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We report the development of a double diffusion encoding (DDE) MRI method to estimate and map the axon diameter distribution (ADD) within an imaging volume. A variety of biological processes, ranging from development to disease and trauma, may lead to changes in the ADD in the central and peripheral nervous systems. Unlike previously proposed methods, this ADD experimental design and estimation framework employs a more general, nonparametric approach, without a priori assumptions about the underlying form of the ADD, making it suitable to analyze abnormal tissue. In the current study, this framework was used on an ex vivo ferret spinal cord, while emphasizing the way in which the ADD can be weighted by either the number or the volume of the axons. The different weightings, which result in different spatial contrasts, were considered throughout this work. DDE data were analyzed to derive spatially resolved maps of average axon diameter, ADD variance, and extra-axonal volume fraction, along with a novel sub-micron restricted structures map. The morphological information contained in these maps was then used to segment white matter into distinct domains by using a proposed k-means clustering algorithm with spatial contiguity and left–right symmetry constraints, resulting in identifiable white matter tracks. The method was validated by comparing histological measures to the estimated ADDs using a quantitative similarity metric, resulting in good agreement. With further acquisition acceleration and experimental parameters adjustments, this ADD estimation framework could be first used preclinically, and eventually clinically, enabling a wide range of neuroimaging applications for improved understanding of neurodegenerative pathologies and assessing microstructural changes resulting from trauma. [Display omitted] •Double diffusion encoding MRI method to map the axon diameter distribution (ADD)•Nonparametric approach without assumptions about the underlying form of the ADD•Axon volume and number-weighted ADDs result in different spatial contrasts.•Highly restricting sub-micron structures accounted for in the model•Validation by comparing histological measures to the estimated ADDs

Axon caliber plays a crucial role in determining conduction velocity and, consequently, in the timing and synchronization of neural activation. Noninvasive measurement of axon radii could have significant impact on the understanding of healthy and diseased neural processes. Until now, accurate axon radius mapping has eluded in vivo neuroimaging, mainly due to a lack of sensitivity of the MRI signal to micron-sized axons. Here, we show how – when confounding factors such as extra-axonal water and axonal orientation dispersion are eliminated – heavily diffusion-weighted MRI signals become sensitive to axon radii. However, diffusion MRI is only capable of estimating a single metric, the effective radius, representing the entire axon radius distribution within a voxel that emphasizes the larger axons. Our findings, both in rodents and humans, enable noninvasive mapping of critical information on axon radii, as well as resolve the long-standing debate on whether axon radii can be quantified.

The engineering of a 3T human MRI scanner equipped with 300mT/m gradients – the strongest gradients ever built for an in vivo human MRI scanner – was a major component of the NIH Blueprint Human Connectome Project (HCP). This effort was motivated by the HCP's goal of mapping, as completely as possible, the macroscopic structural connections of the in vivo healthy, adult human brain using diffusion tractography. Yet, the 300mT/m gradient system is well suited to many additional types of diffusion measurements. Here, we present three initial applications of the 300mT/m gradients that fall outside the immediate scope of the HCP. These include: 1) diffusion tractography to study the anatomy of consciousness and the mechanisms of brain recovery following traumatic coma; 2) q-space measurements of axon diameter distributions in the in vivo human brain and 3) postmortem diffusion tractography as an adjunct to standard histopathological analysis. We show that the improved sensitivity and diffusion-resolution provided by the gradients are rapidly enabling human applications of techniques that were previously possible only for in vitro and animal models on small-bore scanners, thereby creating novel opportunities to map the microstructure of the human brain in health and disease. •Diffusion spectrum imaging to study traumatic coma recovery•In vivo human axon diameter measurements using 300mT/m gradients•High-resolution (0.6mm isotropic) diffusion imaging in whole, fixed human brain

Development of therapies for neurological disorders depends on our ability to non-invasively diagnose and monitor the progression of underlying pathologies at the cellular level. Physics and physiology limit the resolution of human MRI to be orders of magnitude coarser than cell dimensions. Here we identify and quantify the MRI signal coming from within micrometer-thin axons in human white matter tracts in vivo, by utilizing the sensitivity of diffusion MRI to Brownian motion of water molecules restricted by cell walls. We study a specific power-law scaling of the diffusion MRI signal with the diffusion weighting, predicted for water confined to narrow axons, and quantify axonal water fraction and orientation dispersion.

The first phase of the Human Connectome Project pioneered advances in MRI technology for mapping the macroscopic structural connections of the living human brain through the engineering of a whole-body human MRI scanner equipped with maximum gradient strength of 300 mT/m, the highest ever achieved for human imaging. While this instrument has made important contributions to the understanding of macroscale connectional topology, it has also demonstrated the potential of dedicated high-gradient performance scanners to provide unparalleled in vivo assessment of neural tissue microstructure. Building on the initial groundwork laid by the original Connectome scanner, we have now embarked on an international, multi-site effort to build the next-generation human 3T Connectome scanner (Connectome 2.0) optimized for the study of neural tissue microstructure and connectional anatomy across multiple length scales. In order to maximize the resolution of this in vivo microscope for studies of the living human brain, we will push the diffusion resolution limit to unprecedented levels by (1) nearly doubling the current maximum gradient strength from 300 mT/m to 500 mT/m and tripling the maximum slew rate from 200 T/m/s to 600 T/m/s through the design of a one-of-a-kind head gradient coil optimized to minimize peripheral nerve stimulation; (2) developing high-sensitivity multi-channel radiofrequency receive coils for in vivo and ex vivo human brain imaging; (3) incorporating dynamic field monitoring to minimize image distortions and artifacts; (4) developing new pulse sequences to integrate the strongest diffusion encoding and highest spatial resolution ever achieved in the living human brain; and (5) calibrating the measurements obtained from this next-generation instrument through systematic validation of diffusion microstructural metrics in high-fidelity phantoms and ex vivo brain tissue at progressively finer scales with accompanying diffusion simulations in histology-based micro-geometries. We envision creating the ultimate diffusion MRI instrument capable of capturing the complex multi-scale organization of the living human brain – from the microscopic scale needed to probe cellular geometry, heterogeneity and plasticity, to the mesoscopic scale for quantifying the distinctions in cortical structure and connectivity that define cyto- and myeloarchitectonic boundaries, to improvements in estimates of macroscopic connectivity.

This paper aims to identify the minimum requirements for an accurate model of the diffusion MR signal in white matter of the brain. We construct a taxonomy of multi-compartment models of white matter from combinations of simple models for the intra- and the extra-axonal spaces. We devise a new diffusion MRI protocol that provides measurements with a wide range of imaging parameters for diffusion sensitization both parallel and perpendicular to white matter fibres. We use the protocol to acquire data from two fixed rat brains, which allows us to fit, study and compare the different models. The study examines a total of 47 analytic models, including several well-used models from the literature, which we place within the taxonomy. The results show that models that incorporate intra-axonal restriction, such as ball and stick or CHARMED, generally explain the data better than those that do not, such as the DT or the biexponential models. However, three-compartment models which account for restriction parallel to the axons and incorporate pore size explain the measurements most accurately. The best fit comes from combining a full diffusion tensor (DT) model of the extra-axonal space with a cylindrical intra-axonal component of single radius and a third spherical compartment of non-zero radius. We also measure the stability of the non-zero radius intra-axonal models and find that single radius intra-axonal models are more stable than gamma distributed radii models with similar fitting performance. ► Identify least requirements for a precise model of diffusion in white matter. ► Taxonomy of analytic models including well-used models from literature. ► New imaging protocol for model comparison. ► Restriction is essential to explain the data. ► Three-compartment models outperform two-compartments.

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. •85% of the variance in CV is accounted for by axon diameter and g-ratio, which are potentially accessible from in vivo MRI.•CV estimates from MRI are robust to errors in myelin and axonal volume estimates, but sensitive to errors in axon diameter.•CV estimates are feasible for large axons but limitations of in vivo imaging of small axons poses a significant challenge.

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

•Large, high-resolution 3D EM data of human superficial white matter was segmented.•Segmentation results using deep learning were highly accurate.•128,285 myelinated axons were delineated, with 2102 longer than 100 μm.•Local variations in diameter (beading) and direction (undulation) were observed.•Axons had inner diameters ∼0.5 µm, outer diameters ∼1 µm, and g-ratios ∼0.5. Short-range association fibers located in the superficial white matter play an important role in mediating higher-order cognitive function in humans. Detailed morphological characterization of short-range association fibers at the microscopic level promises to yield important insights into the axonal features driving cortico-cortical connectivity in the human brain yet has been difficult to achieve to date due to the challenges of imaging at nanometer-scale resolution over large tissue volumes. This work presents results from multi-beam scanning electron microscopy (EM) data acquired at 4 × 4 × 33 nm3 resolution in a volume of human superficial white matter measuring 200 × 200 × 112 μm3, leveraging automated analysis methods. Myelin and myelinated axons were automatically segmented using deep convolutional neural networks (CNNs), assisted by transfer learning and dropout regularization techniques. A total of 128,285 myelinated axons were segmented, of which 70,321 and 2102 were longer than 10 and 100 μm, respectively. Marked local variations in diameter (i.e., beading) and direction (i.e., undulation) were observed along the length of individual axons. Myelinated axons longer than 10 μm had inner diameters around 0.5 µm, outer diameters around 1 µm, and g-ratios around 0.5. This work fills a gap in knowledge of axonal morphometry in the superficial white matter and provides a large 3D human EM dataset and accurate segmentation results for a variety of future studies in different fields.

Direct measurement of tissue microstructure with diffusion MRI offers a new class of markers, such as axon diameters, that give more specific information about tissue than measures derived from diffusion tensor imaging. The existing techniques of this kind assume a single axon orientation in the tissue model, which may be a reasonable approximation only for the most coherently oriented brain white matter, such as the corpus callosum. For most other areas, orientation dispersion is not negligible and, if unaccounted for, leads to overestimation of the axon diameters, prohibiting their accurate mapping over the whole brain. Here we propose a new model that captures the effect of orientation dispersion explicitly. A numerical scheme is developed to compute the diffusion signal prescribed by the proposed model efficiently, which supports the simultaneous estimation of the axon diameter and orientation dispersion. Synthetic data experiments demonstrate that the new model provides an axon diameter index that is robust to the presence of orientation dispersion. Results on in vivo human data show reduced axon diameter index and better agreement with histology compared to previous methods suggesting improvements in the axon diameter estimate. ► Existing models overestimate axon diameter when orientation dispersion is present. ► A new model for axon diameter estimation in the presence of orientation dispersion. ► New model improves axon diameter estimates in simulation and in vivo human brain data. ► New model additionally provides a useful index of orientation dispersion.