High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity.

Magnetic resonance (MR) diffusion tensor imaging (DTI) can resolve the white matter fiber orientation within a voxel provided that the fibers are strongly aligned. However, a given voxel may contain a distribution of fiber orientations due to, for example, intravoxel fiber crossing. The present study sought to test whether a geodesic, high b-value diffusion gradient sampling scheme could resolve multiple fiber orientations within a single voxel. In regions of fiber crossing the diffusion signal exhibited multiple local maxima/minima as a function of diffusion gradient orientation, indicating the presence of multiple intravoxel fiber orientations. The multimodality of the observed diffusion signal precluded the standard tensor reconstruction, so instead the diffusion signal was modeled as arising from a discrete mixture of Gaussian diffusion processes in slow exchange, and the underlying mixture of tensors was solved for using a gradient descent scheme. The multitensor reconstruction resolved multiple intravoxel fiber populations corresponding to known fiber anatomy. Ma     

In vivo generalized diffusion tensor imaging (GDTI) using higher‐order tensors (HOT)

Generalized diffusion tensor imaging (GDTI) using higher‐order tensor (HOT) statistics generalizes the technique of diffusion tensor imaging by including the effect of nongaussian diffusion on the signal of MRI. In GDTI‐HOT, the effect of nongaussian diffusion is characterized by higher‐order tensor statistics (i.e., the cumulant tensors or the moment tensors), such as the covariance matrix (the second‐order cumulant tensor), the skewness tensor (the third‐order cumulant tensor), and the kurtosis tensor (the fourth‐order cumulant tensor). Previously, Monte Carlo simulations have been applied to verify the validity of this technique in reconstructing complicated fiber structures. However, no in vivo implementation of GDTI‐HOT has been reported. The primary goal of this study is to establish GDTI‐HOT as a feasible in vivo technique for imaging nongaussian diffusion. We show that probability distribution function of the molecular diffusion process can be measured in vivo with GDTI‐HOT and be visualized with three‐dimensional glyphs. By comparing GDTI‐HOT to fiber structures that are revealed by the highest resolution diffusion‐weighted imaging (DWI) possible in vivo, we show that the GDTI‐HOT can accurately predict multiple fiber orientations within one white matter voxel. Furthermore, through bootstrap analysis we demonstrate that in vivo measurement of HOT elements is reproducible, with a small statistical variation that is similar to that of diffusion tensor imaging. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.     

Measurement of fiber orientation distributions using high angular resolution diffusion imaging.

High angular resolution measurements of diffusion are used to estimate the angular distribution and diffusion anisotropy of fibers in a voxel. A simple, axially symmetric model of diffusion in white matter fibers is used to relate diffusion measurements to fiber properties. The new technique is called fiber orientation estimated using continuous axially symmetric tensors (FORECAST). It is tested using both numerical simulation and in vivo measurements. The new method agrees with other methods in voxels containing single fibers, but resolves crossing fibers better, at least at the level of diffusion weighting used in this study (tr(b) = 1480 s/mm2). The simplifying assumptions of the model are tested by comparison with the "model-free" q-ball analysis of in vivo data and the results are shown to be in good agreement. The new method addresses the problem of partial volume averaging in diffusion tensor imaging and provides a basis for more reliable estimates of fiber orientation and fractional anisotropy.     

Tensor kernels for simultaneous fiber model estimation and tractography

This paper proposes a novel framework for joint orientation distribution function estimation and tractography based on a new class of tensor kernels. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the measured signal or estimated fiber orientation. In this work, fiber tracking is formulated as recursive estimation: at each step of tracing the fiber, the current estimate of the orientation distribution function is guided by the previous. To do this, second‐and higher‐order tensor‐based kernels are employed. A weighted mixture of these tensor kernels is used for representing crossing and branching fiber structures. While tracing a fiber, the parameters of the mixture model are estimated based on the orientation distribution function at that location and a smoothness term that penalizes deviation from the previous estimate along the fiber direction. This ensures smooth estimation along the direction of propagation of the fiber. In synthetic experiments, using a mixture of two and three components it is shown that this approach improves the angular resolution at crossings. In vivo experiments using two and three components examine the corpus callosum and corticospinal tract and confirm the ability to trace through regions known to contain such crossing and branching. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Model‐based reconstruction of undersampled diffusion tensor k‐space data

The practical utility of diffusion tensor imaging, especially for 3D high‐resolution spin warp experiments of ex vivo specimens, has been hampered by long acquisition times. To accelerate the acquisition, a compressed sensing framework that uses a model‐based formulation to reconstruct diffusion tensor fields from undersampled k‐space data was presented and evaluated. Accuracies in brain specimen white matter fiber orientation, fractional anisotropy, and mean diffusivity mapping were compared with alternative methods achievable using the same scan time via reduced image resolution, fewer diffusion encoding directions, standard compressed sensing, or asymmetrical sampling reconstruction. The efficiency of the proposed approach was also compared with fully sampled cases across a range of the number of diffusion encoding directions. In general, the proposed approach was found to reduce the image blurring and noise and to provide more accurate fiber orientation, fractional anisotropy, and mean diffusivity measurements compared with the alternative methods. Moreover, depending on the degree of undersampling used and the diffusion tensor imaging parameter examined, the measurement accuracy of the proposed scheme was equivalent to fully sampled diffusion tensor imaging datasets that consist of 33–67% more encoding directions and require proportionally longer scan times. The findings show model‐based compressed sensing to be promising for improving the resolution, accuracy, or scan time of diffusion tensor imaging. Magn Reson Med 70:429–440, 2013. © 2012 Wiley Periodicals, Inc.     

Theory of diffusion tensor imaging and fiber tractography analysis

Magnetic Resonance Imaging (MRI) techniques have been increasingly applied to the study of molecular displacement (diffusion) in biologic tissue. The magnetic resonance measurement of an effective diffusion tensor of water in tissues can provide unique biologically and clinically relevant information that is not available from other imaging modalities. For this purpose Diffusion Tensor Imaging (DTI) is applied. DTI is an MRI variation that may significantly improve our understanding of brain structure and neural connectivity. DTI measures are thought to be representative of brain tissue microstructure and are particularly useful for examining organized brain regions, such as white matter tract areas. DTI measures the water diffusion tensor using diffusion weighted pulse sequences sensitive to microscopic random water motion. The resultant images display and allow for quantification of how water diffuses along axes or diffusion encoding directions. This can help measure and quantify a tissue's orientation and structure, making it an ideal tool for examining cerebral white matter and neural fiber tracts. In this article we discuss the theory on which DTI depends on, how can be used in mapping fiber tracts. Also the fiber tracking algorithms are presented.     

Novel spherical phantoms for Q‐ball imaging under in vivo conditions

For the validation of complex diffusion imaging techniques like q‐ball imaging that aim to resolve multiple fiber directions, appropriate phantoms are highly desirable. However, previous q‐ball imaging phantoms had diffusion anisotropies well below those of in vivo white matter. In this work, fiber phantoms of well‐defined geometry are presented. The fibers are wound on a spherical spindle yielding high packing densities and consequently high diffusion anisotropies (fractional anisotropy 0.93 ± 0.02 at b = 500 s/mm²). Phantoms with 90° and 45° crossing angle were constructed both with two crossing types. In the “stacked” crossing, two fiber strings were wound consecutively to simulate two touching fibers, in the “interleaved” crossing, fibers were wound alternately. The stacked crossing allows the alteration of partial volumes, whereas the interleaved crossing provides constant partial volumes, allowing e.g. the easy alteration of the SNR by varying the slice thickness. Exemplary q‐ball imaging validation measurements using different b‐values and slice thicknesses are presented. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Double‐wave‐vector diffusion‐weighted imaging reveals microscopic diffusion anisotropy in the living human brain

Diffusion‐tensor imaging is widely used to characterize diffusion in biological tissue, however, the derived anisotropy information, e.g., the fractional anisotropy, is ambiguous. For instance, low values of the diffusion anisotropy in brain white matter voxels may reflect a reduced axon density, i.e., a loss of fibers, or a lower fiber coherence within the voxel, e.g., more crossing fibers. This ambiguity can be avoided with experiments involving two diffusion‐weighting periods applied successively in a single acquisition, so‐called double‐wave‐vector or double‐pulsed‐field‐gradient experiments. For a long mixing time between the two periods such experiments are sensitive to the cells' eccentricity, i.e., the diffusion anisotropy present on a microscopic scale. In this study, it is shown that this microscopic diffusion anisotropy can be detected in white matter in the living human brain, even in a macroscopically isotropic region‐of‐interest (fractional anisotropy = 0). The underlying signal difference between parallel and orthogonal wave vector orientations does not show up in standard diffusion‐weighting experiments but is specific to the double‐wave‐vector experiment. Furthermore, the modulation amplitude observed is very similar for regions‐of‐interest with different fractional anisotrpy values. Thus, double‐wave‐vector experiments may provide a direct and reliable access to white matter integrity independent of the actual fiber orientation distribution within the voxel. Magn Reson Med 69:1072–1082, 2013. © 2012 Wiley Periodicals, Inc.     

Characterizing fiber directional uncertainty in diffusion tensor MRI

Image noise in diffusion tensor MRI (DT‐MRI) causes errors in the measured tensor and hence variance in the estimated fiber orientation. Uncertainty in fiber orientation has been described using a circular “cone of uncertainty” (CU) around the principal eigenvector of the DT. The CU has proved to be a useful construct for quantifying and visualizing the variability of DT‐MRI parameters and fiber tractography. The assumption of circularity of the CU has not been tested directly, however. In this work, bootstrap analysis and simple theoretical arguments were used to show that the CU is elliptical and multivariate normal in the vast majority of white matter (WM) voxels for typical measurement conditions. The dependence of the cone angle on the signal‐to‐noise ratio (SNR) and eigenvalue contrast was established. The major and minor cone axes are shown to be coincident with the second and third eigenvectors of the tensor, respectively, in the limit of many uniformly spaced diffusion‐encoding directions. The deviation between the major cone axis and the second eigenvector was quantified for typical sets of diffusion‐weighting (DW) directions. The elliptical CU provides more realistic error information for fiber‐tracking algorithms and a quantitative basis for selecting DT imaging acquisition protocols. Magn Reson Med 60:1408–1421, 2008. © 2008 Wiley‐Liss, Inc.     

Q-ball imaging.

Magnetic resonance diffusion tensor imaging (DTI) provides a powerful tool for mapping neural histoarchitecture in vivo. However, DTI can only resolve a single fiber orientation within each imaging voxel due to the constraints of the tensor model. For example, DTI cannot resolve fibers crossing, bending, or twisting within an individual voxel. Intravoxel fiber crossing can be resolved using q-space diffusion imaging, but q-space imaging requires large pulsed field gradients and time-intensive sampling. It is also possible to resolve intravoxel fiber crossing using mixture model decomposition of the high angular resolution diffusion imaging (HARDI) signal, but mixture modeling requires a model of the underlying diffusion process.Recently, it has been shown that the HARDI signal can be reconstructed model-independently using a spherical tomographic inversion called the Funk-Radon transform, also known as the spherical Radon transform. The resulting imaging method, termed q-ball imaging, can resolve multiple intravoxel fiber orientations and does not require any assumptions on the diffusion process such as Gaussianity or multi-Gaussianity. The present paper reviews the theory of q-ball imaging and describes a simple linear matrix formulation for the q-ball reconstruction based on spherical radial basis function interpolation. Open aspects of the q-ball reconstruction algorithm are discussed.     

Susceptibility tensor imaging

Heterogeneity of magnetic susceptibility within brain tissues creates unique contrast between gray and white matter in magnetic resonance phase images acquired by gradient echo sequences. Detailed understanding of this contrast may provide meaningful diagnostic information. In this communication, we report an observation of extensive anisotropic magnetic susceptibility in the white matter of the central nervous system. Furthermore, we describe a susceptibility tensor imaging technique to measure and quantify this phenomenon. This technique relies on the measurement of resonance frequency offset at different orientations with respect to the main magnetic field. We propose to characterize this orientation variation using an apparent susceptibility tensor. The susceptibility tensor can be decomposed into three eigenvalues (principal susceptibilities) and associated eigenvectors that are coordinate‐system independent. We show that the principal susceptibilities offer strong contrast between gray and white matter, whereas the eigenvectors provide orientation information of an underlying magnetic network. We believe that this network may further offer information of white matter fiber orientation. Magn Reson Med 63:1471–1477, 2010. © 2010 Wiley‐Liss, Inc.     

磁共振弥散张量成像对正常大脑白质纤维束构象的初步研究

目的利用磁共振弥散张量成像(DTI)研究正常成人脑内各部位各向异性程度及正常白质纤维束构象特征.方法对25名正常志愿者进行常规MR及DTI序列检查,重建FA图及三维彩色编码张量图.分别在半卵圆中心、基底节区和大脑脚层面测量主要白质束的FA值.结果DTI显示灰质与白质区各向异性存在显著差异,不同部位的白质纤维束各向异性程度亦不相同,且左右两侧基本对称,重建FA图和三维彩色编码张量图可显示白质内大部分主要的白质纤维束.结论DTI可清晰显示脑内白质纤维束的走行及分布,为了解脑功能与白质通路间关系提供了有力研究手段.     

Usefulness of diffusion tensor imaging of white matter in Alzheimer disease and vascular dementia

Purpose: To evaluate the usefulness of diffusion tensor imaging in detecting the water diffusivity caused by neuropathological change in Alzheimer disease and vascular dementia.

Material and Methods: Twenty patients with Alzheimer disease, 20 with vascular dementia, and 10 control subjects were examined. Diffusion tensor imaging applied diffusion gradient encoding in six non-collinear directions. Fractional anisotropy values were compared in the genu and splenium of the corpus callosum, and anterior and posterior white matter among the three groups.

Results: In the patients with Alzheimer disease, fractional anisotropy values of the posterior white matter were significantly lower than those of controls. In patients with vascular dementia, fractional anisotropy values of the anterior white matter tended to be lower than those of the posterior white matter (P=0.07).

Conclusion: Diffusion tensor imaging reflects the neuropathological changes in the white matter, and may be useful in the diagnosis of Alzheimer disease and vascular dementia.     

Inference of multiple fiber orientations in high angular resolution diffusion imaging.

A method is presented that is capable of determining more than one fiber orientation within a single voxel in high angular resolution diffusion imaging (HARDI) data sets. This method is an extension of the Markov chain method recently introduced to diffusion tensor imaging (DTI) analysis, allowing the probability density function of up to 2 intra-voxel fiber orientations to be inferred. The multiple fiber architecture within a voxel is then assessed by calculating the relative probabilities of a 1 and 2 fiber model. It is demonstrated that for realistic signal to noise ratios, it is possible to accurately characterize the directions of 2 intersecting fibers using a 2 fiber model. The shortcomings of under-fitting a 2 fiber model, or over-fitting a 1 fiber model, are explored. This new algorithm enhances the tools available for fiber tracking.     

q‐space and conventional diffusion imaging of axon and myelin damage in the rat spinal cord after axotomy

Parallel and perpendicular diffusion properties of water in the rat spinal cord were investigated 3 and 30 days after dorsal root axotomy, a specific insult resulting in early axonal degeneration followed by later myelin damage in the dorsal column white matter. Results from q‐space analysis (i.e., the diffusion probability density function) obtained with strong diffusion weighting were compared to conventional anisotropy and diffusivity measurements at low b‐values, as well as to histology for axon and myelin damage. q‐Space contrasts included the height (return to zero displacement probability), full width at half maximum, root mean square displacement, and kurtosis excess of the probability density function, which quantifies the deviation from gaussian diffusion. Following axotomy, a significant increase in perpendicular diffusion (with decreased kurtosis excess) and decrease in parallel diffusion (with increased kurtosis excess) were found in lesions relative to uninjured white matter. Notably, a significant change in abnormal parallel diffusion was detected from 3 to 30 days with full width at half maximum, but not with conventional diffusivity. Also, directional full width at half maximum and root mean square displacement measurements exhibited different sensitivities to white matter damage. When compared to histology, the increase in perpendicular diffusion was not specific to demyelination, whereas combined reduced parallel diffusion and increased perpendicular diffusion was associated with axon damage. Magn Reson Med 63:1323–1335, 2010. © 2010 Wiley‐Liss, Inc.     

Diffusion tensor eigenvector directional color imaging patterns in the evaluation of cerebral white matter tracts altered by tumor

PURPOSE: To categorize the varied appearances of tumor-altered white matter (WM) tracts on diffusion tensor eigenvector directional color maps. MATERIALS AND METHODS: Diffusion tensor imaging (DTI) was obtained preoperatively in 13 patients with brain tumors ranging from benign to high-grade malignant, including primary and metastatic lesions, and maps of apparent diffusion coefficient (ADC), fractional anisotropy (FA), and major eigenvector direction were generated. Regions of interest (ROIs) were drawn within identifiable WM tracts affected by tumor, avoiding grossly cystic and necrotic regions, known fiber crossings, and gray matter. Patterns of WM tract alteration were categorized on the basis of qualitative analysis of directional color maps and correlation analysis of ADC and FA. RESULTS: Four basic patterns of WM alteration were identified: 1) normal or nearly normal FA and ADC, with abnormal tract location or tensor directions attributable to bulk mass displacement, 2) moderately decreased FA and increased ADC with normal tract locations and tensor directions, 3) moderately decreased FA and increased ADC with abnormal tensor directions, and 4) near isotropy. FA and ADC were inversely correlated for Patterns 1-3 but did not discriminate edema from infiltrating tumor. However, in the absence of mass displacement, infiltrating tumor was found to produce tensor directional changes that were not observed with vasogenic edema, suggesting the possibility of discrimination on the basis of directional statistics. CONCLUSION: Tumor alteration of WM tracts tends to produce one of four patterns on FA and directional color maps. Clinical application of these patterns must await further study.     

Axial asymmetry of water diffusion in brain white matter.

The diffusion tensor (DT) is a three-dimensional (3D) model of diffusivity in biological tissues. In white matter (WM), the major eigenvector, which is the direction of greatest diffusivity, is generally assumed to align with the direction of the fiber bundles. The distribution of major eigenvectors in WM has been investigated using color-based maps and WM tractography (WMT). However, anatomical patterns in the medium and minor eigenvector directions have largely been ignored in DTI studies of the human brain. In this study, the patterns of medium and minor eigenvectors in the brain were investigated using both color-based maps and WMT. Specific WM structures, such as the corona radiata, internal and external capsules, sagittal stratum, cingulum, and superior longitudinal fasciculus, demonstrated coherent patterns in the medium and minor eigenvector directions. These patterns were consistent across subjects. The orthogonal or axial diffusion asymmetry may be explained by merging, diverging, or crossing fiber geometries. The effects of orthogonal diffusion asymmetry on WMT were also investigated. This study shows that WM axial asymmetry causes anisotropic dispersion patterns in the estimated tract trajectories. The medium and minor eigenvector patterns may be useful for elucidating the local dispersion distributions of WM tracts.     

Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis.

Diffusion tensor imaging (DTI) accurately delineates white matter pathways when the Gaussian model of diffusion is valid. However, DTI yields erroneous results when diffusion takes on a more complex distribution, as is the case in the brain when fiber tracts cross. High angular resolution diffusion imaging (HARDI) overcomes this limitation of DTI by more fully characterizing the angular dependence of intravoxel diffusion. Among the various HARDI methods that have been proposed, QBI offers advantages such as linearity, model independence, and relatively easy implementation. In this work, reconstruction of the q-ball orientation distribution function (ODF) is reformulated in terms of spherical harmonic basis functions, yielding an analytic solution with useful properties of a frequency domain representation. The harmonic basis is parsimonious for typical b-values, which enables the ODF to be synthesized from a relatively small number of noisy measurements and thus brings the technique closer to clinical feasibility from the standpoint of total imaging time. The proposed method is assessed using Monte Carlo computer simulations and compared with conventional q-ball reconstruction using spherical RBFs. In vivo results from 3T whole-brain HARDI of adult volunteers are also provided to verify the underlying mathematical theory.     

Cross-subject comparison of principal diffusion direction maps.

Diffusion tensor imaging (DTI) data differ fundamentally from most brain imaging data in that values at each voxel are not scalars but 3 x 3 positive definite matrices also called diffusion tensors. Frequently, investigators simplify the data analysis by reducing the tensor to a scalar, such as fractional anisotropy (FA). New statistical methods are needed for analyzing vector and tensor valued imaging data. A statistical model is proposed for the principal eigenvector of the diffusion tensor based on the bipolar Watson distribution. Methods are presented for computing mean direction and dispersion of a sample of directions and for testing whether two samples of directions (e.g., same voxel across two groups of subjects) have the same mean. False discovery rate theory is used to identify voxels for which the two-sample test is significant. These methods are illustrated in a DTI data set collected to study reading ability. It is shown that comparison of directions reveals differences in gross anatomic structure that are invisible to FA.     

Six is enough? Comparison of diffusion parameters measured using six or more diffusion‐encoding gradient directions with deterministic tractography

Diffusion tensor imaging tractography is commonly used to quantify white matter tracts in the human brain via parameters such as fractional anisotropy and mean diffusivity. Simulation studies recommend the use of more than six directions for robust parameter estimates; however, no study has examined the impact of the number of gradient directions on deterministic tractography-derived diffusion parameters in human brain. Here, for 10 major white matter tracts in 11 healthy volunteers at 1.5 T, six-direction diffusion tensor imaging data were compared to 30- or 60-direction data, keeping scan time and number of b = 0 images constant within each test. Mean diffusivity was systematically lower for six-direction protocols (20/40 comparisons); six-direction data had higher fractional anisotropy in the superior longitudinal fasciculus and smaller tract volume for the genu of the corpus callosum. In general, parameter differences due to the number of directions were smaller than those from intersubject variation or signal-to-noise ratio. Despite some absolute differences, standard deviations were significantly different for only one of 160 comparisons. Thus, six-direction data provide diffusion measures with comparable robustness to 30- or 60-direction data and yield appropriate parameter values for most white matter tracts, although there are clear advantages in acquiring higher angular resolution data.