Orientationally invariant indices of axon diameter and density from diffusion MRI

The dot-compartment revealed? Diffusion MRI with ultra-strong gradients and spherical tensor encoding in the living human brain

The so-called “dot-compartment” is conjectured in diffusion MRI to represent small spherical spaces, such as cell bodies, in which the diffusion is restricted in all directions. Previous investigations inferred its existence from data acquired with directional diffusion encoding which does not permit a straightforward separation of signals from ‘sticks’ (axons) and signals from ‘dots’. Here we combine isotropic diffusion encoding with ultra-strong diffusion gradients (240 ​mT/m) to achieve high diffusion-weightings with high signal to noise ratio, while suppressing signal arising from anisotropic water compartments with significant mobility along at least one axis (e.g., axons). A dot-compartment, defined to have apparent diffusion coefficient equal to zero and no exchange, would result in a non-decaying signal at very high b-values (b≳7000s/mm2). With this unique experimental setup, a residual yet slowly decaying signal above the noise floor for b-values as high as 15000s/mm2 was seen clearly in the cerebellar grey matter (GM), and in several white matter (WM) regions to some extent. Upper limits of the dot-signal-fraction were estimated to be 1.8% in cerebellar GM and 0.5% in WM. By relaxing the assumption of zero diffusivity, the signal at high b-values in cerebellar GM could be represented more accurately by an isotropic water pool with a low apparent diffusivity of 0.12 μm2/ms and a substantial signal fraction of 9.7%. The T2 of this component was estimated to be around 61ms. This remaining signal at high b-values has potential to serve as a novel and simple marker for isotropically-restricted water compartments in cerebellar GM.

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The “dot-compartment” is conjectured in diffusion MRI to represent e.g. cell bodies.

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We combine isotropic encoding with ultra-strong gradients to study the dot-compartment.

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A slowly decaying signal for high b-values was seen in cerebellar GM.

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An apparent diffusivity of 0.12 and signal fraction of 9.7% were estimated.

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The signal could serve as a novel and simple marker for spherical compartments.

On the need for bundle-specific microstructure kernels in diffusion MRI

Probing microstructure with diffusion magnetic resonance imaging (dMRI) on a scale orders of magnitude below the imaging resolution relies on biophysical modelling of the signal response in the tissue. The vast majority of these biophysical models of diffusion in white matter assume that the measured dMRI signal is the sum of the signals emanating from each of the constituent compartments, each of which exhibits a distinct behaviour in the b-value and/or orientation domain. Many of these models further assume that the dMRI behaviour of the oriented compartments (e.g. the intra-axonal space) is identical between distinct fibre populations, at least at the level of a single voxel. This implicitly assumes that any potential biological differences between fibre populations are negligible, at least as far as is measurable using dMRI. Here, we validate this assumption by means of a voxel-wise, model-free signal decomposition that, under the assumption above and in the absence of noise, is shown to be rank-1. We evaluate the effect size of signal components beyond this rank-1 representation and use permutation testing to assess their significance. We conclude that in the healthy adult brain, the dMRI signal is adequately represented by a rank-1 model, implying that biologically more realistic, but mathematically more complex fascicle-specific microstructure models do not capture statistically significant or anatomically meaningful structure, even in extended high-b diffusion MRI scans.

Estimating axon conduction velocity in vivo from microstructural MRI

The conduction velocity (CV) of action potentials along axons is a key neurophysiological property central to neural communication. The ability to estimate CV in humans in vivo from non-invasive MRI methods would therefore represent a significant advance in neuroscience. However, there are two major challenges that this paper aims to address: (1) Much of the complexity of the neurophysiology of action potentials cannot be captured with currently available MRI techniques. Therefore, we seek to establish the variability in CV that can be captured when predicting CV purely from parameters that have been reported to be estimatable from MRI: inner axon diameter (AD) and g-ratio. (2) errors inherent in existing MRI-based biophysical models of tissue will propagate through to estimates of CV, the extent to which is currently unknown. Issue (1) is investigated by performing a sensitivity analysis on a comprehensive model of axon electrophysiology and determining the relative sensitivity to various morphological and electrical parameters. The investigations suggest that 85% of the variance in CV is accounted for by variation in AD and g-ratio. The observed dependency of CV on AD and g-ratio is well characterised by the previously reported model by Rushton. Issue (2) is investigated through simulation of diffusion and relaxometry MRI data for a range of axon morphologies, applying models of restricted diffusion and relaxation processes to derive estimates of axon volume fraction (AVF), AD and g-ratio and estimating CV from the derived parameters. The results show that errors in the AVF have the biggest detrimental impact on estimates of CV, particularly for sparse fibre populations (AVF<0.3). For our equipment set-up and acquisition protocol, CV estimates are most accurate (below 5% error) where AVF is above 0.3, g-ratio is between 0.6 and 0.85 and AD is high (above 4μm). CV estimates are robust to errors in g-ratio estimation but are highly sensitive to errors in AD estimation, particularly where ADs are small. We additionally show CV estimates in human corpus callosum in a small number of subjects. In conclusion, we demonstrate accurate CV estimates are possible in regions of the brain where AD is sufficiently large. Problems with estimating ADs for smaller axons presents a problem for estimating CV across the whole CNS and should be the focus of further study.

Single- and double-Diffusion encoding MRI for studying ex vivo apparent axon diameter distribution in spinal cord white matter

Mapping average axon diameter (AAD) and axon diameter distribution (ADD) in neuronal tissues non-invasively is a challenging task that may have a tremendous effect on our understanding of the normal and diseased central nervous system (CNS). Water diffusion is used to probe microstructure in neuronal tissues, however, the different water populations and barriers that are present in these tissues turn this into a complex task. Therefore, it is not surprising that recently we have witnessed a burst in the development of new approaches and models that attempt to obtain, non-invasively, detailed microstructural information in the CNS. In this work, we aim at challenging and comparing the microstructural information obtained from single diffusion encoding (SDE) with double diffusion encoding (DDE) MRI. We first applied SDE and DDE MR spectroscopy (MRS) on microcapillary phantoms and then applied SDE and DDE MRI on an ex vivo porcine spinal cord (SC), using similar experimental conditions. The obtained diffusion MRI data were fitted by the same theoretical model, assuming that the signal in every voxel can be approximated as the superposition of a Gaussian-diffusing component and a series of restricted components having infinite cylindrical geometries. The diffusion MRI results were then compared with histological findings. We found a good agreement between the fittings and the experimental data in white matter (WM) voxels of the SC in both diffusion MRI methods. The microstructural information and apparent AADs extracted from SDE MRI were found to be similar or somewhat larger than those extracted from DDE MRI especially when the diffusion time was set to 40 ms. The apparent ADDs extracted from SDE and DDE MRI show reasonable agreement but somewhat weaker correspondence was observed between the diffusion MRI results and histology. The apparent subtle differences between the microstructural information obtained from SDE and DDE MRI are briefly discussed.

ActiveAxADD : Toward non-parametric and orientationally invariant axon diameter distribution mapping using PGSE

PURPOSE

Non-invasive axon diameter distribution (ADD) mapping using diffusion MRI is an ill-posed problem. Current ADD mapping methods require knowledge of axon orientation before performing the acquisition. Instead, ActiveAx uses a 3D sampling scheme to estimate the orientation from the signal, providing orientationally invariant estimates. The mean diameter is estimated instead of the distribution for the solution to be tractable. Here, we propose an extension (ActiveAx_ADD ) that provides non-parametric and orientationally invariant estimates of the whole distribution.

THEORY

The accelerated microstructure imaging with convex optimization (AMICO) framework accelerates mean diameter estimation using a linear formulation combined with Tikhonov regularization to stabilize the solution. Here, we implement a new formulation (ActiveAx_ADD ) that uses Laplacian regularization to provide robust estimates of the whole ADD.

METHODS

The performance of ActiveAx_ADD was evaluated using Monte Carlo simulations on synthetic white matter samples mimicking axon distributions reported in histological studies.

RESULTS

ActiveAx_ADD provided robust ADD reconstructions when considering the isolated intra-axonal signal. However, our formulation inherited some common microstructure imaging limitations. When accounting for the extra axonal compartment, estimated ADDs showed spurious peaks and increased variability because of the difficulty of disentangling intra and extra axonal contributions.

CONCLUSION

Laplacian regularization solves the ill-posedness regarding the intra axonal compartment. ActiveAx_ADD can potentially provide non-parametric and orientationally invariant ADDs from isolated intra-axonal signals. However, further work is required before ActiveAx_ADD can be applied to real data containing extra-axonal contributions, as disentangling the 2 compartment appears to be an overlooked challenge that affects microstructure imaging methods in general.

The Dmipy Toolbox: Diffusion MRI Multi-Compartment Modeling and Microstructure Recovery Made Easy

Non-invasive estimation of brain microstructure features using diffusion MRI (dMRI)—known as Microstructure Imaging—has become an increasingly diverse and complicated field over the last decades. Multi-compartment (MC)-models, representing the measured diffusion signal as a linear combination of signal models of distinct tissue types, have been developed in many forms to estimate these features. However, a generalized implementation of MC-modeling as a whole, providing deeper insights in its capabilities, remains missing. To address this fact, we present Diffusion Microstructure Imaging in Python (Dmipy), an open-source toolbox implementing PGSE-based MC-modeling in its most general form. Dmipy allows on-the-fly implementation, signal modeling, and optimization of any user-defined MC-model, for any PGSE acquisition scheme. Dmipy follows a “building block”-based philosophy to Microstructure Imaging, meaning MC-models are modularly constructed to include any number and type of tissue models, allowing simultaneous representation of a tissue's diffusivity, orientation, volume fractions, axon orientation dispersion, and axon diameter distribution. In particular, Dmipy is geared toward facilitating reproducible, reliable MC-modeling pipelines, often allowing the whole process from model construction to parameter map recovery in fewer than 10 lines of code. To demonstrate Dmipy's ease of use and potential, we implement a wide range of well-known MC-models, including IVIM, AxCaliber, NODDI(x), Bingham-NODDI, the spherical mean-based SMT and MC-MDI, and spherical convolution-based single- and multi-tissue CSD. By allowing parameter cascading between MC-models, Dmipy also facilitates implementation of advanced approaches like CSD with voxel-varying kernels and single-shell 3-tissue CSD. By providing a well-tested, user-friendly toolbox that simplifies the interaction with the otherwise complicated field of dMRI-based Microstructure Imaging, Dmipy contributes to more reproducible, high-quality research.

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.

Extra-axonal restricted diffusion as an in-vivo marker of reactive microglia

Reactive microgliosis is an important pathological component of neuroinflammation and has been implicated in a wide range of brain diseases including brain tumors, multiple sclerosis, Parkinson's disease, Alzheimer's disease, and schizophrenia. Mapping reactive microglia in-vivo is often performed with PET scanning whose resolution, cost, and availability prevent its widespread use. The advent of diffusion compartment imaging (DCI) to probe tissue microstructure in vivo holds promise to map reactive microglia using MRI scanners. But this potential has never been demonstrated. In this paper, we performed longitudinal DCI in rats that underwent dorsal root axotomy triggering Wallerian degeneration of axons-a pathological process which reliably activates microglia. After the last DCI at 51 days, rats were sacrificed and histology with Iba-1 immunostaining for microglia was performed. The fraction of extra-axonal restricted diffusion from DCI was found to follow the expected temporal dynamics of reactive microgliosis. Furthermore, a strong and significant correlation between this parameter and histological measurement of microglial density was observed. These findings strongly suggest that extra-axonal restricted diffusion is an in-vivo marker of reactive microglia. They pave the way for MRI-based microglial mapping which may be important to characterize the pathogenesis of neurological and psychiatric diseases.

Optimizing the intrinsic parallel diffusivity in NODDI: An extensive empirical evaluation

Purpose

NODDI is widely used in parameterizing microstructural brain properties. The model includes three signal compartments: intracellular, extracellular, and free water. The neurite compartment intrinsic parallel diffusivity (d_∥) is set to 1.7 μm²⋅ms⁻¹, though the effects of this assumption have not been extensively explored. This work investigates the optimality of d_∥ = 1.7 μm²⋅ms⁻¹ under varying imaging protocol, age groups, sex, and tissue type in comparison to other biologically plausible values of d_∥.

Methods

Model residuals were used as the optimality criterion. The model residuals were evaluated in function of d_∥ over the range from 0.5 to 3.0 μm²⋅ms⁻¹. This was done with respect to tissue type (i.e., white matter versus gray matter), sex, age (infancy to late adulthood), and diffusion-weighting protocol (maximum b-value). Variation in the estimated parameters with respect to d_∥ was also explored.

Results

Results show d_∥ = 1.7 μm²⋅ms⁻¹ is appropriate for adult brain white matter but it is suboptimal for gray matter with optimal values being significantly lower. d_∥ = 1.7 μm²⋅ms⁻¹ was also suboptimal in the infant brain for both white and gray matter with optimal values being significantly lower. Minor optimum d_∥ differences were observed versus diffusion protocol. No significant sex effects were observed. Additionally, changes in d_∥ resulted in significant changes to the estimated NODDI parameters.

Conclusion

The default (d_∥) of 1.7 μm²⋅ms⁻¹ is suboptimal in gray matter and infant brains.

Exercise ameliorates deficits in neural microstructure in a Disc1 model of psychiatric illness

Recent studies have investigated the effectiveness of aerobic exercise to improve physical and mental health outcomes in schizophrenia; however, few have explicitly explored the impact of aerobic exercise on neural microstructure, which is hypothesized to mediate the behavioral changes observed. Neural microstructure is influenced by numerous genetic factors including DISC1, which is a major molecular scaffold protein that interacts with partners like GSK3β, NDEL1, and PDE4. DISC1 has been shown to play a role in neurogenesis, neuronal migration, neuronal maturation, and synaptic signaling. As with other genetic variants that present an increased risk for disease, mutations of the DISC1 gene have been implicated in the molecular intersection of schizophrenia and numerous other major psychiatric illnesses. This study investigated whether short-term exercise recovers deficits in neural microstructure in a novel genetic Disc1 svΔ2 rat model. Disc1 svΔ2 animals and age- and sex-matched controls were subjected to a treadmill exercise protocol. Subsequent ex-vivo diffusion tensor imaging (DTI) and neurite orientation dispersion and density imaging (NODDI) compared neural microstructure in regions of interest (ROI) between sedentary and exercise wild-type animals and between sedentary and exercise Disc1 svΔ2 animals. Short-term exercise uncovered no significant differences in neural microstructure between sedentary and exercise control animals but did lead to significant differences between sedentary and exercise Disc1 svΔ2 animals in neocortex, basal ganglia, corpus callosum, and external capsule, suggesting a positive benefit derived from a short-term exercise regimen. Our findings suggest that Disc1 svΔ2 animals are more sensitive to the effects of short-term exercise and highlight the ameliorating potential of positive treatment interventions such as exercise on neural microstructure in genetic backgrounds of psychiatric disease susceptibility.

Mechanisms Linking White Matter Lesions, Tract Integrity, and Depression in Alzheimer Disease

OBJECTIVE

Late-life depression involves the disconnection of white matter tracts that regulate mood. A pathogenic link between poor tract integrity and depressive symptoms is believed to be white matter lesions (WML), however the mechanisms linking tract integrity, WML, and depression remains unexplored. The authors sought to identify whether the association between reduced tract integrity and depressive symptoms is mediated by WML in patients with Alzheimer disease (AD), and whether individual characteristics moderate this effect.

METHODS

This was a cross-sectional study in a tertiary memory clinic. A total of 91 patients with mild AD and 79 healthy elderly, comparable in depressive symptoms, white matter hyperintensities (WMH) volume, cardiovascular risk, age, and sex were chosen. Tract integrity was assessed using diffusion tensor imaging, WML were indexed as WMH, measured using fluid-attenuation inversion recovery imaging, and depressive symptoms were measured with the informant-based Geriatric Depression Scale.

RESULTS

In patients with mild AD, reduced tract integrity in right hemispheric cortical-subcortical tracts and the genu of the corpus callosum was moderately associated with depressive symptoms. This association was fully mediated by WML. Moderation analysis indicated that old age strengthened the association between all tracts and depressive symptoms, as mediated by WML. In cognitively healthy elderly, neither tracts nor WML were related to depressive symptoms.

CONCLUSION

Reduced tract integrity may be important but not sufficient for the manifestation of depressive symptoms in mild AD. Instead, WML may drive the pathogenic link between reduced tract integrity and depressive symptoms.

Histological validation of per-bundle water diffusion metrics within a region of fiber crossing following axonal degeneration

Micro-architectural characteristics of white matter can be inferred through analysis of diffusion-weighted magnetic resonance imaging (dMRI). The diffusion-dependent signal can be analyzed through several methods, with the tensor model being the most frequently used due to its straightforward interpretation and low requirements for acquisition parameters. While valuable information can be gained from the tensor-derived metrics in regions of homogeneous tissue organization, this model does not provide reliable microstructural information at crossing fiber regions, which are pervasive throughout human white matter. Several multiple fiber models have been proposed that seem to overcome the limitations of the tensor, with few providing per-bundle dMRI-derived metrics. However, biological interpretations of such metrics are limited by the lack of histological confirmation. To this end, we developed a straightforward biological validation framework. Unilateral retinal ischemia was induced in ten rats, which resulted in axonal (Wallerian) degeneration of the corresponding optic nerve, while the contralateral was left intact; the intact and injured axonal populations meet at the optic chiasm as they cross the midline, generating a fiber crossing region in which each population has different diffusion properties. Five rats served as controls. High-resolution ex vivo dMRI was acquired five weeks after experimental procedures. We correlated and compared histology to per-bundle descriptors derived from three methodologies for dMRI analysis (constrained spherical deconvolution and two multi-tensor representations). We found a tight correlation between axonal density (as evaluated through automatic segmentation of histological sections) with per-bundle apparent fiber density and fractional anisotropy (derived from dMRI). The multi-fiber methods explored were able to correctly identify the damaged fiber populations in a region of fiber crossings (chiasm). Our results provide validation of metrics that bring substantial and clinically useful information about white-matter tissue at crossing fiber regions. Our proposed framework is useful to validate other current and future dMRI methods.

Diffusion MRI microstructural models in the cervical spinal cord - Application, normative values, and correlations with histological analysis

Multi-compartment tissue modeling using diffusion magnetic resonance imaging has proven valuable in the brain, offering novel indices sensitive to the tissue microstructural environment in vivo on clinical MRI scanners. However, application, characterization, and validation of these models in the spinal cord remain relatively under-studied. In this study, we apply a diffusion "signal" model (diffusion tensor imaging, DTI) and two commonly implemented "microstructural" models (neurite orientation dispersion and density imaging, NODDI; spherical mean technique, SMT) in the human cervical spinal cord of twenty-one healthy controls. We first provide normative values of DTI, SMT, and NODDI indices in a number of white matter ascending and descending pathways, as well as various gray matter regions. We then aim to validate the sensitivity and specificity of these diffusion-derived contrasts by relating these measures to indices of the tissue microenvironment provided by a histological template. We find that DTI indices are sensitive to a number of microstructural features, but lack specificity. The microstructural models also show sensitivity to a number of microstructure features; however, they do not capture the specific microstructural features explicitly modelled. Although often regarded as a simple extension of the brain in the central nervous system, it may be necessary to re-envision, or specifically adapt, diffusion microstructural models for application to the human spinal cord with clinically feasible acquisitions - specifically, adjusting, adapting, and re-validating the modeling as it relates to both theory (i.e. relevant biology, assumptions, and signal regimes) and parameter estimation (for example challenges of acquisition, artifacts, and processing).

On using signal magnitude in diffusion magnetic resonance measurements of restricted motion

Tissue microstructure has significance as a biomarker, however its accurate inference with diffusion magnetic resonance (MR) is still an open problem. With few exceptions, diffusion weighted (DW) MR models either process diffusion MR data using signal magnitude, whereby microstructural information is forcefully confined to symmetry due to Fourier transform properties, or directly use symmetric basis expansions. Herein, information loss from magnitude utilization is demonstrated by numerically simulating particles undergoing diffusion near a fully reflective infinite wall and an orthogonal corner. Simulation results show that the loss of the Hermitian property when using signal magnitude impedes DW-MR from accurately inferring microstructural information in both of the geometries.

Resolving degeneracy in diffusion MRI biophysical model parameter estimation using double diffusion encoding

PURPOSE

Biophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, it has been shown recently that, in the general Standard Model, parameter estimation from dMRI data is ill-conditioned even when very high b-values are applied. We analyze this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from single diffusion encoding (SDE) to double diffusion encoding (DDE) resolves the ill-posedness for intermediate diffusion weightings, producing an increase in accuracy and precision of the parameter estimation.

METHODS

We analyze theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions.

RESULTS

We prove analytically that DDE provides invariant information non-accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space.

CONCLUSIONS

DDE adds additional information for estimating the model parameters, unexplored by SDE. We show, as an example, that this is sufficient to solve the previously reported degeneracies in the NODDIDA model parameter estimation.

Dimensionality reduction of diffusion MRI measures for improved tractometry of the human brain

Various diffusion MRI (dMRI) measures have been proposed for characterising tissue microstructure over the last 15 years. Despite the growing number of experiments using different dMRI measures in assessments of white matter, there has been limited work on: 1) examining their covariance along specific pathways; and on 2) combining these different measures to study tissue microstructure. Indeed, it quickly becomes intractable for existing analysis pipelines to process multiple measurements at each voxel and at each vertex forming a streamline, highlighting the need for new ways to visualise or analyse such high-dimensional data. In a sample of 36 typically developing children aged 8–18 years, we profiled various commonly used dMRI measures across 22 brain pathways. Using a data-reduction approach, we identified two biologically-interpretable components that capture 80% of the variance in these dMRI measures. The first derived component captures properties related to hindrance and restriction in tissue microstructure, while the second component reflects characteristics related to tissue complexity and orientational dispersion. We then demonstrate that the components generated by this approach preserve the biological relevance of the original measurements by showing age-related effects across developmentally sensitive pathways. In summary, our findings demonstrate that dMRI analyses can benefit from dimensionality reduction techniques, to help disentangling the neurobiological underpinnings of white matter organisation.

Diffusion MRI in the brain - Theory and concepts

Over the past two decades, diffusion MRI has become an essential tool in neuroimaging investigations. This is due to its sensitivity to the motion of water molecules as they diffuse through the microstructural environment, allowing diffusion MRI to be used as a 'probe' of tissue microstructure. Furthermore, this sensitivity is strongly direction-dependent, notably in brain white matter, due to the alignment of structures that restrict or hinder the motion of water molecules, notably axonal membranes. This provides a means of inferring the orientation of fibres in vivo, and by use of appropriate fibre-tracking algorithms, of delineating the path of white matter tracts in the brain. The ability to perform so-called tractography in humans in vivo non-invasively is unique to diffusion MRI, and is now used in applications such as neurosurgery planning and more broadly within investigations of brain connectomics. This review describes the theory and concepts of diffusion MRI and describes its most important areas of application in the brain, with a strong focus on tractography.

Fingerprinting Orientation Distribution Functions in diffusion MRI detects smaller crossing angles

Diffusion tractography is routinely used to study white matter architecture and brain connectivity in vivo. A key step for successful tractography of neuronal tracts is the correct identification of tract directions in each voxel. Here we propose a fingerprinting-based methodology to identify these fiber directions in Orientation Distribution Functions, dubbed ODF-Fingerprinting (ODF-FP). In ODF-FP, fiber configurations are selected based on the similarity between measured ODFs and elements in a pre-computed library. In noisy ODFs, the library matching algorithm penalizes the more complex fiber configurations. ODF simulations and analysis of bootstrapped partial and whole-brain in vivo datasets show that the ODF-FP approach improves the detection of fiber pairs with small crossing angles while maintaining fiber direction precision, which leads to better tractography results. Rather than focusing on the ODF maxima, the ODF-FP approach uses the whole ODF shape to infer fiber directions to improve the detection of fiber bundles with small crossing angle. The resulting fiber directions aid tractography algorithms in accurately displaying neuronal tracts and calculating brain connectivity.

Along-axon diameter variation and axonal orientation dispersion revealed with 3D electron microscopy: implications for quantifying brain white matter microstructure with histology and diffusion MRI

Tissue microstructure modeling of diffusion MRI signal is an active research area striving to bridge the gap between macroscopic MRI resolution and cellular-level tissue architecture. Such modeling in neuronal tissue relies on a number of assumptions about the microstructural features of axonal fiber bundles, such as the axonal shape (e.g., perfect cylinders) and the fiber orientation dispersion. However, these assumptions have not yet been validated by sufficiently high-resolution 3-dimensional histology. Here, we reconstructed sequential scanning electron microscopy images in mouse brain corpus callosum, and introduced a random-walker (RaW)-based algorithm to rapidly segment individual intra-axonal spaces and myelin sheaths of myelinated axons. Confirmed by a segmentation based on human annotations initiated with conventional machine-learning-based carving, our semi-automatic algorithm is reliable and less time-consuming. Based on the segmentation, we calculated MRI-relevant estimates of size-related parameters (inner axonal diameter, its distribution, along-axon variation, and myelin g-ratio), and orientation-related parameters (fiber orientation distribution and its rotational invariants; dispersion angle). The reported dispersion angle is consistent with previous 2-dimensional histology studies and diffusion MRI measurements, while the reported diameter exceeds those in other mouse brain studies. Furthermore, we calculated how these quantities would evolve in actual diffusion MRI experiments as a function of diffusion time, thereby providing a coarse-graining window on the microstructure, and showed that the orientation-related metrics have negligible diffusion time-dependence over clinical and pre-clinical diffusion time ranges. However, the MRI-measured inner axonal diameters, dominated by the widest cross sections, effectively decrease with diffusion time by ~ 17% due to the coarse-graining over axonal caliber variations. Furthermore, our 3d measurement showed that there is significant variation of the diameter along the axon. Hence, fiber orientation dispersion estimated from MRI should be relatively stable, while the "apparent" inner axonal diameters are sensitive to experimental settings, and cannot be modeled by perfectly cylindrical axons.

Effects of sustained cognitive activity on white matter microstructure and cognitive outcomes in healthy middle-aged adults: A systematic review

Adults who remain cognitively active may be protected from age-associated changes in white matter (WM) and cognitive decline. To determine if cognitive activity is a precursor for WM plasticity, the available literature was systematically searched for Region of Interest (ROI) and whole-brain studies assessing the efficacy of cognitive training (CT) on WM microstructure using Diffusion Tensor Imaging (DTI) in healthy adults (> 40 years). Seven studies were identified and included in this review. Results suggest there are beneficial effects to WM microstructure after CT in frontal and medial brain regions, with some studies showing improved performance in cognitive outcomes. Benefits of CT were shown to be protective against age-related WM microstructure decline by either maintaining or improving WM after training. These results have implications for determining the capacity for training-dependent WM plasticity in older adults and whether CT can be utilised to prevent age-associated cognitive decline. Additional studies with standardised training and imaging protocols are needed to confirm these outcomes.

Nonparenchymal fluid is the source of increased mean diffusivity in preclinical Alzheimer's disease

Introduction

Although increased mean diffusivity of the white matter has been repeatedly linked to Alzheimer’s disease pathology, the underlying mechanism is not known.

Methods

Here, we used ADNI-3 multishell diffusion magnetic resonance imaging data to separate the diffusion signal of the parenchyma from less hindered fluid pools within the white matter such as perivascular space fluid and fluid-filled cavities.

Results

We found that the source of the pathological increase of the mean diffusivity is the increased nonparenchymal fluid, often found in lacunes and perivascular spaces. In this cohort, the cognitive decline was significantly associated with the fluid increase and not with the microstructural changes of the white matter parenchyma itself. The white matter fluid increase was dominantly observed in the sagittal stratum and anterior thalamic radiation.

Discussion

These findings are positive steps toward understanding the pathophysiology of white matter alteration and its role in the cognitive decline.

Neurite orientation dispersion and density imaging of mouse brain microstructure

Advanced biophysical models like neurite orientation dispersion and density imaging (NODDI) have been developed to estimate the microstructural complexity of voxels enriched in dendrites and axons for both in vivo and ex vivo studies. NODDI metrics derived from high spatial and angular resolution diffusion MRI using the fixed mouse brain as a reference template have not yet been reported due in part to the extremely long scan time required. In this study, we modified the three-dimensional diffusion-weighted spin-echo pulse sequence for multi-shell and undersampling acquisition to reduce the scan time. This allowed us to acquire several exhaustive datasets that would otherwise not be attainable. NODDI metrics were derived from a complex 8-shell diffusion (1000-8000 s/mm²) dataset with 384 diffusion gradient-encoding directions at 50 µm isotropic resolution. These provided a foundation for exploration of tradeoffs among acquisition parameters. A three-shell acquisition strategy covering low, medium, and high b values with at least angular resolution of 64 is essential for ex vivo NODDI experiments. The good agreement between neurite density index (NDI) and the orientation dispersion index (ODI) with the subsequent histochemical analysis of myelin and neuronal density highlights that NODDI could provide new insight into the microstructure of the brain. Furthermore, we found that NDI is sensitive to microstructural variations in the corpus callosum using a well-established demyelination cuprizone model. The study lays the ground work for developing protocols for routine use of high-resolution NODDI method in characterizing brain microstructure in mouse models.

Brain networks and their relevance for stroke rehabilitation

Stroke has long been regarded as focal disease with circumscribed damage leading to neurological deficits. However, advances in methods for assessing the human brain and in statistics have enabled new tools for the examination of the consequences of stroke on brain structure and function. Thereby, it has become evident that stroke has impact on the entire brain and its network properties and can therefore be considered as a network disease. The present review first gives an overview of current methodological opportunities and pitfalls for assessing stroke-induced changes and reorganization in the human brain. We then summarize principles of plasticity after stroke that have emerged from the assessment of networks. Thereby, it is shown that neurological deficits do not only arise from focal tissue damage but also from local and remote changes in white-matter tracts and in neural interactions among wide-spread networks. Similarly, plasticity and clinical improvements are associated with specific compensatory structural and functional patterns of neural network interactions. Innovative treatment approaches have started to target such network patterns to enhance recovery. Network assessments to predict treatment response and to individualize rehabilitation is a promising way to enhance specific treatment effects and overall outcome after stroke.

Fractional Order Complexity Model of the Diffusion Signal Decay in MRI

Fractional calculus models are steadily being incorporated into descriptions of diffusion in complex, heterogeneous materials. Biological tissues, when viewed using diffusion-weighted, magnetic resonance imaging (MRI), hinder and restrict the diffusion of water at the molecular, sub-cellular, and cellular scales. Thus, tissue features can be encoded in the attenuation of the observed MRI signal through the fractional order of the time- and space-derivatives. Specifically, in solving the Bloch-Torrey equation, fractional order imaging biomarkers are identified that connect the continuous time random walk model of Brownian motion to the structure and composition of cells, cell membranes, proteins, and lipids. In this way, the decay of the induced magnetization is influenced by the micro- and meso-structure of tissues, such as the white and gray matter of the brain or the cortex and medulla of the kidney. Fractional calculus provides new functions (Mittag-Leffler and Kilbas-Saigo) that characterize tissue in a concise way. In this paper, we describe the exponential, stretched exponential, and fractional order models that have been proposed and applied in MRI, examine the connection between the model parameters and the underlying tissue structure, and explore the potential for using diffusion-weighted MRI to extract biomarkers associated with normal growth, aging, and the onset of disease.

From micro- to macro-structures in multiple sclerosis: what is the added value of diffusion imaging

Diffusion imaging has been instrumental in understanding damage to the central nervous system as a result of its sensitivity to microstructural changes. Clinical applications of diffusion imaging have grown exponentially over the past couple of decades in many neurological and neurodegenerative diseases, such as multiple sclerosis (MS). For several reasons, MS has been extensively researched using advanced neuroimaging techniques, which makes it an 'example disease' to illustrate the potential of diffusion imaging for clinical applications. In addition, MS pathology is characterized by several key processes competing with each other, such as inflammation, demyelination, remyelination, gliosis and axonal loss, enabling the specificity of diffusion to be challenged. In this review, we describe how diffusion imaging can be exploited to investigate micro-, meso- and macro-scale properties of the brain structure and discuss how they are affected by different pathological substrates. Conclusions from the literature are that larger studies are needed to confirm the exciting results from initial investigations before current trends in diffusion imaging can be translated to the neurology clinic. Also, for a comprehensive understanding of pathological processes, it is essential to take a multiple-level approach, in which information at the micro-, meso- and macroscopic scales is fully integrated.

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.

Towards a 'resolution limit' for DW-MRI tumor microstructural models: A simulation study investigating the feasibility of distinguishing between microstructural changes

PURPOSE

To determine the feasibility of extracting sufficiently precise estimates of cell radius, R, and intracellular volume fraction, fi , from DW-MRI data in order to distinguish between specific microstructural changes tissue may undergo, specifically focusing on cell death in tumors.

METHODS

Simulations with optimized and non-optimized clinical acquisitions were performed for a range of microstructures, using a two-compartment model. The ability to distinguish between (i) cell shrinkage with cell density constant, mimicking apoptosis, and (ii) cell size constant with cell density decreasing, mimicking loss of cells, was evaluated based on the precision of simulated parameter estimates. Relationships between parameter precision, SNR, and the magnitude of specific parameter changes, were used to infer SNR requirements for detecting changes.

RESULTS

Accuracy and precision depended on microstructural properties, SNR, and the acquisition protocol. The main benefit of optimized acquisitions tended to be improved accuracy and precision of R, particularly for small cells. In most cases considered, higher SNR was required for detecting changes in R than for changes in fi .

CONCLUSIONS

Given the relative changes in R and fi due to apoptosis, simulations indicate that, for a range of microstructures, detecting changes in R require higher SNR than detecting changes in fi , and that such SNR is typically not achieved in clinical data. This suggests that if apoptotic cell size decreases are to be detected in clinical settings, improved SNR is required. Comparing measurement precision with the magnitude of expected biological changes should form part of the validation process for potential biomarkers.

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.

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

We review, systematize and discuss models of diffusion in neuronal tissue, by putting them into an overarching physical context of coarse-graining over an increasing diffusion length scale. From this perspective, we view research on quantifying brain microstructure as occurring along three major avenues. The first avenue focusses on transient, or time-dependent, effects in diffusion. These effects signify the gradual coarse-graining of tissue structure, which occurs qualitatively differently in different brain tissue compartments. We show that transient effects contain information about the relevant length scales for neuronal tissue, such as the packing correlation length for neuronal fibers, as well as the degree of structural disorder along the neurites. The second avenue corresponds to the long-time limit, when the observed signal can be approximated as a sum of multiple nonexchanging anisotropic Gaussian components. Here, the challenge lies in parameter estimation and in resolving its hidden degeneracies. The third avenue employs multiple diffusion encoding techniques, able to access information not contained in the conventional diffusion propagator. We conclude with our outlook on future directions that could open exciting possibilities for designing quantitative markers of tissue physiology and pathology, based on methods of studying mesoscopic transport in disordered systems.

Corpus callosum axon diameter relates to cognitive impairment in multiple sclerosis

Objective

To evaluate alterations in apparent axon diameter and axon density obtained by high‐gradient diffusion MRI in the corpus callosum of MS patients and the relationship of these advanced diffusion MRI metrics to neurologic disability and cognitive impairment in MS.

Methods

Thirty people with MS (23 relapsing‐remitting MS [RRMS], 7 progressive MS [PMS]) and 23 healthy controls were scanned on a human 3‐tesla (3T) MRI scanner equipped with 300 mT/m maximum gradient strength using a comprehensive multishell diffusion MRI protocol. Data were fitted to a three‐compartment geometric model of white matter to estimate apparent axon diameter and axon density in the midline corpus callosum. Neurologic disability and cognitive function were measured using the Expanded Disability Status Scale (EDSS), Multiple Sclerosis Functional Composite (MSFC), and Minimal Assessment of Cognitive Function in MS battery.

Results

Apparent axon diameter was significantly larger and axon density reduced in the normal‐appearing corpus callosum (NACC) of MS patients compared to healthy controls, with similar trends seen in PMS compared to RRMS. Larger apparent axon diameter in the NACC of MS patients correlated with greater disability as measured by the EDSS (r = 0.555, P = 0.007) and poorer performance on the Symbol Digits Modalities Test (r = ‐0.593, P = 0.008) and Brief Visuospatial Memory Test–Revised (r = −0.632, P < 0.01), tests of interhemispheric processing speed and new learning and memory, respectively.

Interpretation

Apparent axon diameter in the corpus callosum obtained from high‐gradient diffusion MRI is a potential imaging biomarker that may be used to understand the development and progression of cognitive impairment in MS.

Modeling conduction delays in the corpus callosum using MRI-measured g-ratio

Conduction of action potentials along myelinated axons is affected by their structural features, such as the axonal g-ratio, the ratio between the inner and outer diameters of the myelin sheath surrounding the axon. The effect of g-ratio variance on conduction properties has been quantitatively evaluated using single-axon models. It has recently become possible to estimate a g-ratio weighted measurement in vivo using quantitative MRI. Nevertheless, it is still unclear whether the variance in the g-ratio in the healthy human brain leads to significant differences in conduction velocity. In this work we tested whether the g-ratio MRI measurement can be used to predict conduction delays in the corpus callosum. We present a comprehensive framework in which the structural properties of fibers (i.e. length and g-ratio, measured using MRI), are incorporated in a biophysical model of axon conduction, to model conduction delays of long-range white matter fibers. We applied this framework to the corpus callosum, and found conduction delay estimates that are compatible with previously estimated values of conduction delays. We account for the variance in the velocity given the axon diameter distribution in the splenium, mid-body and genu, to further compare the fibers within the corpus callosum. Conduction delays have been suggested to increase with age. Therefore, we investigated whether there are differences in the g-ratio and the fiber length between young and old adults, and whether this leads to a difference in conduction speed and delays. We found very small differences between the predicted delays of the two groups in the motor fibers of the corpus callosum. We also found that the motor fibers of the corpus callosum have the fastest conduction estimates. Using the axon diameter distributions, we found that the occipital fibers have the slowest estimations, while the frontal and motor fiber tracts have similar estimates. Our study provides a framework for predicting conduction latencies in vivo. The framework could have major implications for future studies of white matter diseases and large range network computations. Our results highlight the need for improving additional in vivo measurements of white matter microstructure.

Quantification of white matter cellularity and damage in preclinical and early symptomatic Alzheimer's disease

Interest in understanding the roles of white matter (WM) inflammation and damage in the pathophysiology of Alzheimer disease (AD) has been growing significantly in recent years. However, in vivo magnetic resonance imaging (MRI) techniques for imaging inflammation are still lacking. An advanced diffusion-based MRI method, neuro-inflammation imaging (NII), has been developed to clinically image and quantify WM inflammation and damage in AD. Here, we employed NII measures in conjunction with cerebrospinal fluid (CSF) biomarker classification (for β-amyloid (Aβ) and neurodegeneration) to evaluate 200 participants in an ongoing study of memory and aging. Elevated NII-derived cellular diffusivity was observed in both preclinical and early symptomatic phases of AD, while disruption of WM integrity, as detected by decreased fractional anisotropy (FA) and increased radial diffusivity (RD), was only observed in the symptomatic phase of AD. This may suggest that WM inflammation occurs earlier than WM damage following abnormal Aβ accumulation in AD. The negative correlation between NII-derived cellular diffusivity and CSF Aβ42 level (a marker of amyloidosis) may indicate that WM inflammation is associated with increasing Aβ burden. NII-derived FA also negatively correlated with CSF t-tau level (a marker of neurodegeneration), suggesting that disruption of WM integrity is associated with increasing neurodegeneration. Our findings demonstrated the capability of NII to simultaneously image and quantify WM cellularity changes and damage in preclinical and early symptomatic AD. NII may serve as a clinically feasible imaging tool to study the individual and composite roles of WM inflammation and damage in AD.

Using GPUs to accelerate computational diffusion MRI: From microstructure estimation to tractography and connectomes

The great potential of computational diffusion MRI (dMRI) relies on indirect inference of tissue microstructure and brain connections, since modelling and tractography frameworks map diffusion measurements to neuroanatomical features. This mapping however can be computationally highly expensive, particularly given the trend of increasing dataset sizes and the complexity in biophysical modelling. Limitations on computing resources can restrict data exploration and methodology development. A step forward is to take advantage of the computational power offered by recent parallel computing architectures, especially Graphics Processing Units (GPUs). GPUs are massive parallel processors that offer trillions of floating point operations per second, and have made possible the solution of computationally-intensive scientific problems that were intractable before. However, they are not inherently suited for all problems. Here, we present two different frameworks for accelerating dMRI computations using GPUs that cover the most typical dMRI applications: a framework for performing biophysical modelling and microstructure estimation, and a second framework for performing tractography and long-range connectivity estimation. The former provides a front-end and automatically generates a GPU executable file from a user-specified biophysical model, allowing accelerated non-linear model fitting in both deterministic and stochastic ways (Bayesian inference). The latter performs probabilistic tractography, can generate whole-brain connectomes and supports new functionality for imposing anatomical constraints, such as inherent consideration of surface meshes (GIFTI files) along with volumetric images. We validate the frameworks against well-established CPU-based implementations and we show that despite the very different challenges for parallelising these problems, a single GPU achieves better performance than 200 CPU cores thanks to our parallel designs.

Learning Compact q -Space Representations for Multi-Shell Diffusion-Weighted MRI

Diffusion-weighted MRI measures the direction and scale of the local diffusion process in every voxel through its spectrum in q -space, typically acquired in one or more shells. Recent developments in microstructure imaging and multi-tissue decomposition have sparked renewed attention in the radial b -value dependence of the signal. Applications in motion correction and outlier rejection, therefore, require a compact linear signal representation that extends over the radial as well as angular domain. Here, we introduce SHARD, a data-driven representation of the q$ -space signal based on spherical harmonics and a radial decomposition into orthonormal components. This representation provides a complete, orthogonal signal basis, tailored to the spherical geometry of q -space, and calibrated to the data at hand. We demonstrate that the rank-reduced decomposition outperforms model-based alternatives in human brain data, while faithfully capturing the micro- and meso-structural information in the signal. Furthermore, we validate the potential of joint radial-spherical as compared with single-shell representations. As such, SHARD is optimally suited for applications that require low-rank signal predictions, such as motion correction and outlier rejection. Finally, we illustrate its application for the latter using outlier robust regression.

Detecting Microglial Density With Quantitative Multi-Compartment Diffusion MRI

Neuroinflammation plays a central role in the neuropathogenesis of a wide-spectrum of neurologic and psychiatric disease, but current neuroimaging methods to detect and characterize neuroinflammation are limited. We explored the sensitivity of quantitative multi-compartment diffusion MRI, and specifically neurite orientation dispersion and density imaging (NODDI), to detect changes in microglial density in the brain. Monte Carlo simulations of water diffusion using a NODDI acquisition scheme were performed to measure changes in a virtual MRI signal following modeled cellular changes within the extra-neurite space. 12-week-old C57BL/6J male mice (n = 48; 24 control, 24 treated with colony stimulating factor 1 receptor (CSF1R) inhibitor, PLX5622) were sacrificed at 0, 1, 3, and 7 days following withdrawal of CSF1R inhibition and were imaged ex-vivo to obtain measures of the orientation dispersion index (ODI). Following imaging, all brains were immunostained with Iba-1, NeuN, and GFAP for quantitative fluorescence microscopy. Cell populations were calculated with the ImageJ particle analyzer tool; correlation between microglial density and mean ODI values were calculated with Kendall's tau. Monte Carlo simulations demonstrate the sensitivity and positive correlation of ODI to increased occupancy in the extra-neurite space. Commensurate with our simulation data, ex-vivo NODDI imaging demonstrates an increase in ODI as microglia repopulate the brain following the withdrawal of CSF1R inhibition. Quantitative immunofluorescence of microglial density reveals that microglial density is positively correlated with ODI and greater hindered diffusion in the extra-neurite space (τ = 0.386, p < 0.05). Our results demonstrate that clinically feasible multi-compartment diffusion weighted imaging techniques such as NODDI are sensitive to microglial density and the cellular changes associated with microglial activation and highlights its potential to improve clinical diagnostic accuracy, patient risk stratification, and therapeutic monitoring of neuroinflammation in neurologic and psychiatric disease.

Working Memory: How Important Is White Matter?

Working memory, the ability to transiently keep, process, and use information as part of ongoing mental processes is an essential feature of cognitive functioning. The largest number of items that people can hold in their working memory, referred to as the capacity of working memory, is limited and varies substantially among individuals. Uncovering the biological factors that underlie these two defining properties of working memory capacity remains a key undertaking of modern cognitive neuroscience since capacity strongly predicts how well we reason, learn, and even do math. In this work we review data that highlights the role white matter, which provides the wiring of the extensive neural networks that activate during working memory tasks, may play in interindividual variations in capacity. We also describe advanced diffusion imaging methods, which may be uniquely suited in capturing those white matter features that are most relevant to capacity. Finally, we discuss several possible mechanisms through which white matter may both contribute to and limit working memory.

Age-related alterations in axonal microstructure in the corpus callosum measured by high-gradient diffusion MRI

Cerebral white matter exhibits age-related degenerative changes during the course of normal aging, including decreases in axon density and alterations in axonal structure. Noninvasive approaches to measure these microstructural alterations throughout the lifespan would be invaluable for understanding the substrate and regional variability of age-related white matter degeneration. Recent advances in diffusion magnetic resonance imaging (MRI) have leveraged high gradient strengths to increase sensitivity toward axonal size and density in the living human brain. Here, we examined the relationship between age and indices of axon diameter and packing density using high-gradient strength diffusion MRI in 36 healthy adults (aged 22-72) in well-defined central white matter tracts in the brain. A recently validated method for inferring the effective axonal compartment size and packing density from diffusion MRI measurements acquired with 300 mT/m maximum gradient strength was applied to the in vivo human brain to obtain indices of axon diameter and density in the corpus callosum, its sub-regions, and adjacent anterior and posterior fibers in the forceps minor and forceps major. The relationships between the axonal metrics, corpus callosum area and regional gray matter volume were also explored. Results revealed a significant increase in axon diameter index with advancing age in the whole corpus callosum. Similar analyses in sub-regions of the corpus callosum showed that age-related alterations in axon diameter index and axon density were most pronounced in the genu of the corpus callosum and relatively absent in the splenium, in keeping with findings from previous histological studies. The significance of these correlations was mirrored in the forceps minor and forceps major, consistent with previously reported decreases in FA in the forceps minor but not in the forceps major with age. Alterations in the axonal imaging metrics paralleled decreases in corpus callosum area and regional gray matter volume with age. Among older adults, results from cognitive testing suggested an association between larger effective compartment size in the corpus callosum, particularly within the genu of the corpus callosum, and lower scores on the Montreal Cognitive Assessment, largely driven by deficits in short-term memory. The current study suggests that high-gradient diffusion MRI may be sensitive to the axonal substrate of age-related white matter degeneration reflected in traditional DTI metrics and provides further evidence for regionally selective alterations in white matter microstructure with advancing age.

Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds

The Bloch-Torrey partial differential equation can be used to describe the evolution of the transverse magnetization of the imaged sample under the influence of diffusion-encoding magnetic field gradients inside the MRI scanner. The integral of the magnetization inside a voxel gives the simulated diffusion MRI signal. This paper proposes a finite element discretization on manifolds in order to efficiently simulate the diffusion MRI signal in domains that have a thin layer or a thin tube geometrical structure. The variable thickness of the three-dimensional domains is included in the weak formulation established on the manifolds. We conducted a numerical study of the proposed approach by simulating the diffusion MRI signals from the extracellular space (a thin layer medium) and from neurons (a thin tube medium), comparing the results with the reference signals obtained using a standard three-dimensional finite element discretization. We show good agreements between the simulated signals using our proposed method and the reference signals for a wide range of diffusion MRI parameters. The approximation becomes better as the diffusion time increases. The method helps to significantly reduce the required simulation time, computational memory, and difficulties associated with mesh generation, thus opening the possibilities to simulating complicated structures at low cost for a better understanding of diffusion MRI in the brain.

Microscopic anisotropy misestimation in spherical-mean single diffusion encoding MRI

Purpose

Microscopic fractional anisotropy (µFA) can disentangle microstructural information from orientation dispersion. While double diffusion encoding (DDE) MRI methods are widely used to extract accurate µFA, it has only recently been proposed that powder‐averaged single diffusion encoding (SDE) signals, when coupled with the diffusion standard model (SM) and a set of constraints, could be used for µFA estimation. This study aims to evaluate µFA as derived from the spherical mean technique (SMT) set of constraints, as well as more generally for powder‐averaged SM signals.

Methods

SDE experiments were performed at 16.4 T on an ex vivo mouse brain (Δ/δ = 12/1.5 ms). The µFA maps obtained from powder‐averaged SDE signals were then compared to maps obtained from DDE‐MRI experiments (Δ/τ/δ = 12/12/1.5 ms), which allow a model‐free estimation of µFA. Theory and simulations that consider different types of heterogeneity are presented for corroborating the experimental findings.

Results

µFA, as well as other estimates derived from powder‐averaged SDE signals produced large deviations from the ground truth in both gray and white matter. Simulations revealed that these misestimations are likely a consequence of factors not considered by the underlying microstructural models (such as intercomponent and intracompartmental kurtosis).

Conclusion

Powder‐averaged SMT and (2‐component) SM are unable to accurately report µFA and other microstructural parameters in ex vivo tissues. Improper model assumptions and constraints can significantly compromise parameter specificity. Further developments and validations are required prior to implementation of these models in clinical or preclinical research.

Ultrahigh field imaging of myelin disease models: Toward specific markers of myelin integrity?

Specific magnetic resonance imaging (MRI) markers of myelin are critical for the evaluation and development of regenerative therapies for demyelinating diseases. Several MRI methods have been developed for myelin imaging, based either on acquisition schemes or on mathematical modeling of the signal. They generally showed good sensitivity but validation for specificity toward myelin is still warranted to allow a reliable interpretation in an in vivo complex pathological environment. Experimental models of dys-/demyelination are characterized by various levels of myelin disorders, axonal damage, gliosis and inflammation, and offer the opportunity for powerful correlative studies between imaging metrics and histology. Here, we review how ultrahigh field MRI markers have been correlated with histology in these models and provide insights into the trends for future developments of MRI tools in human myelin diseases. To this end, we present the biophysical basis of the main MRI methods for myelin imaging based on T₁ , T₂ , water diffusion, and magnetization transfer signal, the characteristics of animal models used and the outcomes of histological validations. To date such studies are limited, and demonstrate partial correlations with immunohistochemical and electron microscopy measures of myelin. These MRI metrics also often correlate with axons, glial, or inflammatory cells in models where axonal degeneration or inflammation occur as potential confounding factors. Therefore, the MRI markers' specificity for myelin is still perfectible and future developments should improve mathematical modeling of the MR signal based on more complex systems or provide multimodal approaches to better disentangle the biological processes underlying the MRI metrics.

Topological principles and developmental algorithms might refine diffusion tractography

The identification and reconstruction of axonal pathways in the living brain or "ex-vivo" is promising a revolution in connectivity studies bridging the gap from animal to human neuroanatomy with extensions to brain structural-functional correlates. Unfortunately, the methods suffer from juvenile drawbacks. In this perspective paper we mention several computational and developmental principles, which might stimulate a new generation of algorithms and a discussion bridging the neuroimaging and neuroanatomy communities.

Generalized Mean Apparent Propagator MRI to Measure and Image Advective and Dispersive Flows in Medicine and Biology

Water transport in biological systems spans different regimes with distinct physical behaviors: diffusion, advection, and dispersion. Identifying these regimes is of paramount importance in many in vivo applications, among them, measuring microcirculation of blood in capillary networks and cerebrospinal fluid transport in the glymphatic system. Diffusion magnetic resonance imaging (dMRI) can be used to encode water displacements, and a Fourier transform of the acquired signal furnishes a displacement probability density function known as the propagator. This transformation normally requires the use of a fast Fourier transform (FFT), which presents major feasibility challenges when scanning in vivo, mainly because of dense signal sampling, resulting in long acquisition times. A second approach to reconstruct the propagator is by using analytical representation of the signal, overcoming many of the FFT's limitations. In all analytical implementations of dMRI to date, the translational motion of water has been assumed to be exclusively diffusive, which is the case only in the absence of flow. However, retaining the phase information from the diffusion signal provides the ability to measure both mean coherent velocity and random diffusion from a single experiment. We implement and extend an analytical framework, mean apparent propagator (MAP), which can account for non-zero flow conditions. We call this method generalized MAP or GMAP. We describe a numerical optimization scheme and implement it on data from an MRI flow phantom constructed from a pack of 10- [Formula: see text] beads. The advantages of GMAP over the FFT-based method in the context of sampling density and low-flow detection were demonstrated, and analytically derived propagator moments were shown to agree with theoretical values even after data subsampling. GMAP would enable the detection of microflow in vivo that could help elucidate many important biological processes.