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.     

Use of capillaries in the construction of an MRI phantom for the assessment of diffusion tensor imaging: demonstration of performance

Although diffusion tensor imaging (DTI) shows great potential for the diagnosis of a variety of pathologies, no consensus for an appropriate assessment standard of DTI exists. This study examined the feasibility of using water-filled arrays of glass capillaries to construct a DTI phantom suitable for making repeated and reproducible measurements required in a quality assessment program. Three phantoms were constructed using arrays of capillaries with three inner diameters (23, 48, and 82 μm). Data were acquired using DTI protocols; the fractional anisotropy (FA), mean apparent diffusion coefficient (ADC) and principal eigenvectors of the diffusion tensors were calculated. This study demonstrated four results: (1) echo-planar images show that susceptibility within the capillary arrays does not lead to substantial differences in precessional frequency in regions containing the arrays and neither do the regions show noticeable image distortion; (2) principal eigenvectors of the diffusion tensors agree to within <10.3° of the array orientations; (3) mean FA values (0.18–0.50) and ADC values (1.40–1.93×10−³ mm²/s) within specified regions of interest are in general agreement with simulations after a simple noise correction; and (4) these array performance characteristics are observable using a typical clinical DTI protocol.     

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.     

Effect of B-value in revealing postinfarct myocardial microstructural remodeling using MR diffusion tensor imaging

Nonmonoexponential diffusion behavior has been previously reported to exist in some biological tissues, making quantification of diffusion tensor imaging (DTI) indices dependent on diffusion sensitivity of b-value. This study aims to investigate the effect of b-value in revealing postinfarct myocardial microstructural remodeling in ex vivo hearts. DTI scans were performed on heart samples 1, 3, 5, and 7 days after infarction induction as well as intact controls with b-values of 500 to 2500 s/mm². DTI indices, including fractional anisotropy (FA), and mean and directional diffusivities, were measured in infarct, adjacent and remote regions with zero and each non-zero b-values respectively using conventional DTI analysis. Experimental results showed that these DTI indices decreased gradually with b-values in all regions and groups. Optimal b-values were found to vary with targeted DTI indices, and could strengthen DTI ability in revealing myocardium degradation with using conventional DTI approach. Specifically, FA showed the most sensitive detection of fiber integrity degradation at moderate b-values (≈ 1500 to 2000 s/mm²), and the greatest ability of mean and directional diffusivities in monitoring diffusivity alteration occurred at relatively small b-values (≤ 1500 s/mm²) during the necrotic and fibrotic phases. These findings may provide useful information for DTI protocol parameter optimization in assessing heart microstructures at other pathological or in vivo states in the future.     

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

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

How does distortion correction correlate with anisotropic indices? A diffusion tensor imaging study

PURPOSE: The purpose of this study was to determine a suitable registration algorithm for diffusion tensor imaging (DTI) using conventional preprocessing tools [statistical parametric mapping (SPM) and automated image registration (AIR)] and to investigate how anisotropic indices for clinical assessments are affected by these distortion corrections. MATERIALS AND METHODS: Brain DTI data from 15 normal healthy volunteers were used to evaluate four spatial registration schemes within subjects to correct image distortions: noncorrection, SPM-based affine registration, AIR-based affine registration and AIR-based nonlinear polynomial warping. The performance of each distortion correction was assessed using: (a) quantitative parameters: tensor-fitting error (Ef), mean dispersion index (MDI), mean fractional anisotropy (MFA) and mean variance (MV) within 11 regions of interest (ROI) defined from homogeneous fiber bundles; and (b) fiber tractography through the uncinate fasciculus and the corpus callosum. Fractional anisotropy (FA) and mean diffusivity (MD) were calculated to demonstrate the effects of distortion correction. Repeated-measures analysis of variance was used to investigate differences among the four registration paradigms. RESULTS: AIR-based nonlinear registration showed the best performance for reducing image distortions with respect to smaller Ef (P<.02), MDI (P<.01) and MV (P<.01) with larger MFA (P<.01). FA was decreased to correct distortions (P<.0001) whether the applied registration was linear or nonlinear and was lowest after nonlinear correction (P<.001). No significant differences were found in MD. CONCLUSION: In conventional DTI processing, anisotropic indices of FA can be misestimated by noncorrection or inappropriate distortion correction, which leads to an erroneous increase in FA. AIR-based nonlinear distortion correction would be required for a more accurate measurement of this diffusion parameter.     

Comparison of mouse brain DTI maps using K-space average,image-space average,or no average approach

Diffusion tensor imaging (DTI) is achieved by collecting a series of diffusion-weighted images (DWIs). Signal averaging of multiple repetitions can be performed in the k-space (k-avg) or in the image space (m-avg) to improve the image quality. Alternatively, one can treat each acquisition as an independent image and use all of the data to reconstruct the DTI without doing any signal averaging (no-avg). To compare these three approaches, in this study, in vivo DTI data were collected from five normal mice. Noisy data with signal-to-noise ratios (SNR) that varied between five and 30 (before averaging) were then simulated. The DTI indices, including relative anisotropy (RA), trace of diffusion tensor (TR), axial diffusivity (λ║), and radial diffusivity (λ ⊥), derived from the k-avg, m-avg, and no-avg, were then compared in the corpus callosum white matter, cortex gray matter, and the ventricles. We found that k-avg and m-avg enhanced the SNR of DWI with no significant differences. However, k-avg produced lower RA in the white matter and higher RA in the gray matter, compared to the m-avg and no-avg, regardless of SNR. The latter two produced similar DTI quantifications. We concluded that k-avg is less preferred for DTI brain imaging.     

Effect of cerebrovascular changes on brain DTI quantitation: a hypercapnia study

Quantitative diffusion tensor imaging (DTI) offers a valuable tool to probe the microstructural changes in neural tissues in vivo, where absolute quantitation accuracy and reproducibility are essential. It has been long recognized that measurement of apparent diffusion coefficient (ADC) using DTI could be influenced by the presence of water molecules in cerebrovasculature. However, little is known about to what extent such blood signal affects DTI quantitation. In this study, we quantitatively examined the effect of cerebral hemodynamic change on DTI indices by using a standard multislice echo planar imaging (EPI) spin echo (SE) DTI acquisition protocol and a rat model of hypercapnia. In response to 5% CO(2) challenge, mean, radial and axial diffusivities measured with diffusion factor (b-value) of b=1.0 ms/μm(2) were found to increase in whole brain (1.52%±0.22%, 1.66%±0.16% and 1.35%±0.37%, respectively), gray matter (1.56%±0.23%, 1.63%±0.14% and 1.47%±0.45%, respectively) and white matter regions (1.45%±0.28%, 1.88%±0.33% and 1.10%±0.26%, respectively). Fractional anisotropy (FA) was found to decrease by 1.67%±0.38%, 1.91%±0.59% and 1.46%±0.30% in whole brain, gray matter and white matter regions, respectively. In addition, these diffusivity increases and FA decreases became more pronounced at a lower b-value (b=0.3 ms/μm(2)). The results indicated that in vivo DTI quantitation in brain can be contaminated by vascular factors on the order of few percentages. Consequently, alterations in cerebrovasculature and hemodynamics can affect the DTI quantitation and its efficacy in characterizing the neural tissue microstructures in normal and diseased states. Caution should be taken in designing and interpreting quantitative DTI studies as all DTI indices can be potentially confounded by physiologic conditions and by cerebrovascular and hemodynamic characteristics.     

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.     

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 theoretical study of the effect of experimental noise on the measurement of anisotropy in diffusion imaging

Diffusion tensor imaging (DTI) is a modality known to be highly sensitive to the detrimental effects of experimental noise. Here, using Monte Carlo simulations, we compare and contrast how noise complicates the measurement of diffusion anisotropy in diffusion tensor and conventional diffusion-weighted imaging (DWI). As the signal-to-noise ratio (SNR) decreases below a value of approximately 20, the eigenvalues (λ_i) of the diffusion tensor D are found to diverge rapidly from their true values, with the result that the measured anisotropy can be significantly in error and isotropic structures falsely assigned a high level of anisotropy. The effect of noise on the rotationally variant indices, calculated from a conventional diffusion-weighted imaging experiment, is found to be much less insidious, because the apparent diffusion coefficients (ADCs) diverge only slowly as the signal-to-noise decreases. Thus, although rotationally variant indices almost always underestimate the true diffusion anisotropy, they show only a small susceptibility to experimental noise and hence, are preferred to their rotationally invariant counterparts when the signal-to-noise ratio is small.     

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     

Looking for the optimal DTI acquisition scheme given a maximum scan time: are more b-values a waste of time?

In this study we used simulated data to investigate how valuable the use of multiple b-values is, in terms of improving the accuracy and reproducibility of Diffusion Tensor Imaging (DTI) results. Our results show that the systematic bias of the estimated scalar diffusion parameters [apparent diffusion coefficient and fractional anisotropy (FA)] - due to the Rician distribution of magnetic resonance noise - can be minimized by increasing the number of b-values and not by increasing the number of sampling directions. In addition, the use of more than one b-value accounts better for the wide range of diffusivities found in the human brain by bringing closer together the FA estimates for fibres with different mean diffusivities. It is also shown that while for tractography studies we should use as many sampling directions as allowed by scan time limitations, for follow-up, intersubject or multicenter studies, the use of more than one b-value will improve the accuracy of the scalar diffusion parameters, as long as the minimum number of directions required for robust estimation of each parameter is still used.     

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.     

Role of diffusion tensor imaging metrics and in vivo proton magnetic resonance spectroscopy in the differential diagnosis of cystic intracranial mass lesions

The purpose of this study was to determine whether proton magnetic resonance spectroscopy (PMRS) and diffusion tensor imaging (DTI) indices, fractional anisotropy (FA) and mean diffusivity (MD) can be used to distinguish brain abscess from cystic brain tumors, which are difficult to distinguish by conventional magnetic resonance imaging (MRI). Fifty-three patients with intracranial cystic mass lesions and 10 normal controls were studied. Conventional MRI, PMRS and DTI of all the patients were performed on a 1.5-T GE scanner. Forty patients were with brain abscess and 13 with cystic tumors. Cytosolic amino acids (AAs) were present in 32 of 40 brain abscess patients. Out of 13 patients with cystic tumors, lactate and choline were seen in 3 and only lactate was present in 10 patients on PMRS. All 40 cases of abscess had high FA, while all 13 cases of tumor cysts had high MD values. We conclude that FA measurements are more sensitive in predicting the abscess, while PMRS and MD are more specific in differentiating abscess from cystic tumors. We suggest that PMRS should be combined with DTI rather than with diffusion-weighted imaging as FA can be used as an additional parameter for separation of abscess from other cystic intracranial mass lesions.     

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.     

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 framework for quality control and parameter optimization in diffusion tensor imaging: theoretical analysis and validation

In this communication, a theoretical framework for quality control and parameter optimization in diffusion tensor imaging (DTI) is presented and validated. The approach is based on the analytical error propagation of the mean diffusivity (D(av)) obtained directly from the diffusion-weighted data acquired using rotationally invariant and uniformly distributed icosahedral encoding schemes. The error propagation of a recently described and validated cylindrical tensor model is further extrapolated to the spherical tensor case (diffusion anisotropy approximately 0) to relate analytically the precision error in fractional tensor anisotropy (FA) with the mean diffusion-to-noise ratio (DNR). The approach provided simple analytical and empirical quality control measures for optimization of diffusion parameter space in an isotropic medium that can be tested using widely available water phantoms.     

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.     

An investigation of motion correction algorithms for pediatric spinal cord DTI in healthy subjects and patients with spinal cord injury

Patient and physiological motion can cause artifacts in DTI of the spinal cord which can impact image quality and diffusion indices. The purpose of this investigation was to determine a reliable motion correction method for pediatric spinal cord DTI and show effects of motion correction on DTI parameters in healthy subjects and patients with spinal cord injury. Ten healthy subjects and ten subjects with spinal cord injury were scanned using a 3 T scanner. Images were acquired with an inner field-of-view DTI sequence covering cervical spine levels C1 to C7. Images were corrected for motion using two types of transformation (rigid and affine) and three cost functions. Corrected images and transformations were examined qualitatively and quantitatively using in-house developed code. Fractional anisotropy (FA) and mean diffusivity (MD) indices were calculated and tested for statistical significance pre- and post- motion correction. Images corrected using rigid methods showed improvements in image quality, while affine methods frequently showed residual distortions in corrected images. Blinded evaluation of pre and post correction images showed significant improvement in cord homogeneity and edge conspicuity in corrected images (p < 0.0001). The average FA changes were statistically significant (p < 0.0001) in the spinal cord injury group, while healthy subjects showed less FA change and were not significant. In both healthy subjects and subjects with spinal cord injury, quantitative and qualitative analysis showed the rigid scaled-least-squares registration technique to be the most reliable and effective in improving image quality.