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.     

Noise and nonlinear estimation with optimal schemes in DTI

In general, the estimation of the diffusion properties for diffusion tensor experiments (DTI) is accomplished via least squares estimation (LSE). The technique requires applying the logarithm to the measurements, which causes bad propagation of errors. Moreover, the way noise is injected to the equations invalidates the least squares estimate as the best linear unbiased estimate. Nonlinear estimation (NE), despite its longer computation time, does not possess any of these problems. However, all of the conditions and optimization methods developed in the past are based on the coefficient matrix obtained in a LSE setup. In this article, NE for DTI is analyzed to demonstrate that any result obtained relatively easily in a linear algebra setup about the coefficient matrix can be applied to the more complicated NE framework. The data, obtained using non-optimal and optimized diffusion gradient schemes, are processed with NE. In comparison with LSE, the results show significant improvements, especially for the optimization criterion. However, NE does not resolve the existing conflicts and ambiguities displayed with LSE methods.     

An MRI denoising method using image data redundancy and local SNR estimation

This paper presents an LMMSE-based method for the three-dimensional (3D) denoising of MR images assuming a Rician noise model. Conventionally, the LMMSE method estimates the noise-less signal values using the observed MR data samples within local neighborhoods. This is not an efficient procedure to deal with this issue while the 3D MR data intrinsically includes many similar samples that can be used to improve the estimation results. To overcome this problem, we model MR data as random fields and establish a principled way which is capable of choosing the samples not only from a local neighborhood but also from a large portion of the given data. To follow the similar samples within the MR data, an effective similarity measure based on the local statistical moments of images is presented. The parameters of the proposed filter are automatically chosen from the estimated local signal-to-noise ratio. To further enhance the denoising performance, a recursive version of the introduced approach is also addressed. The proposed filter is compared with related state-of-the-art filters using both synthetic and real MR datasets. The experimental results demonstrate the superior performance of our proposal in removing the noise and preserving the anatomical structures of MR images.     

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.     

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.     

Noise estimation in single- and multiple-coil magnetic resonance data based on statistical models

Noise estimation is a challenging task in magnetic resonance imaging (MRI), with applications in quality assessment, filtering or diffusion tensor estimation. Main noise estimators based on the Rician model are revisited and classified in this article, and new useful methods are proposed. Additionally, all the surveyed estimators are extended to the noncentral chi model, which applies to multiple-coil MRI and some important parallel imaging algorithms for accelerated acquisitions. The proposed new noise estimation procedures, based on the distribution of local moments, show better performance in terms of smaller variance and unbiased estimation over a wide range of experiments, with the additional advantage of not needing to explicitly segment the background of the image.     

Abdominal apparent diffusion coefficient measurements: effect of diffusion-weighted image quality and usefulness of anisotropic images

This study aimed to assess the effect of diffusion-weighted image (DWI) quality on abdominal apparent diffusion coefficient (ADC) measurements and the usefulness of anisotropic images. Twenty-six patients (10 men and 16 women; mean, 58.1 years) who underwent DW imaging and were diagnosed not to have any abdominal diseases were analyzed. Single-shot spin-echo echo-planar DW imaging was performed, and one isotropic and three orthogonal anisotropic images were created. ADCs were calculated for liver (four segments), spleen, pancreas (head, body, tail) and renal parenchyma. Image quality for each organ part was scored visually. We estimated the correlation between ADC and image quality and evaluated the feasibility of using anisotropic images. ADCs and image quality were affected by motion probing gradient directions in the liver and pancreas. A significant inverse correlation was found between ADC and image quality. The r values for isotropic images were −.46, −.48, −.70 and −.28 for the liver, spleen, pancreas and renal parenchyma, respectively. Anisotropic images had the best quality and lowest ADC in at least one organ part in 17 patients. DWIs with the best quality among isotropic and anisotropic images should be used in the liver and pancreas.     

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.     

描述人体内水分子扩散各向异性特征的新方法

通过核磁共振扩散张量成像(DTI)得到的特定值域的扩散各向异性指数(DAI) 可用于揭示水分子扩散椭球的形态学特征, 定量反映被成像物体内部水分子扩散的优势方向和强度, 间接得到被成像物体内部的组织结构信息. DAI的可靠性直接影响对DTI数据的分析和理解. 本文基于扩散张量椭球的几何学信息, 提出利用扩散椭球几何比(EGR)定量描述水分子扩散的各向异性程度. 通过蒙特卡罗模拟实验和对人脑DTI数据进行分析, 并与当前广泛应用的水分子扩散各向异性分数(FA)和近期文献提出的扩散椭球面积比(EAR)进行对比. 实验发现EGR在不同级别噪声影响下的对比度效果和抗噪性都优于FA及EAR. 而且EGR 加入了体积修正, 增强了盘形扩散张量情况下的敏感性, 能够更好地鉴别神经纤维束交叉情况, 对于各向异性扩散程度较高的白质深层和相对均质的表层都有较好的量化区分结果. 关键词： 扩散系数 各向异性扩散 扩散张量成像 扩散椭球几何比     

Association between visual degeneration of intervertebral discs and the apparent diffusion coefficient

The value of apparent diffusion coefficient (ADC) measurements in intervertebral disc has been studied because ADC provides an estimate of free diffusion of unbound water and could be used as a quantitative tool to estimate degenerative changes. However, the challenging nature of diffusion imaging of spine and limited numbers of subjects in earlier studies has produced contradictory findings. We aimed to determine the relation between ADC and visual degenerative changes in lumbar intervertebral discs in a sufficiently large homogeneous study group. Lumbar spines of 228 volunteer middle-aged men were MR imaged at 1.5 T including anatomic and diffusion-weighted imaging. ADC values, T2 signal intensity and height, and width of the three lowest lumbar intervertebral discs were measured and disc degeneration visually graded. The calculated average ADC of 530 measured discs was 2.01×10⁻³ mm²/s±0.29 (±S.D.). The reduction in ADC between visually normal and moderately degenerated discs was 4%. Severely degenerated discs showed 5% larger ADC values than normal discs, presumably due to free water in cracks and fissures of those discs. T2 signal intensity of the disc was significantly correlated with the ADC values, whereas other measured parameters did not show correlation. There was no evident difference in ADC between the studied anatomic lumbar levels. Because there is considerable overlap between ADC values of normal and degenerated discs, we conclude that ADC measurements of intervertebral discs, at least with current technology, have limited clinical value.     

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.     

Exploratory voxel-based analysis of diffusion indices and hemispheric asymmetry in normal aging

Age-related microstructural changes in brain white matter can be studied by utilizing indices derived from diffusion tensor imaging (DTI): apparent diffusion coefficient (ADC) and fractional anisotropy (FA). The objective of this study is to examine alterations in FA and ADC by employing exploratory voxel-based analysis (VBA) and region(s) of interest (ROI)-based analysis. A highly nonlinear registration algorithm was used to align the ADC and FA image volumes of different subjects to perform accurate voxel-level statistics for two age groups, as well as for hemispheric asymmetry for both age groups. VBA shows significant age-related decline in FA with frontal predominance (frontal white matter, and genu and anterior body of the corpus callosum), superior portions of a splenium and highly oriented fibers of the posterior limb of the internal capsule and the anterior and posterior limbs of the external capsule. Hemispheric asymmetry of FA, as assessed by VBA, showed that for the young-age group, significant right-greater-than-left asymmetry exists in the genu, splenium and body of the corpus callosum and that left-greater-than-right asymmetry exists in the anterior limb of the external capsule and in the posterior limb of the internal capsule, thalamus, cerebral peduncle and temporal-parietal regions. VBA of the hemispheric asymmetry of the middle-age group revealed much less asymmetry. Regions showing age-related changes and hemispheric asymmetry from VBA were, for a majority of the findings, in conformance with ROI analysis and with the known pattern of development and age-related degradation of fiber tracks. The study shows the feasibility of the VBA of DTI indices for exploratory investigations of subtle differences in population cohorts, especially when findings are not localized and/or known a priori.     

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.     

Assessment of hepatocellular carcinoma using apparent diffusion coefficient and diffusion kurtosis indices: preliminary experience in fresh liver explants

Objectives

The objective was to perform ex vivo evaluation of non-Gaussian diffusion kurtosis imaging (DKI) for assessment of hepatocellular carcinoma (HCC), including presence of treatment-related necrosis, using fresh liver explants.

Methods

Twelve liver explants underwent 1.5-T magnetic resonance imaging using a DKI sequence with maximal b-value of 2000 s/mm². A standard monoexponential fit was used to calculate apparent diffusion coefficient (ADC), and a non-Gaussian kurtosis fit was used to calculate K, a measure of excess kurtosis of diffusion, and D, a corrected diffusion coefficient accounting for this non-Gaussian behavior. The mean value of these parameters was measured for 16 HCCs based upon histologic findings. For each metric, HCC-to-liver contrast was calculated, and coefficient of variation (CV) was computed for voxels within the lesion as an indicator of heterogeneity. A single hepatopathologist determined HCC necrosis and cellularity.

Results

The 16 HCCs demonstrated intermediate-to-substantial excess diffusional kurtosis, and mean corrected diffusion coefficient D was 23% greater than mean ADC (P=.002). HCC-to-liver contrast and CV of HCC were greater for K than ADC or D, although these differences were significant only for CV of HCCs (P≤.046). ADC, D and K all showed significant differences between non-, partially and completely necrotic HCCs (P≤.004). Among seven nonnecrotic HCCs, cellularity showed a strong inverse correlation with ADC (r=−0.80), a weaker inverse correlation with D (− 0.24) and a direct correlation with K (r= 0.48).

Conclusions

We observed non-Gaussian diffusion behavior for HCCs ex vivo; this DKI model may have added value in HCC characterization in comparison with a standard monoexponential model of diffusion-weighted imaging.     

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.     

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.     

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.     

麦克斯韦分子速率分布律与扩散方程、扩散系数的初浅推导

从演示统计规律的装置－伽耳顿板实验出发，用初等微积分方法推导高斯误差函数，麦氏速率分布律，扩散方程，扩散系数。     

Comparison of absolute magnitude estimation and relative magnitude estimation for judging the subjective intensity of noise and vibration

The method of magnitude estimation is used in psychophysical studies to obtain numerical values for the intensity of perception of environmental stresses (e.g., noise and vibration). The exponent in a power function relating the subjective magnitude of a stimulus (e.g., the degree of discomfort) to the physical magnitude of the stimulus shows the rate of growth of sensations with increasing stimulus magnitude. When judging noise and vibration, there is no basis for deciding whether magnitude estimation should be performed with a reference stimulus (i.e., relative magnitude estimation, RME) or without a reference stimulus (i.e., absolute magnitude estimation, AME). Twenty subjects rated the discomfort caused by thirteen magnitudes of whole-body vertical vibration and 13 levels of noise, by both RME and AME on three occasions. There were high correlations between magnitude estimates of discomfort and the magnitudes of vibration and noise. Both RME and AME provided rates of growth of discomfort with high consistency over the three repetitions. When judging noise, RME was more consistent than AME, with less inter-subject variability in the exponent, n_s. When judging vibration, RME was also more consistent than AME, but with greater inter-subject variability in the exponent, n_v. When judging vibration, AME may be beneficial because sensations caused by the RME reference stimulus may differ (e.g., occur in a different part of the body) from the sensations caused by the stimuli being judged.