Axon diameter mapping in crossing fibers with diffusion MRI

Reconstruction of ovine axonal cytoarchitecture enables more accurate models of brain biomechanics

There is an increased need and focus to understand how local brain microstructure affects the transport of drug molecules directly administered to the brain tissue, for example in convection-enhanced delivery procedures. This study reports a systematic attempt to characterize the cytoarchitecture of commissural, long association and projection fibres, namely the corpus callosum, the fornix and the corona radiata, with the specific aim to map different regions of the tissue and provide essential information for the development of accurate models of brain biomechanics. Ovine samples are imaged using scanning electron microscopy combined with focused ion beam milling to generate 3D volume reconstructions of the tissue at subcellular spatial resolution. Focus is placed on the characteristic cytological feature of the white matter: the axons and their alignment in the tissue. For each tract, a 3D reconstruction of relatively large volumes, including a significant number of axons, is performed and outer axonal ellipticity, outer axonal cross-sectional area and their relative perimeter are measured. The study of well-resolved microstructural features provides useful insight into the fibrous organization of the tissue, whose micromechanical behaviour is that of a composite material presenting elliptical tortuous tubular axonal structures embedded in the extra-cellular matrix. Drug flow can be captured through microstructurally-based models using 3D volumes, either reconstructed directly from images or generated in silico using parameters extracted from the database of images, leading to a workflow to enable physically-accurate simulations of drug delivery to the targeted tissue.

Imaging and reconstruction of sheep brain axonal cytoarchitecture provides insight for brain biomechanics models that simulate drug delivery and other biological processes governed by interstitial fluid flow and transport.

Bundle-Specific Axon Diameter Index as a New Contrast to Differentiate White Matter Tracts

In the central nervous system of primates, several pathways are characterized by different spectra of axon diameters. In vivo methods, based on diffusion-weighted magnetic resonance imaging, can provide axon diameter index estimates non-invasively. However, such methods report voxel-wise estimates, which vary from voxel-to-voxel for the same white matter bundle due to partial volume contributions from other pathways having different microstructure properties. Here, we propose a novel microstructure-informed tractography approach, COMMITAxSize, to resolve axon diameter index estimates at the streamline level, thus making the estimates invariant along trajectories. Compared to previously proposed voxel-wise methods, our formulation allows the estimation of a distinct axon diameter index value for each streamline, directly, furnishing a complementary measure to the existing calculation of the mean value along the bundle. We demonstrate the favourable performance of our approach comparing our estimates with existing histologically-derived measurements performed in the corpus callosum and the posterior limb of the internal capsule. Overall, our method provides a more robust estimation of the axon diameter index of pathways by jointly estimating the microstructure properties of the tissue and the macroscopic organisation of the white matter connectivity.

Axon diameter index estimation independent of fiber orientation distribution using high-gradient diffusion MRI

Axon diameter mapping using high-gradient diffusion MRI has generated great interest as a noninvasive tool for studying trends in axonal size in the human brain. One of the main barriers to mapping axon diameter across the whole brain is accounting for complex white matter fiber configurations (e.g., crossings and fanning), which are prevalent throughout the brain. Here, we present a framework for generalizing axon diameter index estimation to the whole brain independent of the underlying fiber orientation distribution using the spherical mean technique (SMT). This approach is shown to significantly benefit from the use of real-valued diffusion data with Gaussian noise, which reduces the systematic bias in the estimated parameters resulting from the elevation of the noise floor when using magnitude data with Rician noise. We demonstrate the feasibility of obtaining whole-brain orientationally invariant estimates of axon diameter index and relative volume fractions in six healthy human volunteers using real-valued diffusion data acquired on a dedicated high-gradient 3-Tesla human MRI scanner with 300 mT/m maximum gradient strength. The trends in axon diameter index are consistent with known variations in axon diameter from histology and demonstrate the potential of this generalized framework for revealing coherent patterns in axonal structure throughout the living human brain. The use of real-valued diffusion data provides a viable solution for eliminating the Rician noise floor and should be considered for all spherical mean approaches to microstructural parameter estimation.

ConFiG: Contextual Fibre Growth to generate realistic axonal packing for diffusion MRI simulation

This paper presents Contextual Fibre Growth (ConFiG), an approach to generate white matter numerical phantoms by mimicking natural fibre genesis. ConFiG grows fibres one-by-one, following simple rules motivated by real axonal guidance mechanisms. These simple rules enable ConFiG to generate phantoms with tuneable microstructural features by growing fibres while attempting to meet morphological targets such as user-specified density and orientation distribution. We compare ConFiG to the state-of-the-art approach based on packing fibres together by generating phantoms in a range of fibre configurations including crossing fibre bundles and orientation dispersion. Results demonstrate that ConFiG produces phantoms with up to 20% higher densities than the state-of-the-art, particularly in complex configurations with crossing fibres. We additionally show that the microstructural morphology of ConFiG phantoms is comparable to real tissue, producing diameter and orientation distributions close to electron microscopy estimates from real tissue as well as capturing complex fibre cross sections. Signals simulated from ConFiG phantoms match real diffusion MRI data well, showing that ConFiG phantoms can be used to generate realistic diffusion MRI data. This demonstrates the feasibility of ConFiG to generate realistic synthetic diffusion MRI data for developing and validating microstructure modelling approaches.

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We present ConFiG, a biologically motivated numerical phantom generator for white matter.

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ConFiG produces phantoms with state-of-the-art density and realistic microstructure.

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Diffusion MRI simulations in ConFiG phantoms are comparable to real dMRI signals.

High-gradient diffusion MRI reveals distinct estimates of axon diameter index within different white matter tracts in the in vivo human brain

Axon diameter and density are important microstructural metrics that offer valuable insight into the structural organization of white matter throughout the human brain. We report the systematic acquisition and analysis of a comprehensive diffusion MRI data set acquired with 300 mT/m maximum gradient strength in a cohort of 20 healthy human subjects that yields distinct and consistent patterns of axon diameter index in white matter tracts of arbitrary orientation. We use a straightforward, previously validated approach to estimating indices of axon diameter and volume fraction that involves interpolating the diffusion signal perpendicular to the principal fiber orientation and fitting a three-compartment model of intra-axonal, extra-axonal and free water diffusion. The resultant maps confirm the presence of larger diameter indices in the body of corpus callosum compared to the genu and splenium, as previously reported, and show larger axon diameter index in the corticospinal tracts compared to adjacent white matter tracts such as the cingulum. An anterior-to-posterior gradient in axon diameter index is also observed, with smaller diameter indices in the frontal lobes and larger diameter indices in the parieto-occipital white matter. These observations are consistent with known trends from prior histologic studies in humans and non-human primates. Rather than serving as fully quantitative measures of axon diameter and density, our results may be considered as axon diameter- and volume fraction-weighted images that appear to be modulated by the underlying microstructure and may capture broad trends in axonal size and packing density, acknowledging that the precise origin of such modulation requires further investigation that will be facilitated by the availability of high gradient strengths for in vivo human imaging.

AxTract: Toward microstructure informed tractography

Diffusion-weighted (DW) magnetic resonance imaging (MRI) tractography has become the tool of choice to probe the human brain's white matter in vivo. However, tractography algorithms produce a large number of erroneous streamlines (false positives), largely due to complex ambiguous tissue configurations. Moreover, the relationship between the resulting streamlines and the underlying white matter microstructure characteristics remains poorly understood. In this work, we introduce a new approach to simultaneously reconstruct white matter fascicles and characterize the apparent distribution of axon diameters within fascicles. To achieve this, our method, AxTract, takes full advantage of the recent development DW-MRI microstructure acquisition, modeling, and reconstruction techniques. This enables AxTract to separate parallel fascicles with different microstructure characteristics, hence reducing ambiguities in areas of complex tissue configuration. We report a decrease in the incidence of erroneous streamlines compared to the conventional deterministic tractography algorithms on simulated data. We also report an average increase in streamline density over 15 known fascicles of the 34 healthy subjects. Our results suggest that microstructure information improves tractography in crossing areas of the white matter. Moreover, AxTract provides additional microstructure information along the fascicle that can be studied alongside other streamline-based indices. Overall, AxTract provides the means to distinguish and follow white matter fascicles using their microstructure characteristics, bringing new insights into the white matter organization. This is a step forward in microstructure informed tractography, paving the way to a new generation of algorithms able to deal with intricate configurations of white matter fibers and providing quantitative brain connectivity analysis. Hum Brain Mapp 38:5485-5500, 2017. © 2017 Wiley Periodicals, Inc.

Assessing the validity of the approximation of diffusion-weighted-MRI signals from crossing fascicles by sums of signals from single fascicles

PURPOSE

To assess the validity of the superposition approximation for crossing fascicles, i.e., the assumption that the total diffusion-weighted MRI signal is the sum of the signals arising from each fascicle independently, even when the fascicles intermingle in a voxel.

METHODS

Monte Carlo simulations were used to study the impact of the approximation on the diffusion-weighted MRI signal and to assess whether this approximate model allows microstructural features of interwoven fascicles to be accurately estimated, despite signal differences.

RESULTS

Small normalized signal differences were observed, typically 10-3-10-2. The use of the approximation had little impact on the estimation of the crossing angle, the axonal density index, and the radius index in clinically realistic scenarios wherein the acquisition noise was the predominant source of errors. In the absence of noise, large systematic errors due to the superposition approximation only persisted for the radius index, mainly driven by a low sensitivity of diffusion-weighted MRI signals to small radii in general.

CONCLUSION

The use of the superposition approximation rather than a model of interwoven fascicles does not adversely impact the estimation of microstructural features of interwoven fascicles in most current clinical settings. Magn Reson Med 79:2332-2345, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Microstructure Imaging of Crossing (MIX) White Matter Fibers from diffusion MRI

Diffusion MRI (dMRI) reveals microstructural features of the brain white matter by quantifying the anisotropic diffusion of water molecules within axonal bundles. Yet, identifying features such as axonal orientation dispersion, density, diameter, etc., in complex white matter fiber configurations (e.g. crossings) has proved challenging. Besides optimized data acquisition and advanced biophysical models, computational procedures to fit such models to the data are critical. However, these procedures have been largely overlooked by the dMRI microstructure community and new, more versatile, approaches are needed to solve complex biophysical model fitting problems. Existing methods are limited to models assuming single fiber orientation, relevant to limited brain areas like the corpus callosum, or multiple orientations but without the ability to extract detailed microstructural features. Here, we introduce a new and versatile optimization technique (MIX), which enables microstructure imaging of crossing white matter fibers. We provide a MATLAB implementation of MIX, and demonstrate its applicability to general microstructure models in fiber crossings using synthetic as well as ex-vivo and in-vivo brain data.

Reliable Dual Tensor Model Estimation in Single and Crossing Fibers Based on Jeffreys Prior

Purpose

This paper presents and studies a framework for reliable modeling of diffusion MRI using a data-acquisition adaptive prior.

Methods

Automated relevance determination estimates the mean of the posterior distribution of a rank-2 dual tensor model exploiting Jeffreys prior (JARD). This data-acquisition prior is based on the Fisher information matrix and enables the assessment whether two tensors are mandatory to describe the data. The method is compared to Maximum Likelihood Estimation (MLE) of the dual tensor model and to FSL’s ball-and-stick approach.

Results

Monte Carlo experiments demonstrated that JARD’s volume fractions correlated well with the ground truth for single and crossing fiber configurations. In single fiber configurations JARD automatically reduced the volume fraction of one compartment to (almost) zero. The variance in fractional anisotropy (FA) of the main tensor component was thereby reduced compared to MLE. JARD and MLE gave a comparable outcome in data simulating crossing fibers. On brain data, JARD yielded a smaller spread in FA along the corpus callosum compared to MLE. Tract-based spatial statistics demonstrated a higher sensitivity in detecting age-related white matter atrophy using JARD compared to both MLE and the ball-and-stick approach.

Conclusions

The proposed framework offers accurate and precise estimation of diffusion properties in single and dual fiber regions.

T1 relaxometry of crossing fibres in the human brain

A comprehensive tract-based characterisation of white matter should include the ability to quantify myelin and axonal attributes irrespective of the complexity of fibre organisation within the voxel. Recently, a new experimental framework that combines inversion recovery and diffusion MRI, called inversion recovery diffusion tensor imaging (IR-DTI), was introduced and applied in an animal study. IR-DTI provides the ability to assign to each unique fibre population within a voxel a specific value of the longitudinal relaxation time, T₁, which is a proxy for myelin content. Here, we apply the IR-DTI approach to the human brain in vivo on 7 healthy subjects for the first time. We demonstrate that the approach is able to measure differential tract properties in crossing fibre areas, reflecting the different myelination of tracts. We also show that tract-specific T₁ has less inter-subject variability compared to conventional T₁ in areas of crossing fibres, suggesting increased specificity to distinct fibre populations. Finally we show in simulations that changes in myelination selectively affecting one fibre bundle in crossing fibre areas can potentially be detected earlier using IR-DTI.

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We apply the inversion recovery DTI approach to the human brain in vivo for the first time.

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We demonstrate that IR-DTI can measure tract-specific T1 in crossing fibres.

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IR-DTI T1 has less inter-subject variability compared to conventional T1 in crossing fibres.

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Changes in myelination affecting one fibre in crossing fibres can be detected earlier using IR-DTI.

Iterative Subspace Screening for Rapid Sparse Estimation of Brain Tissue Microstructural Properties

Diffusion magnetic resonance imaging (DMRI) is a powerful imaging modality due to its unique ability to extract microstructural information by utilizing restricted diffusion to probe compartments that are much smaller than the voxel size. Quite commonly, a mixture of models is fitted to the data to infer microstructural properties based on the estimated parameters. The fitting process is often non-linear and computationally very intensive. Recent work by Daducci et al. has shown that speed improvement of several orders of magnitude can be achieved by linearizing and recasting the fitting problem as a linear system, involving the estimation of the volume fractions associated with a set of diffusion basis functions that span the signal space. However, to ensure coverage of the signal space, sufficiently dense sampling of the parameter space is needed. This can be problematic because the number of basis functions increases exponentially with the number of parameters, causing computational intractability. We propose in this paper a method called iterative subspace screening (ISS) for tackling this ultrahigh dimensional problem. ISS requires only solving the problem in a medium-size subspace with a dimension that is much smaller than the original space spanned by all diffusion basis functions but is larger than the expected cardinality of the support of the solution. The solution obtained for this subspace is used to screen the basis functions to identify a new subspace that is pertinent to the target problem. These steps are performed iteratively to seek both the solution subspace and the solution itself. We apply ISS to the estimation of the fiber orientation distribution function (ODF) and demonstrate that it improves estimation robustness and accuracy.

Microstructural parameter estimation in vivo using diffusion MRI and structured prior information

Purpose

Diffusion MRI has recently been used with detailed models to probe tissue microstructure. Much of this work has been performed ex vivo with powerful scanner hardware, to gain sensitivity to parameters such as axon radius. By contrast, performing microstructure imaging on clinical scanners is extremely challenging.

Methods

We use an optimized dual spin‐echo diffusion protocol, and a Bayesian fitting approach, to obtain reproducible contrast (histogram overlap of up to 92%) in estimated maps of axon radius index in healthy adults at a modest, widely‐available gradient strength (35 mT m −1). A key innovation is the use of influential priors.

Results

We demonstrate that our priors can improve precision in axon radius estimates—a 7‐fold reduction in voxelwise coefficient of variation in vivo—without significant bias. Our results may reflect true axon radius differences between white matter regions, but this interpretation should be treated with caution due to the complexity of the tissue relative to our model.

Conclusions

Some sensitivity to relatively large axons (3–15 μm) may be available at clinical field and gradient strengths. Future applications at higher gradient strength will benefit from the favorable eddy current properties of the dual spin‐echo sequence, and greater precision available with suitable priors. Magn Reson Med, 2015. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Magn Reson Med 75:1787–1796, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance.

Resolving relaxometry and diffusion properties within the same voxel in the presence of crossing fibres by combining inversion recovery and diffusion-weighted acquisitions

Purpose

A comprehensive image‐based characterization of white matter should include the ability to quantify myelin and axonal attributes irrespective of the complexity of fibre organization within the voxel. While progress has been made with diffusion MRI‐based approaches to measure axonal morphology, to date available myelin metrics simply assign a single scalar value to the voxel, reflecting some form of average of its constituent fibres. Here, a new experimental framework that combines diffusion MRI and relaxometry is introduced. It provides, for the first time, the ability to assign to each unique fibre system within a voxel, a unique value of the longitudinal relaxation time, T₁, which is largely influenced by the myelin content.

Methods

We demonstrate the method through simulations, in a crossing fibres phantom, in fixed brains and in vivo.

Results

The method is capable of recovering unique values of T₁ for each fibre population.

Conclusion

The ability to extract fibre‐specific relaxometry properties will provide enhanced specificity and, therefore, sensitivity to differences in white matter architecture, which will be invaluable in many neuroimaging studies. Further the enhanced specificity should ultimately lead to earlier diagnosis and access to treatment in a range of white matter diseases where axons are affected. Magn Reson Med 75:372–380, 2016. © 2015 The Authors. Magnetic Resonance in Medicine Published by Wiley Periodicals, Inc. on behalf of International Society of Medicine in Resonance.

Learning a reliable estimate of the number of fiber directions in diffusion MRI

Having to determine an adequate number of fiber directions is a fundamental limitation of multi-compartment models in diffusion MRI. This paper proposes a novel strategy to approach this problem, based on simulating data that closely follows the characteristics of the measured data. This provides the ground truth required to determine the number of directions that optimizes a formal measure of accuracy, while allowing us to transfer the result to real data by support vector regression. The method is shown to result in plausible and reproducible decisions on three repeated scans of the same subject. When combined with the ball-and-stick model, it produces directional estimates comparable to constrained spherical deconvolution, but with significantly smaller variance between re-scans, and at a reduced computational cost.