth function uses intuitive parameters related to delay, rate of change, and expected asymptotic value; all descriptive measures which can answer clinical questions related to quantitative analysis of growth patterns. Results suggest that our proposed framework provides descriptive and quantitative information on growth trajectories that can be interpreted by clinicians using natural language terms that describe growth. Statistical analysis of regional differences between anatomical regions which are known to mature differently demonstrates the potential of the proposed method for quantitative assessment of brain growth and differences thereof. This will eventually lead to a prediction of white matter diffusion properties and associated cognitive development at later stages given imaging data at early stages.

The effect of filter size on VBM analyses of DT-MRI data

Voxel-based morphometry (VBM) has been used to analyze diffusion tensor MRI (DT-MRI) data in a number of studies. In VBM, following spatial normalization, data are smoothed to improve the validity of statistical inferences and to reduce inter-individual variation. However, the size of the smoothing filter used for VBM of DT-MRI data is highly variable across studies. For example, a literature review revealed that Gaussian smoothing kernels ranging in size (full width at half maximum) from zero to 16 mm have been used in DT-MRI VBM type studies. To investigate the effect of varying filter size in such analyses, whole brain DT-MRI data from 14 schizophrenic patients were compared with those of 14 matched control subjects using VBM, when the filter size was varied from zero to 16 mm. Within this range of smoothing, four different conclusions regarding apparent patient control differences could be made: (i) no significant patient-control differences; (ii) reduced FA in right superior temporal gyrus (STG) in patients; (iii) reduced FA in both right STG and left cerebellum in patients; and (iv) reduced FA only in left cerebellum in patients. These findings stress the importance of recognizing the effect of the matched filter theorem on VBM analyses of DT-MRI data. Finally, we investigated whether one of the underlying assumptions of parametric VBM, i.e., the normality of the residuals, is met. Our results suggest that, even with moderate smoothing, a large number of voxels within central white matter regions may have non-normally distributed residuals thus making valid statistical inferences with a parametric approach problematic in these areas.

Estimating intensity variance due to noise in registered images: Applications to diffusion tensor MRI

Image registration techniques which require image interpolation are widely used in neuroimaging research. We show that signal variance in interpolated images differs significantly from the signal variance of the original images in native space. We describe a simple approach to compute the signal variance in registered images based on the signal variance and covariance of the original images, the spatial transformations computed by the registration procedure, and the interpolation or approximation kernel chosen. The method is general and could handle various sources of signal variability, such as thermal noise and physiological noise, provided that their effects can be assessed in the original images. Our approach is applied to diffusion tensor (DT) MRI data, assuming only thermal noise as the source of variability in the data. We show that incorrect noise variance estimates in registered diffusion-weighted images can affect DT parameters, as well as indices of goodness of fit such as chi-square maps. In addition to DT-MRI, we believe that this methodology would be useful any time parameter extraction methods are applied to registered or interpolated data, such as in relaxometry and functional MRI studies.

Mathematical framework for simulating diffusion tensor MR neural fiber bundles

White matter (WM) fiber tractography (i.e., the reconstruction of the 3D architecture of WM fiber pathways) is known to be an important application of diffusion tensor magnetic resonance imaging (DT-MRI). For the quantitative evaluation of several fiber-tracking properties, such as accuracy, noise sensitivity, and robustness, synthetic ground-truth DT-MRI data are required. Moreover, an accurate simulated phantom is also required for optimization of the user-defined tractography parameters, and objective comparisons between fiber-tracking algorithms. Therefore, in this study a mathematical framework for simulating DT-MRI data, based on the physical properties of WM fiber bundles, is presented. We obtained a model of a WM fiber bundle by parameterizing the various features that characterize this bundle. We then evaluated three different synthetic DT-MRI models using experimental data in order to test the proposed methodology, and to determine the optimum model and parameter settings for constructing a realistic simulated DT-MRI phantom. Several examples of how the mathematical framework can be applied to compare fiber-tracking algorithms are presented.