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.     

Study of myocardial fiber pathway using magnetic resonance diffusion tensor imaging

The purpose of this study was to investigate myocardial fiber pathway distribution in order to provide supplemental information on myocardial fiber architecture and cardiac mechanics. Diffusion tensor imaging (DTI) with medium diffusion resolution (15 directions) was performed on normal canine heart samples (N=6) fixed in formalin. With the use of diffusion tensor fiber tracking, left ventricle (LV) myocardial fiber pathways and helix angles were computed pixel by pixel at short-axis slices from base to apex. Distribution of DTI-tracked fiber pathway length and number was analyzed quantitatively as a function of fiber helix angle in step of 9 degrees . The long fiber pathways were found to have small helix angles. They are mostly distributed in the middle myocardium and run circumferentially. Fiber pathways tracked at the middle and upper LV are generally longer than those near the apex. Majority of fiber pathways have small helix angles between -20 degrees and 20 degrees , dominating the fiber architecture in myocardium. Likely, such myocardial fiber pathway measurement by DTI may reflect the spatial connectiveness or connectivity of elastic myofiber bundles along their preferential pathway of electromechanical activation. The dominance of the long and circumferentially running fiber pathways found in the study may explain the circumferential predominance in left ventricular contraction.     

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.     

A framework for voxel-based morphometric analysis of the optic radiation using diffusion tensor imaging in glaucoma

Glaucoma is an optic neuropathy affecting the entire visual system. The understanding of the glaucoma mechanism and causes remains unresolved. Diffusion tensor imaging (DTI) has been used to analyze the optic nerve and optic radiation showing global fiber abnormalities associated with glaucoma. Nevertheless, the complex structure of the optic radiation and the limitations of DTI make the localization of the glaucoma effect a difficult task. The aim of this work is to establish a framework for the determination of the local changes of the optic radiation due to glaucoma using DTI. The proposed system utilizes a semiautomated algorithm to produce an efficient identification of the optic radiation. Segmented optic radiations are transformed to a unified space using shape-based nonrigid registration. Using the deformation fields that resulted from the registration, the maps of the diffusion tensor-derived parameters are transformed to the unified space. This allows for statistical voxel-wise analysis to produce significant abnormality maps. The proposed system is applied to a group of 13 glaucoma patients and a normal control group of 10 subjects. The groups are age matched to eliminate the age effect on the analysis. Diffusion-related parameters (axial, radial and mean diffusivities) and an anisotropy index (fractional anisotropy) are studied. The anisotropy analysis indicates that the majority of the significant voxels show decreased fractional anisotropy in the glaucoma patients compared with the control group. In addition, the significant regions are mainly distributed in the middle (in reference to anterior–posterior orientation) of the optic radiation. Glaucoma subjects have increased radial diffusivity and mean diffusivity significant voxels with a main concentration in the proximal part of the right optic radiation. The proposed analysis provides a framework to capture the significant local changes of the optic radiation due to glaucoma. The preliminary analysis suggests that the glaucomatous optic radiation may suffer from localized white matter degeneration. The framework facilitates further studies and understanding of the pathophysiology of glaucoma.     

Alteration of diffusion tensor parameters in postmortem brain

In autopsy of humans, there is usually an interval of hours to days between death and tissue fixation, during which the cadaver is stored below room temperature to retard tissue autolysis. We have attempted to model this process and evaluate the alteration in diffusion indices of the postmortem brain in pigs, which were kept at 4°C. The pigs were scanned prior to death and at 3, 6, 9, 12, 18, 24, 30, 36, 42, 48 and 72 h postmortem. Regions of interest were placed in the corpus callosum, internal capsule, periventricular and subcortical white matter anteriorly and posteriorly. There was a slight increase in fractional anisotropy (FA) in the first 3 h postmortem. The FA remained stable up to 72 h postmortem. There was a marked decrease in trace, eigenmajor (λmajor), eigenmedium (λmedium) and eigenminor (λminor), particularly in the first 3 h following death. This study supports the utility of measuring diffusion anisotropy if the time elapsed between death and tissue fixation is within 3 days. However, trace and eigenvalues decreased markedly within the first few hours postmortem. Therefore trace and eigenvalues obtained from ex vivo studies cannot be extrapolated to in vivo studies.     

Optimal real-time estimation in diffusion tensor imaging

Diffusion tensor imaging (DTI) constitutes the most used paradigm among the diffusion-weighted magnetic resonance imaging (DW-MRI) techniques due to its simplicity and application potential. Recently, real-time estimation in DW-MRI has deserved special attention, with several proposals aiming at the estimation of meaningful diffusion parameters during the repetition time of the acquisition sequence. Specifically focusing on DTI, the underlying model of the noise present in the acquired data is not taken into account, leading to a suboptimal estimation of the diffusion tensor. In this paper, we propose an optimal real-time estimation framework for DTI reconstruction in single-coil acquisitions. By including an online estimation of the time-changing noise variance associated to the acquisition process, the proposed method achieves the sequential best linear unbiased estimator. Results on both synthetic and real data show that our method outperforms those so far proposed, reaching the best performance of the existing proposals by processing a substantially lower number of diffusion images.     

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.     

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.     

A diffusion gradient optimization framework for spinal cord diffusion tensor imaging

The uncertainty in the estimation of diffusion model parameters in diffusion tensor imaging (DTI) can be reduced by optimally selecting the diffusion gradient directions utilizing some prior structural information. This is beneficial for spinal cord DTI, where the magnetic resonance images have low signal-to-noise ratio and thus high uncertainty in diffusion model parameter estimation. Presented is a gradient optimization scheme based on D-optimality, which reduces the overall estimation uncertainty by minimizing the Rician Cramer-Rao lower bound of the variance of the model parameter estimates. The tensor-based diffusion model for DTI is simplified to a four-parameter axisymmetric DTI model where diffusion transverse to the principal eigenvector of the tensor is assumed isotropic. Through simulations and experimental validation, we demonstrate that an optimized gradient scheme based on D-optimality is able to reduce the overall uncertainty in the estimation of diffusion model parameters for the cervical spinal cord and brain stem white matter tracts.     

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.     

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.     

In vivo structural analysis of articular cartilage using diffusion tensor magnetic resonance imaging

Purpose

The articular cartilage is a small tissue with a matrix structure of three layers between which the orientation of collagen fiber differs. A diffusion-weighted twice-refocused spin-echo echo-planar imaging (SE-EPI) sequence was optimized for the articular cartilage, and the structure of the three layers of human articular cartilage was imaged in vivo from diffusion tensor images.

Materials and Methods

The subjects imaged were five specimens of swine femur head after removal of the flesh around the knee joint, five specimens of swine articular cartilage with flesh present and the knee cartilage of five adult male volunteers. Based on diffusion-weighted images in six directions, the mean diffusivity (MD) and the fractional anisotropy (FA) values were calculated.

Results

Diffusion tensor images of the articular cartilage were obtained by sequence optimization. The MD and FA value of the specimens (each of five examples) under different conditions were estimated. Although the articular cartilage is a small tissue, the matrix structure of each layer in the articular cartilage was obtained by SE-EPI sequence with GRAPPA. The MD and FA values of swine articular cartilage are different between the synovial fluid and saline. In human articular cartilage, the load of the body weight on the knee had an effect on the FA value of the surface layer of the articular cartilage.

Conclusion

This method can be used to create images of the articular cartilage structure, not only in vitro but also in vivo. Therefore, it is suggested that this method should support the elucidation of the in vivo structure and function of the knee joint and might be applied to clinical practice.     

An image-processing toolset for diffusion tensor tractography

Diffusion tensor imaging (DTI)-based fiber tractography holds great promise in delineating neuronal fiber tracts and, hence, providing connectivity maps of the neural networks in the human brain. An array of image-processing techniques has to be developed to turn DTI tractography into a practically useful tool. To this end, we have developed a suite of image-processing tools for fiber tractography with improved reliability. This article summarizes the main technical developments we have made to date, which include anisotropic smoothing, anisotropic interpolation, Bayesian fiber tracking and automatic fiber bundling. A primary focus of these techniques is the robustness to noise and partial volume averaging, the two major hurdles to reliable fiber tractography. Performance of these techniques has been comprehensively examined with simulated and in vivo DTI data, demonstrating improvements in the robustness and reliability of DTI tractography.     

Diffusion tensor imaging in horizontal gaze palsywith progressive scoliosis

Horizontal gaze palsy with progressive scoliosis (HGPPS) is a rare disorder characterized by absence of conjugate horizontal eye movements, preservation of vertical gaze and convergence, progressive scoliosis developing in childhood and adolescence. It is caused by mutations in the ROBO3 gene which are critical for the crossing of long ascending medial lemniscal and descending corticospinal tracts in the medulla. Diffusion tensor imaging on a 14-year-old boy with HGPPS revealed ipsilateral ascending and descending connectivity in the brainstem without any crossing over of the major tracts although normal interhemispheric connections in the corpus callosum was demonstrable. Absent decussation of smaller sized superior cerebellar peduncles but with normal crossing over of the middle cerebellar peduncle was also observed. Tractography is a valuable investigative modality to assess neuronal connections in the brain and is a useful adjunct to the structural magnetic resonance imaging in confirming the diagnosis of HGPPS.     

Novel diffusion tensor imaging methodology to detect and quantify injured regions and affected brain pathways in traumatic brain injury

Purpose

To develop and apply diffusion tensor imaging (DTI)-based normalization methodology for the detection and quantification of sites of traumatic brain injury (TBI) and the impact of injury along specific brain pathways in (a) individual TBI subjects and (b) a TBI group.

Materials and Methods

Normalized DTI tractography was conducted in the native space of 12 TBI and 10 age-matched control subjects using the same number of seeds in each subject, distributed at anatomically equivalent locations. Whole-brain tracts from the control group were mapped onto the head of each TBI subject. Differences in the fractional anisotropy (FA) maps between each TBI subject and the control group were computed in a common space using a t test, transformed back to the individual TBI subject's head space, and thresholded to form regions of interest (ROIs) that were used to sort tracts from the control group and the individual TBI subject. Tract counts for a given ROI in each TBI subject were compared to group mean for the same ROI to quantify the impact of injury along affected pathways. The same procedure was used to compare the TBI group to the control group in a common space.

Results

Sites of injury within individual TBI subjects and affected pathways included hippocampal/fornix, inferior fronto-occipital, inferior longitudinal fasciculus, corpus callosum (genu and splenium), cortico-spinal tracts and the uncinate fasciculus. Most of these regions were also detected in the group study.

Conclusions

The DTI normalization methodology presented here enables automatic delineation of ROIs within the heads of individual subjects (or in a group). These ROIs not only localize and quantify the extent of injury, but also quantify the impact of injury on affected pathways in an individual or in a group of TBI subjects.     

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.     

Effects of random subject rotation on optimised diffusion gradient sampling schemes in diffusion tensor MRI

The choice of the number (N) and orientation of diffusion sampling gradients required to measure accurately the water diffusion tensor remains contentious. Monte Carlo studies have suggested that between 20 and 30 uniformly distributed sampling orientations are required to provide robust estimates of water diffusions parameters. These simulations have not, however, taken into account what effect random subject motion, specifically rotation, might have on optimised gradient schemes, a problem which is especially relevant to clinical diffusion tensor MRI (DT-MRI). Here this question is investigated using Monte Carlo simulations of icosahedral sampling schemes and in vivo data. These polyhedra-based schemes, which have the advantage that large N can be created from optimised subsets of smaller N, appear to be ideal for the study of restless subjects since if scanning needs to be prematurely terminated it should be possible to identify a subset of images that have been acquired with a near optimised sampling scheme. The simulations and in vivo data show that as N increases, the rotational variance of fractional anisotropy (FA) estimates becomes progressively less dependent on the magnitude of subject rotation (), while higher FA values are progressively underestimated as increases. These data indicate that for large subject rotations the B-matrix should be recalculated to provide accurate diffusion anisotropy information.     

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.     

Multivariate analysis of diffusion tensor imaging data improves the detection of microstructural damage in young professional boxers

In this study, we present two different methods of multivariate analysis of voxel-based diffusion tensor imaging (DTI) data, using as an example data derived from 59 professional boxers and 12 age-matched controls. Conventional univariate analysis ignores much of the diffusion information contained in the tensor. Our first multivariate method uses the Hotelling's T² statistic and the second uses linear discriminant analysis to generate the linear discriminant function at each voxel to form a separability metric. Both multivariate methods confirm the findings from the individual metrics of large-scale changes in the bilateral inferior temporal gyri of the boxers, but they also reveal greater sensitivity as well as identifying major subcortical changes that had not been evident in the univariate analyses. Linear discriminant analysis has the added strength of providing a quantitative measure of the relative contribution of each metric to any differences between the two subject groups. This novel adaptation of statistical and mathematical techniques to neuroimaging analysis is important for two reasons. Clinically, it develops the findings of a previous mild head injury study, and, methodologically, it could equally well be applied to multivariate studies of other pathologies.