Including diffusion time dependence in the extra-axonal space improves in vivo estimates of axonal diameter and density in human white matter

Modelling white matter microstructure using diffusion OGSE MRI: Model and analysis choices

Alterations in white matter (WM) microstructure of the central nervous system have been shown to be pathophysiological presentations of various neurodegenerative disorders. Current methods for measuring such WM features require ex vivo tissue samples analyzed using electron microscopy. Magnetic Resonance Imaging (MRI) diffusion-weighted pulse sequences provide a non-invasive tool for estimating such microstructural features in vivo. The current project investigated the use of two methods of analysis, including the ROI-based (Region of Interest, RBA) and voxel-based analysis (VBA), as well as four mathematical models of WM microstructure, including the ActiveAx Frequency-Independent Extra-Axonal Diffusion (AAI), ActiveAx Frequency-Dependent Extra-Axonal Diffusion (AAD), AxCaliber Frequency-Independent Extra-Axonal Diffusion (ACI), and AxCaliber Frequency-Dependent Extra-Axonal Diffusion (ACD) models. Two mice samples imaged at 7 T and 15.2 T were analyzed. Both the AAI and AAD models provide a single value for each of the fit parameters, including mean effective axon diameter AxD¯, packing fraction fin, intra-cellular and Din and extra-cellular Dex diffusion coefficients, as well as the frequency dependence of Dex, βex for the AAD model. The ACI and ACD models provide this, in addition to a distribution of axon diameters for a chosen ROI. VBA extends this, providing a parameter value for each voxel within the selected ROI, at the cost of increased computational load and analysis time. Overall, RBA-ACD and VBA-AAD were found to be optimal for parameter fitting to physically relevant values in a reasonable time frame. A full comparison of each combination of RBA and VBA with AAI, AAD, ACI, and ACD is provided to give the reader sufficient information to make an informed decision of which model is best for their own experiments.

Pore size estimation in axon-mimicking microfibers with diffusion-relaxation MRI

PURPOSE

This study aims to evaluate two distinct approaches for fiber radius estimation using diffusion-relaxation MRI data acquired in biomimetic microfiber phantoms that mimic hollow axons. The methods considered are the spherical mean power-law approach and a T2-based pore size estimation technique.

THEORY AND METHODS

A general diffusion-relaxation theoretical model for the spherical mean signal from water molecules within a distribution of cylinders with varying radii was introduced, encompassing the evaluated models as particular cases. Additionally, a new numerical approach was presented for estimating effective radii (i.e., MRI-visible mean radii) from the ground truth radii distributions, not reliant on previous theoretical approximations and adaptable to various acquisition sequences. The ground truth radii were obtained from scanning electron microscope images.

RESULTS

Both methods show a linear relationship between effective radii estimated from MRI data and ground-truth radii distributions, although some discrepancies were observed. The spherical mean power-law method overestimated fiber radii. Conversely, the T2-based method exhibited higher sensitivity to smaller fiber radii, but faced limitations in accurately estimating the radius in one particular phantom, possibly because of material-specific relaxation changes.

CONCLUSION

The study demonstrates the feasibility of both techniques to predict pore sizes of hollow microfibers. The T2-based technique, unlike the spherical mean power-law method, does not demand ultra-high diffusion gradients, but requires calibration with known radius distributions. This research contributes to the ongoing development and evaluation of neuroimaging techniques for fiber radius estimation, highlights the advantages and limitations of both methods, and provides datasets for reproducible research.

The effects of axonal beading and undulation on axonal diameter estimation from diffusion MRI: Insights from simulations in human axons segmented from three-dimensional electron microscopy

The increasing availability of high-performance gradient systems in human MRI scanners has generated great interest in diffusion microstructural imaging applications such as axonal diameter mapping. Practically, sensitivity to axon diameter in diffusion MRI is attained at strong diffusion weightings b , where the deviation from the expected 1 / b scaling in white matter yields a finite transverse diffusivity, which is then translated into an axon diameter estimate. While axons are usually modeled as perfectly straight, impermeable cylinders, local variations in diameter (caliber variation or beading) and direction (undulation) are known to influence axonal diameter estimates and have been observed in microscopy data of human axons. In this study, we performed Monte Carlo simulations of diffusion in axons reconstructed from three-dimensional electron microscopy of a human temporal lobe specimen using simulated sequence parameters matched to the maximal gradient strength of the next-generation Connectome 2.0 human MRI scanner ( ≲ 500 mT/m). We show that axon diameter estimation is accurate for nonbeaded, nonundulating fibers; however, in fibers with caliber variations and undulations, the axon diameter is heavily underestimated due to caliber variations, and this effect overshadows the known overestimation of the axon diameter due to undulations. This unexpected underestimation may originate from variations in the coarse-grained axial diffusivity due to caliber variations. Given that increased axonal beading and undulations have been observed in pathological tissues, such as traumatic brain injury and ischemia, the interpretation of axon diameter alterations in pathology may be significantly confounded.

A translational MRI approach to validate acute axonal damage detection as an early event in multiple sclerosis

Axonal degeneration is a central pathological feature of multiple sclerosis and is closely associated with irreversible clinical disability. Current noninvasive methods to detect axonal damage in vivo are limited in their specificity and clinical applicability, and by the lack of proper validation. We aimed to validate an MRI framework based on multicompartment modeling of the diffusion signal (AxCaliber) in rats in the presence of axonal pathology, achieved through injection of a neurotoxin damaging the neuronal terminal of axons. We then applied the same MRI protocol to map axonal integrity in the brain of multiple sclerosis relapsing-remitting patients and age-matched healthy controls. AxCaliber is sensitive to acute axonal damage in rats, as demonstrated by a significant increase in the mean axonal caliber along the targeted tract, which correlated with neurofilament staining. Electron microscopy confirmed that increased mean axonal diameter is associated with acute axonal pathology. In humans with multiple sclerosis, we uncovered a diffuse increase in mean axonal caliber in most areas of the normal-appearing white matter, preferentially affecting patients with short disease duration. Our results demonstrate that MRI-based axonal diameter mapping is a sensitive and specific imaging biomarker that links noninvasive imaging contrasts with the underlying biological substrate, uncovering generalized axonal damage in multiple sclerosis as an early event.

Multishell diffusion MRI reveals whole-brain white matter changes in HIV

Diffusion tensor imaging (DTI) and diffusion kurtosis imaging (DKI) have been previously used to explore white matter related to human immunodeficiency virus (HIV) infection. While DTI and DKI suffer from low specificity, the Combined Hindered and Restricted Model of Diffusion (CHARMED) provides additional microstructural specificity. We used these three models to evaluate microstructural differences between 35 HIV-positive patients without neurological impairment and 20 healthy controls who underwent diffusion-weighted imaging using three b-values. While significant group effects were found in all diffusion metrics, CHARMED and DKI analyses uncovered wider involvement (80% vs. 20%) of all white matter tracts in HIV infection compared with DTI. In restricted fraction (FR) analysis, we found significant differences in the left corticospinal tract, middle cerebellar peduncle, right inferior cerebellar peduncle, right corticospinal tract, splenium of the corpus callosum, left superior cerebellar peduncle, left superior cerebellar peduncle, pontine crossing tract, left posterior limb of the internal capsule, and left/right medial lemniscus. These are involved in language, motor, equilibrium, behavior, and proprioception, supporting the functional integration that is frequently impaired in HIV-positivity. Additionally, we employed a machine learning algorithm (XGBoost) to discriminate HIV-positive patients from healthy controls using DTI and CHARMED metrics on an ROIwise basis, and unique contributions to this discrimination were examined using Shapley Explanation values. The CHARMED and DKI estimates produced the best performance. Our results suggest that biophysical multishell imaging, combining additional sensitivity and built-in specificity, provides further information about the brain microstructural changes in multimodal areas involved in attentive, emotional and memory networks often impaired in HIV patients.

Estimating axon radius using diffusion-relaxation MRI: calibrating a surface-based relaxation model with histology

Axon radius is a potential biomarker for brain diseases and a crucial tissue microstructure parameter that determines the speed of action potentials. Diffusion MRI (dMRI) allows non-invasive estimation of axon radius, but accurately estimating the radius of axons in the human brain is challenging. Most axons in the brain have a radius below one micrometer, which falls below the sensitivity limit of dMRI signals even when using the most advanced human MRI scanners. Therefore, new MRI methods that are sensitive to small axon radii are needed. In this proof-of-concept investigation, we examine whether a surface-based axonal relaxation process could mediate a relationship between intra-axonal T2 and T1 times and inner axon radius, as measured using postmortem histology. A unique in vivo human diffusion-T1-T2 relaxation dataset was acquired on a 3T MRI scanner with ultra-strong diffusion gradients, using a strong diffusion-weighting (i.e., b = 6,000 s/mm2) and multiple inversion and echo times. A second reduced diffusion-T2 dataset was collected at various echo times to evaluate the model further. The intra-axonal relaxation times were estimated by fitting a diffusion-relaxation model to the orientation-averaged spherical mean signals. Our analysis revealed that the proposed surface-based relaxation model effectively explains the relationship between the estimated relaxation times and the histological axon radius measured in various corpus callosum regions. Using these histological values, we developed a novel calibration approach to predict axon radius in other areas of the corpus callosum. Notably, the predicted radii and those determined from histological measurements were in close agreement.

The Role of the Corpus Callosum (Micro)Structure in Bimanual Coordination: A Literature Review Update

The characterization of callosal white matter is crucial for understanding the relationship between brain structure and bimanual motor function. An earlier literature review established this. With advancements in neuroimaging and data modeling, we aim to provide an update on the existing literature. Firstly, we highlight new CC parcellation approaches, such as functional MRI- and atlas-informed tractography and in vivo histology. Secondly, we elaborate on recent insights into the CC's role in bimanual coordination, drawing evidence from studies on healthy young and older adults, patients and training-related callosal plasticity. We also reflect on progress in the field and propose future perspectives to inspire research on the underlying mechanisms of structural-functional interactions.

Diffusion time dependency of extracellular diffusion

PURPOSE

To quantify the variations of the power-law dependences on diffusion time t or gradient frequencyf $$ f $$ of extracellular water diffusion measured by diffusion MRI (dMRI).

METHODS

Model cellular systems containing only extracellular water were used to investigate thet / f $$ t/f $$ dependence ofD ex $$ {D}_{ex} $$ , the extracellular diffusion coefficient. Computer simulations used a randomly packed tissue model with realistic intracellular volume fractions and cell sizes. DMRI measurements were performed on samples consisting of liposomes containing heavy water(D2 O, deuterium oxide) dispersed in regular water (H2 O).D ex $$ {D}_{ex} $$ was obtained over a broadt $$ t $$ range (∼1-1000 ms) and then fit power-law equationsD ex ( t ) = D const + const · t - ϑ t $$ {D}_{ex}(t)={D}_{\mathrm{const}}+\mathrm{const}\cdotp {t}^{-{\vartheta}_t} $$ andD ex ( f ) = D const + const · f ϑ f $$ {D}_{ex}(f)={D}_{\mathrm{const}}+\mathrm{const}\cdotp {f}^{\vartheta_f} $$ .

RESULTS

Both simulated and experimental results suggest that no single power-law adequately describes the behavior ofD ex $$ {D}_{ex} $$ over the range of diffusion times of most interest in practical dMRI. Previous theoretical predictions are accurate over only limitedt $$ t $$ ranges; for example,θ t = θ f = - 1 2 $$ {\theta}_t={\theta}_f=-\frac{1}{2} $$ is valid only for short times, whereasθ t = 1 $$ {\theta}_t=1 $$ orθ f = 3 2 $$ {\theta}_f=\frac{3}{2} $$ is valid only for long times but cannot describe other ranges simultaneously. For the specifict $$ t $$ range of 5-70 ms used in typical human dMRI measurements,θ t = θ f = 1 $$ {\theta}_t={\theta}_f=1 $$ matches the data well empirically.

CONCLUSION

The optimal power-law fit of extracellular diffusion varies with diffusion time. The dependency obtained at short or longt $$ t $$ limits cannot be applied to typical dMRI measurements in human cancer or liver. It is essential to determine the appropriate diffusion time range when modeling extracellular diffusion in dMRI-based quantitative microstructural imaging.

Novel insights into axon diameter and myelin content in late childhood and adolescence

White matter microstructural development in late childhood and adolescence is driven predominantly by increasing axon density and myelin thickness. Ex vivo studies suggest that the increase in axon diameter drives developmental increases in axon density observed with pubertal onset. In this cross-sectional study, 50 typically developing participants aged 8-18 years were scanned using an ultra-strong gradient magnetic resonance imaging scanner. Microstructural properties, including apparent axon diameter $({d}_a)$, myelin content, and g-ratio, were estimated in regions of the corpus callosum. We observed age-related differences in ${d}_a$, myelin content, and g-ratio. In early puberty, males had larger ${d}_a$ in the splenium and lower myelin content in the genu and body of the corpus callosum, compared with females. Overall, this work provides novel insights into developmental, pubertal, and cognitive correlates of individual differences in apparent axon diameter and myelin content in the developing human brain.

The influence of axonal beading and undulation on axonal diameter mapping

We consider the effect of non-cylindrical axonal shape on axonal diameter mapping with diffusion MRI. Practical sensitivity to axon diameter is attained at strong diffusion weightings b , where the deviation from the 1 / b scaling yields the finite transverse diffusivity, which is then translated into axon diameter. While axons are usually modeled as perfectly straight, impermeable cylinders, the local variations in diameter (caliber variation or beading) and direction (undulation) have been observed in microscopy data of human axons. Here we quantify the influence of cellular-level features such as caliber variation and undulation on axon diameter estimation. For that, we simulate the diffusion MRI signal in realistic axons segmented from 3-dimensional electron microscopy of a human brain sample. We then create artificial fibers with the same features and tune the amplitude of their caliber variations and undulations. Numerical simulations of diffusion in fibers with such tunable features show that caliber variations and undulations result in under- and over-estimation of axon diameters, correspondingly; this bias can be as large as 100%. Given that increased axonal beading and undulations have been observed in pathological tissues, such as traumatic brain injury and ischemia, the interpretation of axon diameter alterations in pathology may be significantly confounded.

Linear multi-scale modeling of diffusion MRI data: A framework for characterization of oriented structures across length scales

Diffusion-weighted magnetic resonance imaging (DW-MRI) has evolved to provide increasingly sophisticated investigations of the human brain's structural connectome in vivo. Restriction spectrum imaging (RSI) is a method that reconstructs the orientation distribution of diffusion within tissues over a range of length scales. In its original formulation, RSI represented the signal as consisting of a spectrum of Gaussian diffusion response functions. Recent technological advances have enabled the use of ultra-high b-values on human MRI scanners, providing higher sensitivity to intracellular water diffusion in the living human brain. To capture the complex diffusion time dependence of the signal within restricted water compartments, we expand upon the RSI approach to represent restricted water compartments with non-Gaussian response functions, in an extended analysis framework called linear multi-scale modeling (LMM). The LMM approach is designed to resolve length scale and orientation-specific information with greater specificity to tissue microstructure in the restricted and hindered compartments, while retaining the advantages of the RSI approach in its implementation as a linear inverse problem. Using multi-shell, multi-diffusion time DW-MRI data acquired with a state-of-the-art 3 T MRI scanner equipped with 300 mT/m gradients, we demonstrate the ability of the LMM approach to distinguish different anatomical structures in the human brain and the potential to advance mapping of the human connectome through joint estimation of the fiber orientation distributions and compartment size characteristics.

Mapping the human connectome using diffusion MRI at 300 mT/m gradient strength: Methodological advances and scientific impact

Tremendous efforts have been made in the last decade to advance cutting-edge MRI technology in pursuit of mapping structural connectivity in the living human brain with unprecedented sensitivity and speed. The first Connectom 3T MRI scanner equipped with a 300 mT/m whole-body gradient system was installed at the Massachusetts General Hospital in 2011 and was specifically constructed as part of the Human Connectome Project. Since that time, numerous technological advances have been made to enable the broader use of the Connectom high gradient system for diffusion tractography and tissue microstructure studies and leverage its unique advantages and sensitivity to resolving macroscopic and microscopic structural information in neural tissue for clinical and neuroscientific studies. The goal of this review article is to summarize the technical developments that have emerged in the last decade to support and promote large-scale and scientific studies of the human brain using the Connectom scanner. We provide a brief historical perspective on the development of Connectom gradient technology and the efforts that led to the installation of three other Connectom 3T MRI scanners worldwide - one in the United Kingdom in Cardiff, Wales, another in continental Europe in Leipzig, Germany, and the latest in Asia in Shanghai, China. We summarize the key developments in gradient hardware and image acquisition technology that have formed the backbone of Connectom-related research efforts, including the rich array of high-sensitivity receiver coils, pulse sequences, image artifact correction strategies and data preprocessing methods needed to optimize the quality of high-gradient strength diffusion MRI data for subsequent analyses. Finally, we review the scientific impact of the Connectom MRI scanner, including advances in diffusion tractography, tissue microstructural imaging, ex vivo validation, and clinical investigations that have been enabled by Connectom technology. We conclude with brief insights into the unique value of strong gradients for diffusion MRI and where the field is headed in the coming years.

MAGNIMS recommendations for harmonization of MRI data in MS multicenter studies

•

Sharing data from cooperative studies is essential to develop new biomarkers in MS.

•

Differences in MRI acquisition, analysis, storage represent a substantial constraint.

•

We review the state of the art and developments in the harmonization of MRI.

•

We provide recommendations to harmonize large MRI datasets in the MS field.

There is an increasing need of sharing harmonized data from large, cooperative studies as this is essential to develop new diagnostic and prognostic biomarkers. In the field of multiple sclerosis (MS), the issue has become of paramount importance due to the need to translate into the clinical setting some of the most recent MRI achievements. However, differences in MRI acquisition parameters, image analysis and data storage across sites, with their potential bias, represent a substantial constraint. This review focuses on the state of the art, recent technical advances, and desirable future developments of the harmonization of acquisition, analysis and storage of large-scale multicentre MRI data of MS cohorts. Huge efforts are currently being made to achieve all the requirements needed to provide harmonized MRI datasets in the MS field, as proper management of large imaging datasets is one of our greatest opportunities and challenges in the coming years. Recommendations based on these achievements will be provided here. Despite the advances that have been made, the complexity of these tasks requires further research by specialized academical centres, with dedicated technical and human resources. Such collective efforts involving different professional figures are of crucial importance to offer to MS patients a personalised management while minimizing consumption of resources.

Individual variability in the nonlinear development of the corpus callosum during infancy and toddlerhood: a longitudinal MRI analysis

The human brain spends several years bootstrapping itself through intrinsic and extrinsic modulation, thus gradually developing both spatial organization and functions. Based on previous studies on developmental patterns and inter-individual variability of the corpus callosum (CC), we hypothesized that inherent variations of CC shape among infants emerge, depending on the position within the CC, along the developmental timeline. Here we used longitudinal magnetic resonance imaging data from infancy to toddlerhood and investigated the area, thickness, and shape of the midsagittal plane of the CC by applying multilevel modeling. The shape characteristics were extracted using the Procrustes method. We found nonlinearity, region-dependency, and inter-individual variability, as well as intra-individual consistencies, in CC development. Overall, the growth rate is faster in the first year than in the second year, and the trajectory differs between infants; the direction of CC formation in individual infants was determined within six months and maintained to two years. The anterior and posterior subregions increase in area and thickness faster than other subregions. Moreover, we clarified that the growth rate of the middle part of the CC is faster in the second year than in the first year in some individuals. Since the division of regions exhibiting different tendencies coincides with previously reported divisions based on the diameter of axons that make up the region, our results suggest that subregion-dependent individual variability occurs due to the increase in the diameter of the axon caliber, myelination partly due to experience and axon elimination during the early developmental period.

In vivo Correlation Tensor MRI reveals microscopic kurtosis in the human brain on a clinical 3T scanner

Diffusion MRI (dMRI) has become one of the most important imaging modalities for noninvasively probing tissue microstructure. Diffusional Kurtosis MRI (DKI) quantifies the degree of non-gaussian diffusion, which in turn has been shown to increase sensitivity towards, e.g., disease and orientation mapping in neural tissue. However, the specificity of DKI is limited as different sources can contribute to the total intravoxel diffusional kurtosis, including: variance in diffusion tensor magnitudes (K_iso), variance due to diffusion anisotropy (K_aniso), and microscopic kurtosis (μK) related to restricted diffusion, microstructural disorder, and/or exchange. Interestingly, μK is typically ignored in diffusion MRI signal modeling as it is assumed to be negligible in neural tissues. However, recently, Correlation Tensor MRI (CTI) based on Double-Diffusion-Encoding (DDE) was introduced for kurtosis source separation, revealing non negligible μK in preclinical imaging. Here, we implemented CTI for the first time on a clinical 3T scanner and investigated the sources of total kurtosis in healthy subjects. A robust framework for kurtosis source separation in humans is introduced, followed by estimation of μK (and the other kurtosis sources) in the healthy brain. Using this clinical CTI approach, we find that μK significantly contributes to total diffusional kurtosis both in gray and white matter tissue but, as expected, not in the ventricles. The first μK maps of the human brain are presented, revealing that the spatial distribution of μK provides a unique source of contrast, appearing different from isotropic and anisotropic kurtosis counterparts. Moreover, group average templates of these kurtosis sources have been generated for the first time, which corroborated our findings at the underlying individual-level maps. We further show that the common practice of ignoring μK and assuming the multiple gaussian component approximation for kurtosis source estimation introduces significant bias in the estimation of other kurtosis sources and, perhaps even worse, compromises their interpretation. Finally, a twofold acceleration of CTI is discussed in the context of potential future clinical applications. We conclude that CTI has much potential for future in vivo microstructural characterizations in healthy and pathological tissue.

Advanced Diffusion MRI of the Visual System in Glaucoma: From Experimental Animal Models to Humans

Glaucoma is a group of ophthalmologic conditions characterized by progressive retinal ganglion cell death, optic nerve degeneration, and irreversible vision loss. While intraocular pressure is the only clinically modifiable risk factor, glaucoma may continue to progress at controlled intraocular pressure, indicating other major factors in contributing to the disease mechanisms. Recent studies demonstrated the feasibility of advanced diffusion magnetic resonance imaging (dMRI) in visualizing the microstructural integrity of the visual system, opening new possibilities for non-invasive characterization of glaucomatous brain changes for guiding earlier and targeted intervention besides intraocular pressure lowering. In this review, we discuss dMRI methods currently used in visual system investigations, focusing on the eye, optic nerve, optic tract, subcortical visual brain nuclei, optic radiations, and visual cortex. We evaluate how conventional diffusion tensor imaging, higher-order diffusion kurtosis imaging, and other extended dMRI techniques can assess the neuronal and glial integrity of the visual system in both humans and experimental animal models of glaucoma, among other optic neuropathies or neurodegenerative diseases. We also compare the pros and cons of these methods against other imaging modalities. A growing body of dMRI research indicates that this modality holds promise in characterizing early glaucomatous changes in the visual system, determining the disease severity, and identifying potential neurotherapeutic targets, offering more options to slow glaucoma progression and to reduce the prevalence of this world's leading cause of irreversible but preventable blindness.

Practical computation of the diffusion MRI signal based on Laplace eigenfunctions: permeable interfaces

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal, called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the tissue geometry and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. In a previous publication, we presented a simulation framework that we implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for biological cells subject to impermeable membrane boundary conditions. In this work, we extend our simulation framework to include geometries that contain permeable cell membranes. We describe the new computational techniques that allowed this generalization and we analyze the effects of the magnitude of the permeability coefficient on the eigendecomposition of the diffusion and Bloch-Torrey operators. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.

Multi-tissue spherical deconvolution of tensor-valued diffusion MRI

Multi-tissue constrained spherical deconvolution (MT-CSD) leverages the characteristic b-value dependency of each tissue type to estimate both the apparent tissue densities and the white matter fiber orientation distribution function from diffusion MRI data. In this work, we generalize MT-CSD to tensor-valued diffusion encoding with arbitrary b-tensor shapes. This enables the use of data encoded with mixed b-tensors, rather than being limited to the subset of linear (conventional) b-tensors. Using the complete set of data, including all b-tensor shapes, provides a categorical improvement in the estimation of apparent tissue densities, fiber ODF, and resulting tractography. Furthermore, we demonstrate that including multiple b-tensor shapes in the analysis provides improved contrast between tissue types, in particular between gray matter and white matter. We also show that our approach provides high-quality apparent tissue density maps and high-quality fiber tracking from data, even with sparse sampling across b-tensors that yield whole-brain coverage at 2 mm isotropic resolution in approximately 5:15 min.

Validating pore size estimates in a complex microfiber environment on a human MRI system

PURPOSE

Recent advances in diffusion-weighted MRI provide "restricted diffusion signal fraction" and restricting pore size estimates. Materials based on co-electrospun oriented hollow cylinders have been introduced to provide validation for such methods. This study extends this work, exploring accuracy and repeatability using an extended acquisition on a 300 mT/m gradient human MRI scanner, in substrates closely mimicking tissue, that is, non-circular cross-sections, intra-voxel fiber crossing, intra-voxel distributions of pore-sizes, and smaller pore-sizes overall.

METHODS

In a single-blind experiment, diffusion-weighted data were collected from a biomimetic phantom on a 3T Connectom system using multiple gradient directions/diffusion times. Repeated scans established short-term and long-term repeatability. The total scan time (54 min) matched similar protocols used in human studies. The number of distinct fiber populations was estimated using spherical deconvolution, and median pore size estimated through the combination of CHARMED and AxCaliber3D framework. Diffusion-based estimates were compared with measurements derived from scanning electron microscopy.

RESULTS

The phantom contained substrates with different orientations, fiber configurations, and pore size distributions. Irrespective of one or two populations within the voxel, the pore-size estimates (~5 μm) and orientation-estimates showed excellent agreement with the median values of pore-size derived from scanning electron microscope and phantom configuration. Measurement repeatability depended on substrate complexity, with lower values seen in samples containing crossing-fibers. Sample-level repeatability was found to be good.

CONCLUSION

While no phantom mimics tissue completely, this study takes a step closer to validating diffusion microstructure measurements for use in vivo by demonstrating the ability to quantify microgeometry in relatively complex configurations.

Indices of callosal axonal density and radius from diffusion MRI relate to upper and lower limb motor performance

Understanding the relationship between human brain structure and functional outcome is of critical importance in systems neuroscience. Diffusion MRI (dMRI) studies show that fractional anisotropy (FA) is predictive of motor control, underscoring the importance of white matter (WM). However, as FA is a surrogate marker of WM, we aim to shed new light on the structural underpinnings of this relationship by applying a multi-compartment microstructure model providing axonal density/radius indices. Sixteen young adults (7 males / 9 females), performed a hand/foot tapping task and a Multi Limb Reaction Time task. Furthermore, diffusion (STEAM &HARDI) and fMRI (localizer hand/foot activations) data were obtained. Sphere ROIs were placed on activation clusters with highest t value to guide interhemispheric WM tractography. Axonal radius/density indices of callosal parts intersecting with tractography were calculated from STEAM, using the diffusion-time dependent AxCaliber model, and correlated with behavior. Results indicated a possible association between larger apparent axonal radii of callosal motor fibers of the hand and higher tapping scores of both hands, and faster selection-related processing (normalized reaction) times (RTs) on diagonal limb combinations. Additionally, a trend was present for faster selection-related processing (normalized reaction) times for lower limbs being related with higher axonal density of callosal foot motor fibers, and for higher FA values of callosal motor fibers in general being related with better tapping and faster selection-related processing (normalized reaction) times. Whereas FA is sensitive in demonstrating associations with motor behavior, axon radius/density (i.e., fiber geometry) measures are promising to explain the physiological source behind the observed FA changes, contributing to deeper insights into brain-behavior interactions.

Scan-rescan repeatability of axonal imaging metrics using high-gradient diffusion MRI and statistical implications for study design

Axon diameter mapping using diffusion MRI in the living human brain has attracted growing interests with the increasing availability of high gradient strength MRI systems. A systematic assessment of the consistency of axon diameter estimates within and between individuals is needed to gain a comprehensive understanding of how such methods extend to quantifying differences in axon diameter index between groups and facilitate the design of neurobiological studies using such measures. We examined the scan-rescan repeatability of axon diameter index estimation based on the spherical mean technique (SMT) approach using diffusion MRI data acquired with gradient strengths up to 300 mT/m on a 3T Connectom system in 7 healthy volunteers. We performed statistical power analyses using data acquired with the same protocol in a larger cohort consisting of 15 healthy adults to investigate the implications for study design. Results revealed a high degree of repeatability in voxel-wise restricted volume fraction estimates and tract-wise estimates of axon diameter index derived from high-gradient diffusion MRI data. On the region of interest (ROI) level, across white matter tracts in the whole brain, the Pearson’s correlation coefficient of the axon diameter index estimated between scan and rescan experiments was r = 0.72 with an absolute deviation of 0.18 μm. For an anticipated 10% effect size in studies of axon diameter index, most white matter regions required a sample size of less than 15 people to observe a measurable difference between groups using an ROI-based approach. To facilitate the use of high-gradient strength diffusion MRI data for neuroscientific studies of axonal microstructure, the comprehensive multi-gradient strength, multi-diffusion time data used in this work will be made publicly available, in support of open science and increasing the accessibility of such data to the greater scientific community.

MESMERISED: Super-accelerating T1 relaxometry and diffusion MRI with STEAM at 7 T for quantitative multi-contrast and diffusion imaging

There is an increasing interest in quantitative imaging of T₁, T₂ and diffusion contrast in the brain due to greater robustness against bias fields and artifacts, as well as better biophysical interpretability in terms of microstructure. However, acquisition time constraints are a challenge, particularly when multiple quantitative contrasts are desired and when extensive sampling of diffusion directions, high b-values or long diffusion times are needed for multi-compartment microstructure modeling. Although ultra-high fields of 7 T and above have desirable properties for many MR modalities, the shortening T₂ and the high specific absorption rate (SAR) of inversion and refocusing pulses bring great challenges to quantitative T₁, T₂ and diffusion imaging. Here, we present the MESMERISED sequence (Multiplexed Echo Shifted Multiband Excited and Recalled Imaging of STEAM Encoded Diffusion). MESMERISED removes the dead time in Stimulated Echo Acquisition Mode (STEAM) imaging by an echo-shifting mechanism. The echo-shift (ES) factor is independent of multiband (MB) acceleration and allows for very high multiplicative (ESxMB) acceleration factors, particularly under moderate and long mixing times. This results in super-acceleration and high time efficiency at 7 T for quantitative T₁ and diffusion imaging, while also retaining the capacity to perform quantitative T₂ and B₁ mapping. We demonstrate the super-acceleration of MESMERISED for whole-brain T₁ relaxometry with total acceleration factors up to 36 at 1.8 mm isotropic resolution, and up to 54 at 1.25 mm resolution qT₁ imaging, corresponding to a 6x and 9x speedup, respectively, compared to MB-only accelerated acquisitions. We then demonstrate highly efficient diffusion MRI with high b-values and long diffusion times in two separate cases. First, we show that super-accelerated multi-shell diffusion acquisitions with 370 whole-brain diffusion volumes over 8 b-value shells up to b = 7000 s/mm² can be generated at 2 mm isotropic in under 8 minutes, a data rate of almost a volume per second, or at 1.8 mm isotropic in under 11 minutes, achieving up to 3.4x speedup compared to MB-only. A comparison of b = 7000 s/mm² MESMERISED against standard MB pulsed gradient spin echo (PGSE) diffusion imaging shows 70% higher SNR efficiency and greater effectiveness in supporting complex diffusion signal modeling. Second, we demonstrate time-efficient sampling of different diffusion times with 1.8 mm isotropic diffusion data acquired at four diffusion times up to 290 ms, which supports both Diffusion Tensor Imaging (DTI) and Diffusion Kurtosis Imaging (DKI) at each diffusion time. Finally, we demonstrate how adding quantitative T₂ and B₁⁺ mapping to super-accelerated qT₁ and diffusion imaging enables efficient quantitative multi-contrast mapping with the same MESMERISED sequence and the same readout train. MESMERISED extends possibilities to efficiently probe T₁, T₂ and diffusion contrast for multi-component modeling of tissue microstructure.

Beyond the diffusion standard model in fixed rat spinal cord with combined linear and planar encoding

Information about tissue on the microscopic and mesoscopic scales can be accessed by modelling diffusion MRI signals, with the aim of extracting microstructure-specific biomarkers. The standard model (SM) of diffusion, currently the most broadly adopted microstructural model, describes diffusion in white matter (WM) tissues by two Gaussian components, one of which has zero radial diffusivity, to represent diffusion in intra- and extra-axonal water, respectively. Here, we reappraise these SM assumptions by collecting comprehensive double diffusion encoded (DDE) MRI data with both linear and planar encodings, which was recently shown to substantially enhance the ability to estimate SM parameters. We find however, that the SM is unable to account for data recorded in fixed rat spinal cord at an ultrahigh field of 16.4 T, suggesting that its underlying assumptions are violated in our experimental data. We offer three model extensions to mitigate this problem: first, we generalize the SM to accommodate finite radii (axons) by releasing the constraint of zero radial diffusivity in the intra-axonal compartment. Second, we include intracompartmental kurtosis to account for non-Gaussian behaviour. Third, we introduce an additional (third) compartment. The ability of these models to account for our experimental data are compared based on parameter feasibility and Bayesian information criterion. Our analysis identifies the three-compartment description as the optimal model. The third compartment exhibits slow diffusion with a minor but non-negligible signal fraction (∼12%). We demonstrate how failure to take the presence of such a compartment into account severely misguides inferences about WM microstructure. Our findings bear significance for microstructural modelling at large and can impact the interpretation of biomarkers extracted from the standard model of diffusion.

The sensitivity of diffusion MRI to microstructural properties and experimental factors

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

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

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

In vivo observation and biophysical interpretation of time-dependent diffusion in human cortical gray matter

The dependence of the diffusion MRI signal on the diffusion time t is a hallmark of tissue microstructure at the scale of the diffusion length. Here we measure the time-dependence of the mean diffusivity D(t) and mean kurtosis K(t) in cortical gray matter and in 25 ​gray matter sub-regions, in 10 healthy subjects. Significant diffusivity and kurtosis time-dependence is observed for t=21.2-100 ​ms, and is characterized by a power-law tail ∼t-ϑ with dynamical exponent ϑ. To interpret our measurements, we systematize the relevant scenarios and mechanisms for diffusion time-dependence in the brain. Using the effective medium theory formalism, we derive an exact relation between the power-law tails in D(t) and K(t). The estimated dynamical exponent ϑ≃1/2 in both D(t) and K(t) is consistent with one-dimensional diffusion in the presence of randomly positioned restrictions along neurites. We analyze the short-range disordered statistics of synapses on axon collaterals in the cortex, and perform one-dimensional Monte Carlo simulations of diffusion restricted by permeable barriers with a similar randomness in their placement, to confirm the ϑ=1/2 exponent. In contrast, the Kärger model of exchange is less consistent with the data since it does not capture the diffusivity time-dependence, and the estimated exchange time from K(t) falls below our measured t-range. Although we cannot exclude exchange as a contributing factor, we argue that structural disorder along neurites is mainly responsible for the observed time-dependence of diffusivity and kurtosis. Our observation and theoretical interpretation of the t-1/2 tail in D(t) and K(t) altogether establish the sensitivity of a macroscopic MRI signal to micrometer-scale structural heterogeneities along neurites in human gray matter in vivo.

Mesoscale diffusion magnetic resonance imaging of the ex vivo human hippocampus

Mesoscale diffusion magnetic resonance imaging (MRI) endeavors to bridge the gap between macroscopic white matter tractography and microscopic studies investigating the cytoarchitecture of human brain tissue. To ensure a robust measurement of diffusion at the mesoscale, acquisition parameters were arrayed to investigate their effects on scalar indices (mean, radial, axial diffusivity, and fractional anisotropy) and streamlines (i.e., graphical representation of axonal tracts) in hippocampal layers. A mesoscale resolution afforded segementation of the pyramidal cell layer (CA1-4), the dentate gyrus, as well as stratum moleculare, radiatum, and oriens. Using ex vivo samples, surgically excised from patients with intractable epilepsy (n = 3), we found that shorter diffusion times (23.7 ms) with a b-value of 4,000 s/mm2 were advantageous at the mesoscale, providing a compromise between mean diffusivity and fractional anisotropy measurements. Spatial resolution and sample orientation exerted a major effect on tractography, whereas the number of diffusion gradient encoding directions minimally affected scalar indices and streamline density. A sample temperature of 15°C provided a compromise between increasing signal-to-noise ratio and increasing the diffusion properties of the tissue. Optimization of the acquisition afforded a system's view of intra- and extra-hippocampal connections. Tractography reflected histological boundaries of hippocampal layers. Individual layer connectivity was visualized, as well as streamlines emanating from individual sub-fields. The perforant path, subiculum and angular bundle demonstrated extra-hippocampal connections. Histology of the samples confirmed individual cell layers corresponding to ROIs defined on MR images. We anticipate that this ex vivo mesoscale imaging will yield novel insights into human hippocampal connectivity.

Practical computation of the diffusion MRI signal of realistic neurons based on Laplace eigenfunctions

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the biological cell and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. Up to now, this representation, though mathematically elegant, has not been often used as a practical model of the diffusion MRI signal, due to the difficulties of calculating the Laplace eigendecomposition in complicated geometries. In this paper, we present a simulation framework that we have implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for realistic neurons using the finite element method. We show that the matrix formalism representation requires a few hundred eigenmodes to match the reference signal computed by solving the Bloch-Torrey equation when the cell geometry originates from realistic neurons. As expected, the number of eigenmodes required to match the reference signal increases with smaller diffusion time and higher b-values. We also convert the eigenvalues to a length scale and illustrate the link between the length scale and the oscillation frequency of the eigenmode in the cell geometry. We give the transformation that links the Laplace eigenfunctions to the eigenfunctions of the Bloch-Torrey operator and compute the Bloch-Torrey eigenfunctions and eigenvalues. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.

Challenges for biophysical modeling of microstructure

The biophysical modeling efforts in diffusion MRI have grown considerably over the past 25 years. In this review, we dwell on the various challenges along the journey of bringing a biophysical model from initial design to clinical implementation, identifying both hurdles that have been already overcome and outstanding issues. First, we describe the critical initial task of selecting which features of tissue microstructure can be estimated using a model and which acquisition protocol needs to be implemented to make the estimation possible. The model performance should necessarily be tested in realistic numerical simulations and in experimental data - adapting the fitting strategy accordingly, and parameter estimates should be validated against complementary techniques, when/if available. Secondly, the model performance and validity should be explored in pathological conditions, and, if appropriate, dedicated models for pathology should be developed. We build on examples from tumors, ischemia and demyelinating diseases. We then discuss the challenges associated with clinical translation and added value. Finally, we single out four major unresolved challenges that are related to: the availability of a microstructural ground truth, the validation of model parameters which cannot be accessed with complementary techniques, the development of a generalized standard model for any brain region and pathology, and the seamless communication between different parties involved in the development and application of biophysical models of diffusion.

Dcf1 deficiency induces hypomyelination by activating Wnt signaling

Myelination is extremely important in achieving neural function. Hypomyelination causes a variety of neurological diseases. However, little is known about how hypomyelination occurs. Here we investigated the effect of dendritic cell factor 1(Dcf1) on myelination, using in vitro and in vivo models and found that Dcf1 is essential for normal myelination, motor coordination and balance. Lack of Dcf1 downregulated myelin-associated proteins, such as myelin basic protein (MBP), myelin associated glycoprotein (MAG), and 2'3'-cyclic nucleotide 3'-phosphodiesterase (CNPase) in the hippocampus and corpus callosum of Dcf1-null mice, as a result, the myelin sheath of these mice became thinner. Transmission electron microscopy revealed hypomyelination in Dcf1-deficient mice. Motor coordination and balance tests confirmed impaired neurological function in Dcf1-null mice. Gain-of-function analysis via In utero electroporation showed that hypomyelination could be rescued by re-expression of Dcf1 in Dcf1-null mouse brain. Dcf1-null mice exhibited a phenotype similar to that of cuprizone-induced demyelinated mice, thereby supporting the finding of hypomyelination caused by Dcf1 knockout. Mechanistically, we further revealed that insufficient Dcf1 leads to hyperactivation of the Wnt/β-catenin signaling pathway. Our work describes the role of Dcf1 in maintaining normal myelination, and this could help improve the current understanding of hypomyelination and its pathogenesis.

A time-dependent diffusion MRI signature of axon caliber variations and beading

MRI provides a unique non-invasive window into the brain, yet is limited to millimeter resolution, orders of magnitude coarser than cell dimensions. Here, we show that diffusion MRI is sensitive to the micrometer-scale variations in axon caliber or pathological beading, by identifying a signature power-law diffusion time-dependence of the along-fiber diffusion coefficient. We observe this signature in human brain white matter and identify its origins by Monte Carlo simulations in realistic substrates from 3-dimensional electron microscopy of mouse corpus callosum. Simulations reveal that the time-dependence originates from axon caliber variation, rather than from mitochondria or axonal undulations. We report a decreased amplitude of time-dependence in multiple sclerosis lesions, illustrating the potential sensitivity of our method to axonal beading in a plethora of neurodegenerative disorders. This specificity to microstructure offers an exciting possibility of bridging across scales to image cellular-level pathology with a clinically feasible MRI technique.

Robust Monte-Carlo Simulations in Diffusion-MRI: Effect of the Substrate Complexity and Parameter Choice on the Reproducibility of Results

Monte-Carlo Diffusion Simulations (MCDS) have been used extensively as a ground truth tool for the validation of microstructure models for Diffusion-Weighted MRI. However, methodological pitfalls in the design of the biomimicking geometrical configurations and the simulation parameters can lead to approximation biases. Such pitfalls affect the reliability of the estimated signal, as well as its validity and reproducibility as ground truth data. In this work, we first present a set of experiments in order to study three critical pitfalls encountered in the design of MCDS in the literature, namely, the number of simulated particles and time steps, simplifications in the intra-axonal substrate representation, and the impact of the substrate's size on the signal stemming from the extra-axonal space. The results obtained show important changes in the simulated signals and the recovered microstructure features when changes in those parameters are introduced. Thereupon, driven by our findings from the first studies, we outline a general framework able to generate complex substrates. We show the framework's capability to overcome the aforementioned simplifications by generating a complex crossing substrate, which preserves the volume in the crossing area and achieves a high packing density. The results presented in this work, along with the simulator developed, pave the way toward more realistic and reproducible Monte-Carlo simulations for Diffusion-Weighted MRI.

Oscillating diffusion-encoding with a high gradient-amplitude and high slew-rate head-only gradient for human brain imaging

PURPOSE

We investigate the importance of high gradient-amplitude and high slew-rate on oscillating gradient spin echo (OGSE) diffusion imaging for human brain imaging and evaluate human brain imaging with OGSE on the MAGNUS head-gradient insert (200 mT/m amplitude and 500 T/m/s slew rate).

METHODS

Simulations with cosine-modulated and trapezoidal-cosine OGSE at various gradient amplitudes and slew rates were performed. Six healthy subjects were imaged with the MAGNUS gradient at 3T with OGSE at frequencies up to 100 Hz and b = 450 s/mm² . Comparisons were made against standard pulsed gradient spin echo (PGSE) diffusion in vivo and in an isotropic diffusion phantom.

RESULTS

Simulations show that to achieve high frequency and b-value simultaneously for OGSE, high gradient amplitude, high slew rates, and high peripheral nerve stimulation limits are required. A strong linear trend for increased diffusivity (mean: 8-19%, radial: 9-27%, parallel: 8-15%) was observed in normal white matter with OGSE (20 Hz to 100 Hz) as compared to PGSE. Linear fitting to frequency provided excellent correlation, and using a short-range disorder model provided radial long-term diffusivities of D_∞,MD = 911 ± 72 µm² /s, D_∞,PD = 1519 ± 164 µm² /s, and D_∞,RD = 640 ± 111 µm² /s and correlation lengths of l_{c ,MD} = 0.802 ± 0.156 µm, l_{c ,PD} = 0.837 ± 0.172 µm, and l_{c ,RD} = 0.780 ± 0.174 µm. Diffusivity changes with OGSE frequency were negligible in the phantom, as expected.

CONCLUSION

The high gradient amplitude, high slew rate, and high peripheral nerve stimulation thresholds of the MAGNUS head-gradient enables OGSE acquisition for in vivo human brain imaging.

Diffusion time dependency along the human corpus callosum and exploration of age and sex differences as assessed by oscillating gradient spin-echo diffusion tensor imaging

Conventional diffusion imaging uses pulsed gradient spin echo (PGSE) waveforms with diffusion times of tens of milliseconds (ms) to infer differences of white matter microstructure. The combined use of these long diffusion times with short diffusion times (<10 ​ms) enabled by oscillating gradient spin echo (OGSE) waveforms can enable more sensitivity to changes of restrictive boundaries on the scale of white matter microstructure (e.g. membranes reflecting the axon diameters). Here, PGSE and OGSE images were acquired at 4.7 ​T from 20 healthy volunteers aged 20-73 years (10 males). Mean, radial, and axial diffusivity, as well as fractional anisotropy were calculated in the genu, body and splenium of the corpus callosum (CC). Monte Carlo simulations were also conducted to examine the relationship of intra- and extra-axonal radial diffusivity with diffusion time over a range of axon diameters and distributions. The results showed elevated diffusivities with OGSE relative to PGSE in the genu and splenium (but not the body) in both males and females, but the OGSE-PGSE difference was greater in the genu for males. Females showed positive correlations of OGSE-PGSE diffusivity difference with age across the CC, whereas there were no such age correlations in males. Simulations of radial diffusion demonstrated that for axon sizes in human brain both OGSE and PGSE diffusivities were dominated by extra-axonal water, but the OGSE-PGSE difference nonetheless increased with area-weighted outer-axon diameter. Therefore, the lack of OGSE-PGSE difference in the body is not entirely consistent with literature that suggests it is composed predominantly of axons with large diameter. The greater OGSE-PGSE difference in the genu of males could reflect larger axon diameters than females. The OGSE-PGSE difference correlation with age in females could reflect loss of smaller axons at older ages. The use of OGSE with short diffusion times to sample the microstructural scale of restriction implies regional differences of axon diameters along the corpus callosum with preliminary results suggesting a dependence on age and sex.

Diffusion Kurtosis Imaging maps neural damage in the EAE model of multiple sclerosis

Diffusion kurtosis imaging (DKI) is an imaging modality that yields novel disease biomarkers and in combination with nervous tissue modeling, provides access to microstructural parameters. Recently, DKI and subsequent estimation of microstructural model parameters has been used for assessment of tissue changes in neurodegenerative diseases and associated animal models. In this study, mouse spinal cords from the experimental autoimmune encephalomyelitis (EAE) model of multiple sclerosis (MS) were investigated for the first time using DKI in combination with biophysical modeling to study the relationship between microstructural metrics and degree of animal dysfunction. Thirteen spinal cords were extracted from animals with varied grades of disability and scanned in a high-field MRI scanner along with five control specimen. Diffusion weighted data were acquired together with high resolution T₂* images. Diffusion data were fit to estimate diffusion and kurtosis tensors and white matter modeling parameters, which were all used for subsequent statistical analysis using a linear mixed effects model. T₂* images were used to delineate focal demyelination/inflammation. Our results reveal a strong relationship between disability and measured microstructural parameters in normal appearing white matter and gray matter. Relationships between disability and mean of the kurtosis tensor, radial kurtosis, radial diffusivity were similar to what has been found in other hypomyelinating MS models, and in patients. However, the changes in biophysical modeling parameters and in particular in extra-axonal axial diffusivity were clearly different from previous studies employing other animal models of MS. In conclusion, our data suggest that DKI and microstructural modeling can provide a unique contrast capable of detecting EAE-specific changes correlating with clinical disability.

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.

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.

Peripheral nerve stimulation limits of a high amplitude and slew rate magnetic field gradient coil for neuroimaging

PURPOSE

To establish peripheral nerve stimulation (PNS) thresholds for an ultra-high performance magnetic field gradient subsystem (simultaneous 200-mT/m gradient amplitude and 500-T/m/s gradient slew rate; 1 MVA per axis [MAGNUS]) designed for neuroimaging with asymmetric transverse gradients and 42-cm inner diameter, and to determine PNS threshold dependencies on gender, age, patient positioning within the gradient subsystem, and anatomical landmarks.

METHODS

The MAGNUS head gradient was installed in a whole-body 3T scanner with a custom 16-rung bird-cage transmit/receive RF coil compatible with phased-array receiver brain coils. Twenty adult subjects (10 male, mean ± SD age = 40.4 ± 11.1 years) underwent the imaging and PNS study. The tests were repeated by displacing subject positions by 2-4 cm in the superior-inferior and anterior-posterior directions.

RESULTS

The x-axis (left-right) yielded mostly facial stimulation, with mean ΔG_min = 111 ± 6 mT/m, chronaxie = 766 ± 76 µsec. The z-axis (superior-inferior) yielded mostly chest/shoulder stimulation (123 ± 7 mT/m, 620 ± 62 µsec). Y-axis (anterior-posterior) stimulation was negligible. X-axis and z-axis thresholds tended to increase with age, and there was negligible dependency with gender. Translation in the inferior and posterior directions tended to increase the x-axis and z-axis thresholds, respectively. Electric field simulations showed good agreement with the PNS results. Imaging at MAGNUS gradient performance with increased PNS threshold provided a 35% reduction in noise-to-diffusion contrast as compared with whole-body performance (80 mT/m gradient amplitude, 200 T/m/sec gradient slew rate).

CONCLUSION

The PNS threshold of MAGNUS is significantly higher than that for whole-body gradients, which allows for diffusion gradients with short rise times (under 1 msec), important for interrogating brain microstructure length scales.

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.

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.

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.

The role of diffusion MRI in neuroscience

Diffusion-weighted imaging has pushed the boundaries of neuroscience by allowing us to examine the white matter microstructure of the living human brain. By doing so, it has provided answers to fundamental neuroscientific questions, launching a new field of research that had been largely inaccessible. We briefly summarize key questions that have historically been raised in neuroscience concerning the brain's white matter. We then expand on the benefits of diffusion-weighted imaging and its contribution to the fields of brain anatomy, functional models and plasticity. In doing so, this review highlights the invaluable contribution of diffusion-weighted imaging in neuroscience, presents its limitations and proposes new challenges for future generations who may wish to exploit this powerful technology to gain novel insights.

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.

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 time dependence of microstructural parameters in fixed spinal cord

Biophysical modelling of diffusion MRI is necessary to provide specific microstructural tissue properties. However, estimating model parameters from data with limited diffusion gradient strength, such as clinical scanners, has proven unreliable due to a shallow optimization landscape. On the other hand, estimation of diffusion kurtosis (DKI) parameters is more robust, and its parameters may be connected to microstructural parameters, given an appropriate biophysical model. However, it was previously shown that this procedure still does not provide sufficient information to uniquely determine all model parameters. In particular, a parameter degeneracy related to the relative magnitude of intra-axonal and extra-axonal diffusivities remains. Here we develop a model of diffusion in white matter including axonal dispersion and demonstrate stable estimation of all model parameters from DKI in fixed pig spinal cord. By employing the recently developed fast axisymmetric DKI, we use stimulated echo acquisition mode to collect data over a two orders of magnitude diffusion time range with very narrow diffusion gradient pulses, enabling finely resolved measurements of diffusion time dependence of both net diffusion and kurtosis metrics, as well as model intra- and extra-axonal diffusivities, and axonal dispersion. Our results demonstrate substantial time dependence of all parameters except volume fractions, and the additional time dimension provides support for intra-axonal diffusivity to be larger than extra-axonal diffusivity in spinal cord white matter, although not unambiguously. We compare our findings for the time-dependent compartmental diffusivities to predictions from effective medium theory with reasonable agreement.

Physical and numerical phantoms for the validation of brain microstructural MRI: A cookbook

Phantoms, both numerical (software) and physical (hardware), can serve as a gold standard for the validation of MRI methods probing the brain microstructure. This review aims to provide guidelines on how to build, implement, or choose the right phantom for a particular application, along with an overview of the current state-of-the-art of phantoms dedicated to study brain microstructure with MRI. For physical phantoms, we discuss the essential requirements and relevant characteristics of both the (NMR visible) liquid and (NMR invisible) phantom materials that induce relevant microstructural features detectable via MRI, based on diffusion, intra-voxel incoherent motion, magnetization transfer or magnetic susceptibility weighted contrast. In particular, for diffusion MRI, many useful phantoms have been proposed, ranging from simple liquids to advanced biomimetic phantoms consisting of hollow or plain microfibers and capillaries. For numerical phantoms, the focus is on Monte Carlo simulations of random walk, for which the basic principles, along with useful criteria to check and potential pitfalls are reviewed, in addition to a literature overview highlighting recent advances. While many phantoms exist already, the current review aims to stimulate further research in the field and to address remaining needs.