Quantitative analysis of diffusion tensor orientation: theoretical framework.

Diffusion-tensor MRI (DT-MRI) yields information about the magnitude, anisotropy, and orientation of water diffusion of brain tissues. Although white matter tractography and eigenvector color maps provide visually appealing displays of white matter tract organization, they do not easily lend themselves to quantitative and statistical analysis. In this study, a set of visual and quantitative tools for the investigation of tensor orientations in the human brain was developed. Visual tools included rose diagrams, which are spherical coordinate histograms of the major eigenvector directions, and 3D scatterplots of the major eigenvector angles. A scatter matrix of major eigenvector directions was used to describe the distribution of major eigenvectors in a defined anatomic region. A measure of eigenvector dispersion was developed to describe the degree of eigenvector coherence in the selected region. These tools were used to evaluate directional organization and the interhemispheric symmetry of DT-MRI data in five healthy human brains and two patients with infiltrative diseases of the white matter tracts. In normal anatomical white matter tracts, a high degree of directional coherence and interhemispheric symmetry was observed. The infiltrative diseases appeared to alter the eigenvector properties of affected white matter tracts, showing decreased eigenvector coherence and interhemispheric symmetry. This novel approach distills the rich, 3D information available from the diffusion tensor into a form that lends itself to quantitative analysis and statistical hypothesis testing.     

Effects of signal-to-noise ratio on the accuracy and reproducibility of diffusion tensor imaging-derived fractional anisotropy, mean diffusivity, and principal eigenvector measurements at 1.5 T

PURPOSE: To develop an experimental protocol to calculate the precision and accuracy of fractional anisotropy (FA), mean diffusivity (MD), and the orientation of the principal eigenvector (PEV) as a function of the signal-to-noise ratio (SNR) in vivo. MATERIALS AND METHODS: A healthy male volunteer was scanned in three separate scanning sessions, yielding a total of 45 diffusion tensor imaging (DTI) scans. To provide FA, MD, and PEV as a function of SNR, sequential scans from a scan session were grouped into nonintersecting sets. Analysis of the accuracy and precision of the DTI-derived contrasts was done in both a voxel-wise and region of interest (ROI)-based manner. RESULTS: An upward bias of FA and no significant bias in MD were present as SNR decreased, confirming results from simulation-based studies. Notably, while the precision of the PEV became worse at low SNR, no bias in the PEV orientation was observed. Overall, an accurate and precise quantification of FA values in GM requires substantially more SNR than the quantification of white matter (WM) FA values CONCLUSION: This study provides guidance for FA, MD, and PEV quantification and a means to investigate the minimal detectable differences within and across scan sessions as a function of SNR.     

Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI.

Diffusion tensor MRI (DT-MRI) permits determination of the dominant orientation of structured tissue within an image voxel. This has led to the development of 2D graphical methods for representing fiber orientation and DT-MRI "tractography," which aims to reconstruct the 3D trajectories of white matter fasciculi. Most contemporary fiber orientation mapping schemes and tractography algorithms employ the directional information contained in the eigenvectors of the diffusion tensor to approximate white matter fiber orientation. However, while the uncertainty associated with every estimate of an eigenvector has long been recognized, no attempts to quantify this uncertainty in vivo have been reported. Here, a method is proposed for determining confidence intervals in fiber orientation from real DT-MRI data using the bootstrap method. This is used to construct maps of the "cone of uncertainty," allowing simultaneous viewing of fiber orientation and its uncertainty, and to examine the relationship between orientation uncertainty and tissue anisotropy.     

Clinical applications of diffusion tensor imaging

Directionally-ordered cellular structures that impede water motion, such as cell membranes and myelin, result in water mobility that is also directionally-dependent. Diffusion tensor imaging characterizes this directional nature of water motion and thereby provides structural information that cannot be obtained by standard anatomic imaging. Quantitative apparent diffusion coefficients and fractional anisotropy have emerged from being primarily research tools to methods enabling valuable clinical applications. This review describes the clinical utility of diffusion tensor imaging, including the basic principles of the technique, acquisition, data analysis, and the major clinical applications.     

Novel diffusion anisotropy indices: an evaluation

PURPOSE: To systematically evaluate diffusion anisotropy (DA) using newly defined indices based on the diffusion deviation and mean diffusivity approach. MATERIALS AND METHODS: Measures of amplitude, area, and volume of the DA index (DAI) were measured and compared with regard to their sensitivity to changes in DA, susceptibility to noise in the original diffusion-weighted (DW) images, and contrast-to-noise ratio (CNR) in homogenous regions. Simulations were performed under different levels of noise and DA. Human DTI data were acquired from eight normal volunteers. RESULTS: Indices of area and volume measures provided improved resolution for characterizing the DA compared to the eigenvalue ratio. The amplitude measure showed consistent performances with good CNR and less susceptibility to noise in the original data. CONCLUSION: These indices are rotationally invariant without the requirement of eigenvalue sorting. At low anisotropy, all indices have a similar CNR. For larger DA, the first index (the deviation tensor divided by the DT) shows improved sensitivity, contrast-to-noise ratio (CNR), and noise immunity compared to the other indices.     

Water diffusion anisotropy in white and gray matter of the human spinal cord

PURPOSE: To develop a reliable technique for diffusion imaging of the human spinal cord at 1.5 Tesla and to assess potential differences in diffusion anisotropy in cross-sectional images. MATERIALS AND METHODS: A single-shot echo-planar imaging sequence with double spin-echo diffusion preparation was optimized regarding cerebrospinal fluid artifacts, effective resolution, and contrast-to-noise ratios. Eleven healthy volunteers participated in the study for quantitative characterization of diffusion anisotropy in white matter (WM) and gray matter (GM) by means of two diffusion encoding schemes: octahedral-six-directions for fractional anisotropy (FA) evaluation and orthogonal-three-directions for anisotropy index (AI) calculation. RESULTS: Pulse-trigger gated sequences with optimal matrix size (read x phase = 64 x 32) and b-value (700 s/mm(2)) allowed the acquisition of high-resolved images (voxel size = 0.9 x 0.9 x 5.0 mm(3)). The GM butterfly shape was recognizable in both AI and FA maps. Both encoding schemes yielded high diffusion anisotropy in dorsal WM (FA = 0.79 +/- 0.07; AI = 0.39 +/- 0.04). Lateral WM showed slightly lower anisotropy (FA = 0.69 +/- 0.08; AI = 0.35 +/- 0.03) than dorsal WM. Clearly smaller anisotropy was found in regions containing GM (FA = 0.45 +/- 0.06; AI = 0.21 +/- 0.05). CONCLUSION: Diffusion anisotropy data of the spinal cord can be obtained in a clinical setting. Its application seems promising for the assessment of neurological disorders.     

Relative indices of water diffusion anisotropy are equivalent in live and formalin-fixed mouse brains.

Formalin fixation of tissue is a common laboratory practice. A direct comparison of diffusion tensor imaging (DTI) parameters from mouse brains before (in vivo) and after (ex vivo) formalin fixation is reported herein. Five diffusion indices were examined in a cohort of seven mice: relative anisotropy (RA), directional correlation (DC), trace (Tr(D)), trace-normalized axial diffusivity (D(axially)), and radial diffusivity (D(radially)). Seven regions of interest (ROIs), including five in white matter and two in gray matter, were selected for examination. Consistent with previous findings, a significant decrease of Tr(D) was observed for all ROIs after fixation. However, water diffusion anisotropy, as defined by the indices RA, DC, D(axially), and D(radially), remained unchanged after fixation. Thus, fixation does not appear to alter diffusion anisotropy in the mouse brain. This finding supports the utility of diffusion anisotropy analysis of fixed tissue. The combination of DTI measurements and standard histology may shed light on the microstructural determinants of diffusion anisotropy in normal and disease states.     

Analytical expressions for the NMR apparent diffusion coefficients in an anisotropic system and a simplified method for determining fiber orientation

NMR measurements of anisotropic diffusion were studied using a three-dimensional random-walk model. It was found that the apparent diffusion coefficient can be expressed in a canonical form as the product of a diagonal matrix, an orthonormal rotation matrix, and a vector representing the encoding magnetic field gradient. The diffusion coefficient can be interpreted as the sum of the corresponding coefficients measured along the principal diffusion axes, weighted by the squares of the directional cosines of the encoding direction with respect to the principal axes. The analysis revealed that determining the orientation of anisotropy, in a cylindrically symmetric system, requires a minimum of four diffusion measurements. A special pulse sequence which minimized gradient cross-terms and possible restricted diffusion effects was used to characterize diffusion anisotropy in cut chicken gizzards. Diffusion coefficients parallel to the muscle fibers were found to be approximately two to three times larger than those in the transverse direction. Furthermore, the method was successful in detecting the angular change when the sample was rotated by 30°. Results indicate that the proposed approach to measure fiber orientation is valid and may be used to improve the time efficiency of diffusion anisotropy measurements.     

In vivo diffusion tensor imaging of the human calf muscle

PURPOSE: To demonstrate the feasibility of in vivo calf muscle fiber tracking in human subjects. MATERIALS AND METHODS: An EPI-based diffusion tensor imaging (DTI) sequence with six-direction diffusion gradient sensitization was implemented, and DT images were acquired at 3 Tesla on five subjects using an extremity coil. The mean diffusivity, fractional anisotropy (FA), and fiber angle (with respect to the magnet z-axis) were measured in different muscles, and fibers were tracked from several regions of interest (ROIs). RESULTS: The fiber orientations in the current DTI studies agree well with those determined in previous spectroscopic studies. The orientation angles ranged from 13.4 degrees in the lateral gastrocnemius to 48.5 degrees in the medial soleus. The diffusion ellipsoid in muscle tissue is anisotropic and approximates a prolate model, as shown by color maps of the anisotropy. Fibers were tracked from the different muscle regions, and the unipennate and bipennate structure of muscle fibers was visualized. CONCLUSION: The study clearly shows that in vivo fiber tracking of muscle fibers is feasible and could potentially be applied to study muscle structure function relationships.     

Dependence on diffusion time of apparent diffusion tensor of ex vivo calf tongue and heart.

The time dependence of the apparent diffusion tensor of ex vivo calf heart and tongue was measured for diffusion times (tau(d)) between 32 and 810 ms. The results showed evidence of restricted diffusion in the muscle tissues of both organs. In regions where the myofibers are parallel, the largest eigenvalue (lambda(1)) of the diffusion tensor remained the same for all diffusion times measured, while the other eigenvalues (lambda(2), lambda(3)) decreased by 29-36% between tau(d) = 32 ms and tau(d) = 400 ms. In regions where the fibers cross, the lambda(1) also changed, decreasing by 17% between tau(d) = 32 ms and tau(d) = 400 ms. The restricting compartment size and volume fraction were effectively estimated by fitting the time courses of the eigenvalues to a model consisting of a nonrestricted compartment and a cylindrically restricted compartment. To our knowledge, this study is the first demonstrating diffusion time dependence of measured water diffusion tensor in muscular tissue. With improvement in scanning technology, future studies may permit noninvasive, in vivo detection of changes in muscle myoarchitecture due to disease, treatment, and exercise.     

Increased diffusion sensitivity with hyperechos.

It is shown that the introduction of a 180 degrees refocusing pulse into a standard diffusion weighted stimulated echo sequence is equivalent to the simplest hyperecho sequence with identical diffusion weighting but equal or greater signal-to-noise (SNR) and thus equal or greater diffusion contrast. For high b-value imaging, the hyperecho sequence thus possesses the high diffusion contrast in the presence of small T(1)/T(2) ratios characteristic of stimulated echo sequences but with less than the 50% loss in SNR that is associated with the stimulated echo. For low b-value imaging, the hyperecho signal converges to that of the standard spin echo. The advantages of the two-pulse diffusion weighted hyperecho sequence are demonstrated theoretically. Experimental results are shown in the application to high angular resolution diffusion encoding (HARD) in normal human brain.     

Single-step nonlinear diffusion tensor estimation in the presence of microscopic and macroscopic motion.

Patient motion can cause serious artifacts in diffusion tensor imaging (DTI), diminishing the reliability of the estimated diffusion tensor information. Studies in this field have so far been limited mainly to the correction of miniscule physiological motion. In order to correct for gross patient motion it is not sufficient to correct for misregistration between successive shots; the change in the diffusion-encoding direction must also be accounted for. This becomes particularly important for multishot sequences, whereby-in the presence of motion-each shot is encoded with a different diffusion weighting. In this study a general mathematical framework to correct for gross patient motion present in a multishot and multicoil DTI scan is presented. A signal model is presented that includes the effect of rotational and translational motion in the patient frame of reference. This model was used to create a nonlinear least-squares formulation, from which the diffusion tensors were obtained using a nonlinear conjugate gradient algorithm. Applications to both phantom simulations and in vivo studies showed that in the case of gross motion the proposed algorithm performs superiorly compared to conventional methods used for tensor estimation.     

Conventional DTI vs. slow and fast diffusion tensors in cat visual cortex.

Diffusion tensor imaging (DTI) uses water diffusion anisotropy in axonal fibers to provide a tool for analyzing and tracking those fibers in brain white matter. In the present work, multidirectional diffusion MRI data were collected from a cat brain and decomposed into slow and fast diffusion tensors and directly compared with conventional DTI data from the same imaging slice. The fractional anisotropy of the slow diffusing component (D(slow)) was significantly higher than the anisotropy measured by conventional DTI while reflecting a similar directionality and appeared to account for most of the anisotropy observed in gray matter, where the fiber density is notoriously low. Preliminary results of fiber tracking based on the slow diffusion component are shown. Fibers generated based on the slow diffusion component appear to follow the vertical fibers in gray matter. D(slow)TI may provide a way for increasing the sensitivity to anisotropic structures in cortical gray matter.     

Total magnitude of diffusion tensor imaging as an effective tool for the differentiation of glioma

Objectives

The study aims to evaluate the difference in diffusion properties between high grade glioma and low grade glioma by measuring the total magnitude of diffusion tensor (L), and its isotropic (p) and anisotropic (q) components.

Methods

The diffusion tensor parameters p, q, L and FA from the tumor area, adjacent area to the tumor and corresponding contra lateral normal area of 30 high grade glioma and 49 low grade glioma were calculated. Chi square analysis was done to find the changes in age and sex. One Way ANOVA was performed to compare the mean and ROC curve analysis to confirm the discriminative sensitivity.

Results

Major variation in the mean values of p, L and FA was observed in different brain areas considered. Variation in the p and L values between low grade and high grade glioma were statistically significant (p < 0.001) and their ROC curve analysis yielded 93.9% and 91.8% sensitivity and 53.3% specificity respectively.

Conclusion

Measurement of the isotropic component p and the total value of diffusion tensor L can be effectively correlated with different grades of glioma and can be used to study the diffusion properties of tumor affected brain.     

Contrast-to-noise ratios of diffusion anisotropy indices.

The degree of diffusion anisotropy in different brain regions is usually measured by a diffusion anisotropy index (DAI) such as relative anisotropy (RA) and fractional anisotropy (FA). FA has been reported to have a higher contrast-to-noise ratio (CNR) than RA. The present work compares the CNRs of seven DAIs in theoretical propagation-of-error calculations, in simulations, and in human brain measurements over small and large anisotropy differences. In simulations all seven CNRs were similar for small anisotropy differences. Small differences among the DAIs appeared at higher anisotropy levels and lower signal-to-noise ratios with certain tensor orientations. The DAIs fell into three groups based on algebraic relationships and small CNR differences. The group with RA and FA had the best CNR. Human brain regions with small anisotropy differences had similar CNR for all seven DAIs, and the scatter in the data was greater than any expected differences. With large anisotropy differences, a small advantage appeared for RA over FA in some simulations and for FA over RA in other simulations. The CNR between brain regions with very different anisotropies was different for each DAI. The apparent reported advantage of FA over RA is explained by biologic heterogeneity and by noise-induced bias in the DAI values and their standard deviations.