The tensor distribution function

Mapping Along-Tract White Matter Microstructural Differences in Autism

Previous diffusion magnetic resonance imaging (dMRI) research has indicated altered white matter microstructure in autism, but the implicated regions are highly inconsistent across studies. Such prior work has largely used conventional dMRI analysis methods, including the traditional microstructure model, based on diffusion tensor imaging (DTI). However, these methods are limited in their ability to precisely map microstructural differences and accurately resolve complex fiber configurations. In our study, we investigated white matter microstructure alterations in autism using the refined along-tract analytic approach, BUndle ANalytics (BUAN), and an advanced microstructure model, the tensor distribution function (TDF). We analyzed dMRI data from 365 autistic and neurotypical participants (5-24 years; 34% female) from 10 cohorts to examine commissural and association tracts. Autism was associated with lower fractional anisotropy and higher diffusivity in localized portions of nearly every commissural and association tract examined; these tracts inter-connected a wide range of brain regions, including frontal, temporal, parietal, and occipital. Taken together, BUAN and TDF allow robust and spatially precise mapping of microstructural properties in autism. Our findings rigorously demonstrate that white matter microstructure alterations in autism may be greater within specific regions of individual tracts, and that the implicated tracts are distributed across the brain.

In vivo rat brain mapping of multiple gray matter water populations using nonparametric D(ω)-R1-R2 distributions MRI

Massively multidimensional diffusion magnetic resonance imaging combines tensor-valued encoding, oscillating gradients, and diffusion-relaxation correlation to provide multicomponent subvoxel parameters depicting some tissue microstructural features. This method was successfully implemented ex vivo in microimaging systems and clinical conditions with tensor-valued gradient waveform of variable duration giving access to a narrow diffusion frequency (ω) range. We demonstrate here its preclinical in vivo implementation with a protocol of 389 contrast images probing a wide diffusion frequency range of 18 to 92 Hz at b-values up to 2.1 ms/μm2 enabled by the use of modulated gradient waveforms and combined with multislice high-resolution and low-distortion echo planar imaging acquisition with segmented and full reversed phase-encode acquisition. This framework allows the identification of diffusion ω-dependence in the rat cerebellum and olfactory bulb gray matter (GM), and the parameter distributions are shown to resolve two water pools in the cerebellum GM with different diffusion coefficients, shapes, ω-dependence, relaxation rates, and spatial repartition whose attribution to specific microstructure could modify the current understanding of the origin of restriction in GM.

A diffusion kurtosis imaging study of the relationship between whole brain microstructure and cognitive function in older adults with mild cognitive impairment

BACKGROUND

The association of Mini-Mental State Examination (MMSE) with microstructure of individual regions across the entire brain remains unexplored.

PURPOSE

To investigate the relationship between cognitive function and the microstructure of each brain region in the gray matter using diffusion kurtosis imaging (DKI) in older adults with mild cognitive impairment (MCI), which is the transitional stage before the onset of dementia.

MATERIAL AND METHODS

DKI and MMSE were obtained for 34 older adults with MCI and 16 cognitively normal (CN) individuals aged 65-85 years. The DKI parameters were measured from 31 distinct regions of interest in the gray matter. A multiple regression analysis was used to examine the association between DKI parameters and MMSE scores; subsequently, interactions between the DKI parameters and the groups (MCI and CN) were examined.

RESULTS

The mean (±SD) MMSE score for the MCI group was 27.67 ± 1.90. Significant positive correlations were observed between MMSE score and mean kurtosis (MK) in the superior frontal, middle frontal, inferior frontal, precentral, postcentral, angular, middle temporal, and inferior occipital gyri, and superior parietal lobe for the MCI group. In addition, the interaction term of the MK in the middle frontal, precentral, postcentral, and angular gyri, and the groups was statistically significant.

CONCLUSION

Older adults with MCI may exhibit histological damage in certain regions of the brain, such as the middle frontal and angular gyri, as observed in this study. The findings could provide insights into understanding the pathophysiology of cognitive decline in this population group.

Nonparametric distributions of tensor-valued Lorentzian diffusion spectra for model-free data inversion in multidimensional diffusion MRI

Magnetic resonance imaging (MRI) is the method of choice for noninvasive studies of micrometer-scale structures in biological tissues via their effects on the time- and frequency-dependent (restricted) and anisotropic self-diffusion of water. While new designs of time-dependent magnetic field gradient waveforms have enabled disambiguation between different aspects of translational motion that are convolved in traditional MRI methods relying on single pairs of field gradient pulses, data analysis for complex heterogeneous materials remains a challenge. Here, we propose and demonstrate nonparametric distributions of tensor-valued Lorentzian diffusion spectra, or "D(ω) distributions," as a general representation with sufficient flexibility to describe the MRI signal response from a wide range of model systems and biological tissues investigated with modulated gradient waveforms separating and correlating the effects of restricted and anisotropic diffusion.

Sex Differences in the Brain's White Matter Microstructure during Development assessed using Advanced Diffusion MRI Models

Typical sex differences in white matter (WM) microstructure during development are incompletely understood. Here we evaluated sex differences in WM microstructure during typical brain development using a sample of neurotypical individuals across a wide developmental age (N=239, aged 5-22 years). We used the conventional diffusion-weighted MRI (dMRI) model, diffusion tensor imaging (DTI), and two advanced dMRI models, the tensor distribution function (TDF) and neurite orientation dispersion density imaging (NODDI) to assess WM microstructure. WM microstructure exhibited significant, regionally consistent sex differences across the brain during typical development. Additionally, the TDF model was most sensitive in detecting sex differences. These findings highlight the importance of considering sex in neurodevelopmental research and underscore the value of the advanced TDF model.

Deep Normative Tractometry for Identifying Joint White Matter Macro- and Micro-structural Abnormalities in Alzheimer's Disease

This study introduces the Deep Normative Tractometry (DNT) framework, that encodes the joint distribution of both macrostructural and microstructural profiles of the brain white matter tracts through a variational autoencoder (VAE). By training on data from healthy controls, DNT learns the normative distribution of tract data, and can delineate along-tract micro- and macro-structural abnormalities. Leveraging a large sample size via generative pre-training, we assess DNT's generalizability using transfer learning on data from an independent cohort acquired in India. Our findings demonstrate DNT's capacity to detect widespread diffusivity abnormalities along tracts in mild cognitive impairment and Alzheimer's disease, aligning closely with results from the Bundle Analytics (BUAN) tractometry pipeline. By incorporating tract geometry information, DNT may be able to distinguish disease-related abnormalities in anisotropy from tract macrostructure, and shows promise in enhancing fine-scale mapping and detection of white matter alterations in neurodegenerative conditions.

Sex Differences in the Brain's White Matter Microstructure during Development assessed using Advanced Diffusion MRI Models

Typical sex differences in white matter (WM) microstructure during development are incompletely understood. Here we evaluated sex differences in WM microstructure during typical brain development using a sample of neurotypical individuals across a wide developmental age (N=239, aged 5-22 years). We used the conventional diffusion-weighted MRI (dMRI) model, diffusion tensor imaging (DTI), and two advanced dMRI models, the tensor distribution function (TDF) and neurite orientation dispersion density imaging (NODDI) to assess WM microstructure. WM microstructure exhibited significant, regionally consistent sex differences across the brain during typical development. Additionally, the TDF model was most sensitive in detecting sex differences. These findings highlight the importance of considering sex in neurodevelopmental research and underscore the value of the advanced TDF model.

Deep Normative Tractometry for Identifying Joint White Matter Macro- and Micro-structural Abnormalities in Alzheimer's Disease

This study introduces the Deep Normative Tractometry (DNT) framework, that encodes the joint distribution of both macrostructural and microstructural profiles of the brain white matter tracts through a variational autoencoder (VAE). By training on data from healthy controls, DNT learns the normative distribution of tract data, and can delineate along-tract micro-and macro-structural abnormalities. Leveraging a large sample size via generative pre-training, we assess DNT's generalizability using transfer learning on data from an independent cohort acquired in India. Our findings demonstrate DNT's capacity to detect widespread diffusivity abnormalities along tracts in mild cognitive impairment and Alzheimer's disease, aligning closely with results from the Bundle Analytics (BUAN) tractometry pipeline. By incorporating tract geometry information, DNT may be able to distinguish disease-related abnormalities in anisotropy from tract macrostructure, and shows promise in enhancing fine-scale mapping and detection of white matter alterations in neurodegenerative conditions.

BrainGB: A Benchmark for Brain Network Analysis With Graph Neural Networks

Mapping the connectome of the human brain using structural or functional connectivity has become one of the most pervasive paradigms for neuroimaging analysis. Recently, Graph Neural Networks (GNNs) motivated from geometric deep learning have attracted broad interest due to their established power for modeling complex networked data. Despite their superior performance in many fields, there has not yet been a systematic study of how to design effective GNNs for brain network analysis. To bridge this gap, we present BrainGB, a benchmark for brain network analysis with GNNs. BrainGB standardizes the process by (1) summarizing brain network construction pipelines for both functional and structural neuroimaging modalities and (2) modularizing the implementation of GNN designs. We conduct extensive experiments on datasets across cohorts and modalities and recommend a set of general recipes for effective GNN designs on brain networks. To support open and reproducible research on GNN-based brain network analysis, we host the BrainGB website at https://braingb.us with models, tutorials, examples, as well as an out-of-box Python package. We hope that this work will provide useful empirical evidence and offer insights for future research in this novel and promising direction.

Age and sex effects on advanced white matter microstructure measures in 15,628 older adults: A UK biobank study

A comprehensive characterization of the brain's white matter is critical for improving our understanding of healthy and diseased aging. Here we used diffusion-weighted magnetic resonance imaging (dMRI) to estimate age and sex effects on white matter microstructure in a cross-sectional sample of 15,628 adults aged 45-80 years old (47.6% male, 52.4% female). Microstructure was assessed using the following four models: a conventional single-shell model, diffusion tensor imaging (DTI); a more advanced single-shell model, the tensor distribution function (TDF); an advanced multi-shell model, neurite orientation dispersion and density imaging (NODDI); and another advanced multi-shell model, mean apparent propagator MRI (MAPMRI). Age was modeled using a data-driven statistical approach, and normative centile curves were created to provide sex-stratified white matter reference charts. Participant age and sex substantially impacted many aspects of white matter microstructure across the brain, with the advanced dMRI models TDF and NODDI detecting such effects the most sensitively. These findings and the normative reference curves provide an important foundation for the study of healthy and diseased brain aging.

A new framework for MR diffusion tensor distribution

The ability to characterize heterogeneous and anisotropic water diffusion processes within macroscopic MRI voxels non-invasively and in vivo is a desideratum in biology, neuroscience, and medicine. While an MRI voxel may contain approximately a microliter of tissue, our goal is to examine intravoxel diffusion processes on the order of picoliters. Here we propose a new theoretical framework and efficient experimental design to describe and measure such intravoxel structural heterogeneity and anisotropy. We assume that a constrained normal tensor-variate distribution (CNTVD) describes the variability of positive definite diffusion tensors within a voxel which extends its applicability to a wide range of b-values while preserving the richness of diffusion tensor distribution (DTD) paradigm unlike existing models. We introduce a new Monte Carlo (MC) scheme to synthesize realistic 6D DTD numerical phantoms and invert the MR signal. We show that the signal inversion is well-posed and estimate the CNTVD parameters parsimoniously by exploiting the different symmetries of the mean and covariance tensors of CNTVD. The robustness of the estimation pipeline is assessed by adding noise to calculated MR signals and compared with the ground truth. A family of invariant parameters and glyphs which characterize microscopic shape, size and orientation heterogeneity within a voxel are also presented.

The sensitivity of diffusion MRI to microstructural properties and experimental factors

Diffusion MRI is a non-invasive technique to study brain microstructure. Differences in the microstructural properties of tissue, including size and anisotropy, can be represented in the signal if the appropriate method of acquisition is used. However, to depict the underlying properties, special care must be taken when designing the acquisition protocol as any changes in the procedure might impact on quantitative measurements. This work reviews state-of-the-art methods for studying brain microstructure using diffusion MRI and their sensitivity to microstructural differences and various experimental factors. Microstructural properties of the tissue at a micrometer scale can be linked to the diffusion signal at a millimeter-scale using modeling. In this paper, we first give an introduction to diffusion MRI and different encoding schemes. Then, signal representation-based methods and multi-compartment models are explained briefly. The sensitivity of the diffusion MRI signal to the microstructural components and the effects of curvedness of axonal trajectories on the diffusion signal are reviewed. Factors that impact on the quality (accuracy and precision) of derived metrics are then reviewed, including the impact of random noise, and variations in the acquisition parameters (i.e., number of sampled signals, b-value and number of acquisition shells). Finally, yet importantly, typical approaches to deal with experimental factors are depicted, including unbiased measures and harmonization. We conclude the review with some future directions and recommendations on this topic.

Neuroimaging Advances in Diagnosis and Differentiation of HIV, Comorbidities, and Aging in the cART Era

In the "cART era" of more widely available and accessible treatment, aging and HIV-related comorbidities, including symptoms of brain dysfunction, remain common among HIV-infected individuals on suppressive treatment. A better understanding of the neurobiological consequences of HIV infection is essential for developing thorough treatment guidelines and for optimizing long-term neuropsychological outcomes and overall brain health. In this chapter, we first summarize magnetic resonance imaging (MRI) methods used in over two decades of neuroHIV research. These methods evaluate brain volumetric differences and circuitry disruptions in adults living with HIV, and help map clinical correlations with brain function and tissue microstructure. We then introduce and discuss aging and associated neurological complications in people living with HIV, and processes by which infection may contribute to the risk for late-onset dementias. We describe how new technologies and large-scale international collaborations are helping to disentangle the effect of genetic and environmental risk factors on brain aging and neurodegenerative diseases. We provide insights into how these advances, which are now at the forefront of Alzheimer's disease research, may advance the field of neuroHIV. We conclude with a summary of how we see the field of neuroHIV research advancing in the decades to come and highlight potential clinical implications.

Accuracy and precision of statistical descriptors obtained from multidimensional diffusion signal inversion algorithms

In biological tissues, typical MRI voxels comprise multiple microscopic environments, the local organization of which can be captured by microscopic diffusion tensors. The measured diffusion MRI signal can, therefore, be written as the multidimensional Laplace transform of an intravoxel diffusion tensor distribution (DTD). Tensor-valued diffusion encoding schemes have been designed to probe specific features of the DTD, and several algorithms have been introduced to invert such data and estimate statistical descriptors of the DTD, such as the mean diffusivity, the variance of isotropic diffusivities, and the mean squared diffusion anisotropy. However, the accuracy and precision of these estimations have not been assessed systematically and compared across methods. In this article, we perform and compare such estimations in silico for a one-dimensional Gamma fit, a generalized two-term cumulant approach, and two-dimensional and four-dimensional Monte-Carlo-based inversion techniques, using a clinically feasible tensor-valued acquisition scheme. In particular, we compare their performance at different signal-to-noise ratios (SNRs) for voxel contents varying in terms of the aforementioned statistical descriptors, orientational order, and fractions of isotropic and anisotropic components. We find that all inversion techniques share similar precision (except for a lower precision of the two-dimensional Monte Carlo inversion) but differ in terms of accuracy. While the Gamma fit exhibits infinite-SNR biases when the signal deviates strongly from monoexponentiality and is unaffected by orientational order, the generalized cumulant approach shows infinite-SNR biases when this deviation originates from the variance in isotropic diffusivities or from the low orientational order of anisotropic diffusion components. The two-dimensional Monte Carlo inversion shows remarkable accuracy in all systems studied, given that the acquisition scheme possesses enough directions to yield a rotationally invariant powder average. The four-dimensional Monte Carlo inversion presents no infinite-SNR bias, but suffers significantly from noise in the data, while preserving good contrast in most systems investigated.

Direct and specific assessment of axonal injury and spinal cord microenvironments using diffusion correlation imaging

We describe a practical two-dimensional (2D) diffusion MRI framework to deliver specificity and improve sensitivity to axonal injury in the spinal cord. This approach provides intravoxel distributions of correlations of water mobilities in orthogonal directions, revealing sub-voxel diffusion components. Here we use it to investigate water diffusivities along axial and radial orientations within spinal cord specimens with confirmed, tract-specific axonal injury. First, we show using transmission electron microscopy and immunohistochemistry that tract-specific axonal beading occurs following Wallerian degeneration in the cortico-spinal tract as direct sequelae to closed head injury. We demonstrate that although some voxel-averaged diffusion tensor imaging (DTI) metrics are sensitive to this axonal injury, they are non-specific, i.e., they do not reveal an underlying biophysical mechanism of injury. Then we employ 2D diffusion correlation imaging (DCI) to improve discrimination of different water microenvironments by measuring and mapping the joint water mobility distributions perpendicular and parallel to the spinal cord axis. We determine six distinct diffusion spectral components that differ according to their microscopic anisotropy and mobility. We show that at the injury site a highly anisotropic diffusion component completely disappears and instead becomes more isotropic. Based on these findings, an injury-specific MR image of the spinal cord was generated, and a radiological-pathological correlation with histological silver staining % area was performed. The resulting strong and significant correlation (r=0.70,p < 0.0001) indicates the high specificity with which DCI detects injury-induced tissue alterations. We predict that the ability to selectively image microstructural changes following axonal injury in the spinal cord can be useful in clinical and research applications by enabling specific detection and increased sensitivity to injury-induced microstructural alterations. These results also encourage us to translate DCI to higher spatial dimensions to enable assessment of traumatic axonal injury, and possibly other diseases and disorders in the brain.

Diffusion tensor distribution imaging

Conventional diffusion MRI yields voxel-averaged parameters that suffer from ambiguities for heterogeneous anisotropic materials such as brain tissue. Using principles from solid-state NMR spectroscopy, we have previously introduced the shape of the diffusion encoding tensor as a separate acquisition dimension that disentangles isotropic and anisotropic contributions to the observed diffusivities, thereby allowing for unconstrained data inversion into diffusion tensor distributions with "size," "shape," and orientation dimensions. Here we combine our recent non-parametric data inversion algorithm and data acquisition protocol with an imaging pulse sequence to demonstrate spatial mapping of diffusion tensor distributions using a previously developed composite phantom with multiple isotropic and anisotropic components. We propose a compact format for visualizing two-dimensional arrays of the distributions, new scalar parameters quantifying intra-voxel heterogeneity, and a binning procedure giving maps of all relevant parameters for each of the components resolved in the multidimensional distribution space.

Imaging brain microstructure with diffusion MRI: practicality and applications

This article gives an overview of microstructure imaging of the brain with diffusion MRI and reviews the state of the art. The microstructure-imaging paradigm aims to estimate and map microscopic properties of tissue using a model that links these properties to the voxel scale MR signal. Imaging techniques of this type are just starting to make the transition from the technical research domain to wide application in biomedical studies. We focus here on the practicalities of both implementing such techniques and using them in applications. Specifically, the article summarizes the relevant aspects of brain microanatomy and the range of diffusion-weighted MR measurements that provide sensitivity to them. It then reviews the evolution of mathematical and computational models that relate the diffusion MR signal to brain tissue microstructure, as well as the expanding areas of application. Next we focus on practicalities of designing a working microstructure imaging technique: model selection, experiment design, parameter estimation, validation, and the pipeline of development of this class of technique. The article concludes with some future perspectives on opportunities in this topic and expectations on how the field will evolve in the short-to-medium term.

Diffusion MRI Indices and Their Relation to Cognitive Impairment in Brain Aging: The Updated Multi-protocol Approach in ADNI3

Brain imaging with diffusion-weighted MRI (dMRI) is sensitive to microstructural white matter (WM) changes associated with brain aging and neurodegeneration. In its third phase, the Alzheimer's Disease Neuroimaging Initiative (ADNI3) is collecting data across multiple sites and scanners using different dMRI acquisition protocols, to better understand disease effects. It is vital to understand when data can be pooled across scanners, and how the choice of dMRI protocol affects the sensitivity of extracted measures to differences in clinical impairment. Here, we analyzed ADNI3 data from 317 participants (mean age: 75.4 ± 7.9 years; 143 men/174 women), who were each scanned at one of 47 sites with one of six dMRI protocols using scanners from three different manufacturers. We computed four standard diffusion tensor imaging (DTI) indices including fractional anisotropy (FA^DTI) and mean, radial, and axial diffusivity, and one FA index based on the tensor distribution function (FA^TDF), in 24 bilaterally averaged WM regions of interest. We found that protocol differences significantly affected dMRI indices, in particular FA^DTI. We ranked the diffusion indices for their strength of association with four clinical assessments. In addition to diagnosis, we evaluated cognitive impairment as indexed by three commonly used screening tools for detecting dementia and AD: the AD Assessment Scale (ADAS-cog), the Mini-Mental State Examination (MMSE), and the Clinical Dementia Rating scale sum-of-boxes (CDR-sob). Using a nested random-effects regression model to account for protocol and site, we found that across all dMRI indices and clinical measures, the hippocampal-cingulum and fornix (crus)/stria terminalis regions most consistently showed strong associations with clinical impairment. Overall, the greatest effect sizes were detected in the hippocampal-cingulum (CGH) and uncinate fasciculus (UNC) for associations between axial or mean diffusivity and CDR-sob. FA^TDF detected robust widespread associations with clinical measures, while FA^DTI was the weakest of the five indices for detecting associations. Ultimately, we were able to successfully pool dMRI data from multiple acquisition protocols from ADNI3 and detect consistent and robust associations with clinical impairment and age.

Multidimensional correlation of nuclear relaxation rates and diffusion tensors for model-free investigations of heterogeneous anisotropic porous materials

Despite their widespread use in non-invasive studies of porous materials, conventional MRI methods yield ambiguous results for microscopically heterogeneous materials such as brain tissue. While the forward link between microstructure and MRI observables is well understood, the inverse problem of separating the signal contributions from different microscopic pores is notoriously difficult. Here, we introduce an experimental protocol where heterogeneity is resolved by establishing 6D correlations between the individual values of isotropic diffusivity, diffusion anisotropy, orientation of the diffusion tensor, and relaxation rates of distinct populations. Such procedure renders the acquired signal highly specific to the sample's microstructure, and allows characterization of the underlying pore space without prior assumptions on the number and nature of distinct microscopic environments. The experimental feasibility of the suggested method is demonstrated on a sample designed to mimic the properties of nerve tissue. If matched to the constraints of whole body scanners, this protocol could allow for the unconstrained determination of the different types of tissue that compose the living human brain.

Diffusion Tensor Magnetic Resonance Imaging Strategies for Color Mapping of Human Brain Anatomy

BACKGROUND

A color mapping of fiber tract orientation using diffusion tensor imaging (DTI) can be prominent in clinical practice. The goal of this paper is to perform a comparative study of visualized diffusion anisotropy in the human brain anatomical entities using three different color-mapping techniques based on diffusion-weighted imaging (DWI) and DTI.

METHODS

The first technique is based on calculating a color map from DWIs measured in three perpendicular directions. The second technique is based on eigenvalues derived from the diffusion tensor. The last technique is based on three eigenvectors corresponding to sorted eigenvalues derived from the diffusion tensor. All magnetic resonance imaging measurements were achieved using a 1.5 Tesla Siemens Vision whole body imaging system. A single-shot DW echoplanar imaging sequence used a Stejskal-Tanner approach. Trapezoidal diffusion gradients are used. The slice orientation was transverse. The basic measurement yielded a set of 13 images. Each series consists of a single image without diffusion weighting, besides two DWIs for each of the next six noncollinear magnetic field gradient directions.

RESULTS

The three types of color maps were calculated consequently using the DWI obtained and the DTI. Indeed, we established an excellent similarity between the image data in the color maps and the fiber directions of known anatomical structures (e.g., corpus callosum and gray matter).

CONCLUSIONS

In the meantime, rotationally invariant quantities such as the eigenvectors of the diffusion tensor reflected better, the real orientation found in the studied tissue.

An advanced white matter tract analysis in frontotemporal dementia and early-onset Alzheimer's disease

Cortical and subcortical nuclei degenerate in the dementias, but less is known about changes in the white matter tracts that connect them. To better understand white matter changes in behavioral variant frontotemporal dementia (bvFTD) and early-onset Alzheimer’s disease (EOAD), we used a novel approach to extract full 3D profiles of fiber bundles from diffusion-weighted MRI (DWI) and map white matter abnormalities onto detailed models of each pathway. The result is a spatially complex picture of tract-by-tract microstructural changes. Our atlas of tracts for each disease consists of 21 anatomically clustered and recognizable white matter tracts generated from whole-brain tractography in 20 patients with bvFTD, 23 with age-matched EOAD, and 33 healthy elderly controls. To analyze the landscape of white matter abnormalities, we used a point-wise tract correspondence method along the 3D profiles of the tracts and quantified the pathway disruptions using common diffusion metrics – fractional anisotropy, mean, radial, and axial diffusivity. We tested the hypothesis that bvFTD and EOAD are associated with preferential degeneration in specific neural networks. We mapped axonal tract damage that was best detected with mean and radial diffusivity metrics, supporting our network hypothesis, highly statistically significant and more sensitive than widely studied fractional anisotropy reductions. From white matter diffusivity, we identified abnormalities in bvFTD in all 21 tracts of interest but especially in the bilateral uncinate fasciculus, frontal callosum, anterior thalamic radiations, cingulum bundles and left superior longitudinal fasciculus. This network of white matter alterations extends beyond the most commonly studied tracts, showing greater white matter abnormalities in bvFTD versus controls and EOAD patients. In EOAD, network alterations involved more posterior white matter – the parietal sector of the corpus callosum and parahipoccampal cingulum bilaterally. Widespread but distinctive white matter alterations are a key feature of the pathophysiology of these two forms of dementia.

MAPPING AGE EFFECTS ALONG FIBER TRACTS IN YOUNG ADULTS

Brain development is a protracted and dynamic process. Many studies have charted the trajectory of white matter development, but here we sought to map these effects in greater detail, based on a large set of fiber tracts automatically extracted from HARDI (high angular resolution diffusion imaging) at 4 tesla. We used autoMATE (automated multi-atlas tract extraction) to extract diffusivity measures along 18 of the brain's major fiber bundles in 667 young adults, aged 18-30. We examined linear and non-linear age effects on diffusivity measures, pointwise along tracts. All diffusivity measures showed both linear and non-linear age effects. Tracts with the most pronounced age effects were those that connected the temporal lobe to the rest of the brain. Nonlinear age effects were picked up strongly in the anterior corpus callosum and right temporo-parietal tracts.

Fractional anisotropy derived from the diffusion tensor distribution function boosts power to detect Alzheimer's disease deficits

PURPOSE

In diffusion MRI (dMRI), fractional anisotropy derived from the single-tensor model (FA^DTI ) is the most widely used metric to characterize white matter (WM) microarchitecture, despite known limitations in regions with crossing fibers. Due to time constraints when scanning patients in clinical settings, high angular resolution diffusion imaging acquisition protocols, often used to overcome these limitations, are still rare in clinical population studies. However, the tensor distribution function (TDF) may be used to model multiple underlying fibers by representing the diffusion profile as a probabilistic mixture of tensors.

METHODS

We compared the ability of standard FA^DTI and TDF-derived FA (FA^TDF ), calculated from a range of dMRI angular resolutions (41, 30, 15, and 7 gradient directions), to profile WM deficits in 251 individuals from the Alzheimer's Disease Neuroimaging Initiative and to detect associations with 1) Alzheimer's disease diagnosis, 2) Clinical Dementia Rating scores, and 3) average hippocampal volume.

RESULTS

Across angular resolutions and statistical tests, FA^TDF showed larger effect sizes than FA^DTI , particularly in regions preferentially affected by Alzheimer's disease, and was less susceptible to crossing fiber anomalies.

CONCLUSION

The TDF "corrected" form of FA may be a more sensitive and accurate alternative to the commonly used FA^DTI , even in clinical quality dMRI data. Magn Reson Med 78:2322-2333, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Heritability and genetic correlation between the cerebral cortex and associated white matter connections

The aim of this study is to investigate the genetic influence on the cerebral cortex, based on the analyses of heritability and genetic correlation between grey matter (GM) thickness, derived from structural MR images (sMRI), and associated white matter (WM) connections obtained from diffusion MRI (dMRI). We measured on sMRI the cortical thickness (CT) from a large twin imaging cohort using a surface-based approach (N = 308, average age 22.8 ± 2.3 SD). An ACE model was employed to compute the heritability of CT. WM connections were estimated based on probabilistic tractography using fiber orientation distributions (FOD) from dMRI. We then fitted the ACE model to estimate the heritability of CT and FOD peak measures along WM fiber tracts. The WM fiber tracts where genetic influence was detected were mapped onto the cortical surface. Bivariate genetic modeling was performed to estimate the cross-trait genetic correlation between the CT and the FOD-based connectivity of the tracts associated with the cortical regions. We found some cortical regions displaying heritable and genetically correlated GM thickness and WM connectivity, forming networks under stronger genetic influence. Significant heritability and genetic correlations between the CT and WM connectivity were found in regions including the right postcentral gyrus, left posterior cingulate gyrus, right middle temporal gyri, suggesting common genetic factors influencing both GM and WM. Hum Brain Mapp 37:2331-2347, 2016. © 2016 Wiley Periodicals, Inc.

Characterizing brain tissue by assessment of the distribution of anisotropic microstructural environments in diffusion-compartment imaging (DIAMOND)

PURPOSE

To develop a statistical model for the tridimensional diffusion MRI signal at each voxel that describes the signal arising from each tissue compartment in each voxel.

THEORY AND METHODS

In prior work, a statistical model of the apparent diffusion coefficient was shown to well-characterize the diffusivity and heterogeneity of the mono-directional diffusion MRI signal. However, this model was unable to characterize the three-dimensional anisotropic diffusion observed in the brain. We introduce a new model that extends the statistical distribution representation to be fully tridimensional, in which apparent diffusion coefficients are extended to be diffusion tensors. The set of compartments present at a voxel is modeled by a finite sum of unimodal continuous distributions of diffusion tensors. Each distribution provides measures of each compartment microstructural diffusivity and heterogeneity.

RESULTS

The ability to estimate the tridimensional diffusivity and heterogeneity of multiple fascicles and of free diffusion is demonstrated.

CONCLUSION

Our novel tissue model allows for the characterization of the intra-voxel orientational heterogeneity, a prerequisite for accurate tractography while also characterizing the overall tridimensional diffusivity and heterogeneity of each tissue compartment. The model parameters can be estimated from short duration acquisitions. The diffusivity and heterogeneity microstructural parameters may provide novel indicator of the presence of disease or injury. Magn Reson Med 76:963-977, 2016. © 2015 Wiley Periodicals, Inc.

State-of-the-art MRI techniques in neuroradiology: principles, pitfalls, and clinical applications

This article reviews the most relevant state-of-the-art magnetic resonance (MR) techniques, which are clinically available to investigate brain diseases. MR acquisition techniques addressed include notably diffusion imaging (diffusion-weighted imaging (DWI), diffusion tensor imaging (DTI), and diffusion kurtosis imaging (DKI)) as well as perfusion imaging (dynamic susceptibility contrast (DSC), arterial spin labeling (ASL), and dynamic contrast enhanced (DCE)). The underlying models used to process these images are described, as well as the theoretic underpinnings of quantitative diffusion and perfusion MR imaging-based methods. The technical requirements and how they may help to understand, classify, or follow-up neurological pathologies are briefly summarized. Techniques, principles, advantages but also intrinsic limitations, typical artifacts, and alternative solutions developed to overcome them are discussed. In this article, we also review routinely available three-dimensional (3D) techniques in neuro MRI, including state-of-the-art and emerging angiography sequences, and briefly introduce more recently proposed 3D quantitative neuro-anatomy sequences, and new technology, such as multi-slice and multi-transmit imaging.

Diffusion weighted imaging-based maximum density path analysis and classification of Alzheimer's disease

Characterizing brain changes in Alzheimer's disease (AD) is important for patient prognosis and for assessing brain deterioration in clinical trials. In this diffusion weighted imaging study, we used a new fiber-tract modeling method to investigate white matter integrity in 50 elderly controls (CTL), 113 people with mild cognitive impairment, and 37 AD patients. After clustering tractography using a region-of-interest atlas, we used a shortest path graph search through each bundle's fiber density map to derive maximum density paths (MDPs), which we registered across subjects. We calculated the fractional anisotropy (FA) and mean diffusivity (MD) along all MDPs and found significant MD and FA differences between AD patients and CTL subjects, as well as MD differences between CTL and late mild cognitive impairment subjects. MD and FA were also associated with widely used clinical scores. As an MDP is a compact low-dimensional representation of white matter organization, we tested the utility of diffusion tensor imaging measures along these MDPs as features for support vector machine based classification of AD.

Altered white matter microstructure is associated with social cognition and psychotic symptoms in 22q11.2 microdeletion syndrome

22q11.2 Microdeletion Syndrome (22q11DS) is a highly penetrant genetic mutation associated with a significantly increased risk for psychosis. Aberrant neurodevelopment may lead to inappropriate neural circuit formation and cerebral dysconnectivity in 22q11DS, which may contribute to symptom development. Here we examined: (1) differences between 22q11DS participants and typically developing controls in diffusion tensor imaging (DTI) measures within white matter tracts; (2) whether there is an altered age-related trajectory of white matter pathways in 22q11DS; and (3) relationships between DTI measures, social cognition task performance, and positive symptoms of psychosis in 22q11DS and typically developing controls. Sixty-four direction diffusion weighted imaging data were acquired on 65 participants (36 22q11DS, 29 controls). We examined differences between 22q11DS vs. controls in measures of fractional anisotropy (FA), axial diffusivity (AD), and radial diffusivity (RD), using both a voxel-based and region of interest approach. Social cognition domains assessed were: Theory of Mind and emotion recognition. Positive symptoms were assessed using the Structured Interview for Prodromal Syndromes. Compared to typically developing controls, 22q11DS participants showed significantly lower AD and RD in multiple white matter tracts, with effects of greatest magnitude for AD in the superior longitudinal fasciculus. Additionally, 22q11DS participants failed to show typical age-associated changes in FA and RD in the left inferior longitudinal fasciculus. Higher AD in the left inferior fronto-occipital fasciculus (IFO) and left uncinate fasciculus was associated with better social cognition in 22q11DS and controls. In contrast, greater severity of positive symptoms was associated with lower AD in bilateral regions of the IFO in 22q11DS. White matter microstructure in tracts relevant to social cognition is disrupted in 22q11DS, and may contribute to psychosis risk.

Investigating brain connectivity heritability in a twin study using diffusion imaging data

Heritability of brain anatomical connectivity has been studied with diffusion-weighted imaging (DWI) mainly by modeling each voxel's diffusion pattern as a tensor (e.g., to compute fractional anisotropy), but this method cannot accurately represent the many crossing connections present in the brain. We hypothesized that different brain networks (i.e., their component fibers) might have different heritability and we investigated brain connectivity using High Angular Resolution Diffusion Imaging (HARDI) in a cohort of twins comprising 328 subjects that included 70 pairs of monozygotic and 91 pairs of dizygotic twins. Water diffusion was modeled in each voxel with a Fiber Orientation Distribution (FOD) function to study heritability for multiple fiber orientations in each voxel. Precision was estimated in a test-retest experiment on a sub-cohort of 39 subjects. This was taken into account when computing heritability of FOD peaks using an ACE model on the monozygotic and dizygotic twins. Our results confirmed the overall heritability of the major white matter tracts but also identified differences in heritability between connectivity networks. Inter-hemispheric connections tended to be more heritable than intra-hemispheric and cortico-spinal connections. The highly heritable tracts were found to connect particular cortical regions, such as medial frontal cortices, postcentral, paracentral gyri, and the right hippocampus.

Automatic clustering and population analysis of white matter tracts using maximum density paths

We introduce a framework for population analysis of white matter tracts based on diffusion-weighted images of the brain. The framework enables extraction of fibers from high angular resolution diffusion images (HARDI); clustering of the fibers based partly on prior knowledge from an atlas; representation of the fiber bundles compactly using a path following points of highest density (maximum density path; MDP); and registration of these paths together using geodesic curve matching to find local correspondences across a population. We demonstrate our method on 4-Tesla HARDI scans from 565 young adults to compute localized statistics across 50 white matter tracts based on fractional anisotropy (FA). Experimental results show increased sensitivity in the determination of genetic influences on principal fiber tracts compared to the tract-based spatial statistics (TBSS) method. Our results show that the MDP representation reveals important parts of the white matter structure and considerably reduces the dimensionality over comparable fiber matching approaches.

Segmentation of high angular resolution diffusion MRI using sparse riemannian manifold clustering

We address the problem of segmenting high angular resolution diffusion imaging (HARDI) data into multiple regions (or fiber tracts) with distinct diffusion properties. We use the orientation distribution function (ODF) to model diffusion and cast the ODF segmentation problem as a clustering problem in the space of ODFs. Our approach integrates tools from sparse representation theory and Riemannian geometry into a graph theoretic segmentation framework. By exploiting the Riemannian properties of the space of ODFs, we learn a sparse representation for each ODF and infer the segmentation by applying spectral clustering to a similarity matrix built from these representations. In cases where regions with similar (resp. distinct) diffusion properties belong to different (resp. same) fiber tracts, we obtain the segmentation by incorporating spatial and user-specified pairwise relationships into the formulation. Experiments on synthetic data evaluate the sensitivity of our method to image noise and to the concentration parameters, and show its superior performance compared to alternative methods when analyzing complex fiber configurations. Experiments on phantom and real data demonstrate the accuracy of the proposed method in segmenting simulated fibers and white matter fiber tracts of clinical importance.

Effectiveness of regional DTI measures in distinguishing Alzheimer's disease, MCI, and normal aging

The Alzheimer's Disease Neuroimaging Initiative (ADNI) recently added diffusion tensor imaging (DTI), among several other new imaging modalities, in an effort to identify sensitive biomarkers of Alzheimer's disease (AD). While anatomical MRI is the main structural neuroimaging method used in most AD studies and clinical trials, DTI is sensitive to microscopic white matter (WM) changes not detectable with standard MRI, offering additional markers of neurodegeneration. Prior DTI studies of AD report lower fractional anisotropy (FA), and increased mean, axial, and radial diffusivity (MD, AxD, RD) throughout WM. Here we assessed which DTI measures may best identify differences among AD, mild cognitive impairment (MCI), and cognitively healthy elderly control (NC) groups, in region of interest (ROI) and voxel-based analyses of 155 ADNI participants (mean age: 73.5 ± 7.4; 90 M/65 F; 44 NC, 88 MCI, 23 AD). Both VBA and ROI analyses revealed widespread group differences in FA and all diffusivity measures. DTI maps were strongly correlated with widely-used clinical ratings (MMSE, CDR-sob, and ADAS-cog). When effect sizes were ranked, FA analyses were least sensitive for picking up group differences. Diffusivity measures could detect more subtle MCI differences, where FA could not. ROIs showing strongest group differentiation (lowest p-values) included tracts that pass through the temporal lobe, and posterior brain regions. The left hippocampal component of the cingulum showed consistently high effect sizes for distinguishing groups, across all diffusivity and anisotropy measures, and in correlations with cognitive scores.

White matter microstructure in body dysmorphic disorder and its clinical correlates

Body dysmorphic disorder (BDD) is characterized by an often-delusional preoccupation with misperceived defects of appearance, causing significant distress and disability. Although previous studies have found functional abnormalities in visual processing, frontostriatal, and limbic systems, no study to date has investigated the microstructure of white matter connecting these systems in BDD. Participants comprised 14 medication-free individuals with BDD and 16 healthy controls who were scanned using diffusion-weighted magnetic resonance imaging (MRI). We utilized probabilistic tractography to reconstruct tracts of interest, and tract-based spatial statistics to investigate whole brain white matter. To estimate white matter microstructure, we used fractional anisotropy (FA), mean diffusivity (MD), and linear and planar anisotropy (c(l) and c(p)). We correlated diffusion measures with clinical measures of symptom severity and poor insight/delusionality. Poor insight negatively correlated with FA and c(l) and positively correlated with MD in the inferior longitudinal fasciculus (ILF) and the forceps major (FM). FA and c(l) were lower in the ILF and the inferior fronto-occipital fasciculus and higher in the FM in the BDD group, but differences were nonsignificant. This is the first diffusion-weighted MR investigation of white matter in BDD. Results suggest a relationship between impairments in insight, a clinically important phenotype, and fiber disorganization in tracts connecting visual with emotion/memory processing systems.

Magnetic resonance field strength effects on diffusion measures and brain connectivity networks

The quest to map brain connectivity is being pursued worldwide using diffusion imaging, among other techniques. Even so, we know little about how brain connectivity measures depend on the magnetic field strength of the scanner. To investigate this, we scanned 10 healthy subjects at 7 and 3 tesla-using 128-gradient high-angular resolution diffusion imaging. For each subject and scan, whole-brain tractography was used to estimate connectivity between 113 cortical and subcortical regions. We examined how scanner field strength affects (i) the signal-to-noise ratio (SNR) of the non-diffusion-sensitized reference images (b(0)); (ii) diffusion tensor imaging (DTI)-derived fractional anisotropy (FA), mean, radial, and axial diffusivity (MD/RD/AD), in atlas-defined regions; (iii) whole-brain tractography; (iv) the 113 × 113 brain connectivity maps; and (v) five commonly used network topology measures. We also assessed effects of the multi-channel reconstruction methods (sum-of-squares, SOS, at 7T; adaptive recombine, AC, at 3T). At 7T with SOS, the b0 images had 18.3% higher SNR than with 3T-AC. FA was similar for most regions of interest (ROIs) derived from an online DTI atlas (ICBM81), but higher at 7T in the cerebral peduncle and internal capsule. MD, AD, and RD were lower at 7T for most ROIs. The apparent fiber density between some subcortical regions was greater at 7T-SOS than 3T-AC, with a consistent connection pattern overall. Suggesting the need for caution, the recovered brain network was apparently more efficient at 7T, which cannot be biologically true as the same subjects were assessed. Care is needed when comparing network measures across studies, and when interpreting apparently discrepant findings.

Linear transforms for Fourier data on the sphere: application to high angular resolution diffusion MRI of the brain

This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk-Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data. The new family of transforms is characterized theoretically, and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics. After these general discussions, attention is focused on a particular new transform from this family that we name the Funk-Radon and Cosine Transform (FRACT). Based on theoretical arguments, it is expected that FRACT-based analysis should yield significantly better orientation information (e.g., improved accuracy and higher angular resolution) than FRT-based analysis, while maintaining the strong characterizability and computational efficiency of the FRT. Simulations are used to confirm these theoretical characteristics, and the practical significance of the proposed approach is illustrated with real diffusion weighted MRI brain data. These experiments demonstrate that, in addition to having strong theoretical characteristics, the proposed approach can outperform existing state-of-the-art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors.

Extended Broca's area in the functional connectome of language in adults: combined cortical and subcortical single-subject analysis using fMRI and DTI tractography

Traditional models of the human language circuitry encompass three cortical areas, Broca's, Geschwind's and Wernicke's, and their connectivity through white matter fascicles. The neural connectivity deep to these cortical areas remains poorly understood, as does the macroscopic functional organization of the cortico-subcortical language circuitry. In an effort to expand current knowledge, we combined functional MRI (fMRI) and diffusion tensor imaging to explore subject-specific structural and functional macroscopic connectivity, focusing on Broca's area. Fascicles were studied using diffusion tensor imaging fiber tracking seeded from volumes placed manually within the white matter. White matter fascicles and fMRI-derived clusters (antonym-generation task) of positive and negative blood-oxygen-level-dependent (BOLD) signal were co-registered with 3-D renderings of the brain in 12 healthy subjects. Fascicles connecting BOLD-derived clusters were analyzed within specific cortical areas: Broca's, with the pars triangularis, the pars opercularis, and the pars orbitaris; Geschwind's and Wernicke's; the premotor cortex, the dorsal supplementary motor area, the middle temporal gyrus, the dorsal prefrontal cortex and the frontopolar region. We found a functional connectome divisible into three systems-anterior, superior and inferior-around the insula, more complex than previously thought, particularly with respect to a new extended Broca's area. The extended Broca's area involves two new fascicles: the operculo-premotor fascicle comprised of well-organized U-shaped fibers that connect the pars opercularis with the premotor region; and (2) the triangulo-orbitaris system comprised of intermingled U-shaped fibers that connect the pars triangularis with the pars orbitaris. The findings enhance our understanding of language function.

Angular versus spatial resolution trade-offs for diffusion imaging under time constraints

Diffusion weighted magnetic resonance imaging (DW-MRI) are now widely used to assess brain integrity in clinical populations. The growing interest in mapping brain connectivity has made it vital to consider what scanning parameters affect the accuracy, stability, and signal-to-noise of diffusion measures. Trade-offs between scan parameters can only be optimized if their effects on various commonly-derived measures are better understood. To explore angular versus spatial resolution trade-offs in standard tensor-derived measures, and in measures that use the full angular information in diffusion signal, we scanned eight subjects twice, 2 weeks apart, using three protocols that took the same amount of time (7 min). Scans with 3.0, 2.7, 2.5 mm isotropic voxels were collected using 48, 41, and 37 diffusion-sensitized gradients to equalize scan times. A specially designed DTI phantom was also scanned with the same protocols, and different b-values. We assessed how several diffusion measures including fractional anisotropy (FA), mean diffusivity (MD), and the full 3D orientation distribution function (ODF) depended on the spatial/angular resolution and the SNR. We also created maps of stability over time in the FA, MD, ODF, skeleton FA of 14 TBSS-derived ROIs, and an information uncertainty index derived from the tensor distribution function, which models the signal using a continuous mixture of tensors. In scans of the same duration, higher angular resolution and larger voxels boosted SNR and improved stability over time. The increased partial voluming in large voxels also led to bias in estimating FA, but this was partially addressed by using "beyond-tensor" models of diffusion.

Quantitative tract-specific measures of uncinate and cingulum in major depression using diffusion tensor imaging

Previous findings suggested the role of the prefrontal cortex, hippocampus, and cingulate gyrus in major depressive disorders (MDD), but the white matter microstructural abnormalities of the fibers connecting these brain structures are not known. The purpose of this study was to test the hypothesis that white matter abnormalities are present in association fibers of the uncinate fasciculus (UF) and cingulum bundle (CB) among MDD subjects. A total of 21 MDD subjects aged between 30 and 65 years and 21 age-matched healthy controls (HC) were recruited. All subjects were right-handed and without history of diabetes or other cardiac diseases. We extracted quantitative tract-specific measures based on diffusion tensor imaging tractography to examine both diffusivity and geometric properties of the UF and CB. Significantly decreased fractional anisotropy (FA) and increased radial diffusivity of the right UF were observed in MDD patients compared with HC (p<0.05), while their geometric characteristics remained relatively unchanged. Among MDD subjects, depression severity had a significant negative correlation with normalized number of fibers (NNF) in the right UF (r=-0.53, p=0.02). We also found significant age effect (old<young) in HC group and laterality effect (L>R) in both groups in the FA measure of the CB. Our study demonstrates novel findings of white matter microstructural abnormalities of the right UF in MDD. In the MDD group, the severity of depression is associated with reduced NNF in the right UF. These findings have implications for both clinical manifestations of depression as well as its pathophysiology.

Nonparametric Bayesian inference of the fiber orientation distribution from diffusion-weighted MR images

Diffusion MR imaging provides a unique tool to probe the microgeometry of nervous tissue and to explore the wiring diagram of the neural connections noninvasively. Generally, a forward model is established to map the intra-voxel fiber architecture onto the observable diffusion signals, which is reformulated in this article by adopting a measure-theoretic approach. However, the inverse problem, i.e., the spherical deconvolution of the fiber orientation density from noisy MR measurements, is ill-posed. We propose a nonparametric representation of the tangential distribution of the nerve fibers in terms of a Dirichlet process mixture. Given a second-order approximation of the impulse response of a fiber segment, the specified problem is solved by Bayesian statistics under a Rician noise model, using an adaptive reversible jump Markov chain Monte Carlo sampler. The density estimation framework is demonstrated by various experiments with a diffusion MR dataset featuring high angular resolution, uncovering the fiber orientation field in the cerebral white matter of the living human brain.

Ball and rackets: Inferring fiber fanning from diffusion-weighted MRI

A number of methods have been proposed for resolving crossing fibers from diffusion-weighted (DW) MRI. However, other complex fiber geometries have drawn minimal attention. In this study, we focus on fiber orientation dispersion induced by within-voxel fanning. We use a multi-compartment, model-based approach to estimate fiber dispersion. Bingham distributions are employed to represent continuous distributions of fiber orientations, centered around a main orientation, and capturing anisotropic dispersion. We evaluate the accuracy of the model for different simulated fanning geometries, under different acquisition protocols and we illustrate the high SNR and angular resolution needs. We also perform a qualitative comparison between our parametric approach and five popular non-parametric techniques that are based on orientation distribution functions (ODFs). This comparison illustrates how the same underlying geometry can be depicted by different methods. We apply the proposed model on high-quality, post-mortem macaque data and present whole-brain maps of fiber dispersion, as well as exquisite details on the local anatomy of fiber distributions in various white matter regions.

Determination of axonal and dendritic orientation distributions within the developing cerebral cortex by diffusion tensor imaging

As neurons of the developing brain form functional circuits, they undergo morphological differentiation. In immature cerebral cortex, radially-oriented cellular processes of undifferentiated neurons impede water diffusion parallel, but not perpendicular, to the pial surface, as measured via diffusion-weighted magnetic resonance imaging, and give rise to water diffusion anisotropy. As the cerebral cortex matures, the loss of water diffusion anisotropy accompanies cellular morphological differentiation. A quantitative relationship is proposed here to relate water diffusion anisotropy measurements directly to characteristics of neuronal morphology. This expression incorporates the effects of local diffusion anisotropy within cellular processes, as well as the effects of anisotropy in the orientations of cellular processes. To obtain experimental support for the proposed relationship, tissue from 13 and 31 day-old ferrets was stained using the rapid Golgi technique, and the 3-D orientation distribution of neuronal processes was characterized using confocal microscopic examination of reflected visible light images. Coregistration of the MRI and Golgi data enables a quantitative evaluation of the proposed theory, and excellent agreement with the theoretical results, as well as agreement with previously published values for locally-induced water diffusion anisotropy and volume fraction of the neuropil, is observed.

MEASURING INTER-HEMISPHERIC INTEGRATION IN BIPOLAR AFFECTIVE DISORDER USING BRAIN NETWORK ANALYSES AND HARDI

Bipolar disorder is characterized by extreme mood swings, including both manic and depressive episodes commonly accompanied by psychosis. Many imaging studies have investigated white matter changes in bipolar illness, and the results have suggested abnormal intra- and inter-hemispheric white matter structures, particularly in the fronto-limbic and callosal systems. However, some inconsistency remains in the literature, and no study to-date has utilized brain network analysis using graph theory. Here, we acquired 64-direction diffusion weighted imaging (DWI) on 25 euthymic bipolar I subjects and 25 gender/age matched healthy subjects. White matter integrity measures were computed and compared in 50 white matter ROIs. The results indicated impaired integrity in the corpus callosum. Guided by this, we constructed whole brain structural connectivity networks using graph theory. We devised brain network metrics (inter-hemispheric path length and efficiency) to further probe inter-hemispheric integration, and demonstrated relatively preserved intra-hemispheric but significantly impaired inter-hemispheric integration in our bipolar subjects.

A VARIATIONAL MODEL FOR DENOISING HIGH ANGULAR RESOLUTION DIFFUSION IMAGING

The presence of noise in High Angular Resolution Diffusion Imaging (HARDI) data of the brain can limit the accuracy with which fiber pathways of the brain can be extracted. In this work, we present a variational model to denoise HARDI data corrupted by Rician noise. Numerical experiments are performed on three types of data: 2D synthetic data, 3D diffusion-weighted Magnetic Resonance Imaging (DW-MRI) data of a hardware phantom containing synthetic fibers, and 3D real HARDI brain data. Experiments show that our model is effective for denoising HARDI-type data while preserving important aspects of the fiber pathways such as fractional anisotropy and the orientation distribution functions.

A nonparametric Riemannian framework for processing high angular resolution diffusion images and its applications to ODF-based morphometry

High angular resolution diffusion imaging (HARDI) has become an important technique for imaging complex oriented structures in the brain and other anatomical tissues. This has motivated the recent development of several methods for computing the orientation probability density function (PDF) at each voxel. However, much less work has been done on developing techniques for filtering, interpolation, averaging and principal geodesic analysis of orientation PDF fields. In this paper, we present a Riemannian framework for performing such operations. The proposed framework does not require that the orientation PDFs be represented by any fixed parameterization, such as a mixture of von Mises-Fisher distributions or a spherical harmonic expansion. Instead, we use a nonparametric representation of the orientation PDF. We exploit the fact that under the square-root re-parameterization, the space of orientation PDFs forms a Riemannian manifold: the positive orthant of the unit Hilbert sphere. We show that various orientation PDF processing operations, such as filtering, interpolation, averaging and principal geodesic analysis, may be posed as optimization problems on the Hilbert sphere, and can be solved using Riemannian gradient descent. We illustrate these concepts with numerous experiments on synthetic, phantom and real datasets. We show their application to studying left/right brain asymmetries.

White matter anatomy of the human deep brain revisited with high resolution DTI fibre tracking

BACKGROUND AND PURPOSE

Deep white matter (WM) fascicles play a major, yet poorly understood, role in the overall connectivity of human brain. Better knowledge of their anatomy is requisite to understand the clinical correlates of their lesions and develop targeted treatments. We investigated whether MR-based diffusion tensor imaging (DTI) and fibre tracking could reveal in vivo, in explicit details, the 3D WM architecture within the subthalamic region and the internal capsule.

METHODS

High-resolution DTI images were acquired on six healthy volunteers on a three Tesla MR scanner. We studied using single-subject analysis WM fascicles within the subthalamic region and the internal capsule, as follows: DTI deterministic fibre tracking (FT) of fascicles; embedding fascicles in the volume-rendered brain coupled with a triplanar view; rigorous anatomic labelling of each fascicle according to classical knowledge as described by pioneer neuroanatomists. Deterministic FT effects were taken into account.

RESULTS

We charted most of WM fascicles of the deep brain, in particular large and complex fascicles such as the basal forebrain bundle and the ansa lenticularis. A topographic classification of subthalamic fascicles was proposed into three groups: the cerebellorubral, the reticulo-dorsal and the tegmento-peripheral one.

CONCLUSIONS

Beyond to demonstrate the feasibility of imaging the deepest WM fascicles in vivo, our results pave the way for a better understanding of the brain connectivity and for developing targeted neuromodulation.

Diffeomorphic image registration of diffusion MRI using spherical harmonics

Nonrigid registration of diffusion magnetic resonance imaging (MRI) is crucial for group analyses and building white matter and fiber tract atlases. Most current diffusion MRI registration techniques are limited to the alignment of diffusion tensor imaging (DTI) data. We propose a novel diffeomorphic registration method for high angular resolution diffusion images by mapping their orientation distribution functions (ODFs). ODFs can be reconstructed using q-ball imaging (QBI) techniques and represented by spherical harmonics (SHs) to resolve intra-voxel fiber crossings. The registration is based on optimizing a diffeomorphic demons cost function. Unlike scalar images, deforming ODF maps requires ODF reorientation to maintain its consistency with the local fiber orientations. Our method simultaneously reorients the ODFs by computing a Wigner rotation matrix at each voxel, and applies it to the SH coefficients during registration. Rotation of the coefficients avoids the estimation of principal directions, which has no analytical solution and is time consuming. The proposed method was validated on both simulated and real data sets with various metrics, which include the distance between the estimated and simulated transformation fields, the standard deviation of the general fractional anisotropy and the directional consistency of the deformed and reference images. The registration performance using SHs with different maximum orders were compared using these metrics. Results show that the diffeomorphic registration improved the affine alignment, and registration using SHs with higher order SHs further improved the registration accuracy by reducing the shape difference and improving the directional consistency of the registered and reference ODF maps.