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Preclinical diffusion MRI (dMRI) has proven value in methods development and validation, characterizing the biological basis of diffusion phenomena, and comparative anatomy. While dMRI enables in vivo non-invasive characterization of tissue, ex vivo dMRI is increasingly being used to probe tissue microstructure and brain connectivity. Ex vivo dMRI has several experimental advantages that facilitate high spatial resolution and high signal-to-noise ratio (SNR) images, cutting-edge diffusion contrasts, and direct comparison with histological data as a methodological validation. However, there are a number of considerations that must be made when performing ex vivo experiments. The steps from tissue preparation, image acquisition and processing, and interpretation of results are complex, with many decisions that not only differ dramatically from in vivo imaging of small animals, but ultimately affect what questions can be answered using the data. This work concludes a 3-part series of recommendations and considerations for preclinical dMRI. Herein, we describe best practices for dMRI of ex vivo tissue, with a focus on image pre-processing, data processing and model fitting, and tractography. In each section, we attempt to provide guidelines and recommendations, but also highlight areas for which no guidelines exist (and why), and where future work should lie. We end by providing guidelines on code sharing and data sharing, and point towards open-source software and databases specific to small animal and ex vivo imaging., Comment: Part 3 of 3 in "Considerations and recommendations for preclinical diffusion MRI"

Water diffusion gives rise to micrometer-scale sensitivity of diffusion MRI (dMRI) to cellular-level tissue structure. The advent of precision medicine and quantitative imaging hinges on revealing the information content of dMRI, and providing its parsimonious basis- and hardware-independent "fingerprint". Here we reveal the geometry of a multi-dimensional dMRI signal, classify all 21 invariants of diffusion and covariance tensors in terms of irreducible representations of the group of rotations, and relate them to tissue properties. Previously studied dMRI contrasts are expressed via 7 invariants, while the remaining 14 provide novel complementary information. We design acquisitions based on icosahedral vertices guaranteeing minimal number of measurements to determine 3-4 most used invariants in only 1-2 minutes for the whole brain. Representing dMRI signals via scalar invariant maps with definite symmetries will underpin machine learning classifiers of brain pathology, development, and aging, while fast protocols will enable translation of advanced dMRI into clinical practice.

The clinical translation of diffusion MRI (dMRI)-derived quantitative contrasts hinges on robust reproducibility, minimizing both same-scanner and cross-scanner variability. This study evaluates the reproducibility of higher-order diffusion metrics (beyond conventional diffusion tensor imaging), at the voxel and region-of-interest levels on magnitude and complex-valued dMRI data, using denoising with and without harmonization. We compared same-scanner, cross-scanner, and cross-protocol variability for a multi-shell dMRI protocol in 20 subjects. We first evaluated the effectiveness of denoising strategies for both magnitude and complex data to mitigate noise-induced bias and variance, to improve dMRI parametric maps and reproducibility. We examined the impact of denoising under different analysis approaches, comparing voxel-wise and region of interest (ROI)-based methods. We also evaluated the role of denoising when harmonizing dMRI across scanners and protocols. DTI and DKI maps visually improve after MPPCA denoising, with noticeably fewer outliers in kurtosis maps. Denoising enhances voxel-wise reproducibility, with test-retest variability of kurtosis indices reduced from 15-20% to 5-10% after denoising. Complex dMRI denoising reduces the noise floor by up to 60%. In ROI-analyses, denoising also increased statistical power, with reduction in sample size requirements by up to 40% for detecting differences across populations. Combining denoising with linear-RISH harmonization, in voxel-wise assessments, improved intra-scanner intraclass correlation coefficients for FA from moderate to excellent repeatability over harmonization alone. The enhancement in data quality and precision due to denoising facilitates the broader application and acceptance of these advanced imaging techniques in both clinical practice and large-scale neuroimaging studies.

Joint modeling of diffusion and relaxation has seen growing interest due to its potential to provide complementary information about tissue microstructure. For brain white matter, we designed an optimal diffusion-relaxometry MRI protocol that samples multiple b-values, B-tensor shapes, and echo times (TE). This variable-TE protocol (27 min) has as subsets a fixed-TE protocol (15 min) and a 2-shell dMRI protocol (7 min), both characterizing diffusion only. We assessed the sensitivity, specificity and reproducibility of these protocols with synthetic experiments and in six healthy volunteers. Compared with the fixed-TE protocol, the variable-TE protocol enables estimation of free water fractions while also capturing compartmental $T_2$ relaxation times. Jointly measuring diffusion and relaxation offers increased sensitivity and specificity to microstructure parameters in brain white matter with voxelwise coefficients of variation below 10%., Comment: 8 figures

Biophysical modeling of diffusion MRI (dMRI) offers the exciting potential of bridging the gap between the macroscopic MRI resolution and microscopic cellular features, effectively turning the MRI scanner into a noninvasive in vivo microscope. In brain white matter, the Standard Model (SM) interprets the dMRI signal in terms of axon dispersion, intra- and extra-axonal water fractions and diffusivities. However, for SM to be fully applicable and correctly interpreted, it needs to be carefully evaluated using histology. Here, we perform a comprehensive histological validation of the SM parameters, by characterizing WM microstructure in sham and injured rat brains using volume (3d) electron microscopy (EM) and ex vivo dMRI. Sensitivity is evaluated by how close each SM metric is to its histological counterpart, and specificity by how independent it is from other, non-corresponding histological features. This comparison reveals that SM is sensitive and specific to microscopic properties, clearing the way for the clinical adoption of in vivo dMRI derived SM parameters as biomarkers for neurological disorders., Comment: 19 pages, 5 figures, 1 table, 5 supplementary figures

Diffusion magnetic resonance imaging offers unique in vivo sensitivity to tissue microstructure in brain white matter, which undergoes significant changes during development and is compromised in virtually every neurological disorder. Yet, the challenge is to develop biomarkers that are specific to micrometer-scale cellular features in a human MRI scan of a few minutes. Here we quantify the sensitivity and specificity of a multicompartment diffusion modeling framework to the density, orientation and integrity of axons. We demonstrate that using a machine learning based estimator, our biophysical model captures the morphological changes of axons in early development, acute ischemia and multiple sclerosis (total N=821). The methodology of microstructure mapping is widely applicable in clinical settings and in large imaging consortium data to study development, aging and pathology., Comment: 4 figures, 5 supplementary figures, 1 supplementary table

Various diffusion MRI (dMRI) preprocessing pipelines are currently available to yield more accurate diffusion parameters. Here, we evaluated accuracy and robustness of the optimized Diffusion parameter EStImation with Gibbs and NoisE Removal (DESIGNER) pipeline in a large clinical dMRI dataset and using ground truth phantoms. DESIGNER has been modified to improve denoising and target Gibbs ringing for partial Fourier acquisitions. We compared the revisited DESIGNER (Dv2) (including denoising, Gibbs removal, correction for motion, EPI distortion, and eddy currents) against the original DESIGNER (Dv1) pipeline, minimal preprocessing (including correction for motion, EPI distortion, and eddy currents only), and no preprocessing on a large clinical dMRI dataset of 524 control subjects with ages between 25 and 75 years old. We evaluated the effect of specific processing steps on age correlations in white matter with DTI and DKI metrics. We also evaluated the added effect of minimal Gaussian smoothing to deal with noise and to reduce outliers in parameter maps compared to DESIGNER (Dv2)'s noise removal method. Moreover, DESIGNER (Dv2)'s updated noise and Gibbs removal methods were assessed using ground truth dMRI phantom to evaluate accuracy. Results show age correlation in white matter with DTI and DKI metrics were affected by the preprocessing pipeline, causing systematic differences in absolute parameter values and loss or gain of statistical significance. Both in clinical dMRI and ground truth phantoms, DESIGNER (Dv2) pipeline resulted in the smallest number of outlier voxels and improved accuracy in DTI and DKI metrics as noise was reduced and Gibbs removal was improved. Thus, DESIGNER (Dv2) provides more accurate and robust DTI and DKI parameter maps as compared to no preprocessing or minimal preprocessing.

The value of preclinical diffusion MRI (dMRI) is substantial. While dMRI enables in vivo non-invasive characterization of tissue, ex vivo dMRI is increasingly used to probe tissue microstructure and brain connectivity. Ex vivo dMRI has several experimental advantages including higher signal-to-noise ratio and spatial resolution compared to in vivo studies, and enabling more advanced diffusion contrasts. Another major advantage of ex vivo dMRI is the direct comparison with histological data as a methodological validation. However, there are a number of considerations that must be made when performing ex vivo experiments. The steps from tissue preparation, image acquisition and processing, and interpretation of results are complex, with decisions that not only differ dramatically from in vivo imaging of small animals, but ultimately affect what questions can be answered using the data. This work represents "Part 2" of a 3-part series of recommendations and considerations for preclinical dMRI. We describe best practices for dMRI of ex vivo tissue, with a focus on the value that ex vivo imaging adds to the field of dMRI and considerations in ex vivo image acquisition. We give general considerations and foundational knowledge that must be considered when designing experiments. We describe differences in specimens and models and discuss why some may be more or less appropriate for different studies. We then give guidelines for ex vivo protocols, including tissue fixation, sample preparation, and MR scanning. In each section, we attempt to provide guidelines and recommendations, but also highlight areas for which no guidelines exist (and why), and where future work should lie. An overarching goal herein is to enhance the rigor and reproducibility of ex vivo dMRI acquisitions and analyses, and thereby advance biomedical knowledge., Comment: Part 2 of 3 in "Considerations and recommendations for preclinical diffusion MRI"

Small-animal diffusion MRI (dMRI) has been used for methodological development and validation, characterizing the biological basis of diffusion phenomena, and comparative anatomy. The steps from animal setup and monitoring, to acquisition, analysis, and interpretation are complex, with many decisions that may ultimately affect what questions can be answered using the resultant data. This work aims to present selected recommendations and guidelines from the diffusion community, on best practices for preclinical dMRI of in vivo animals. We describe the general considerations and foundational knowledge that must be considered when designing experiments. We briefly describe differences in animal species and disease models and discuss why some may be more or less appropriate for different studies. We then give guidelines for in vivo acquisition protocols, including decisions on hardware, animal preparation, and imaging sequences, followed by advice for data processing including pre-processing, model-fitting, and tractography. Finally, we provide an online resource which lists publicly available preclinical dMRI datasets and software packages, to promote responsible and reproducible research. In each section, we attempt to provide guides and recommendations, but also highlight areas for which no guidelines exist (and why), and where future work should focus. While we mainly cover the central nervous system (on which most preclinical dMRI studies are focused), we also provide, where possible and applicable, recommendations for other organs of interest. An overarching goal herein is to enhance the rigor and reproducibility of small animal dMRI acquisitions and analyses, and thereby advance biomedical knowledge., Comment: 47 pages, 5 figures, 1 table

Estimating intra- and extra-axonal microstructure parameters, such as volume fractions and diffusivities, has been one of the major efforts in brain microstructure imaging with MRI. The Standard Model (SM) of diffusion in white matter has unified various modeling approaches based on impermeable narrow cylinders embedded in locally anisotropic extra-axonal space. However, estimating the SM parameters from a set of conventional diffusion MRI (dMRI) measurements is ill-conditioned. Multidimensional dMRI helps resolve the estimation degeneracies, but there remains a need for clinically feasible acquisitions that yield robust parameter maps. Here we find optimal multidimensional protocols by minimizing the mean-squared error of machine learning-based SM parameter estimates for two 3T scanners with corresponding gradient strengths of $40$ and $80\,\unit{mT/m}$. We assess intra-scanner and inter-scanner repeatability for 15-minute optimal protocols by scanning 20 healthy volunteers twice on both scanners. The coefficients of variation all SM parameters except free water fraction are $\lesssim 10\%$ voxelwise and $1-4 \%$ for their region-averaged values. As the achieved SM reproducibility outcomes are similar to those of conventional diffusion tensor imaging, our results enable robust in vivo mapping of white matter microstructure in neuroscience research and in the clinic., Comment: 17 pages, 7 figures

Background: Monte Carlo simulations of diffusion are commonly used as a model validation tool as they are especially suitable for generating the diffusion MRI signal in complicated tissue microgeometries. New method: Here we describe the details of implementing Monte Carlo simulations in three-dimensional (3d) voxelized segmentations of cells in microscopy images. Using the concept of the corner reflector, we largely reduce the computational load of simulating diffusion within and exchange between multiple cells. Precision is further achieved by GPU-based parallel computations. Results: Our simulation of diffusion in white matter axons segmented from a mouse brain demonstrates its value in validating biophysical models. Furthermore, we provide the theoretical background for implementing a discretized diffusion process, and consider the finite-step effects of the particle-membrane reflection and permeation events, needed for efficient simulation of interactions with irregular boundaries, spatially variable diffusion coefficient, and exchange. Comparison with existing methods: To our knowledge, this is the first Monte Carlo pipeline for MR signal simulations in a substrate composed of numerous realistic cells, accounting for their permeable and irregularly-shaped membranes. Conclusions: The proposed RMS pipeline makes it possible to achieve fast and accurate simulations of diffusion in realistic tissue microgeometry, as well as the interplay with other MR contrasts. Presently, RMS focuses on simulations of diffusion, exchange, and T1 and T2 NMR relaxation in static tissues, with a possibility to straightforwardly account for susceptibility-induced T2* effects and flow.

To study axonal microstructure with diffusion MRI, axons are typically modeled as straight impermeable cylinders, whereby the transverse diffusion MRI signal can be made sensitive to the cylinder's inner diameter. However, the shape of a real axon varies along the axon direction, which couples the longitudinal and transverse diffusion of the overall axon direction. Here we develop a theory of the intra-axonal diffusion MRI signal based on coarse-graining of the axonal shape by 3d diffusion. We demonstrate how the estimate of the inner diameter is confounded by the diameter variations (beading), and by the local variations in direction (undulations) along the axon. We analytically relate diffusion MRI metrics, such as time-dependent radial diffusivity D(t) and kurtosis K(t), to the axonal shape, and validate our theory using Monte Carlo simulations in synthetic undulating axons with randomly positioned beads, and in realistic axons reconstructed from electron microscopy images of mouse brain white matter. We show that (i) In the narrow pulse limit, the inner diameter from D(t) is overestimated by about twofold due to a combination of axon caliber variations and undulations (each contributing a comparable effect size); (ii) The narrow-pulse kurtosis K$_{t\to\infty}$ deviates from that in an ideal cylinder due to caliber variations; we also numerically calculate the fourth-order cumulant for an ideal cylinder in the wide pulse limit, which is relevant for inner diameter overestimation; (iii) In the wide pulse limit, the axon diameter overestimation is mainly due to undulations at low diffusion weightings b; and (iv) The effect of undulations can be considerably reduced by directional averaging of high-b signals, with the apparent inner diameter given by a combination of the axon caliber (dominated by the thickest axons), caliber variations, and the residual contribution of undulations.

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 $\sim t^{-\vartheta}$ with dynamical exponent $\vartheta$. To interpret our measurements, we systematize the relevant scenarios and mechanisms for diffusion time-dependence in the brain. Using effective medium theory formalisms, we derive an exact relation between the power-law tails in $D(t)$ and $K(t)$. The estimated power-law dynamical exponent $\vartheta\simeq1/2$ 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 $\vartheta=1/2$ exponent. In contrast, the K\"arger 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 $K(t)$ alltogether establish the sensitivity of a macroscopic MRI signal to micrometer-scale structural heterogeneities along neurites in human gray matter in vivo.

Mild Traumatic Brain Injury (mTBI) is a significant public health problem. The most troubling symptoms after mTBI are cognitive complaints. Studies show measurable differences between patients with mTBI and healthy controls with respect to tissue microstructure using diffusion MRI. However, it remains unclear which diffusion measures are the most informative with regard to cognitive functions in both the healthy state as well as after injury. In this study, we use diffusion MRI to formulate a predictive model for performance on working memory based on the most relevant MRI features. The key challenge is to identify relevant features over a large feature space with high accuracy in an efficient manner. To tackle this challenge, we propose a novel improvement of the best first search approach with crossover operators inspired by genetic algorithm. Compared against other heuristic feature selection algorithms, the proposed method achieves significantly more accurate predictions and yields clinically interpretable selected features.

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 uncover its origins by Monte Carlo simulations in realistic substrates from 3d 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 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.

We develop and evaluate a neural network-based method for Gibbs artifact and noise removal. A convolutional neural network (CNN) was designed for artifact removal in diffusion-weighted imaging data. Two implementations were considered: one for magnitude images and one for complex images. Both models were based on the same encoder-decoder structure and were trained by simulating MRI acquisitions on synthetic non-MRI images. Both machine learning methods were able to mitigate artifacts in diffusion-weighted images and diffusion parameter maps. The CNN for complex images was also able to reduce artifacts in partial Fourier acquisitions. The proposed CNNs extend the ability of artifact correction in diffusion MRI. The machine learning method described here can be applied on each imaging slice independently, allowing it to be used flexibly in clinical applications., Comment: Pre-print prior to submission to Magnetic Resonance in Medicine

In this work, we propose bag of adversarial features (BAF) for identifying mild traumatic brain injury (MTBI) patients from their diffusion magnetic resonance images (MRI) (obtained within one month of injury) by incorporating unsupervised feature learning techniques. MTBI is a growing public health problem with an estimated incidence of over 1.7 million people annually in US. Diagnosis is based on clinical history and symptoms, and accurate, concrete measures of injury are lacking. Unlike most of previous works, which use hand-crafted features extracted from different parts of brain for MTBI classification, we employ feature learning algorithms to learn more discriminative representation for this task. A major challenge in this field thus far is the relatively small number of subjects available for training. This makes it difficult to use an end-to-end convolutional neural network to directly classify a subject from MR images. To overcome this challenge, we first apply an adversarial auto-encoder (with convolutional structure) to learn patch-level features, from overlapping image patches extracted from different brain regions. We then aggregate these features through a bag-of-word approach. We perform an extensive experimental study on a dataset of 227 subjects (including 109 MTBI patients, and 118 age and sex matched healthy controls), and compare the bag-of-deep-features with several previous approaches. Our experimental results show that the BAF significantly outperforms earlier works relying on the mean values of MR metrics in selected brain regions., Comment: IEEE Transactions on Medical Imaging

Mild traumatic brain injury is a growing public health problem with an estimated incidence of over 1.7 million people annually in US. Diagnosis is based on clinical history and symptoms, and accurate, concrete measures of injury are lacking. This work aims to directly use diffusion MR images obtained within one month of trauma to detect injury, by incorporating deep learning techniques. To overcome the challenge due to limited training data, we describe each brain region using the bag of word representation, which specifies the distribution of representative patch patterns. We apply a convolutional auto-encoder to learn the patch-level features, from overlapping image patches extracted from the MR images, to learn features from diffusion MR images of brain using an unsupervised approach. Our experimental results show that the bag of word representation using patch level features learnt by the auto encoder provides similar performance as that using the raw patch patterns, both significantly outperform earlier work relying on the mean values of MR metrics in selected brain regions., Comment: arXiv admin note: text overlap with arXiv:1710.06824

Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests are used to both assess the patient condition and to monitor the patient progress. This work aims to directly use MR images taken shortly after injury to detect whether a patient suffers from mTBI, by incorporating machine learning and computer vision techniques to learn features suitable discriminating between mTBI and normal patients. We focus on 3 regions in brain, and extract multiple patches from them, and use bag-of-visual-word technique to represent each subject as a histogram of representative patterns derived from patches from all training subjects. After extracting the features, we use greedy forward feature selection, to choose a subset of features which achieves highest accuracy. We show through experimental studies that BoW features perform better than the simple mean value features which were used previously.

Big data initiatives such as the Enhancing NeuroImaging Genetics through Meta-Analysis consortium (ENIGMA), combine data collected by independent studies worldwide to achieve more accurate estimates of effect sizes and more reliable and reproducible outcomes. Such efforts require harmonized analyses protocols to consistently extract phenotypes. Even so, challenges include wide variability of fMRI protocols and scanner platforms; this leads to site-to-site variance in quality, resolution and temporal signal-to-noise ratio (tSNR). An effective harmonization should provide optimal measures for data of different qualities. We developed a multi-site rsfMRI analysis pipeline to allow research groups around the world to process rsfMRI scans in a harmonized way, to extract consistent and quantitative measurements of connectivity and to perform coordinated statistical tests. We used the single-modality ENIGMA rsfMRI pipeline based on model-free Marchenko-Pastor PCA based denoising to verify and replicate findings of significant heritability of measures from resting state networks. We analyzed two independent cohorts, GOBS (Genetics of Brain Structure) and HCP (the Human Connectome Project), which collected data using conventional and connectomics oriented fMRI protocols. We used seed-based connectivity and dual-regression approaches to show that rsfMRI signal is consistently heritable across twenty major functional network measures. Heritability values of 20-40% were observed across both cohorts., Comment: 12 pages, 3 figures, PSB 2018

While diffusion MRI has been extremely promising in the study of MTBI, identifying patients with recent MTBI remains a challenge. The literature is mixed with regard to localizing injury in these patients, however, gray matter such as the thalamus and white matter including the corpus callosum and frontal deep white matter have been repeatedly implicated as areas at high risk for injury. The purpose of this study is to develop a machine learning framework to classify MTBI patients and controls using features derived from multi-shell diffusion MRI in the thalamus, frontal white matter and corpus callosum.

Brownian motion of water molecules provides an essential length scale, the diffusion length, commensurate with cell dimensions in biological tissues. Measuring the diffusion coefficient as a function of diffusion time makes in vivo diffusion MRI uniquely sensitive to the cellular features about three orders of magnitude below imaging resolution. However, there is a longstanding debate, regarding which contribution --- intra- or extra-cellular --- is more relevant in the overall time-dependence of the diffusion metrics. Here we resolve this debate in the human brain white matter. By varying not just the diffusion time, but also the gradient pulse duration of a standard diffusion pulse sequence, we identify a functional form of the measured time-dependent diffusion coefficient transverse to white matter tracts in 5 healthy volunteers. This specific functional form is shown to originate from the extra-axonal space, and provides estimates of the fiber packing correlation length for axons in a bundle. Our results offer a metric for the outer axonal diameter, a promising candidate marker for demyelination in neurodegenerative diseases. From the methodological perspective, our analysis demonstrates how competing models, which describe different physics yet interpolate standard measurements equally well, can be distinguished based on their prediction for an independent "orthogonal" measurement.

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 the three major avenues. The first avenue focusses on the 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 studying the transient effects has the potential to quantify the relevant length scales for neuronal tissue, such as the packing correlation length for neuronal fibers, the degree of neuronal beading, and compartment sizes. The second avenue corresponds to the long-time limit, when the observed signal can be approximated as a sum of multiple non-exchanging 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 the future directions which can open exciting possibilities for designing quantitative markers of tissue physiology and pathology, based on methods of studying mesoscopic transport in disordered systems., Comment: 50 pages, 13 figures, revtex4-1

We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational invariants and their expansion in the powers of diffusion weighting, we analytically uncover the nontrivial topology of the parameter estimation landscape, showing that multiple branches of parameters describe the measurement almost equally well, with only one of them corresponding to the biophysical reality. A comprehensive acquisition shows that the branch choice varies across the brain. Our framework reveals hidden degeneracies in MRI parameter estimation for neuronal tissue, provides microstructural and orientational maps in the whole brain without constraints or priors, and connects modern biophysical modeling with clinical MRI., Comment: 25 pages, 12 figures, elsarticle two-column

Development of successful therapies for neurological disorders depends on our ability to diagnose and monitor the progression of underlying pathologies at the cellular level. Physics and physiology limit the resolution of human MRI to millimeters, three orders of magnitude coarser than the cell dimensions of microns. A promising way to access cellular structure is provided by diffusion-weighted MRI (dMRI), a modality which exploits the sensitivity of the MRI signal to micron-level Brownian motion of water molecules strongly hindered by cell walls. By analyzing diffusion of water molecules in human subjects, here we demonstrate that biophysical modeling has the potential to break the intrinsic MRI resolution limits. The observation of a universal power-law scaling of the dMRI signal identifies the contribution from water specifically confined inside narrow impermeable axons, validating the overarching assumption behind models of diffusion in neuronal tissue. This scaling behavior establishes dMRI as an in vivo instrument able to quantify intra-axonal properties orders of magnitude below the nominal MRI resolution, spurring our understanding of brain anatomy and function., Comment: 7 pages, 4 figures, revtex4-1

We report on an experimental observation of classical diffusion distinguishing between structural universality classes of disordered systems in one dimension. Samples of hyperuniform and short-range disorder were designed, characterized by the statistics of the placement of $\mu$m-thin parallel permeable barriers, and the time-dependent diffusion coefficient was measured by NMR methods over three orders of magnitude in time. The relation between the structural exponent, characterizing disorder universality class, and the dynamical exponent of the diffusion coefficient is experimentally verified. The experimentally established relation between structure and transport exemplifies the hierarchical nature of structural complexity --- dynamics are mainly determined by the universality class, whereas microscopic parameters affect the non-universal coefficients. These results open the way for non-invasive characterization of structural correlations in porous media, complex materials, and biological tissues via a bulk diffusion measurement., Comment: 5 pages, 3 Figures

Molecular diffusion measurements are widely used to probe microstructure in materials and living organisms noninvasively. The precise relation of diffusion metrics to microstructure remains a major challenge: In complex samples, it is often unclear which structural features are most relevant and can be quantified. Here we classify the structural complexity in terms of the long time tail exponent in the molecular velocity autocorrelation function. The specific values of the dynamical exponent let us identify the relevant tissue microanatomy affecting water diffusion measured with MRI in muscles and in brain, and the microstructural changes in ischemic stroke. Our framework presents a systematic way to identify the most relevant part of structural complexity using transport measured with a variety of techniques., Comment: 5 pages + supplementary material