Diffusion tensor imaging at low SNR: nonmonotonic behaviors of tensor contrasts

Diffusion tensor imaging (DTI) provides measurements of directional diffusivities and has been widely used to characterize changes in the tissue microarchitecture of the brain. DTI is gaining prominence in applications outside of the brain, where resolution, motion and short T2 values often limit the achievable signal-to-noise ratio (SNR). Consequently, it is important to revisit the topic of tensor estimation in low-SNR regimes. A theoretical framework is developed to model noise in DTI, and by using simulations based on this theory, the degree to which the noise, tensor estimation method and acquisition protocol affect tensor-derived quantities, such as fractional anisotropy and apparent diffusion coefficient, is clarified. These results are then validated against clinical data. It is shown that reliability of tensor contrasts depends on the noise level, estimation method, diffusion-weighting scheme and underlying anatomy. The propensity for bias and errors does not monotonically increase with noise. Comparative results are shown in both graphical and tabular forms, so that decisions about suitable acquisition protocols and processing methods can be made on a case-by-case basis without exhaustive experimentation.     

A practical approach to in vivo high-resolution diffusion tensor imaging of rhesus monkeys on a 3-T human scanner

The nonhuman primate brain study provides important supplemental means for human brain exploration since the two species share close anatomical and functional similarities. MR diffusion tensor imaging (DTI) in human brain has revealed exquisite details of brain structures especially in the brain white matter. However, most previous monkey brain DTI results lack the spatial resolution in comparison to the conventional tracing and postmortem imaging methods, especially when it is acquired in commonly available human MRI scanners of field strength of 3 T or lower. To meet the increasing demands for nonhuman primate DTI studies, we proposed an in vivo high-resolution monkey DTI acquisition protocol that is practically feasible and combined it with an improved postprocessing procedure for a 3-T human scanner. The acquisition protocol, susceptibility distortion correction method with phase reversal acquisition, and postprocessing steps were proved to be effective in our study of rhesus monkeys. Results from diffusion tensor estimations and fiber tractography at 1 x 1 x 1 mm(3) resolution were found to be comparable to previous ex vivo DTI studies with much longer acquisition times. Effects of image resolution were evaluated and it was confirmed that the partial volume effect due to the larger voxel size in low-resolution data biased the diffusion tensor estimation and produced erroneous fiber tractography. Our results suggest that in vivo high-resolution monkey brain DTI can be achieved within practical time, which allows accurate diffusion tensor estimation and fiber tractography in monkey brains, so that the complex anatomical structures within many small but important anatomic structures can be delineated.     

Condition number as a measure of noise performance of diffusion tensor data acquisition schemes with MRI

Diffusion tensor mapping with MRI can noninvasively track neural connectivity and has great potential for neural scientific research and clinical applications. For each diffusion tensor imaging (DTI) data acquisition scheme, the diffusion tensor is related to the measured apparent diffusion coefficients (ADC) by a transformation matrix. With theoretical analysis we demonstrate that the noise performance of a DTI scheme is dependent on the condition number of the transformation matrix. To test the theoretical framework, we compared the noise performances of different DTI schemes using Monte-Carlo computer simulations and experimental DTI measurements. Both the simulation and the experimental results confirmed that the noise performances of different DTI schemes are significantly correlated with the condition number of the associated transformation matrices. We therefore applied numerical algorithms to optimize a DTI scheme by minimizing the condition number, hence improving the robustness to experimental noise. In the determination of anisotropic diffusion tensors with different orientations, MRI data acquisitions using a single optimum b value based on the mean diffusivity can produce ADC maps with regional differences in noise level. This will give rise to rotational variances of eigenvalues and anisotropy when diffusion tensor mapping is performed using a DTI scheme with a limited number of diffusion-weighting gradient directions. To reduce this type of artifact, a DTI scheme with not only a small condition number but also a large number of evenly distributed diffusion-weighting gradients in 3D is preferable.     

Importance of exactb-tensor calculation for quantitative diffusion tensor imaging and tracking of neuronal fiber bundles

Quantitative diffusion tensor imaging (DTI) is a novel method of magnetic resonance (MR) imaging providing information on the brain’s microstructure in vivo. DTI can be effectively measured with modern clinical MR scanners. However, imaging sequence details required for accurateb matrix calculation and for following DTI quantification are normally unknown to the user. In this work, we investigated the accuracy ofb value approximation if theb matrix is calculated without taking into account the effect of imaging gradients. It was found that an error of more than 4% in DTI estimation arises for a quite typical brain imaging protocol. The errors in mean diffusivity and fractional anisotropy index depend on diffusion tensor shape and eigenvectors orientation and exceed noise level in DTI quantification. These errors however have a strong impact on fiber tracking — up to 30% difference was found between the fiber tracks corresponding to exact and approximate calculated DTI data. Since these errors are dependent on imaging parameters and sequence implementation, accurateb matrix calculations are important for adequate comparison between data acquired on different MR scanners and also for data measured with the different imaging protocols.     

Brain tissue classification based on DTI using an improved Fuzzy C-means algorithm with spatial constraints

We present an effective method for brain tissue classification based on diffusion tensor imaging (DTI) data. The method accounts for two main DTI segmentation obstacles: random noise and magnetic field inhomogeneities. In the proposed method, DTI parametric maps were used to resolve intensity inhomogeneities of brain tissue segmentation because they could provide complementary information for tissues and define accurate tissue maps. An improved fuzzy c-means with spatial constraints proposal was used to enhance the noise and artifact robustness of DTI segmentation. Fuzzy c-means clustering with spatial constraints (FCM_S) could effectively segment images corrupted by noise, outliers, and other imaging artifacts. Its effectiveness contributes not only to the introduction of fuzziness for belongingness of each pixel but also to the exploitation of spatial contextual information. We proposed an improved FCM_S applied on DTI parametric maps, which explores the mean and covariance of the feature spatial information for automated segmentation of DTI. The experiments on synthetic images and real-world datasets showed that our proposed algorithms, especially with new spatial constraints, were more effective.     

Diffusion tensor encoding schemes optimized for white matter fibers with selected orientations

A method to produce gradient encoding schemes that minimize the noise of diffusion tensor imaging (DTI) indices for selected fiber orientations has been developed. The accuracy of DTI measurements depends on the gradient encoding scheme used. Most current acquisition schemes contain diffusion directions uniformly distributed in 3D space in order to provide equal noise levels for fibers in any orientation. However, when considering specific fiber bundles such as the corticospinal tract (CST) or parts of fiber bundles, the range of fiber orientations of interest may be limited. We hypothesized that, when studying fiber tracts with a limited range of orientations, measuring diffusion in directions that are uniformly distributed in 3D space may be suboptimal for the noise levels of various DTI indices. Therefore, we first used simulations to determine six diffusion directions that minimize the noise of DTI measurements for selected fiber orientations. The resulting optimized set of directions was then tested on the right CST of a healthy human subject, and its performance was compared with that of conventional acquisition strategies. Both the simulations and the experiments on the human subject demonstrated that the new scheme significantly reduced the standard deviation of DTI indices for tensors with primary eigenvectors within a selected range of orientations.     

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     

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.     

扩散张量成像的人脑模板构建

扩散张量脑模板包含丰富的大脑白质组织信息,在空间标准化或者脑图谱创建中具有重要价值,然而基于扩散张量模型构建的脑模板精度不高,特别是在脑部复杂的神经元微观结构区域中应用受到限制.针对这一问题,研究者们提出了基于高分辨率扩散成像构建大脑模板的方法.本文对使用扩散张量成像方法进行脑模板构建的研究进展进行了综述,首先介绍了扩散张量脑模板构建的发展进程,阐述了脑模板构建中解决的技术问题及同时存在的局限性;接着详细论述了基于扩散频谱成像及高角度分辨率扩散成像构建脑模板的不同方法间的差异,并总结了这些研究方法取得的重要进展;最后通过分析目前研究进展提出该研究问题中存在的不足以及未来的发展趋势.     

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.     

Learning-based structurally-guided construction of resting-state functional correlation tensors

Functional magnetic resonance imaging (fMRI) measures changes in blood-oxygenation-level-dependent (BOLD) signals to detect brain activities. It has been recently reported that the spatial correlation patterns of resting-state BOLD signals in the white matter (WM) also give WM information often measured by diffusion tensor imaging (DTI). These correlation patterns can be captured using functional correlation tensor (FCT), which is analogous to the diffusion tensor (DT) obtained from DTI. In this paper, we propose a noise-robust FCT method aiming at further improving its quality, and making it eligible for further neuroscience study. The novel FCT estimation method consists of three major steps: First, we estimate the initial FCT using a patch-based approach for BOLD signal correlation to improve the noise robustness. Second, by utilizing the relationship between functional and diffusion data, we employ a regression forest model to learn the mapping between the initial FCTs and the corresponding DTs using the training data. The learned forest can then be applied to predict the DTI-like tensors given the initial FCTs from the testing fMRI data. Third, we re-estimate the enhanced FCT by utilizing the DTI-like tensors as a feedback guidance to further improve FCT computation. We have demonstrated the utility of our enhanced FCTs in Alzheimer's disease (AD) diagnosis by identifying mild cognitive impairment (MCI) patients from normal subjects.     

Minimal gradient encoding for robust estimation of diffusion anisotropy

This study has investigated the relationship between the noise sensitivity of measurement by magnetic resonance imaging (MRI) of the diffusion tensor (D) of water and the number N of diffusion-weighting (DW) gradient directions, using computer simulations of strongly anisotropic fibers with variable orientation. The DW directions uniformly sampled the diffusion ellipsoid surface. It is shown that the variation of the signal-to-noise ratio (SNR) of three ideally rotationally invariant scalars of D due to variable fiber orientation provides an objective quantitative measure for the diffusion ellipsoid sampling efficiency, which is independent of the SNR value of the baseline signal obtained without DW; the SNR variation decreased asymptotically with increasing N. The minimum number N(0) of DW directions, which minimized the SNR variation of the three scalars of D was determined, thereby achieving the most efficient ellipsoid sampling. The resulting time efficient diffusion tensor imaging (DTI) protocols provide robust estimation of diffusion anisotropy in the presence of noise and can improve the repeatability/reliability of DTI experiments when there is high variability in the orientation of similar anisotropic structures, as for example, in studies which require repeated measurement of one individual, intersubject comparisons or multicenter studies.     

Estimation error bound for GRAPPA diffusion-weighted MRI

In recent years, diffusion weight magnetic resonance imaging (DW-MRI) has become one of the most important MRI imaging modalities. The importance of the DW-MRI grew thanks to the combination of parallel magnetic resonance imaging (pMRI) techniques with the echo-planar imaging (EPI), which minimize scan time and lead to reduced distortion, allowing the DW-MRI to become a routine clinical exam. Additionally, this has brought various new parameters that influence image quality and biomarkers used in DW-MRI. This work aims to investigate the effects of these parameters on the estimation quality, by using the Cramér-Rao bound tool, which gives analytical expressions of the lower limit on the estimation error variance of different DW-MRI variables when using the pMRI technique. In particular, these bounds will be used to study and optimize the impact of different factors of generalized autocalibrating partially parallel acquisition (GRAPPA) technique and system parameters on the estimation quality of the desired clinical metrics. Moreover, the obtained results of this study can be exploited and adapted in all human body DW-MRI clinical routines, further improving disease diagnosis, and tractography studies.     

Adaptive registration of diffusion tensor images on lie groups

With diffusion tensor imaging (DTI), more exquisite information on tissue microstructure is provided for medical image processing. In this paper, we present a locally adaptive topology preserving method for DTI registration on Lie groups. The method aims to obtain more plausible diffeomorphisms for spatial transformations via accurate approximation for the local tangent space on the Lie group manifold. In order to capture an exact geometric structure of the Lie group, the local linear approximation is efficiently optimized by using the adaptive selection of the local neighborhood sizes on the given set of data points. Furthermore, numerical comparative experiments are conducted on both synthetic data and real DTI data to demonstrate that the proposed method yields a higher degree of topology preservation on a dense deformation tensor field while improving the registration accuracy.     

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.     

A Monte Carlo simulation of image misalignment effects in diffusion tensor imaging

Diffusion tensor imaging (DTI) and tractography are noninvasive MRI methods, providing an insight on microscopic structural information of anisotropic tissues in vivo. The success of this technique stems on a watchful choice of imaging parameters and post-acquisition reconstruction. In the present work, we have focused on the problem of residual linear image misalignment in the DTI data and its effects on the parameters of the diffusion tensor and fiber tracking in human brain. We demonstrate substantial sensitivity of the reconstructed diffusion tensor and fiber tractography on increasing amplitude of artificially induced random image misalignment in the DTI. We show that already a submillimeter image misalignment in the DTI is an important source of error, which may potentially mask pathological presentations of the diseases and may partially explain variations in the results obtained from the DTI. Finally, we evaluated four implementations of image registrations and demonstrate their variable performance. This further supports the fact that a robust image registration must be performed to ensure reliable and reproducible diffusion tensor mapping and reconstruction of white matter (WM) fibers.     

磁共振扩散张量成像中扩散敏感梯度磁场方向分布方案的研究进展

磁共振扩散张量成像可以定量无创研究人体内水分子在三维空间中的各向异性扩散规律,进而获取重要的病理及生理信息.为了得到水分子各向异性扩散信息,需要按照一定的方案依次施加不同方向的扩散敏感梯度磁场,测量水分子在这些方向上的扩散系数用以估算扩散张量.扩散张量成像测量结果的准确程度受梯度磁场方向分布方案的影响,本文对扩散敏感梯度磁场方向分布方案进行综述,包括完全随机方案、启发式方案、规则多面体式方案和数值优化方案等,分析这些方案的优势与局限性,并提出需进一步研究的问题.     

Estimation and application of spatially variable noise fields in diffusion tensor imaging

Optimal interpretation of magnetic resonance image content often requires an estimate of the underlying image noise, which is typically realized as a spatially invariant estimate of the noise distribution. This is not an ideal practice in diffusion tensor imaging because the noise distribution is usually spatially varying due to the use of fast imaging and noise suppression techniques. A new estimation approach for spatially varying noise fields (NFs) is proposed in this article. The approach is based on a noise invariance property in scenarios in which more than one image, each with potentially different signal levels, is acquired on each slice, as in diffusion-weighted MRI. This technique leads to improved NF estimates in simulations, phantom experiments and in vivo studies when compared to traditional NF estimators that use regional variability or background intensity histograms. The proposed method reduces the NF estimation error by a factor of 100 in simulations, shows a strong linear correlation (R²=0.99) between theoretical and estimated noise changes in phantoms and demonstrates consistent (<5% variability) NF estimates in vivo. The advantages of spatially varying NF estimation are demonstrated for power analysis, outlier detection and tensor estimation.     

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.