The ellipsoidal area ratio: an alternative anisotropy index for diffusion tensor imaging

In the processing and analysis of diffusion tensor imaging (DTI) data, certain predefined morphological features of diffusion tensors are often represented as simplified scalar indices, termed diffusion anisotropy indices (DAIs). When comparing tensor morphologies across differing voxels of an image, or across corresponding voxels in different images, DAIs are mathematically and statistically more tractable than are the full tensors, which are probabilistic ellipsoids consisting of three orthogonal vectors that each has a direction and an associated scalar magnitude. We have developed a new DAI, the "ellipsoidal area ratio" (EAR), to represent the degree of anisotropy in the morphological features of a diffusion tensor. The EAR is a normalized geometrical measure of surface curvature in the 3D diffusion ellipsoid. Monte Carlo simulations and applications to the study of in vivo human data demonstrate that, at low noise levels, EAR provides a similar contrast-to-noise ratio (CNR) but a higher signal-to-noise ratio (SNR) than does fractional anisotropy (FA), which is currently the most popular anisotropy index in active use. Moreover, at the high noise levels encountered most commonly in real-world DTI datasets, EAR compared with FA is consistently much more robust to perturbations from noise and it provides a higher CNR, features useful for the analysis of DTI data that are inherently noise sensitive.     

Automated assessment of the quality of diffusion tensor imaging data using color cast of color-encoded fractional anisotropy images

Diffusion tensor imaging (DTI) data often suffer from artifacts caused by motion. These artifacts are especially severe in DTI data from infants, and implementing tight quality controls is therefore imperative for DTI studies of infants. Currently, routine procedures for quality assurance of DTI data involve the slice-wise visual inspection of color-encoded, fractional anisotropy (CFA) images. Such procedures often yield inconsistent results across different data sets, across different operators who are examining those data sets, and sometimes even across time when the same operator inspects the same data set on two different occasions. We propose a more consistent, reliable, and effective method to evaluate the quality of CFA images automatically using their color cast, which is calculated on the distribution statistics of the 2D histogram in the color space as defined by the International Commission on Illumination (CIE) on lightness and a and b (LAB) for the color-opponent dimensions (also known as the CIELAB color space) of the images. Experimental results using DTI data acquired from neonates verified that this proposed method is rapid and accurate. The method thus provides a new tool for real-time quality assurance for DTI data.     

Validation of the anisotropy index ellipsoidal area ratio in diffusion tensor imaging

A new diffusion anisotropy index, ellipsoidal area ratio (EAR), was described recently and proved to be less noise-sensitive than fractional anisotropy (FA) by theory and simulation. Here we show that EAR has higher signal-to-noise ratios than FA in average diffusion tensor imaging data from 40 normal subjects. EAR was also more sensitive than FA in detecting white matter abnormalities in a patient with widespread diffuse axonal injury. Monte Carlo simulation showed that EAR's mean values are more biased by noise than FA when anisotropy is small, both for single fiber tracts and when fiber tracts cross. However, the improved signal-to-noise ratio of EAR relative to FA suggests that EAR may be a superior measure of anisotropy both in quantifying both deep white matter with relatively uniform fiber tracts and pericortical white matter structure with relatively low anisotropy and fiber crossings.     

Removal of partial volume averaging with free water in MR diffusion tensor imaging using inversion recovery for b0 image

Purpose

To remove the partial volume averaging effect of free water in MR diffusion imaging of neural tissues by use of the fluid attenuated inversion recovery (FLAIR) without the penalty of an extended scan time.

Materials and methods

The magnetic resonance images were obtained from a normal volunteer in a coronal slice orientation at 3 T with the 20-channel rf coil. In diffusion imaging only the b0 images were obtained with the FLAIR contrast while the diffusion weighted images were obtained without the FLAIR contrast. A composition of FLAIR b0 and non-FLAIR diffusion weighted images was used in calculating the diffusion tensor and fractional anisotropy after compensating the reduced signal amplitude due to the inversion recovery in the FLAIR b0 images. The fractional anisotropy of the non-FLAIR, FLAIR, and the composite methods were analyzed for the mean and histogram in the corpus callosum, cervical spine, and the fornix tracts.

Results

The partial volume averaging effect was observed in the corpus callosum, the cervical spine, and the fornix tracts in the non-FLAIR b0 and diffusion images. The partial volume averaging effect was removed in the FLAIR diffusion images which took more than twice the scan time than the non-FLAIR diffusion imaging. The proposed composite FLAIR diffusion imaging removed the partial volume averaging effect as in the FLAIR diffusion imaging. The distribution of the FA histogram was very different between the non-FLAIR and FLAIR diffusion images, while it was very similar between the FLAIR and the composite FLAIR after correcting the white matter signal in the FLAIR b0 images.

Conclusions

The proposed composite FLAIR diffusion imaging method was equally effective in removing the partial volume averaging effect as the FLAIR diffusion imaging at a limited increase of the scan time since only a small number of b0 images needed to be obtained with the FLAIR contrast.     

Simultaneous magnetic resonance imaging of diffusion anisotropy and diffusion gradient

The theory of diffusion gradient-weighted MRI (DGWI) is presented in this paper. The Bloch-Torrey equation was modified to include the effect of intravoxel spatial-location variation of water diffusion (diffusion gradient) on MRI signal, in addition to the effect of intravoxel spatial-direction variation of water diffusion (diffusion anisotropy). An analytical solution for a diffusion-encoding spin-echo pulse sequence was derived. Unlike water diffusion which attenuates the image signal intensity, this newly derived solution relates the spatial gradient of the water diffusion with the phase of the image signal. This novel MRI technique directly measures both the water diffusion and its spatial gradient, and thus offers a noninvasive imaging tool to simultaneously investigate the intravoxel inhomogeneity and anisotropy of tissue structures. In addition, as demonstrated with our preliminary data, this new method may be utilized to delineate the interfaces of tissues with different diffusion. This method is an extension of the successful diffusion tensor MRI (DTI), but requires no additional data acquisition. In addition to the measured diffusion tensor, this new method provides measurements of the spatial derivatives of the three principal diffusivities of the tensor, thereby providing additional information for improving white matter fiber tractography.     

Cerebral infarction associated with moyamoya disease: histogram-based quantitative analysis of diffusion tensor imaging -- a preliminary study

Moyamoya disease (MMD) is a rare disorder of unknown etiology in which terminal portions of the internal carotid arteries become steno-occlusive, with fine collateral "moyamoya vessels" formed secondarily, resulting in serial ischemic strokes throughout its clinical course. Whole-brain histogram (WBH) of diffusion tensor imaging (WBH-DTI) is an analytical tool whose feasibility has been ascertained in various pathologies. To elucidate whether WBH-DTI could detect any difference between ischemic MMD and normal controls, we examined 27 consecutive MMD patients without hemorrhage and 48 normal controls in this prospective study using a 3.0-T magnetic resonance scanner. WBHs of fractional anisotropy (FA) (WBH-FA) and mean diffusivity (MD) (WBH-MD) were compared among three groups: Group 1, MMD patients with infarct (n=15); Group 2, MMD patients without infarct (n=12); and Group 3, normal controls (n=48). Group 1 showed significantly higher peak height and significantly lower mean value on WBH-FA, as well as significantly lower peak height and significantly higher mean value on WBH-MD, compared with Groups 2 and 3. No significant difference was seen in parameters at either WBH-FA or WBH-MD between Groups 2 and 3. These results might reflect the pathological severity of each group, and WBH-DTI could feasibly detect differences between ischemic MMD with infarction and MMD without infarction and normal controls.     

Influence of steady background gradients on the accuracy of molecular diffusion anisotropy measurements

Spatial susceptibility variations of body components lead to local gradients of the static magnetic field. Effects of such background gradients on fractional diffusion anisotropy (FA) measurements on whole-body magnetic resonance units operating at 1.5, 3.0 and 7.0 T were analyzed theoretically and experimentally. Analytical expressions were derived for the cases of diffusion occurring in isotropic media and in tissues with cylindrical symmetry (e.g., white matter tracts or skeletal musculature). Typical magnitudes of background gradient strengths were estimated from in vivo and in vitro measurements with B0 field mapping sequences. Additionally, numerical simulations of magnetic field distributions and resulting field gradients were performed considering tissue-air interfaces in simplified geometrical arrangements. For media with isotropic diffusion, both measurements and analytical calculations showed increasing FA inaccuracy with stronger coupling between diffusion-encoding and background gradients. For cylindrical symmetry, FA values were estimated for a standard diffusion tensor imaging protocol in a realistic scenario. At 1 mm distance from a water-air interface, susceptibility-related background gradients amount to approximately 9 mT/m at 7 T and lead to a relative error of the measured FA of up to 48%. The error in the anisotropy assessment rises considerably with increasing field strength and must be taken into account especially for experimental and clinical studies on modern high-field systems.     

Quantitative assessment of motion correction for high angular resolution diffusion imaging

Several methods have been proposed for motion correction of high angular resolution diffusion imaging (HARDI) data. There have been few comparisons of these methods, partly due to a lack of quantitative metrics of performance. We compare two motion correction strategies using two figures of merit: displacement introduced by the motion correction and the 95% confidence interval of the cone of uncertainty of voxels with prolate tensors. What follows is a general approach for assessing motion correction of HARDI data that may have broad application for quality assurance and optimization of postprocessing protocols. Our analysis demonstrates two important issues related to motion correction of HARDI data: (1) although neither method we tested was dramatically superior in performance, both were dramatically better than performing no motion correction, and (2) iteration of motion correction can improve the final results. Based on the results demonstrated here, iterative motion correction is strongly recommended for HARDI acquisitions.     

On the effects of dephasing due to local gradients in diffusion tensor imaging experiments: relevance for diffusion tensor imaging fiber phantoms

The effect of susceptibility differences between fluid and fibers on the properties of DTI fiber phantoms was investigated. Thereto, machine-made, easily producible and inexpensive DTI fiber phantoms were constructed by winding polyamide fibers of 15 microm diameter around a circular acrylic glass spindle. The achieved fractional anisotropy was 0.78+/-0.02. It is shown by phantom measurements and Monte Carlo simulations that the transversal relaxation time T(2) strongly depends on the angle between the fibers and the B(0) field if the susceptibilities of the fibers and fluid are not identical. In the phantoms, the measured T(2) time at 3 T decreased by 60% for fibers running perpendicular to B(0). Monte Carlo simulations confirmed this result and revealed that the exact relaxation time depends strongly on the exact packing of the fibers. In the phantoms, the measured diffusion was independent of fiber orientation. Monte Carlo simulations revealed that the measured diffusion strongly depends on the exact fiber packing and that field strength and -orientation dependencies of measured diffusion may be minimal for hexagonal packing while the diffusion can be underestimated by more than 50% for cubic packing at 3 T. To overcome these effects, the susceptibilities of fibers and fluid were matched using an aqueous sodium chloride solution (83 g NaCl per kilogram of water). This enables an orientation independent and reliable use of DTI phantoms for evaluation purposes.     

Keyhole and zero-padding approaches for reduced-encoding diffusion tensor imaging of the mouse brains

Keyhole diffusion tensor imaging (keyhole DTI) was previously proposed in cardiac imaging to reconstruct DTI maps from the reduced phase-encoding images. To evaluate the feasibility of keyhole DTI in brain imaging, keyhole and zero-padding DTI algorithms were employed on in vivo mouse brain. The reduced phase-encoding portion, also termed as the sharing rate, was varied from 50% to 90% of the full k-space. Our data showed that zero-padding DTI resulted in decreased fractional anisotropy (FA) and decreased mean apparent diffusion coefficient (mean ADC) in white matter (WM) regions. Keyhole DTI showed a better edge preservation on mean ADC maps but not on FA maps as compared to the zero-padding DTI. When increasing the sharing rate in keyhole approach, an underestimation of FA and an over- or underestimation of mean ADC were measured in WM depending on the selected reference image. The inconsistency of keyhole DTI may add a challenge for the wide use of this modality. However, with a carefully selected directive diffusion-weighted image to serve as the reference image in the keyhole approach, this study demonstrated that one may obtain DTI indices of reduced-encoding images with high consistency to those derived with full k-space DTI.     

Intersubject variability in the analysis of diffusion tensor images at the group level: fractional anisotropy mapping and fiber tracking techniques

Introduction

Diffusion tensor imaging (DTI) provides comprehensive information about quantitative diffusion and connectivity in the human brain. Transformation into stereotactic standard space is a prerequisite for group studies and requires thorough data processing to preserve directional inter-dependencies. The objective of the present study was to optimize technical approaches for this preservation of quantitative and directional information during spatial normalization in data analyses at the group level.

Methods

Different averaging methods for mean diffusion-weighted images containing DTI information were compared, i.e., region of interest-based fractional anisotropy (FA) mapping, fiber tracking (FT) and corresponding tractwise FA statistics (TFAS). The novel technique of intersubject FT that takes into account directional information of single data sets during the FT process was compared to standard FT techniques. Application of the methods was shown in the comparison of normal subjects and subjects with defined white matter pathology (alterations of the corpus callosum).

Results

Fiber tracking was applied to averaged data sets and showed similar results compared with FT on single subject data. The application of TFAS to averaged data showed averaged FA values around 0.4 for normal controls. The values were in the range of the standard deviation for averaged FA values for TFAS applied to single subject data. These results were independent of the applied averaging technique. A significant reduction of the averaged FA values was found in comparison to TFAS applied to data from subjects with defined white matter pathology (FA around 0.2).

Conclusion

The applicability of FT techniques in the analysis of different subjects at the group level was demonstrated. Group comparisons as well as FT on group averaged data were shown to be feasible. The objective of this work was to identify the most appropriate method for intersubject averaging and group comparison which incorporates intersubject variability of the directional information.     

Recollections about our 1996 JMR paper on diffusion anisotropy

We provide scientific background information and personal accounts relating to our publication of “Microstructural and Physiological Features of Tissues Elucidated by Quantitative-Diffusion-Tensor MRI” in the Journal of Magnetic Resonance B. This paper provided a framework for measuring and mapping intrinsic features of diffusion anisotropy obtained from diffusion tensor MRI (DTI) data.     

Analyzing diffusion tensor images with ghosting artifacts: the effects of direct and indirect normalization

The current study aims to assess the applicability of direct or indirect normalization for the analysis of fractional anisotropy (FA) maps in the context of diffusion-weighted images (DWIs) contaminated by ghosting artifacts. We found that FA maps acquired by direct normalization showed generally higher anisotropy than indirect normalization, and the disparities were aggravated by the presence of ghosting artifacts in DWIs. The voxel-wise statistical comparisons demonstrated that indirect normalization reduced the influence of artifacts and enhanced the sensitivity of detecting anisotropy differences between groups. This suggested that images contaminated with ghosting artifacts can be sensibly analyzed using indirect normalization.     

Geometric analysis of the b-dependent effects of Rician signal noise on diffusion tensor imaging estimates and determining an optimal b value

The optimal diffusion weighting (DW) factor, b, for use in diffusion tensor imaging (DTI) studies remains uncertain. In this study, the geometric relations of DW quantities are examined, in particular, the effects of Rician noise in the measured magnetic resonance signal. This geometric analysis is used to make theoretical predictions for selecting a b value to reduce the influence of noise. It is shown that the optimal b value for DTI studies in healthy human parenchyma is approximately b=1200 s mm⁻², with a simple relation given as well for a given expected apparent diffusion coefficient. Monte-Carlo simulations on sets of realistic DTI measures are then performed, verifying the optimal DW for minimizing estimate errors. The effects of noise on various DTI parameters such as anisotropy indices (fractional anisotropy and scaled relative anisotropy), mean diffusivity, radial diffusivity, eigenvalues and the direction of the first eigenvector are investigated as well.     

Dependence of the fractional anisotropy in cervical spine from the number of diffusion gradients,repeated acquisition and voxel size

The aim of this study is to investigate the consequences of using different gradient schemes, number of repeated measurements and voxel size on the fractional anisotropy (FA) value in a diffusion tensor imaging (DTI) sequence on the cervical tract of the spinal cord. Twenty healthy volunteers underwent a total of 86 DTI axial acquisitions performed by using different voxel size and number of diffusion gradient directions (NDGDs). Three different diffusion gradient schemes were applied, named 6, 15 and 32 according to the NDGD. Furthermore, some acquisitions were repeated to investigate the effects of image averaging on FA value.     

Aging effects on cerebral asymmetry: a voxel-based morphometry and diffusion tensor imaging study

The hemispheres of the human brain are functionally and structurally asymmetric. The purpose of this study was to evaluate the effects of aging on gray and white matter asymmetry. Two hundred twenty-six right-handed normal volunteers aged 21–71 years were included in this study. The effects of aging on gray matter volume asymmetry and white matter fractional anisotropy asymmetry were evaluated with use of voxel-based morphometry and voxel-based analysis of fractional anisotropy maps derived from diffusion tensor imaging (DTI), respectively. The voxel-based morphometry showed no significant correlation between age and gray matter volume asymmetry. The voxel-based analysis of DTI also showed no significant correlation between age and white matter fractional anisotropy asymmetry. Our results showed no significant effects of aging on either gray matter volume asymmetry or white matter fractional anisotropy asymmetry.     

Correlation of CSF neuroinflammatory molecules with leptomeningeal cortical subcortical white matter fractional anisotropy in neonatal meningitis

It has been previously hypothesized that the high fractional anisotropy (FA) values in leptomeningeal cortical subcortical white matter (LCSWM) regions of neonatal brain with bacterial meningitis is due to the presence of adhesion molecules in the subarachnoid space, which are responsible for adherence of inflammatory cells over the subarachnoid membrane. The aim of this study was to look for any relationship between FA values in LCSWM regions and various neuroinflammatory molecules (NMs) in cerebrospinal fluid (CSF) measured in neonates with bacterial meningitis. Diffusion tensor imaging was performed on 18 term neonates (median age, 10.5 days) having bacterial meningitis and 10 age-/sex-matched healthy controls. CSF enzyme-linked immunosorbent assay was performed to quantify NMs [soluble intracellular adhesion molecules (sICAM), tumor necrosis factor-alpha (TNF-alpha) and interleukin-1beta (IL-1beta)]. Significantly increased FA values were observed in LCSWM regions of the patients compared to controls. A significant positive correlation was observed between FA values in LCSWM regions and NMs [sICAM (r=0.67, P=.006), TNF-alpha (r=0.69, P=.005) and IL-1beta (r=0.82, P=.000)] in CSF of these patients. No difference in FA values (P=.99) in LCSWM regions was observed between patients with sterile (0.12+/-0.02) and culture-positive CSF study (0.12+/-0.02). FA may be used as noninvasive surrogate marker of NMs in neonatal meningitis in assessing therapeutic response in future.     

Evaluation of diffusion models of fiber tracts using diffusion tensor magnetic resonance imaging

Modeling of water diffusion in white matter is useful for revealing microstructure of the brain tissue and hence diagnosis and evaluation of white matter diseases. Researchers have modeled diffusion in white matter using mathematical and mechanical analysis at the cellular level. However, less work has been devoted to evaluate these models using macroscopic real data such as diffusion tensor magnetic resonance imaging (DTMRI) data. DTMRI is a noninvasive tool for evaluating white matter microstructure by measuring random motion of water molecules referred to as diffusion. It reflects directional information of microscopic structures such as fibers. Thus, it is applicable for evaluation and modification of mathematical models of white matter. Nevertheless, a realistic relation between a fiber model and imaging data does not exist. This work opens a promising avenue for relating DTMRI data to microstructural parameters of white matter. First, we propose a strategy for relating DTMRI and fiber model parameters to evaluate mathematical models in light of real data. The proposed strategy is then applied to evaluate and extend an existing model of white matter based on clinically available DTMRI data. Next, the proposed strategy is used to estimate microstructural characteristics of fiber tracts. We illustrate this approach through its application to approximation of myelin sheath thickness and fraction of volume occupied by fibers. Using sufficiently small imaging voxels, the proposed approach is capable of estimating model parameters with desirable precision.     

Diffusional kurtosis imaging of cingulate fibers in Parkinson disease: Comparison with conventional diffusion tensor imaging

Objective

The pathological changes in Parkinson disease begin in the brainstem; reach the limbic system and ultimately spread to the cerebral cortex. In Parkinson disease (PD) patients, we evaluated the alteration of cingulate fibers, which comprise part of the limbic system, by using diffusional kurtosis imaging (DKI).

Methods

Seventeen patients with PD and 15 age-matched healthy controls underwent DKI with a 3-T MR imager. Diffusion tensor tractography images of the anterior and posterior cingulum were generated. The mean kurtosis (MK) and conventional diffusion tensor parameters measured along the images in the anterior and posterior cingulum were compared between the groups. Receiver operating characteristic (ROC) analysis was also performed to compare the diagnostic abilities of the MK and conventional diffusion tensor parameters.

Results

The MK and fractional anisotropy (FA) in the anterior cingulum were significantly lower in PD patients than in healthy controls. The area under the ROC curve was 0.912 for MK and 0.747 for FA in the anterior cingulum. MK in the anterior cingulum had the best diagnostic performance (mean cutoff, 0.967; sensitivity, 0.87; specificity, 0.94).

Conclusions

DKI can detect alterations of the anterior cingulum in PD patients more sensitively than can conventional diffusion tensor imaging. Use of DKI can be expected to improve the ability to diagnose PD.