Quantifying the brain's sheet structure with normalized convolution

COnstrained Reference frame diffusion TEnsor Correlation Spectroscopic (CORTECS) MRI: A practical framework for high-resolution diffusion tensor distribution imaging

High-resolution imaging studies have consistently shown that in cortical tissue water diffuses preferentially along radial and tangential orientations with respect to the cortical surface, in agreement with histology. These dominant orientations do not change significantly even if the relative contributions from microscopic water pools to the net voxel signal vary across experiments that use different diffusion times, b-values, TEs, and TRs. With this in mind, we propose a practical new framework for imaging non-parametric diffusion tensor distributions (DTDs) by constraining the microscopic diffusion tensors of the DTD to be diagonalized using the same orthonormal reference frame of the mesoscopic voxel. In each voxel, the constrained DTD (cDTD) is completely determined by the correlation spectrum of the microscopic principal diffusivities associated with the axes of the voxel reference frame. Consequently, all cDTDs are inherently limited to the domain of positive definite tensors and can be reconstructed efficiently using Inverse Laplace Transform methods. Moreover, the cDTD reconstruction can be performed using only data acquired efficiently with single diffusion encoding, although it also supports datasets with multiple diffusion encoding. In tissues with a well-defined architecture, such as the cortex, we can further constrain the cDTD to contain only cylindrically symmetric diffusion tensors and measure the 2D correlation spectra of principal diffusivities along the radial and tangential orientation with respect to the cortical surface. To demonstrate this framework, we perform numerical simulations and analyze high-resolution dMRI data from a fixed macaque monkey brain. We estimate 2D cDTDs in the cortex and derive, in each voxel, the marginal distributions of the microscopic principal diffusivities, the corresponding distributions of the microscopic fractional anisotropies and mean diffusivities along with their 2D correlation spectra to quantify the cDTD shape-size characteristics. Signal components corresponding to specific bands in these cDTD-derived spectra show high specificity to cortical laminar structures observed with histology. Our framework drastically simplifies the measurement of non-parametric DTDs in high-resolution datasets with mesoscopic voxel sizes much smaller than the radius of curvature of the underlying anatomy, e.g., cortical surface, and can be applied retrospectively to analyze existing diffusion MRI data from fixed cortical tissues.

Prevalence of white matter pathways coming into a single white matter voxel orientation: The bottleneck issue in tractography

Characterizing and understanding the limitations of diffusion MRI fiber tractography is a prerequisite for methodological advances and innovations which will allow these techniques to accurately map the connections of the human brain. The so-called "crossing fiber problem" has received tremendous attention and has continuously triggered the community to develop novel approaches for disentangling distinctly oriented fiber populations. Perhaps an even greater challenge occurs when multiple white matter bundles converge within a single voxel, or throughout a single brain region, and share the same parallel orientation, before diverging and continuing towards their final cortical or sub-cortical terminations. These so-called "bottleneck" regions contribute to the ill-posed nature of the tractography process, and lead to both false positive and false negative estimated connections. Yet, as opposed to the extent of crossing fibers, a thorough characterization of bottleneck regions has not been performed. The aim of this study is to quantify the prevalence of bottleneck regions. To do this, we use diffusion tractography to segment known white matter bundles of the brain, and assign each bundle to voxels they pass through and to specific orientations within those voxels (i.e. fixels). We demonstrate that bottlenecks occur in greater than 50-70% of fixels in the white matter of the human brain. We find that all projection, association, and commissural fibers contribute to, and are affected by, this phenomenon, and show that even regions traditionally considered "single fiber voxels" often contain multiple fiber populations. Together, this study shows that a majority of white matter presents bottlenecks for tractography which may lead to incorrect or erroneous estimates of brain connectivity or quantitative tractography (i.e., tractometry), and underscores the need for a paradigm shift in the process of tractography and bundle segmentation for studying the fiber pathways of the human brain.

Fiber orientation distribution from diffusion MRI: Effects of inaccurate response function calibration

Background and Purpose

Diffusion MRI of the brain enables to quantify white matter fiber orientations noninvasively. Several approaches have been proposed to estimate such characteristics from diffusion MRI data with spherical deconvolution being one of the most widely used methods. Spherical deconvolution requires to define––or derive from the data––a response function, which is used to compute the fiber orientation distribution (FOD). Different characteristics of the response function are expected to affect the FOD computation and the subsequent fiber tracking.

Methods

In this work, we explored the effects of inaccuracies in the shape factors of the response function on the FOD characteristics.

Results

With simulations, we show that the apparent fiber density could be doubled in the presence of underestimated shape factors in the response functions, whereas the overestimation of the shape factor will cause more spurious peaks in the FOD, especially when the signal‐to‐noise ratio is below 15. Moreover, crossing fiber populations with a separation angle smaller than 60° were more sensitive to inaccuracies in the response function than fiber populations with more orthogonal separation angles. Results with in vivo data demonstrate angular deviations in the FODs and spurious peaks as a result of modified shape factors of the response function, while the reconstruction of the main parts of fiber bundles is well preserved.

Conclusions

This work sheds light on how specific aspects of the response function shape can affect the estimated FODs, and highlights the importance of a proper calibration/definition of the response function.

Probing tissue microstructure by diffusion skewness tensor imaging

Probing the cellular structure of in vivo biological tissue is a fundamental problem in biomedical imaging and medical science. This work introduces an approach for analyzing diffusion magnetic resonance imaging data acquired by the novel tensor-valued encoding technique for characterizing tissue microstructure. Our approach first uses a signal model to estimate the variance and skewness of the distribution of apparent diffusion tensors modeling the underlying tissue. Then several novel imaging indices, such as weighted microscopic anisotropy and microscopic skewness, are derived to characterize different ensembles of diffusion processes that are indistinguishable by existing techniques. The contributions of this work also include a theoretical proof that shows that, to estimate the skewness of a diffusion tensor distribution, the encoding protocol needs to include full-rank tensor diffusion encoding. This proof provides a guideline for the application of this technique. The properties of the proposed indices are illustrated using both synthetic data and in vivo data acquired from a human brain.

Patterning of corpus callosum integrity in glioma observed by MRI: Effect of 2D bi-axial lamellar brain architecture

PURPOSE

Corpus callosum (CC) is a main channel histologically for glioma spreading, downgrading the prognosis, the infiltration occurring through cellular reaction-diffusion process. Preliminary clinical trial indicates that CC's surgical interruption appreciably enhances clinical outcome. We aim to find how high-grade glioma phenomenology is reflected in CC parameters, including various 3D diffusion eigenvalues differentially, whereby this information may be utilized for planning radiotherapy and surgical intervention.

METHODS

Using 3 Tesla MRI diffusion-tensor imaging of glioma patients and matched controls, we formulated the callosal volume, fibre count, and 3D directional diffusivity eigenvalues (λ₁-λ₂-λ₃), utilizing FDT/FMRIB-based analysis.

RESULTS

In glioma, the callosal volume, fibre count and normalized volume decreases (p < 0.001), while axial diffusivity λ₁ and radial diffusivity component λ₂ significantly increase (p = 0.03, p = 0.04). Though not expected, the other radial diffusivity component λ₃ remains unchanged (p = 0.11). Increase of λ₁ and λ₂ is due to gliomatous migration across the two directions (eigenvectors of λ₁, λ₂), which correlate respectively with medio-lateral commissural fibres and dorso-ventral perforating fibres in CC. These are corroborated by collateral radiological findings and immunohistological staining of those two fibre-systems in cat and human.

CONCLUSION

In glioma, the two diffusivities (λ₁, λ₂), enhance due to fluidic edema permeation through CC's bi-axial lamina-type structural scaffold, formed by mediolateral commissural fibres and dorsoventral perforating cingulo-septal fibres. On other hand, the two radial diffusivities (λ₂, λ₃) are physiologically different and can be distinguished as lamellar diffusivity and focal diffusivity respectively. Lamellar diffusivity λ₂ needs to be considered for MRI-assisted surgical intervention and radiotherapy planning in glioma.

Advances in computational and statistical diffusion MRI

Computational methods are crucial for the analysis of diffusion magnetic resonance imaging (MRI) of the brain. Computational diffusion MRI can provide rich information at many size scales, including local microstructure measures such as diffusion anisotropies or apparent axon diameters, whole-brain connectivity information that describes the brain's wiring diagram and population-based studies in health and disease. Many of the diffusion MRI analyses performed today were not possible five, ten or twenty years ago, due to the requirements for large amounts of computer memory or processor time. In addition, mathematical frameworks had to be developed or adapted from other fields to create new ways to analyze diffusion MRI data. The purpose of this review is to highlight recent computational and statistical advances in diffusion MRI and to put these advances into context by comparison with the more traditional computational methods that are in popular clinical and scientific use. We aim to provide a high-level overview of interest to diffusion MRI researchers, with a more in-depth treatment to illustrate selected computational advances.

Diffusion MRI visualization

Modern diffusion magnetic resonance imaging (dMRI) acquires intricate volume datasets and biological meaning can only be found in the relationship between its different measurements. Suitable strategies for visualizing these complicated data have been key to interpretation by physicians and neuroscientists, for drawing conclusions on brain connectivity and for quality control. This article provides an overview of visualization solutions that have been proposed to date, ranging from basic grayscale and color encodings to glyph representations and renderings of fiber tractography. A particular focus is on ongoing and possible future developments in dMRI visualization, including comparative, uncertainty, interactive and dense visualizations.

The Nomenclature of Human White Matter Association Pathways: Proposal for a Systematic Taxonomic Anatomical Classification

The heterogeneity and complexity of white matter (WM) pathways of the human brain were discretely described by pioneers such as Willis, Stenon, Malpighi, Vieussens and Vicq d'Azyr up to the beginning of the 19th century. Subsequently, novel approaches to the gross dissection of brain internal structures have led to a new understanding of WM organization, notably due to the works of Reil, Gall and Burdach highlighting the fascicular organization of WM. Meynert then proposed a definitive tripartite organization in association, commissural and projection WM pathways. The enduring anatomical work of Dejerine at the turn of the 20th century describing WM pathways in detail has been the paramount authority on this topic (including its terminology) for over a century, enriched sporadically by studies based on blunt Klingler dissection. Currently, diffusion-weighted magnetic resonance imaging (DWI) is used to reveal the WM fiber tracts of the human brain in vivo by measuring the diffusion of water molecules, especially along axons. It is then possible by tractography to reconstitute the WM pathways of the human brain step by step at an unprecedented level of precision in large cohorts. However, tractography algorithms, although powerful, still face the complexity of the organization of WM pathways, and there is a crucial need to benefit from the exact definitions of the trajectories and endings of all WM fascicles. Beyond such definitions, the emergence of DWI-based tractography has mostly revealed strong heterogeneity in naming the different bundles, especially the long-range association pathways. This review addresses the various terminologies known for the WM association bundles, aiming to describe the rules of arrangements followed by these bundles and to propose a new nomenclature based on the structural wiring diagram of the human brain.

DT-MRI Streamsurfaces Revisited

DT-MRI streamsurfaces, defined as surfaces that are everywhere tangential to the major and medium eigenvector fields, have been proposed as a tool for visualizing regions of predominantly planar behavior in diffusion tensor MRI. Even though it has long been known that their construction assumes that the involved eigenvector fields satisfy an integrability condition, it has never been tested systematically whether this condition is met in real-world data. We introduce a suitable and efficiently computable test to the visualization literature, demonstrate that it can be used to distinguish integrable from nonintegrable configurations in simulations, and apply it to whole-brain datasets of 15 healthy subjects. We conclude that streamsurface integrability is approximately satisfied in a substantial part of the brain, but not everywhere, including some regions of planarity. As a consequence, algorithms for streamsurface extraction should explicitly test local integrability. Finally, we propose a novel patch-based approch to streamsurface visualization that reduces visual artifacts, and is shown to more fully sample the extent of streamsurfaces.

Fast and accurate Slicewise OutLIer Detection (SOLID) with informed model estimation for diffusion MRI data

The accurate characterization of the diffusion process in tissue using diffusion MRI is greatly challenged by the presence of artefacts. Subject motion causes not only spatial misalignments between diffusion weighted images, but often also slicewise signal intensity errors. Voxelwise robust model estimation is commonly used to exclude intensity errors as outliers. Slicewise outliers, however, become distributed over multiple adjacent slices after image registration and transformation. This challenges outlier detection with voxelwise procedures due to partial volume effects. Detecting the outlier slices before any transformations are applied to diffusion weighted images is therefore required. In this work, we present i) an automated tool coined SOLID for slicewise outlier detection prior to geometrical image transformation, and ii) a framework to naturally interpret data uncertainty information from SOLID and include it as such in model estimators. SOLID uses a straightforward intensity metric, is independent of the choice of the diffusion MRI model, and can handle datasets with a few or irregularly distributed gradient directions. The SOLID-informed estimation framework prevents the need to completely reject diffusion weighted images or individual voxel measurements by downweighting measurements with their degree of uncertainty, thereby supporting convergence and well-conditioning of iterative estimation algorithms. In comprehensive simulation experiments, SOLID detects outliers with a high sensitivity and specificity, and can achieve higher or at least similar sensitivity and specificity compared to other tools that are based on more complex and time-consuming procedures for the scenarios investigated. SOLID was further validated on data from 54 neonatal subjects which were visually inspected for outlier slices with the interactive tool developed as part of this study, showing its potential to quickly highlight problematic volumes and slices in large population studies. The informed model estimation framework was evaluated both in simulations and in vivo human data.

Multidimensional encoding of brain connectomes

The ability to map brain networks in living individuals is fundamental in efforts to chart the relation between human behavior, health and disease. Advances in network neuroscience may benefit from developing new frameworks for mapping brain connectomes. We present a framework to encode structural brain connectomes and diffusion-weighted magnetic resonance (dMRI) data using multidimensional arrays. The framework integrates the relation between connectome nodes, edges, white matter fascicles and diffusion data. We demonstrate the utility of the framework for in vivo white matter mapping and anatomical computing by evaluating 1,490 connectomes, thirteen tractography methods, and three data sets. The framework dramatically reduces storage requirements for connectome evaluation methods, with up to 40x compression factors. Evaluation of multiple, diverse datasets demonstrates the importance of spatial resolution in dMRI. We measured large increases in connectome resolution as function of data spatial resolution (up to 52%). Moreover, we demonstrate that the framework allows performing anatomical manipulations on white matter tracts for statistical inference and to study the white matter geometrical organization. Finally, we provide open-source software implementing the method and data to reproduce the results.