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.     

Minimum SNR and acquisition for bias-free estimation of fractional anisotropy in diffusion tensor imaging - a comparison of two analytical techniques and field strengths

Although it is known that low signal-to-noise ratio (SNR) can affect tensor metrics, few studies reporting disease or treatment effects on fractional anisotropy (FA) report SNR; the implicit assumption is that SNR is adequate. However, the level at which low SNR causes bias in FA may vary with tissue FA, field strength and analytical methodology. We determined the SNR thresholds at 1.5 T vs. 3 T in regions of white matter (WM) with different FA and compared FA derived using manual region-of-interest (ROI) analysis to tract-based spatial statistics (TBSS), an operator-independent whole-brain analysis tool. Using ROI analysis, SNR thresholds on our hardware-software magnetic resonance platforms were 25 at 1.5 T and 20 at 3 T in the callosal genu (CG), 40 at 1.5 and 3 T in the anterior corona radiata (ACR), and 50 at 1.5 T and 70 at 3 T in the putamen (PUT). Using TBSS, SNR thresholds were 20 at 1.5 T and 3 T in the CG, and 35 at 1.5 T and 40 at 3 T in the ACR. Below these thresholds, the mean FA increased logarithmically, and the standard deviations widened. Achieving bias-free SNR in the PUT required at least nine acquisitions at 1.5 T and six acquisitions at 3 T. In the CG and ACR, bias-free SNR was achieved with at least three acquisitions at 1.5 T and one acquisition at 3 T. Using diffusion tensor imaging (DTI) to study regions of low FA, e.g., basal ganglia, cerebral cortex, and WM in the abnormal brain, SNR should be documented. SNR thresholds below which FA is biased varied with the analytical technique, inherent tissue FA and field strength. Studies using DTI to study WM injury should document that bias-free SNR has been achieved in the region of the brain being studied as part of quality control.     

Reduced anisotropy of water diffusion in structural cerebral abnormalities demonstrated with diffusion tensor imaging

We used diffusion tensor imaging (DTI) to investigate the behavior of water diffusion in cerebral structural abnormalities. The fractional anisotropy, a measure of directionality of the molecular motion of water, and the mean diffusivity, a measure of the magnitude of the molecular motion of water, were measured in 18 patients with longstanding partial epilepsy and structural abnormalities on standard magnetic resonance imaging and the results compared with measurements in the white matter of 10 control subjects. Structural abnormalities were brain damage (postsurgical brain damage, nonspecific brain damage, perinatal brain damage, perinatal infarct, ischemic infarct, perinatal hypoxia, traumatic brain damage (n = 3), mitochondrial cytopathy and mesiotemporal sclerosis), dysgenesis (cortical dysplasia (n = 2) and heterotopia) and tumors (meningioma (n = 2), hypothalamic hamartoma and glioma). Anisotropy was reduced in all structural abnormalities. In the majority of abnormalities this was associated with an increased mean diffusivity; however, 30% of all structural abnormalities (some patients with brain damage and dysgenesis) had a normal mean diffusivity in combination with a reduced anisotropy. There was no correlation between fractional anisotropy and mean diffusivity measurements in structural abnormalities (r = -0.1). Our findings suggest that DTI is sensitive for the detection of a variety of structural abnormalities, that a reduced anisotropy is the common denominator in structural cerebral abnormalities of different etiologies and that mean diffusivity and fractional anisotropy may be, in part, independent. Combined measurements of mean diffusivity and fractional anisotropy are likely to increase the specificity of DTI.     

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.     

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.     

Robust tensor estimation in diffusion tensor imaging

The signal response measured in diffusion tensor imaging is subject to detrimental influences caused by noise. Noise fields arise due to various contributions such as thermal and physiological noise and sources related to the hardware imperfection. As a result, diffusion tensors estimated by different linear and non-linear least squares methods in absence of a proper noise correction tend to be substantially corrupted. In this work, we propose an advanced tensor estimation approach based on the least median squares method of the robust statistics. Both constrained and non-constrained versions of the method are considered. The performance of the developed algorithm is compared to that of the conventional least squares method and of the alternative robust methods proposed in the literature. Two examples of simulated diffusion attenuations and experimental in vivo diffusion data sets were used as a basis for comparison. The robust algorithms were shown to be advantageous compared to the least squares method in the cases where elimination of the outliers is desirable. Additionally, the constraints were applied in order to prevent generation of the non-positive definite tensors and reduce related artefacts in the maps of fractional anisotropy. The developed method can potentially be exploited also by other MR techniques where a robust regression or outlier localisation is required.     

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.     

Noise considerations in the determination of diffusion tensor anisotropy

In this study the noise sensitivity of various anisotropy indices has been investigated by Monte-Carlo computer simulations and magnetic resonance imaging (MRI) measurements in a phantom and 5 healthy volunteers. Particularly, we compared the noise performance of indices defined solely in terms of eigenvalues and those based on both the eigenvalues and eigenvectors. It is found that anisotropy indices based on both eigenvalues and eigenvectors are less sensitive to noise, and spatial averaging with neighboring pixels can further reduce the standard deviation. To reduce the partial volume effect caused by the spatial averaging with neighboring voxels, an averaging method in the time domain based on the orientation coherence of eigenvectors in repeated experiments has been proposed.     

A theoretical validation of the B-matrix spatial distribution approach to diffusion tensor imaging

The recently presented B-matrix Spatial Distribution (BSD) approach is a calibration technique which derives the actual distribution of the B-matrix in space. It is claimed that taking into account the spatial variability of the B-matrix improves the accuracy of diffusion tensor imaging (DTI). The purpose of this study is to verify this approach theoretically through computer simulations.Assuming three different spatial distributions of the B-matrix, diffusion weighted signals were calculated for the six orientations of a model anisotropic phantom. Subsequently two variants of the BSD calibration were performed for each of the three cases; one with the assumption of high uniformity of the model phantom (uBSD-DTI) and the other taking into account imperfections in phantom structure (BSD-DTI). Several cases of varying degrees of phantom uniformity were analyzed and the distributions of the B-matrix obtained were used for the calculation of the diffusion tensor of a model isotropic phantom. The results were compared with standard diffusion tensor calculation.The simulations confirmed the improvement of accuracy in the determination of the diffusion tensor after the calibration. BSD-DTI improves accuracy independent of both the degree of uniformity of the phantom and the inhomogeneity of the B-matrix. In cases of a relatively good uniformity of the phantom and minor distortions in the spatial distribution of the B-matrix, the uBSD-DTI approach is sufficient.     

Cosmic ray anisotropy in fractional differential models of anomalous diffusion

The problem of galactic cosmic ray anisotropy is considered in two versions of the fractional differential model for anomalous diffusion. The simplest problem of cosmic ray propagation from a point instantaneous source in an unbounded medium is used as an example to show that the transition from the standard diffusion model to the Lagutin-Uchaikin fractional differential model (with characteristic exponent α = 3/5 and a finite velocity of free particle motion), which gives rise to a knee in the energy spectrum at 10⁶ GeV, increases the anisotropy coefficient only by 20%, while the anisotropy coefficient in the Lagutin-Tyumentsev model (with exponents α = 0.3 and β = 0.8, a long stay of particles in traps, and an infinite velocity of their jumps) is close to one. This is because the parameters of the Lagutin-Tyumentsev model have been chosen improperly.     

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.     

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.     

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (相似文献   

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.     

Comparison of compressed sensing diffusion spectrum imaging and diffusion tensor imaging in patients with intracranial masses

PurposeTo compare compressed diffusion spectrum imaging (CS-DSI) with diffusion tensor imaging (DTI) in patients with intracranial masses. We hypothesized that CS-DSI would provide superior visualization of the motor and language tracts.Materials and methodsWe retrospectively analyzed 25 consecutive patients with intracranial masses who underwent DTI and CS-DSI for preoperative planning. Directionally-encoded anisotropy maps, and streamline hand corticospinal motor tracts and arcuate fasciculus language tracts were graded according to a 3-point scale. Tract counts, anisotropy, and lengths were also calculated. Comparisons were made using exact marginal homogeneity, McNemar's and Wilcoxon signed-rank tests.ResultsReaders preferred the CS-DSI over DTI anisotropy maps in 92% of the cases, and the CS-DSI over DTI tracts in 84%. The motor tracts were graded as excellent in 80% of cases for CS-DSI versus 52% for DTI; 58% of the motor tracts graded as acceptable in DTI were graded as excellent in CS-DSI (p = 0.02). The language tracts were graded as excellent in 68% for CS-DSI versus none for DTI; 78% of the language tracts graded as acceptable by DTI were graded as excellent by CS-DSI (p < 0.001). CS-DSI demonstrated smaller normalized mean differences than DTI for motor tract counts, anisotropy and language tract counts (p ≤ 0.01).ConclusionCS-DSI was preferred over DTI for the evaluation of motor and language white matter tracts in patients with intracranial masses. Results suggest that CS-DSI may be more useful than DTI for preoperative planning purposes.     

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.     

Correlation of proton MR spectroscopy and diffusion tensor imaging

Proton magnetic resonance spectroscopy ((1)H-MRS) provides indices of neuronal damage. Diffusion tensor imaging (DTI) relates to water diffusivity and fiber tract orientation. A method to compare (1)H-MRS and DTI findings was developed, tested on phantom and applied on normal brain. Point-resolved spectroscopy (T(R)/T(E)=1500/135) was used for chemical shift imaging of a supraventricular volume of interest of 8 x 8 x 2 cm(3) (64 voxels). In DTI, a segmental spin-echo sequence (T(R)/T(E)=5500/91) was used and slices were stacked to reproduce the slab used in MRS. The spatial distributions of choline and N-acetylaspartate (NAA) correlated to mean fractional anisotropy and apparent diffusion coefficient (ADC) for the inner 6 x 6=36 voxels defined in MRS, most notably NAA and ADC value (r=-.70, P<.00001; correlation across four subjects, 144 data pairs). This is the first association of neuron metabolite contents in volunteers with structure as indicated by DTI.     

Comparison of multimesh hp-FEM to interpolation and projection methods for spatial coupling of thermal and neutron diffusion calculations

Multiphysics solution challenges are legion within the field of nuclear reactor design and analysis. One major issue concerns the coupling between heat and neutron flow (neutronics) within the reactor assembly. These phenomena are usually very tightly interdependent, as large amounts of heat are quickly produced with an increase in fission events within the fuel, which raises the temperature that affects the neutron cross section of the fuel. Furthermore, there typically is a large diversity of time and spatial scales between mathematical models of heat and neutronics. Indeed, the different spatial resolution requirements often lead to the use of very different meshes for the two phenomena. As the equations are coupled, one must take care in exchanging solution data between them, or significant error can be introduced into the coupled problem. We propose a novel approach to the discretization of the coupled problem on different meshes based on an adaptive multimesh higher-order finite element method (hp-FEM), and compare it to popular interpolation and projection methods. We show that the multimesh hp-FEM method is significantly more accurate than the interpolation and projection approaches considered in this study.     

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.     

Glaucoma classification based on visual pathway analysis using diffusion tensor imaging

Most of the existing methods for diagnosing glaucoma analyze the eye with a main focus on the retina, despite the transsynaptic nature of the fiber degeneration caused by glaucoma. Thus, they ignore a significant part of the visual system represented by the visual pathway in the brain. The advances in neuroimaging, especially diffusion tensor imaging (DTI), enable the identification and characterization of white matter fibers. In this work, we propose a system based on DTI analysis of the visual pathway fibers in the optic radiation for detecting and discriminating different glaucoma entities. The optic radiation is identified semi-automatically. DTI provides information about the fiber orientation as well as a set of derived parameters describing the degree of diffusion anisotropy and diffusivity. Features for each DTI derived measure are extracted from a specified region of interest on the optic radiation. The features are grouped into three sets: Histogram, co-occurrence matrices, and Laws features. For feature selection, the features are ranked using a support vector machine classifier. The highest ranked features are used for classification. A support vector machine classifier is used for classification in a 10-fold cross validation setup. The system is applied to three age-matched subjects’ categories containing 27 healthy, 39 primary open angle glaucoma (POAG), and 18 normal tension glaucoma (NTG) subjects. The discrimination accuracy between healthy and glaucoma (POAG and NTG) subjects is 94.1% with an area under the ROC of 0.97. Classification accuracy of 92.4% is obtained for the normal and the POAG groups while it increased to 100% in case of healthy and NTG groups. In addition, the system could differentiate between glaucoma types (POAG and NTG) with an accuracy of 98.3%. A complementary analysis was performed to estimate the selection bias in the obtained accuracy. The bias ranged from 10% to 20% depending on the group pair under consideration. The classification results indicate the high performance of the system compared to retina-based glaucoma detection systems. The proposed approach utilizes visual pathway analysis rather than the conventional eye analysis which presents a new trend in glaucoma detection. Analyzing the entire visual system could provide significant information that can improve the glaucoma examination flow and treatment.