Towards inference of human brain connectivity from MR diffusion tensor data

Non-local means based Rician noise filtering for diffusion tensor and kurtosis imaging in human brain and spinal cord

BACKGROUND

To investigate the effect of using a Rician nonlocal means (NLM) filter on quantification of diffusion tensor (DT)- and diffusion kurtosis (DK)-derived metrics in various anatomical regions of the human brain and the spinal cord, when combined with a constrained linear least squares (CLLS) approach.

METHODS

Prospective brain data from 9 healthy subjects and retrospective spinal cord data from 5 healthy subjects from a 3 T MRI scanner were included in the study. Prior to tensor estimation, registered diffusion weighted images were denoised by an optimized blockwise NLM filter with CLLS. Mean kurtosis (MK), radial kurtosis (RK), axial kurtosis (AK), mean diffusivity (MD), radial diffusivity (RD), axial diffusivity (AD) and fractional anisotropy (FA), were determined in anatomical structures of the brain and the spinal cord. DTI and DKI metrics, signal-to-noise ratio (SNR) and Chi-square values were quantified in distinct anatomical regions for all subjects, with and without Rician denoising.

RESULTS

The averaged SNR significantly increased with Rician denoising by a factor of 2 while the averaged Chi-square values significantly decreased up to 61% in the brain and up to 43% in the spinal cord after Rician NLM filtering. In the brain, the mean MK varied from 0.70 (putamen) to 1.27 (internal capsule) while AK and RK varied from 0.58 (corpus callosum) to 0.92 (cingulum) and from 0.70 (putamen) to 1.98 (corpus callosum), respectively. In the spinal cord, FA varied from 0.78 in lateral column to 0.81 in dorsal column while MD varied from 0.91 × 10^-3 mm²/s (lateral) to 0.93 × 10^-3 mm²/s (dorsal). RD varied from 0.34 × 10^-3 mm²/s (dorsal) to 0.38 × 10^-3 mm²/s (lateral) and AD varied from 1.96 × 10^-3 mm²/s (lateral) to 2.11 × 10^-3 mm²/s (dorsal).

CONCLUSIONS

Our results show a Rician denoising NLM filter incorporated with CLLS significantly increases SNR and reduces estimation errors of DT- and KT-derived metrics, providing the reliable metrics estimation with adequate SNR levels.

Cellular Automata Tractography: Fast Geodesic Diffusion MR Tractography and Connectivity Based Segmentation on the GPU

Geodesic based tractography on diffusion magnetic resonance data is a method to devise long distance connectivities among the brain regions. In this study, cellular automata technique is applied to the geodesic tractography problem and the algorithm is implemented on a graphics processing unit. Cellular automaton based method is preferable to current techniques due to its parallel nature and ability to solve the connectivity based segmentation problem with the same computational complexity, which has important applications in neuroimaging. An application to prior-less tracking and connectivity based segmentation of corpus callosum fibers is presented as an example. A geodesic tractography based corpus callosum atlas is provided, which reveals high projections to the cortical language areas. The developed method not only allows fast computation especially for segmentation but also provides a powerful and intuitive framework, suitable to derive new algorithms to perform connectivity calculations and allowing novel applications.

Denoise diffusion-weighted images using higher-order singular value decomposition

Noise usually affects the reliability of quantitative analysis in diffusion-weighted (DW) magnetic resonance imaging (MRI), especially at high b-values and/or high spatial resolution. Higher-order singular value decomposition (HOSVD) has recently emerged as a simple, effective, and adaptive transform to exploit sparseness within multidimensional data. In particular, the patch-based HOSVD denoising has demonstrated superb performance when applied to T1-, T2-, and proton density-weighted MRI data. In this study, we aim to investigate the feasibility of denoising DW data using the HOSVD transform. With the low signal-to-noise ratio in typical DW data, the patch-based HOSVD denoising suffers from stripe artifacts in homogeneous regions because of the HOSVD bases learned from the noisy patches. To address this problem, we propose a novel denoising method. It first introduces a global HOSVD-based denoising as a prefiltering stage to guide the subsequent patch-based HOSVD denoising stage. The HOSVD bases from the patch groups in prefiltered images are then used to transform the noisy patch groups in original DW data. Experiments were performed using simulated and in vivo DW data. Results show that the proposed method significantly reduces stripe artifacts compared with conventional patch-based HOSVD denoising methods, and outperforms two state-of-the-art denoising methods in terms of denoising quality and diffusion parameters estimation.

Volumetric and fiber-tracing MRI methods for gray and white matter

Magnetic resonance imaging (MRI) is capable of generating high-resolution brain images with fine anatomic detail and unique tissue contrasts that reveal structures that are not visible to the eye. Sharply defined gray- and white-matter interfaces allow for quantitative anatomic analysis that can be accurately performed with largely automated segmentation methods. In an analogous fashion, diffusion MRI in the brain provides structural information based on contrasts derived from the diffusivity of water in brain tissue, which can highlight the orientation of neuronal axons. Also using largely automated methods, diffusion MRI can be used to generate models of white-matter tracts throughout the brain, a method known as tractography, as well as characterize the microstructural integrity of neuronal axons. Tractographic analysis has helped to define connectivity in the brain that powerfully informs understanding of brain function, and, together with other diffusion metrics, is useful in evaluation of the normal and diseased brain. The quantitative methods of brain segmentation, tractography, and diffusion MRI extend MRI into a realm beyond visual inspection and provide otherwise unachievable sensitivity and specificity in the analysis of brain structure and function.

Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI): A framework for single-subject analysis in diffusion tensor imaging

The purpose of this work is to develop a framework for single-subject analysis of diffusion tensor imaging (DTI) data. This framework is termed Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI) because it is capable of testing whether an individual tract as represented by the major eigenvector of the diffusion tensor and its corresponding angular dispersion are significantly different from a group of tracts on a voxel-by-voxel basis. This work develops two complementary statistical tests based on the elliptical cone of uncertainty, which is a model of uncertainty or dispersion of the major eigenvector of the diffusion tensor. The orientation deviation test examines whether the major eigenvector from a single subject is within the average elliptical cone of uncertainty formed by a collection of elliptical cones of uncertainty. The shape deviation test is based on the two-tailed Wilcoxon-Mann-Whitney two-sample test between the normalized shape measures (area and circumference) of the elliptical cones of uncertainty of the single subject against a group of controls. The False Discovery Rate (FDR) and False Non-discovery Rate (FNR) were incorporated in the orientation deviation test. The shape deviation test uses FDR only. TOADDI was found to be numerically accurate and statistically effective. Clinical data from two Traumatic Brain Injury (TBI) patients and one non-TBI subject were tested against the data obtained from a group of 45 non-TBI controls to illustrate the application of the proposed framework in single-subject analysis. The frontal portion of the superior longitudinal fasciculus seemed to be implicated in both tests (orientation and shape) as significantly different from that of the control group. The TBI patients and the single non-TBI subject were well separated under the shape deviation test at the chosen FDR level of 0.0005. TOADDI is a simple but novel geometrically based statistical framework for analyzing DTI data. TOADDI may be found useful in single-subject, graph-theoretic and group analyses of DTI data or DTI-based tractography techniques.

Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description

In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal-Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain.

Why do stroke patients with negative motor evoked potential show poor limb motor function recovery?

Negative motor evoked potentials after cerebral infarction, indicative of poor recovery of limb motor function, tend to be accompanied by changes in fractional anisotropy values and the cerebral peduncle area on the affected side, but the characteristics of these changes have not been reported. This study included 57 cases of cerebral infarction whose motor evoked potentials were tested in the 24 hours after the first inspection for diffusion tensor imaging, in which 29 cases were in the negative group and 28 cases in the positive group. Twenty-nine patients with negative motor evoked potentials were divided into two groups according to fractional anisotropy on the affected side of the cerebral peduncle: a fractional anisotropy < 0.36 group and a fractional anisotropy ≥ 0.36 group. All patients underwent a regular magnetic resonance imaging and a diffusion tensor imaging examination at 1 week, 1, 3, 6 and 12 months after cerebral infarction. The Fugl-Meyer scores of their hemiplegic limbs were tested before the magnetic resonance and diffusion tensor imaging tions. In the negative motor evoked potential group, fractional anisotropy in the affected cerebral peduncle declined progressively, which was most obvious in the first 1-3 months after the onset of cerebral infarction. The areas and area asymmetries of the cerebral peduncle on the affected side were significantly decreased at 6 and 12 months after onset. At 12 months after onset, the area asymmetries of the cerebral peduncle on the affected side were lower than the normal lower limit value of 0.83. Fugl-Meyer scores in the fractional anisotropy ≥ 0.36 group were significantly higher than in the fractional anisotropy < 0.36 group at 3-12 months after onset. The fractional anisotropy of the cerebral peduncle in the positive motor evoked potential group decreased in the first 1 month after onset, and stayed unchanged from 3-12 months; there was no change in the area of the cerebral peduncle in the first 1-12 months after cerebral infarction. These findings confirmed that if the fractional anisotropy of the cerebral peduncle on the affected side is < 0.36 and the area asymmetries < 0.83 in patients with negative motor evoked potential after cerebral infarction, then poor hemiplegic limb motor function recovery may occur.

Knowledge-based automated reconstruction of human brain white matter tracts using a path-finding approach with dynamic programming

It has been shown that the anatomy of major white matter tracts can be delineated using diffusion tensor imaging (DTI) data. Tract reconstruction, however, often suffers from a large number of false-negative results when a simple line propagation algorithm is used. This limits the application of this technique to only the core of prominent white matter tracts. By employing probabilistic path-generation algorithms, connectivity between a larger number of anatomical regions can be studied, but an increase in the number of false-positive results is inevitable. One of the causes of the inaccuracy is the complex axonal anatomy within a voxel; however, high-angular resolution (HAR) methods have been proposed to ameliorate this limitation. However, HAR data are relatively rare due to the long scan times required and the low signal-to-noise ratio. In this study, we tested a probabilistic path-finding method in which two anatomical regions with known connectivity were pre-defined and a path that maximized agreement with the DTI data was searched. To increase the accuracy of the trajectories, knowledge-based anatomical constraints were applied. The reconstruction protocols were tested using DTI data from 19 normal subjects to examine test-retest reproducibility and cross-subject variability. Fifty-two tracts were found to be reliably reconstructed using this approach, which can be viewed on our website.

Reliability of two clinically relevant fiber pathways reconstructed with constrained spherical deconvolution

The single diffusion tensor model is inadequate for the reconstruction of fiber pathways in brain regions with multiple fiber orientations. To overcome this limitation, constrained spherical deconvolution has been proposed. A high reliability of constrained spherical deconvolution is, however, a pre-requisite for its use in clinical applications. Reliability of reconstructed fiber pathways can be assessed in terms of architectural (addressing their spatial configuration) and microstructural (addressing diffusion-derived measures along the fibers) reproducibility. We assess the reliability for two clinically relevant fiber pathways: the corticospinal tract and arcuate fasciculus. The fiber pathways were reconstructed using constrained spherical deconvolution in 11 healthy subjects who were scanned on three occasions. Coefficients of variations of diffusion-derived measures were used to assess the microstructural reproducibility. Image correlation and fiber overlap were used to assess the architectural reproducibility. The mean correlation between sessions was 72% for both the corticospinal tract and arcuate fasciculus. The mean overlap between sessions was 63% for the corticospinal tract and 58% for the arcuate fasciculus. Coefficients of variations of diffusion-derived measures showed very low variation (all measures <3.1%). These results are comparable with reliability results based on the diffusion tensor model, which is commonly used in clinical settings. The reliability results found here are, therefore, promising to further investigate the use of constrained spherical deconvolution in clinical practice.

Clinical applications of diffusion tensor imaging

The potential utility of diffusion tensor (DT) imaging in clinical practice is broad, and new applications continue to evolve as technology advances. Clinical applications of DT imaging and tractography include tissue characterization, lesion localization, and mapping of white matter tracts. DT imaging metrics are sensitive to microstructural changes associated with central nervous system disease; however, further research is needed to enhance specificity so as to facilitate more widespread clinical application. Preoperative tract mapping, with either directionally encoded color maps or tractography, provides useful information to the neurosurgeon and has been shown to improve clinical outcomes.

Diffusion MR imaging: How to get the maximum from the experimental time

Diffusion-based MR imaging is the only non-invasive method for characterising the microstructural organization of brain tissue in vivo. Diffusion tensor MRI (DT-MRI) is currently routinely used in both research and clinical practice. However, other diffusion approaches are gaining more and more popularity and an increasing number of researchers express interest in using them concomitantly with DT-MRI. While non tensor-based methods hold great promises for increasing the specificity of diffusion MR imaging, including them in the experimental routine inevitably leads to longer experimental times. In most cases, this may preclude the translation of the full protocol to clinical practice, especially when these methods are to be used with subjects that are not compatible with long scanning sessions (e.g., with elderly and pediatric subjects who have difficulties in maintaining a fixed head position during a long imaging session).

The aim of this review is to guide the end-users on obtaining the maximum from the experimental time allocated to collecting diffusion MRI data. This is done by: (i) briefly reviewing non tensor-based approaches; (ii) reviewing the optimal protocols for both tensor and non tensor-based imaging; and (iii) drawing the conclusions for different experimental times.

Diffusion tensor imaging of diffuse axonal injury in a rat brain trauma model

Diffusion tensor imaging (DTI) was used to study traumatic brain injury. The impact-acceleration trauma model was used in rats. Here, in addition to diffusivities (mean, axial and radial), fractional anisotropy (FA) was used, in particular, as a parameter to characterize the cerebral tissue early after trauma. DTI was implemented at 7 T using fast spiral k-space sampling and the twice-refocused spin echo radiofrequency sequence for eddy current minimization. The method was carefully validated on different phantom measurements. DTI of a trauma group (n = 5), as well as a sham group (n = 5), was performed at different time points during 6 h following traumatic brain injury. Two cerebral regions, the cortex and corpus callosum, were analyzed carefully. A significant decrease in diffusivity in the trauma group versus the sham group was observed, suggesting the predominance of cellular edema in both cerebral regions. No significant FA change was detected in the cortex. In the corpus callosum of the trauma group, the FA indices were significantly lower. A net discontinuity in fiber reconstructions in the corpus callosum was observed by fiber tracking using DTI. Histological analysis using Hoechst, myelin basic protein and Bielschowsky staining showed fiber disorganization in the corpus callosum in the brains of the trauma group. On the basis of our histology results and the characteristics of the impact-acceleration model responsible for the presence of diffuse axonal injury, the detection of low FA caused by a drastic reduction in axial diffusivity and the presence of fiber disconnections of the DTI track in the corpus callosum were considered to be related to the presence of diffuse axonal injury.

CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking

Diffusion Tensor Imaging (DTI) allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU). This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times.

A pointwise correspondence based DT-MRI fiber similarity measure

Diffusion Tensor Magnetic Resonance Imaging (DTI) fiber tractography is a way to reconstruct fiber tracts underlying data according to local anisotropic diffusion characteristics. Reliability of fiber tracts as a result of tractography decreases due to noise in the data, error accumulation during integration and stochastic nature of the underlying data. We proposed a new similarity measure based on point-wise correspondence between tracts. Laplacian Eigenmaps are used to embed the fiber tracts into ℜ(3) based on the new similarity measure. We compared our method with a previously proposed method, on real and phantom data, that uses a 9D feature space to measure fiber similarity and showed that the new similarity measure results in a low dimensional manifold representing the fiber bundles. We presented preliminary results demonstrating that the fibers that fall far from this manifold correspond to outliers.

Cortical Projection Topography of the Human Splenium: Hemispheric Asymmetry and Individual Differences

The corpus callosum is the largest white matter pathway in the human brain. The most posterior portion, known as the splenium, is critical for interhemispheric communication between visual areas. The current study employed diffusion tensor imaging to delineate the complete cortical projection topography of the human splenium. Homotopic and heterotopic connections were revealed between the splenium and the posterior visual areas, including the occipital and the posterior parietal cortices. In nearly one third of participants, there were homotopic connections between the primary visual cortices, suggesting interindividual differences in splenial connectivity. There were also more instances of connections with the right hemisphere, indicating a hemispheric asymmetry in interhemispheric connectivity within the splenium. Combined, these findings demonstrate unique aspects of human interhemispheric connectivity and provide anatomical bases for hemispheric asymmetries in visual processing and a long-described hemispheric asymmetry in speed of interhemispheric communication for visual information.

MR diffusion tensor imaging: a window into white matter integrity of the working brain

As Norman Geschwind asserted in 1965, syndromes resulting from white matter lesions could produce deficits in higher-order functions and "disconnexion" or the interruption of connection between gray matter regions could be as disruptive as trauma to those regions per se. The advent of in vivo diffusion tensor imaging, which allows quantitative characterization of white matter fiber integrity in health and disease, has served to strengthen Geschwind's proposal. Here we present an overview of the principles of diffusion tensor imaging (DTI) and its contribution to progress in our current understanding of normal and pathological brain function.

Contribution of callosal connections to the interhemispheric integration of visuomotor and cognitive processes

In recent years, cognitive neuroscience has been concerned with the role of the corpus callosum and interhemispheric communication for lower-level processes and higher-order cognitive functions. There is empirical evidence that not only callosal disconnection but also subtle degradation of the corpus callosum can influence the transfer of information and integration between the hemispheres. The reviewed studies on patients with callosal degradation with and without disconnection indicate a dissociation of callosal functions: while anterior callosal regions were associated with interhemispheric inhibition in situations of semantic (Stroop) and visuospatial (hierarchical letters) competition, posterior callosal areas were associated with interhemispheric facilitation from redundant information at visuomotor and cognitive levels. Together, the reviewed research on selective cognitive functions provides evidence that the corpus callosum contributes to the integration of perception and action within a subcortico-cortical network promoting a unified experience of the way we perceive the visual world and prepare our actions.

Mesh-based spherical deconvolution: a flexible approach to reconstruction of non-negative fiber orientation distributions

Diffusion-weighted MRI has enabled the imaging of white matter architecture in vivo. Fiber orientations have classically been assumed to lie along the major eigenvector of the diffusion tensor, but this approach has well-characterized shortcomings in voxels containing multiple fiber populations. Recently proposed methods for recovery of fiber orientation via spherical deconvolution utilize a spherical harmonics framework and are susceptible to noise, yielding physically-invalid results even when additional measures are taken to minimize such artifacts. In this work, we reformulate the spherical deconvolution problem onto a discrete spherical mesh. We demonstrate how this formulation enables the estimation of fiber orientation distributions which strictly satisfy the physical constraints of realness, symmetry, and non-negativity. Moreover, we analyze the influence of the flexible regularization parameters included in our formulation for tuning the smoothness of the resultant fiber orientation distribution (FOD). We show that the method is robust and reliable by reconstructing known crossing fiber anatomy in multiple subjects. Finally, we provide a software tool for computing the FOD using our new formulation in hopes of simplifying and encouraging the adoption of spherical deconvolution techniques.

MR connectomics: Principles and challenges

MR connectomics is an emerging framework in neuro-science that combines diffusion MRI and whole brain tractography methodologies with the analytical tools of network science. In the present work we review the current methods enabling structural connectivity mapping with MRI and show how such data can be used to infer new information of both brain structure and function. We also list the technical challenges that should be addressed in the future to achieve high-resolution maps of structural connectivity. From the resulting tremendous amount of data that is going to be accumulated soon, we discuss what new challenges must be tackled in terms of methods for advanced network analysis and visualization, as well data organization and distribution. This new framework is well suited to investigate key questions on brain complexity and we try to foresee what fields will most benefit from these approaches.

A voxelized model of direct infusion into the corpus callosum and hippocampus of the rat brain: model development and parameter analysis

Recent experimental studies have shown convective-enhanced delivery (CED) to be useful for transporting macromolecular therapeutic agents over large tissue volumes in the central nervous system (CNS). There are limited tools currently available for predicting tissue distributions in the brain. We have developed a voxelized modeling methodology in which CNS tissues are modeled as porous media, and transport properties and anatomical boundaries are determined semi-automatically on a voxel-by-voxel basis using diffusion tensor imaging (DTI). By using this methodology, 3D extracellular transport models of the rat brain were developed. Macromolecular tracer distributions following CED in two different infusion sites (corpus callosum and hippocampus) were predicted. Sensitivity of models to changes in infusion parameters, transport properties, and modeling parameters was determined. Predicted tracer distributions were most sensitive to changes in segmentation threshold, DTI resolution, tissue porosity, and infusion site. This DTI-based voxelized modeling methodology provides a potentially rapid means of estimating CED transport.

Voxelized model of interstitial transport in the rat spinal cord following direct infusion into white matter

Direct tissue infusion, e.g., convection-enhanced delivery (CED), is a promising local delivery technique for treating diseases of the central nervous system. Predictive models of spatial drug distribution during and following direct tissue infusion are necessary for treatment optimization and planning of surgery. In this study, a 3D interstitial transport modeling approach in which tissue properties and anatomical boundaries are assigned on a voxel-by-voxel basis using tissue alignment data from diffusion tensor imaging (DTI) is presented. The modeling approach is semi-automatic and utilizes porous media transport theory to estimate interstitial transport in isotropic and anisotropic tissue regions. Rat spinal cord studies compared predicted distributions of albumin tracer (for varying DTI resolution) following infusion into the dorsal horn with tracer distributions measured by Wood et al. in a previous study. Tissue distribution volumes compared favorably for small infusion volumes (<4 microl). The presented DTI-based methodology provides a rapid means of estimating interstitial flows and tracer distributions following CED into the spinal cord. Quantification of these transport fields provides an important step toward development of drug-specific transport models of infusion.

Diffusion tensor tractography in mesencephalic bundles: relation to mental flexibility in detoxified alcohol-dependent subjects

Components of the corticocerebellar circuit and the midbrain individually play a central role in addictive processes and have been associated with altered volumes and impairment of cognitive flexibility in alcohol-dependent subjects. The microstructure of white matter bundles composing the corticocerebellar network and passing through the midbrain was studied using diffusion tensor imaging in a group of detoxified alcohol-dependent men (n=20) and a group of healthy men (n=24). The relationship between properties of these white matter bundles and cognitive flexibility performance was investigated in alcohol-dependent subjects. Bundles connecting two regions of interest were analyzed using a fiber-tracking quantitative approach, which provided estimates of the fractional anisotropy and the apparent diffusion coefficient, as well as the number of tracked fibers normalized by the volume of regions of interest. Within the bundles running between the midbrain and pons, a mean of 18% fewer fibers per unit volume were tracked in alcohol-dependent men than in healthy controls. In addition, the normalized number of these fibers correlated with the performance in the Trail-Making Test part-B. Even though the alcohol-dependent subjects were detoxified and apparently neurologically intact, their earlier excessive use of alcohol seems to be associated with altered neural microstructure of mesencephalic white matter bundles, which may contribute to their cognitive flexibility impairment.

The elliptical cone of uncertainty and its normalized measures in diffusion tensor imaging

Diffusion tensor magnetic resonance imaging (DT-MRI) is capable of providing quantitative insights into tissue microstructure in the brain. An important piece of information offered by DT-MRI is the directional preference of diffusing water molecules within a voxel. Building upon this local directional information, DT-MRI tractography attempts to construct global connectivity of white matter tracts. The interplay between local directional information and global structural information is crucial in understanding changes in tissue microstructure as well as in white matter tracts. To this end, the right circular cone of uncertainty was proposed by Basser as a local measure of tract dispersion. Recent experimental observations by Jeong et al. and Lazar et al. that the cones of uncertainty in the brain are mostly elliptical motivate the present study to investigate analytical approaches to quantify their findings. Two analytical approaches for constructing the elliptical cone of uncertainty, based on the first-order matrix perturbation and the error propagation method via diffusion tensor representations, are presented and their theoretical equivalence is established. We propose two normalized measures, circumferential and areal, to quantify the uncertainty of the major eigenvector of the diffusion tensor. We also describe a new technique of visualizing the cone of uncertainty in 3-D.

Diffusion spectrum magnetic resonance imaging (DSI) tractography of crossing fibers

MRI tractography is the mapping of neural fiber pathways based on diffusion MRI of tissue diffusion anisotropy. Tractography based on diffusion tensor imaging (DTI) cannot directly image multiple fiber orientations within a single voxel. To address this limitation, diffusion spectrum MRI (DSI) and related methods were developed to image complex distributions of intravoxel fiber orientation. Here we demonstrate that tractography based on DSI has the capacity to image crossing fibers in neural tissue. DSI was performed in formalin-fixed brains of adult macaque and in the brains of healthy human subjects. Fiber tract solutions were constructed by a streamline procedure, following directions of maximum diffusion at every point, and analyzed in an interactive visualization environment (TrackVis). We report that DSI tractography accurately shows the known anatomic fiber crossings in optic chiasm, centrum semiovale, and brainstem; fiber intersections in gray matter, including cerebellar folia and the caudate nucleus; and radial fiber architecture in cerebral cortex. In contrast, none of these examples of fiber crossing and complex structure was identified by DTI analysis of the same data sets. These findings indicate that DSI tractography is able to image crossing fibers in neural tissue, an essential step toward non-invasive imaging of connectional neuroanatomy.

Elevating tensor rank increases anisotropy in brain areas associated with intra-voxel orientational heterogeneity (IVOH): a generalised DTI (GDTI) study

Rank-2 tensors are unable to represent multi-modal diffusion associated with intra-voxel orientational heterogeneity (IVOH), which occurs where axons are incoherently oriented, such as where bundles intersect or diverge. Under this condition, they are oblate or spheroidally shaped, resulting in artefactually low anisotropy, potentially masking reduced axonal density, myelinisation and integrity. Higher rank tensors can represent multi-modal diffusion, and suitable metrics such as generalised anisotropy (GA) and scaled entropy (SE) have been introduced. The effect of tensor rank was studied through simulations, and analysing high angular resolution diffusion imaging (HARDI) data from two volunteers, fit with rank-2, rank-4 and rank-6 tensors. The variation of GA and SE as a function of rank was investigated through difference maps and region of interest (ROI)-based comparisons. Results were correlated with orientation distribution functions (ODF) reconstructed with q-ball, and with colour-maps of the principal and second eigenvectors. Simulations revealed that rank-4 tensors are able to represent multi-modal diffusion, and that increasing rank further has a minor effect on measurements. IVOH was detected in subcortical regions of the corona radiata, along the superior longitudinal fasciculus, in the radiations of the genu of the corpus callosum, in peritrigonal white matter and along the inferior fronto-occipital and longitudinal fascicula. In these regions, elevating tensor rank increased anisotropy. This was also true for the corpus callosum, cingulum and anterior limb of the internal capsule, where increasing tensor rank resulted in patterns that, although mono-modal, were more anisotropic. In these regions the second eigenvector was coherently oriented. As rank-4 tensors have only 15 distinct elements, they can be determined without acquiring a large number of directions. By removing artefactual underestimation of anisotropy, their use may increase the sensitivity to pathological change.

Stochastic DT-MRI connectivity mapping on the GPU

We present a method for stochastic fiber tract mapping from diffusion tensor MRI (DT-MRI) implemented on graphics hardware. From the simulated fibers we compute a connectivity map that gives an indication of the probability that two points in the dataset are connected by a neuronal fiber path. A Bayesian formulation of the fiber model is given and it is shown that the inversion method can be used to construct plausible connectivity. An implementation of this fiber model on the graphics processing unit (GPU) is presented. Since the fiber paths can be stochastically generated independently of one another, the algorithm is highly parallelizable. This allows us to exploit the data-parallel nature of the GPU fragment processors. We also present a framework for the connectivity computation on the GPU. Our implementation allows the user to interactively select regions of interest and observe the evolving connectivity results during computation. Results are presented from the stochastic generation of over 250,000 fiber steps per iteration at interactive frame rates on consumer-grade graphics hardware.

Riemannian graph diffusion for DT-MRI regularization

A new method for diffusion tensor MRI (DT-MRI) regularization is presented that relies on graph diffusion. We represent a DT image using a weighted graph, where the weights of edges are functions of the geodesic distances between tensors. Diffusion across this graph with time is captured by the heat-equation, and the solution, i.e. the heat kernel, is found by exponentiating the Laplacian eigen-system with time. Tensor regularization is accomplished by computing the Riemannian weighted mean using the heat kernel as its weights. The method can efficiently remove noise, while preserving the fine details of images. Experiments on synthetic and real-world datasets illustrate the effectiveness of the method.

How accurately can the diffusion profiles indicate multiple fiber orientations? A study on general fiber crossings in diffusion MRI

The q-space imaging techniques and high angular resolution diffusion (HARD) imaging have shown promise to identify intravoxel multiple fibers. The measured orientation distribution function (ODF) and apparent diffusion coefficient (ADC) profiles can be used to identify the orientations of the actual intravoxel fibers. The present study aims to examine the accuracy of these profile-based orientation methods by comparing the angular deviations between the estimated local maxima of the profiles and the real fiber orientation for a fiber crossing simulated with various intersection angles under different b values in diffusion-weighted MRI experiments. Both noisy and noise-free environments were investigated. The diffusion spectrum imaging (DSI), q-ball imaging (QBI), and HARD techniques were used to generate ODF and ADC profiles. To provide a better comparison between ODF and ADC techniques, the phase-corrected angular deviations were also presented for the ADC method based on a circular spectrum mapping method. The results indicate that systematic angular deviations exist between the actual fiber orientations and the corresponding local maxima of either the ADC or ODF profiles. All methods are apt to underestimation of acute intersection and overestimation of obtuse intersection angle. For a typical slow-exchange fiber crossing, the ODF methods have a non-deviation zone around the 90 degrees intersection. Before the phase-correction, the deviation of ADC profiles approaches a peak at the 90 degrees intersection, while after the correction the ADC deviations are significantly reduced. When the b factor is larger than 1000 s/mm2, the ODF methods have smaller angular deviations than the ADC methods for the intersections close to 90 degrees . QBI method demonstrates a slight yet consistent advantage over the DSI method under the same conditions. In the noisy environment, the mean value of the deviation angles shows a high consistency with the corresponding deviation in the nose-free condition.

Model-based variational smoothing and segmentation for diffusion tensor imaging in the brain

This article applies a unified approach to variational smoothing and segmentation to brain diffusion tensor image data along user-selected attributes derived from the tensor, with the aim of extracting detailed brain structure information. The application of this framework simultaneously segments and denoises to produce edges and smoothed regions within the white matter of the brain that are relatively homogeneous with respect to the diffusion tensor attributes of choice. This approach enables the visualization of a smoothed, scale invariant representation of the tensor data field in a variety of diverse forms. In addition to known attributes such as fractional anisotropy, these representations include selected directional tensor components and additionally associated continuous valued edge fields that might be used for further segmentation. A comparison is presented of the results of three different data model selections with respect to their ability to resolve white matter structure. The resulting images are integrated to provide better perspective of the model properties (edges, smoothed image, and so forth) and their relationship to the underlying brain anatomy. The improvement in brain image quality is illustrated both qualitatively and quantitatively, and the robust performance of the algorithm in the presence of added noise is shown. Smoothing occurs without loss of edge features because of the simultaneous segmentation aspect of the variational approach, and the output enables better delineation of tensors representative of local and long-range association, projection, and commissural fiber systems.

Fibertract segmentation in position orientation space from high angular resolution diffusion MRI

In diffusion MRI, standard approaches for fibertract identification are based on algorithms that generate lines of coherent diffusion, currently known as tractography. A tract is then identified as a set of such lines selected on some criteria. In the present study, we investigate whether fibertract identification can be formulated as a segmentation task that recognizes a fibertract as a region where diffusion is intense and coherent. Indeed, we show that it is possible to segment efficiently well-known fibertracts with classical image processing methods provided that the problem is formulated in a five-dimensional space of position and orientation. As an example, we choose to adapt to this newly defined high-dimensional non-Euclidean space, called position orientation space, an algorithm based on the hidden Markov random field framework. Structures such as the cerebellar peduncles, corticospinal tract, association bundles can be identified and represented in three dimensions by a back projection technique similar to maximum intensity projection. Potential advantages and drawbacks as compared to classical tractography are discussed; for example, it appears that our formulation handles naturally crossing tracts and is not biased by human intervention.

A Bayesian approach for stochastic white matter tractography

White matter fiber bundles in the human brain can be located by tracing the local water diffusion in diffusion weighted magnetic resonance imaging (MRI) images. In this paper, a novel Bayesian modeling approach for white matter tractography is presented. The uncertainty associated with estimated white matter fiber paths is investigated, and a method for calculating the probability of a connection between two areas in the brain is introduced. The main merits of the presented methodology are its simple implementation and its ability to handle noise in a theoretically justified way. Theory for estimating global connectivity is also presented, as well as a theorem that facilitates the estimation of the parameters in a constrained tensor model of the local water diffusion profile.

Computational model of interstitial transport in the spinal cord using diffusion tensor imaging

Local drug delivery methods, including convection-enhanced delivery (CED), are being used to increase distribution in selected regions of nervous tissue. There is a need for 3D models that predict spatial drug distribution within these tissues. A methodology was developed to process magnetic resonance microscopy (MRM) and diffusion tensor imaging (DTI) scans, segment gray and white matter regions, assign tissue transport properties, and model the interstitial transport of macromolecules. Fiber tract orientation was derived from DTI data and used to assign directional dependence of hydraulic conductivity, K, and tracer diffusivity, Dt, transport tensors. Porous media solutions for interstitial fluid pressure, velocity, and albumin distribution were solved using a finite volume method. To test this DTI-based methodology, a rat spinal cord transport model was developed to simulate CED into the dorsal white matter column. Predicted distribution results correspond well with small volume (approximately 1 microl) trends found experimentally, although albumin loss was greater at larger infusion volumes (>2 microl). Simulations were similar to those using fixed transport properties due to the bulk alignment of white matter fibers along the cord axis. These findings help to validate the DTI-based methodology which can be applied to modeling regions where fiber tract organization is more complex, e.g., the brain.

Diffusion tensor imaging and tractography of distal peripheral nerves at 3 T

OBJECTIVE

We studied whether distal peripheral nerves could be imaged using quantitative diffusion tensor imaging (DTI) with a 3-T MRI scanner, and visualized using tractography.

METHODS

Altogether 6 healthy subjects were studied. The diffusion was quantified with apparent diffusion coefficient (ADC) and fractional anisotropy (FA) maps, and the direction of main diffusivity was visualized with color-coded orientation maps and tractography.

RESULTS

We present the first DTI and tractography results of human distal peripheral nerves. The courses of median, ulnar, and radial nerves in the upper limb and of tibial and peroneal nerves in the lower limb were first analyzed quantifying ADC and FA, and then visualized in 3D with tractography. Tractography illustrated nicely the 3D courses of both upper and lower limb nerves which were reliably distinguished from the surrounding muscle tissue and ligaments.

CONCLUSIONS

Quantitative DTI and tractography can be used to image and visualize distal peripheral nerves.

SIGNIFICANCE

DTI is a quantitative method that could provide useful information for the diagnosis and follow-up of nerve lesions, entrapments, and regeneration. Peripheral nerves as well-delineated structures also containing abundant branching into bundles of different diameters, could be used as 'living phantoms' for testing and validating different tractography methods.

White matter fiber tractography via anisotropic diffusion simulation in the human brain

A novel approach to noninvasively tracing brain white matter fiber tracts is presented using diffusion tensor magnetic resonance imaging (DT-MRI). This technique is based on successive anisotropic diffusion simulations over the human brain, which are utilized to construct three dimensional diffusion fronts. The fiber pathways are determined by evaluating the distance and orientation from the fronts to their corresponding diffusion seeds. Synthetic and real DT-MRI data are employed to demonstrate the tracking scheme. It is shown that the synthetic tracts are accurately replicated, and several major white matter fiber pathways can be reproduced noninvasively, with the tract branching being allowed. Since simulating the diffusion process, which is truly a physical phenomenon reflecting the underlying architecture of cerebral tissues, makes full use of the diffusion tensor data, including both the magnitude and orientation information, the proposed approach is expected to enhance robustness and reliability in white matter fiber reconstruction.

Exploring connectivity of the brain's white matter with dynamic queries

Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging method that can be used to measure local information about the structure of white matter within the human brain. Combining DTI data with the computational methods of MR tractography, neuroscientists can estimate the locations and sizes of nerve bundles (white matter pathways) that course through the human brain. Neuroscientists have used visualization techniques to better understand tractography data, but they often struggle with the abundance and complexity of the pathways. In this paper, we describe a novel set of interaction techniques that make it easier to explore and interpret such pathways. Specifically, our application allows neuroscientists to place and interactively manipulate box or ellipsoid-shaped regions to selectively display pathways that pass through specific anatomical areas. These regions can be used in coordination with a simple and flexible query language which allows for arbitrary combinations of these queries using Boolean logic operators. A representation of the cortical surface is provided for specifying queries of pathways that may be relevant to gray matter structures and for displaying activation information obtained from functional magnetic resonance imaging. By precomputing the pathways and their statistical properties, we obtain the speed necessary for interactive question-and-answer sessions with brain researchers. We survey some questions that researchers have been asking about tractography data and show how our system can be used to answer these questions efficiently.

Apparent Diffusion Coefficient Approximation and Diffusion Anisotropy Characterization in DWI

We present a new approximation for the apparent diffusion coefficient (ADC) of non-Gaussian water diffusion with at most two fiber orientations within a voxel. The proposed model approximates ADC profiles by product of two spherical harmonic series (SHS) up to order 2 from High Angular Resolution Diffusion-weighted (HARD) MRI data. The coefficients of SHS are estimated and regularized simultaneously by solving a constrained minimization problem. An equivalent but non-constrained version of the approach is also provided to reduce the complexity and increase the efficiency in computation. Moreover we use the Cumulative Residual Entropy (CRE) as a measurement to characterize diffusion anisotropy. By using CRE we can get reasonable results with two thresholds, while the existing methods either can only be used to characterize Gaussian diffusion or need more measurements and thresholds to classify anisotropic diffusion with two fiber orientations. The experiments on HARD MRI human brain data indicate the effectiveness of the method in the recovery of ADC profiles. The characterization of diffusion based on the proposed method shows a consistency between our results and known neuroanatomy.

Mindboggle: a scatterbrained approach to automate brain labeling

Mindboggle (http://www.binarybottle.com/mindboggle.html) is a fully automated, feature matching approach to label cortical structures and activity anatomically in human brain MRI data. This approach does not assume that the existence of component structures and their relative spatial relationship is preserved from brain to brain, but instead disassembles a labeled atlas and reassembles its pieces to match corresponding pieces in an unlabeled subject brain before labeling. Mindboggle: (1) converts linearly coregistered subject and atlas MRI data into sulcus pieces, (2) matches each atlas piece with a combination of subject pieces by minimizing a cost function, (3) transforms atlas label boundaries to the matching subject pieces, (4) warps atlas labels to their transformed boundaries, and (5) propagates labels to fill remaining gaps in a mask derived from the subject brain. We compared Mindboggle with four registration methods: linear registration, and nonlinear registration using SPM2, AIR, and ANIMAL. Automated labeling by all of the nonlinear methods was found to be at least comparable with linear registration. Mindboggle outperformed every other method, as measured by the agreement between overlapping atlas labels and manually assigned subject labels, with respect to the union or the intersection of voxels. After applying the same procedure that Mindboggle uses to fill a subject's segmented gray matter mask with labels (step 5), the results of the other methods improved. However, after performing a one-way ANOVA (and Tukey's honestly significant difference criterion) in a multiple comparison between the results obtained by the different methods, Mindboggle was still found to be the only nonlinear method whose labeling performance was significantly better than that of linear registration or SPM2. Further advantages to Mindboggle include a high degree of robustness against image artifacts, poor image quality, and incomplete brain data. We tested the latter hypothesis by conducting all of the tests again, this time registering the atlas to an artificially lesioned version of itself, and found that Mindboggle was the only method whose performance did not degrade significantly as the lesion size increased.

Mapping the orientation of intravoxel crossing fibers based on the phase information of diffusion circular spectrum

A new method is presented to map the orientation of intravoxel crossing fibers by using the phase of the diffusion circular spectrum harmonics. In a previous study [Zhan, W., Gu, H., Xu, S., Silbersweig, D.A., Stern, E., Yang, Y., 2003. Circular spectrum mapping for intravoxel fiber structures based on high angular resolution apparent diffusion coefficients. Magn. Reson. Med. 49, 1077-1088], we demonstrated that the magnitude of the 4th-order harmonic of the diffusion circular spectrum can be used to identify the existence of fiber crossings. However, the orientation of the intravoxel crossing fibers remained unknown. This study extends the diffusion circular spectrum mapping method so that it is able to identify the orientation of the intravoxel crossing fibers by utilizing the phase information of the circular spectrum. In general, the phase of the circular harmonic determines the rotation of the apparent diffusion coefficient (ADC) profile on the sampling circle that is spanned by the major and medium eigenvector of the diffusion tensor and thus can be used to determine the orientation of the crossing fibers. Simulation results show that the regular tensor-based major eigenvector maps have obvious artifacts in the fiber-crossing area, whereas the estimated crossing fibers by the proposed method are much more consistent with the orientation of the actual intravoxel fibers. Diffusion MRI experiments were performed on five healthy human brains using a 3T scanner. The brain regions with fiber crossings were selected by thresholding the magnitudes of the 4th-order circular spectrum map. Intravoxel crossing fibers were estimated by the phase of the 4th-order harmonic for each voxel within these areas. The estimated intravoxel crossing fibers demonstrated a clear consistency with the orientations of fiber tracks in the surrounding tissues, reducing the fiber orientation discontinuity of the regular major eigenvector map.

A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from DWI

In this paper, we present a novel constrained variational principle for simultaneous smoothing and estimation of the diffusion tensor field from diffusion weighted imaging (DWI). The constrained variational principle involves the minimization of a regularization term in an LP norm, subject to a nonlinear inequality constraint on the data. The data term we employ is the original Stejskal-Tanner equation instead of the linearized version usually employed in literature. The original nonlinear form leads to a more accurate (when compared to the linearized form) estimated tensor field. The inequality constraint requires that the nonlinear least squares data term be bounded from above by a possibly known tolerance factor. Finally, in order to accommodate the positive definite constraint on the diffusion tensor, it is expressed in terms of cholesky factors and estimated. variational principle is solved using the augmented Lagrangian technique in conjunction with the limited memory quasi-Newton method. Both synthetic and real data experiments are shown to depict the performance of the tensor field estimation algorithm. Fiber tracts in a rat brain are then mapped using a particle system based visualization technique.

A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI

In this paper, we present a novel constrained variational principle for simultaneous smoothing and estimation of the diffusion tensor field from complex valued diffusion-weighted images (DWI). The constrained variational principle involves the minimization of a regularization term of L(P) norms, subject to a nonlinear inequality constraint on the data. The data term we employ is the original Stejskal-Tanner equation instead of the linearized version usually employed in literature. The complex valued nonlinear form leads to a more accurate (when compared to the linearized version) estimate of the tensor field. The inequality constraint requires that the nonlinear least squares data term be bounded from above by a known tolerance factor. Finally, in order to accommodate the positive definite constraint on the diffusion tensor, it is expressed in terms of Cholesky factors and estimated. The constrained variational principle is solved using the augmented Lagrangian technique in conjunction with the limited memory quasi-Newton method. Experiments with complex-valued synthetic and real data are shown to depict the performance of our tensor field estimation and smoothing algorithm.

A generic framework for the parcellation of the cortical surface into gyri using geodesic Voronoï diagrams

In this paper we propose a generic automatic approach for the parcellation of the cortical surface into labeled gyri. These gyri are defined from a set of pairs of sulci selected by the user. The selected sulci are first automatically identified in the data, then projected onto the cortical surface. The parcellation stems from two nested Voronoï diagrams computed geodesically to the cortical surface. The first diagram provides the zones of influence of the sulci. The boundary between the two zones of influence of each selected pair of sulci stands for a gyrus seed. A second diagram yields the gyrus parcellation. The distance underlying the Voronoï diagram allows the method to interpolate the gyrus boundaries where the limiting sulci are interrupted. The method is illustrated with 12 different hemispheres.

Diffusion tensor magnetic resonance image regularization

As multi-dimensional complex data become more common, new regularization schemes tailored to those data are needed. In this paper we present a scheme for regularising diffusion tensor magnetic resonance (DT-MR) data, and more generally multi-dimensional data defined by a direction map and one or several magnitude maps. The scheme is divided in two steps. First, a variational method is proposed to restore direction fields with preservation of discontinuities. Its theoretical aspects are presented, as well as its application to the direction field that defines the main orientation of the diffusion tensors. The second step makes use of an anisotropic diffusion process to regularize the magnitude maps. The main idea is that for a range of data it is possible to use the restored direction as a prior to drive the regularization process in a way that preserves discontinuities and respects the local coherence of the magnitude map. We show that anisotropic diffusion is a convenient framework to implement that idea, and define a regularization process for the magnitude maps from our DT-MR data. Both steps are illustated on synthetic and real diffusion tensor magnetic resonance data.

Assessing brain development using neurophysiologic and behavioral measures

One critical aspect of pediatric research is the assessment of outcome measures after treatment or intervention. Behavioral measures of physical growth, school achievement, and general intelligence have proven to be important scales for assessing gross developmental outcome and differences between pediatric treatment groups. However, more subtle and sophisticated measures may be required to assess finer grained differences in brain development at the structural and functional levels. Advances in noninvasive brain imaging techniques over the past decade have improved our ability to link specific cognitive functions to changes in brain structure and function in healthy infants and children. This paper highlights some of the ways that electrophysiologic and functional magnetic resonance imaging methods have been combined with behavioral measures of cognitive and emotional function to advance our understanding of brain-behavior relations. Such combined neurophysiologic and behavioral methods may help to identify the role specific interventions have on long-term developmental outcomes in childhood.

Fiber-tracking method reveals sensorimotor pathway involvement in stroke patients

BACKGROUND AND PURPOSE

We tested the feasibility of a new MRI technique that provides visualization of the sensorimotor tracts in vivo in a group of stroke victims.

SUMMARY OF REPORT

Fourteen patients with small infarctions involving the white matter of the supratentorial brain were evaluated. Sensorimotor tracts on the lesional and contralesional sides were successfully depicted in all cases. The position of the sensorimotor tracts relative to the infarct was in good agreement with clinical symptoms. The overall sensitivity and specificity for sensorimotor tract involvement were 100% and 77%, respectively.

CONCLUSIONS

Our proposed fiber-tracking method was shown to be a clinically feasible technique that correlates well with clinical symptoms.

DTI mapping of human brain connectivity: statistical fibre tracking and virtual dissection

Several approaches have been used to trace axonal trajectories from diffusion MRI data. If such techniques were first developed in a deterministic framework reducing the diffusion information to one single main direction, more recent approaches emerged that were statistical in nature and that took into account the whole diffusion information. Based on diffusion tensor MRI data coming from normal brains, this paper presents how brain connectivity could be modelled globally by means of a random walk algorithm. The mass of connections thus generated was then virtually dissected to uncover different tracts. Corticospinal, corticobulbar, and corticothalamic tracts, the corpus callosum, the limbic system, several cortical association bundles, the cerebellar peduncles, and the medial lemniscus were all investigated. The results were then displayed in the form of an in vivo brain connectivity atlas. The connectivity pattern and the individual fibre tracts were then compared to known anatomical data; a good matching was found.

Circular spectrum mapping for intravoxel fiber structures based on high angular resolution apparent diffusion coefficients

A method is presented for mapping intravoxel fiber structures using spectral decomposition onto a circular distribution of measured apparent diffusion coefficients (ADCs). The zeroth-, second-, and fourth-order harmonic components of the ADC distribution on the circle spanned by the major and median eigenvectors of the diffusion tensor can be used to provide quantitative indices for isotropic, linear, and fiber-crossing diffusion, respectively. A diffusion-weighted MRI technique with 90 encoding orientations was implemented to estimate the circular ADC distribution and calculate the circular spectrum. A digital phantom was used to simulate various diffusion patterns. Comparisons were made between the circular spectrum and regular DTI-based index maps. The results indicated that the zeroth- and second-order circular spectrum maps exhibited a strong consistency with the DTI-based mean diffusivity and linear indices, respectively, and the fourth-order circular spectrum map was able to identify the fiber crossings. MRI experiments were performed on seven healthy human brains using a 3T scanner. The in vivo fourth-order maps showed significantly higher densities in several brain regions, including the corpus callosum, cingulum bundle, superior longitudinal fasciculus, corticospinal tract, and middle cerebellar peduncle, which indicated the existence of fiber crossings in these regions.