Detection of microscopic anisotropy in gray matter and in a novel tissue phantom using double Pulsed Gradient Spin Echo MR

Novel pore size-controlled, susceptibility matched, 3D-printed MRI phantoms

PURPOSE

We report the design concept and fabrication of MRI phantoms, containing blocks of aligned microcapillaires that can be stacked into larger arrays to construct diameter distribution phantoms or fractured, to create a "powder-averaged" emulsion of randomly oriented blocks for vetting or calibrating advanced MRI methods, that is, diffusion tensor imaging, AxCaliber MRI, MAP-MRI, and multiple pulsed field gradient or double diffusion-encoded microstructure imaging methods. The goal was to create a susceptibility-matched microscopically anisotropic but macroscopically isotropic phantom with a ground truth diameter that could be used to vet advanced diffusion methods for diameter determination in fibrous tissues.

METHODS

Two-photon polymerization, a novel three-dimensional printing method is used to fabricate blocks of capillaries. Double diffusion encoding methods were employed and analyzed to estimate the expected MRI diameter.

RESULTS

Susceptibility-matched microcapillary blocks or modules that can be assembled into large-scale MRI phantoms have been fabricated and measured using advanced diffusion methods, resulting in microscopic anisotropy and random orientation.

CONCLUSION

This phantom can vet and calibrate various advanced MRI methods and multiple pulsed field gradient or diffusion-encoded microstructure imaging methods. We demonstrated that two double diffusion encoding methods underestimated the ground truth diameter.

Biophysical Principles and Computational Modeling of Deep Brain Stimulation

BACKGROUND

Deep brain stimulation (DBS) has revolutionized the treatment of neurological disorders, yet the mechanisms of DBS are still under investigation. Computational models are important in silico tools for elucidating these underlying principles and potentially for personalizing DBS therapy to individual patients. The basic principles underlying neurostimulation computational models, however, are not well known in the clinical neuromodulation community.

OBJECTIVE

In this study, we present a tutorial on the derivation of computational models of DBS and outline the biophysical contributions of electrodes, stimulation parameters, and tissue substrates to the effects of DBS.

RESULTS

Given that many aspects of DBS are difficult to characterize experimentally, computational models have played an important role in understanding how material, size, shape, and contact segmentation influence device biocompatibility, energy efficiency, the spatial spread of the electric field, and the specificity of neural activation. Neural activation is dictated by stimulation parameters including frequency, current vs voltage control, amplitude, pulse width, polarity configurations, and waveform. These parameters also affect the potential for tissue damage, energy efficiency, the spatial spread of the electric field, and the specificity of neural activation. Activation of the neural substrate also is influenced by the encapsulation layer surrounding the electrode, the conductivity of the surrounding tissue, and the size and orientation of white matter fibers. These properties modulate the effects of the electric field and determine the ultimate therapeutic response.

CONCLUSION

This article describes biophysical principles that are useful for understanding the mechanisms of neurostimulation.

Double pulsed field gradient diffusion MRI to assess skeletal muscle microstructure

PURPOSE

Preliminary study to determine whether double pulsed field gradient (PFG) diffusion MRI is sensitive to key features of muscle microstructure related to function.

METHODS

The restricted diffusion profile of molecules in models of muscle microstructure derived from histology were systematically simulated using a numerical simulation approach. Diffusion tensor subspace imaging analysis of the diffusion signal was performed, and spherical anisotropy (SA) was calculated for each model. Linear regression was used to determine the predictive capacity of SA on the fiber area, fiber diameter, and surface area to volume ratio of the models. Additionally, a rat model of muscle hypertrophy was scanned using a single PFG and a double PFG pulse sequence, and the restricted diffusion measurements were compared with histological measurements of microstructure.

RESULTS

Excellent agreement between SA and muscle fiber area (r2  = 0.71; p < 0.0001), fiber diameter (r2  = 0.83; p < 0.0001), and surface area to volume ratio (r2  = 0.97; p < 0.0001) in simulated models was found. In a scanned rat leg, the distribution of these microstructural features measured from histology was broad and demonstrated that there is a wide variance in the microstructural features observed, similar to the SA distributions. However, the distribution of fractional anisotropy measurements in the same tissue was narrow.

CONCLUSIONS

This study demonstrates that SA-a scalar value from diffusion tensor subspace imaging analysis-is highly sensitive to muscle microstructural features predictive of function. Furthermore, these techniques and analysis tools can be translated to real experiments in skeletal muscle. The increased dynamic range of SA compared with fractional anisotropy in the same tissue suggests increased sensitivity to detecting changes in tissue microstructure.

Extra-axonal contribution to double diffusion encoding-based pore size estimates in the corticospinal tract

OBJECTIVE

To study the origin of compartment size overestimation in double diffusion encoding MRI (DDE) in vivo experiments in the human corticospinal tract. Here, the extracellular space is hypothesized to be the origin of the DDE signal. By exploiting the DDE sensitivity to pore shape, it could be possible to identify the origin of the measured signal. The signal difference between parallel and perpendicular diffusion gradient orientation can indicate if a compartment is regular or eccentric in shape. As extracellular space can be considered an eccentric compartment, a positive difference would mean a high contribution to the compartment size estimates.

MATERIALS AND METHODS

Computer simulations using MISST and in vivo experiments in eight healthy volunteers were performed. DDE experiments using a double spin-echo preparation with eight perpendicular directions were measured in vivo. The difference between parallel and perpendicular gradient orientations was analyzed using a Wilcoxon signed-rank test and a Mann-Whitney U test.

RESULTS

Simulations and MR experiments showed a statistically significant difference between parallel and perpendicular diffusion gradient orientation signals ([Formula: see text]).

CONCLUSION

The results suggest that the DDE-based size estimate may be considerably influenced by the extra-axonal compartment. However, the experimental results are also consistent with purely intra-axonal contributions in combination with a large fiber orientation dispersion.

A novel framework for in-vivo diffusion tensor distribution MRI of the human brain

Neural tissue microstructure plays an important role in developmental, physiological and pathophysiological processes. Diffusion tensor distribution (DTD) MRI helps probe subvoxel heterogeneity by describing water diffusion within a voxel using an ensemble of non-exchanging compartments characterized by a probability density function of diffusion tensors. In this study, we provide a new framework for acquiring multiple diffusion encoding (MDE) images and estimating DTD from them in the human brain in vivo. We interfused pulsed field gradients (iPFG) in a single spin echo to generate arbitrary b-tensors of rank one, two, or three without introducing concomitant gradient artifacts. Employing well-defined diffusion encoding parameters we show that iPFG retains salient features of a traditional multiple-PFG (mPFG/MDE) sequence while reducing the echo time and coherence pathway artifacts thereby extending its applications beyond DTD MRI. Our DTD is a maximum entropy tensor-variate normal distribution whose tensor random variables are constrained to be positive definite to ensure their physicality. In each voxel, the second-order mean and fourth-order covariance tensors of the DTD are estimated using a Monte Carlo method that synthesizes micro-diffusion tensors with corresponding size, shape, and orientation distributions to best fit the measured MDE images. From these tensors we obtain the spectrum of diffusion tensor ellipsoid sizes and shapes, and the microscopic orientation distribution function (μODF) and microscopic fractional anisotropy (μFA) that disentangle the underlying heterogeneity within a voxel. Using the DTD-derived μODF, we introduce a new method to perform fiber tractography capable of resolving complex fiber configurations. The results revealed microscopic anisotropy in various gray and white matter regions and skewed MD distributions in cerebellar gray matter not observed previously. DTD MRI tractography captured complex white matter fiber organization consistent with known anatomy. DTD MRI also resolved some degeneracies associated with diffusion tensor imaging (DTI) and elucidated the source of diffusion heterogeneity which may help improve the diagnosis of various neurological diseases and disorders.

COnstrained Reference frame diffusion TEnsor Correlation Spectroscopic (CORTECS) MRI: A practical framework for high-resolution diffusion tensor distribution imaging

High-resolution imaging studies have consistently shown that in cortical tissue water diffuses preferentially along radial and tangential orientations with respect to the cortical surface, in agreement with histology. These dominant orientations do not change significantly even if the relative contributions from microscopic water pools to the net voxel signal vary across experiments that use different diffusion times, b-values, TEs, and TRs. With this in mind, we propose a practical new framework for imaging non-parametric diffusion tensor distributions (DTDs) by constraining the microscopic diffusion tensors of the DTD to be diagonalized using the same orthonormal reference frame of the mesoscopic voxel. In each voxel, the constrained DTD (cDTD) is completely determined by the correlation spectrum of the microscopic principal diffusivities associated with the axes of the voxel reference frame. Consequently, all cDTDs are inherently limited to the domain of positive definite tensors and can be reconstructed efficiently using Inverse Laplace Transform methods. Moreover, the cDTD reconstruction can be performed using only data acquired efficiently with single diffusion encoding, although it also supports datasets with multiple diffusion encoding. In tissues with a well-defined architecture, such as the cortex, we can further constrain the cDTD to contain only cylindrically symmetric diffusion tensors and measure the 2D correlation spectra of principal diffusivities along the radial and tangential orientation with respect to the cortical surface. To demonstrate this framework, we perform numerical simulations and analyze high-resolution dMRI data from a fixed macaque monkey brain. We estimate 2D cDTDs in the cortex and derive, in each voxel, the marginal distributions of the microscopic principal diffusivities, the corresponding distributions of the microscopic fractional anisotropies and mean diffusivities along with their 2D correlation spectra to quantify the cDTD shape-size characteristics. Signal components corresponding to specific bands in these cDTD-derived spectra show high specificity to cortical laminar structures observed with histology. Our framework drastically simplifies the measurement of non-parametric DTDs in high-resolution datasets with mesoscopic voxel sizes much smaller than the radius of curvature of the underlying anatomy, e.g., cortical surface, and can be applied retrospectively to analyze existing diffusion MRI data from fixed cortical tissues.

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.

Diffusion time dependence, power-law scaling, and exchange in gray matter

Characterizing neural tissue microstructure is a critical goal for future neuroimaging. Diffusion MRI (dMRI) provides contrasts that reflect diffusing spins’ interactions with myriad microstructural features of biological systems. However, the specificity of dMRI remains limited due to the ambiguity of its signals vis-à-vis the underlying microstructure. To improve specificity, biophysical models of white matter (WM) typically express dMRI signals according to the Standard Model (SM) and have more recently in gray matter (GM) taken spherical compartments into account (the SANDI model) in attempts to represent cell soma. The validity of the assumptions underlying these models, however, remains largely undetermined, especially in GM. To validate these assumptions experimentally, observing their unique, functional properties, such as the b^−1/2 power-law associated with one-dimensional diffusion, has emerged as a fruitful strategy. The absence of this signature in GM, in turn, has been explained by neurite water exchange, non-linear morphology, and/or by obscuring soma signal contributions. Here, we present diffusion simulations in realistic neurons demonstrating that curvature and branching does not destroy the stick power-law behavior in impermeable neurites, but also that their signal is drowned by the soma signal under typical experimental conditions. Nevertheless, by studying the GM dMRI signal's behavior as a function of diffusion weighting as well as time, we identify an attainable experimental regime in which the neurite signal dominates. Furthermore, we find that exchange-driven time dependence produces a signal behavior opposite to that which would be expected from restricted diffusion, thereby providing a functional signature that disambiguates the two effects. We present data from dMRI experiments in ex vivo rat brain at ultrahigh field of 16.4T and observe a time dependence that is consistent with substantial exchange but also with a GM stick power-law. The first finding suggests significant water exchange between neurites and the extracellular space while the second suggests a small sub-population of impermeable neurites. To quantify these observations, we harness the Kärger exchange model and incorporate the corresponding signal time dependence in the SM and SANDI models.

Disentangling the effects of restriction and exchange with diffusion exchange spectroscopy

Diffusion exchange spectroscopy (DEXSY) is a multidimensional NMR technique that can reveal how water molecules exchange between compartments within heterogeneous media, such as biological tissue. Data from DEXSY experiments is typically processed using numerical inverse Laplace transforms (ILTs) to produce a diffusion-diffusion spectrum. A tacit assumption of this ILT approach is that the signal behavior is Gaussian - i.e., the spin echo intensity decays exponentially with the degree of diffusion weighting. The assumptions that underlie Gaussian signal behavior may be violated, however, depending on the gradient strength applied and the sample under study. We argue that non-Gaussian signal behavior due to restrictions is to be expected in the study of biological tissue using diffusion NMR. Further, we argue that this signal behavior can produce confounding features in the diffusion-diffusion spectra obtained from numerical ILTs of DEXSY data - entangling the effects of restriction and exchange. Specifically, restricted signal behavior can result in broadening of peaks and in the appearance of illusory exchanging compartments with distributed diffusivities, which pearl into multiple peaks if not highly regularized. We demonstrate these effects on simulated data. That said, we suggest the use of features in the signal acquisition domain that can be used to rapidly probe exchange without employing an ILT. We also propose a means to characterize the non-Gaussian signal behavior due to restrictions within a sample using DEXSY measurements with a near zero mixing time or storage interval. We propose a combined acquisition scheme to independently characterize restriction and exchange with various DEXSY measurements, which we term Restriction and Exchange from Equally-weighted Double and Single Diffusion Encodings (REEDS-DE). We test this method on ex vivo neonatal mouse spinal cord - a sample consisting primarily of gray matter - using a low-field, static gradient NMR system. In sum, we highlight critical shortcomings of prevailing DEXSY analysis methods that conflate the effects of restriction and exchange, and suggest a viable experimental approach to disentangle them.

Connectome 2.0: Developing the next-generation ultra-high gradient strength human MRI scanner for bridging studies of the micro-, meso- and macro-connectome

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.

On the potential for mapping apparent neural soma density via a clinically viable diffusion MRI protocol

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B-tensor encoding enables estimation of spherical cellular structures in the brain.

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Spherical compartments may provide markers for apparent neural soma density.

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Model parameters can be estimated in a fast and robust way using deep learning.

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Practical acquisition times are achievable on widely available clinical scanners.

Diffusion MRI is a valuable tool for probing tissue microstructure in the brain noninvasively. Today, model-based techniques are widely available and used for white matter characterisation where their development is relatively mature. Conversely, tissue modelling in grey matter is more challenging, and no generally accepted models exist. With advances in measurement technology and modelling efforts, a clinically viable technique that reveals salient features of grey matter microstructure, such as the density of quasi-spherical cell bodies and quasi-cylindrical cell projections, is an exciting prospect. As a step towards capturing the microscopic architecture of grey matter in clinically feasible settings, this work uses a biophysical model that is designed to disentangle the diffusion signatures of spherical and cylindrical structures in the presence of orientation heterogeneity, and takes advantage of B-tensor encoding measurements, which provide additional sensitivity compared to standard single diffusion encoding sequences. For the fast and robust estimation of microstructural parameters, we leverage recent advances in machine learning and replace conventional fitting techniques with an artificial neural network that fits complex biophysical models within seconds. Our results demonstrate apparent markers of spherical and cylindrical geometries in healthy human subjects, and in particular an increased volume fraction of spherical compartments in grey matter compared to white matter. We evaluate the extent to which spherical and cylindrical geometries may be interpreted as correlates of neural soma and neural projections, respectively, and quantify parameter estimation errors in the presence of various departures from the modelling assumptions. While further work is necessary to translate the ideas presented in this work to the clinic, we suggest that biomarkers focussing on quasi-spherical cellular geometries may be valuable for the enhanced assessment of neurodevelopmental disorders and neurodegenerative diseases.

Compartmental diffusion and microstructural properties of human brain gray and white matter studied with double diffusion encoding magnetic resonance spectroscopy of metabolites and water

Double diffusion encoding (DDE) of the water signal offers a unique ability to separate the effect of microscopic anisotropic diffusion in structural units of tissue from the overall macroscopic orientational distribution of cells. However, the specificity in detected microscopic anisotropy is limited as the signal is averaged over different cell types and across tissue compartments. Performing side-by-side water and metabolite DDE spectroscopic (DDES) experiments provides complementary measures from which intracellular and extracellular microscopic fractional anisotropies (μFA) and diffusivities can be estimated. Metabolites are largely confined to the intracellular space and therefore provide a benchmark for intracellular μFA and diffusivities of specific cell types. By contrast, water DDES measurements allow examination of the separate contributions to water μFA and diffusivity from the intra- and extracellular spaces, by using a wide range of b values to gradually eliminate the extracellular contribution. Here, we aimed to estimate tissue and compartment specific human brain microstructure by combining water and metabolites DDES experiments. We performed our DDES measurements in two brain regions that contain widely different amounts of white matter (WM) and gray matter (GM): parietal white matter (PWM) and occipital gray matter (OGM) in a total of 20 healthy volunteers at 7 Tesla. Metabolite DDES measurements were performed at b = 7199 s/mm², while water DDES measurements were performed with a range of b values from 918 to 7199 s/mm². The experimental framework we employed here resulted in a set of insights pertaining to the morphology of the intracellular and extracellular spaces in both gray and white matter. Results of the metabolite DDES experiments in both PWM and OGM suggest a highly anisotropic intracellular space within neurons and glia, with the possible exception of gray matter glia. The water μFA obtained from the DDES results at high b values in both regions converged with that of the metabolite DDES, suggesting that the signal from the extracellular space is indeed effectively suppressed at the highest b value. The μFA measured in the OGM significantly decreased at lower b values, suggesting a considerably lower anisotropy of the extracellular space in GM compared to WM. In PWM, the water μFA remained high even at the lowest b value, indicating a high degree of organization in the interstitial space in WM. Tortuosity values in the cytoplasm for water and tNAA, obtained with correlation analysis of microscopic parallel diffusivity with respect to GM/WM tissue fraction in the volume of interest, are remarkably similar for both molecules, while exhibiting a clear difference between gray and white matter, suggesting a more crowded cytoplasm and more complex cytomorphology of neuronal cell bodies and dendrites in GM than those found in long-range axons in WM.

A new framework for MR diffusion tensor distribution

The ability to characterize heterogeneous and anisotropic water diffusion processes within macroscopic MRI voxels non-invasively and in vivo is a desideratum in biology, neuroscience, and medicine. While an MRI voxel may contain approximately a microliter of tissue, our goal is to examine intravoxel diffusion processes on the order of picoliters. Here we propose a new theoretical framework and efficient experimental design to describe and measure such intravoxel structural heterogeneity and anisotropy. We assume that a constrained normal tensor-variate distribution (CNTVD) describes the variability of positive definite diffusion tensors within a voxel which extends its applicability to a wide range of b-values while preserving the richness of diffusion tensor distribution (DTD) paradigm unlike existing models. We introduce a new Monte Carlo (MC) scheme to synthesize realistic 6D DTD numerical phantoms and invert the MR signal. We show that the signal inversion is well-posed and estimate the CNTVD parameters parsimoniously by exploiting the different symmetries of the mean and covariance tensors of CNTVD. The robustness of the estimation pipeline is assessed by adding noise to calculated MR signals and compared with the ground truth. A family of invariant parameters and glyphs which characterize microscopic shape, size and orientation heterogeneity within a voxel are also presented.

Gradient waveform design for tensor-valued encoding in diffusion MRI

Diffusion encoding along multiple spatial directions per signal acquisition can be described in terms of a b-tensor. The benefit of tensor-valued diffusion encoding is that it unlocks the 'shape of the b-tensor' as a new encoding dimension. By modulating the b-tensor shape, we can control the sensitivity to microscopic diffusion anisotropy which can be used as a contrast mechanism; a feature that is inaccessible by conventional diffusion encoding. Since imaging methods based on tensor-valued diffusion encoding are finding an increasing number of applications we are prompted to highlight the challenge of designing the optimal gradient waveforms for any given application. In this review, we first establish the basic design objectives in creating field gradient waveforms for tensor-valued diffusion MRI. We also survey additional design considerations related to limitations imposed by hardware and physiology, potential confounding effects that cannot be captured by the b-tensor, and artifacts related to the diffusion encoding waveform. Throughout, we discuss the expected compromises and tradeoffs with an aim to establish a more complete understanding of gradient waveform design and its impact on accurate measurements and interpretations of data.

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.

Double diffusion encoding and applications for biomedical imaging

Diffusion Magnetic Resonance Imaging (dMRI) is one of the most important contemporary non-invasive modalities for probing tissue structure at the microscopic scale. The majority of dMRI techniques employ standard single diffusion encoding (SDE) measurements, covering different sequence parameter ranges depending on the complexity of the method. Although many signal representations and biophysical models have been proposed for SDE data, they are intrinsically limited by a lack of specificity. Advanced dMRI methods have been proposed to provide additional microstructural information beyond what can be inferred from SDE. These enhanced contrasts can play important roles in characterizing biological tissues, for instance upon diseases (e.g. neurodegenerative, cancer, stroke), aging, learning, and development. In this review we focus on double diffusion encoding (DDE), which stands out among other advanced acquisitions for its versatility, ability to probe more specific diffusion correlations, and feasibility for preclinical and clinical applications. Various DDE methodologies have been employed to probe compartment sizes (Section 3), decouple the effects of microscopic diffusion anisotropy from orientation dispersion (Section 4), probe displacement correlations, study exchange, or suppress fast diffusing compartments (Section 6). DDE measurements can also be used to improve the robustness of biophysical models (Section 5) and study intra-cellular diffusion via magnetic resonance spectroscopy of metabolites (Section 7). This review discusses all these topics as well as important practical aspects related to the implementation and contrast in preclinical and clinical settings (Section 9) and aims to provide the readers a guide for deciding on the right DDE acquisition for their specific application.

Brain White-Matter Degeneration Due to Aging and Parkinson Disease as Revealed by Double Diffusion Encoding

Microstructure imaging by means of multidimensional diffusion encoding is increasingly applied in clinical research, with expectations that it yields a parameter that better correlates with clinical disability than current methods based on single diffusion encoding. Under the assumption that diffusion within a voxel can be well described by a collection of diffusion tensors, several parameters of this diffusion tensor distribution can be derived, including mean size, variance of sizes, orientational dispersion, and microscopic anisotropy. The information provided by multidimensional diffusion encoding also enables us to decompose the sources of the conventional fractional anisotropy and mean kurtosis. In this study, we explored the utility of the diffusion tensor distribution approach for characterizing white-matter degeneration in aging and in Parkinson disease by using double diffusion encoding. Data from 23 healthy older subjects and 27 patients with Parkinson disease were analyzed. Advanced age was associated with greater mean size and size variances, as well as smaller microscopic anisotropy. By analyzing the parameters underlying diffusion kurtosis, we found that the reductions of kurtosis in aging and Parkinson disease reported in the literature are likely driven by the reduction in microscopic anisotropy. Furthermore, microscopic anisotropy correlated with the severity of motor impairment in the patients with Parkinson disease. The present results support the use of multidimensional diffusion encoding in clinical studies and are encouraging for its future clinical implementation.

Microstructure with diffusion MRI: what scale we are sensitive to?

Diffusion-weighted MRI is the forerunner of the rapidly developed microstructure MRI (μMRI) aimed at in vivo evaluation of the cellular tissue architecture. This brief review focuses on the spatiotemporal scales of the microstructure that are accessible using different diffusion MRI techniques and the need to weight the measurability against the interpretability of results. Diffusion phenomena and models are first classified in two-dimensional space (the q-t-plane) of the measurement with narrow gradient pulses. Three-dimensional parameter space of the Stejskal-Tanner diffusion weighting adds more phenomena to this collection. Modern measurement techniques with larger number of parameters are briefly discussed under the overarching idea of diffusion weighting matching the geometry of the targeted cell species.

Direct and specific assessment of axonal injury and spinal cord microenvironments using diffusion correlation imaging

We describe a practical two-dimensional (2D) diffusion MRI framework to deliver specificity and improve sensitivity to axonal injury in the spinal cord. This approach provides intravoxel distributions of correlations of water mobilities in orthogonal directions, revealing sub-voxel diffusion components. Here we use it to investigate water diffusivities along axial and radial orientations within spinal cord specimens with confirmed, tract-specific axonal injury. First, we show using transmission electron microscopy and immunohistochemistry that tract-specific axonal beading occurs following Wallerian degeneration in the cortico-spinal tract as direct sequelae to closed head injury. We demonstrate that although some voxel-averaged diffusion tensor imaging (DTI) metrics are sensitive to this axonal injury, they are non-specific, i.e., they do not reveal an underlying biophysical mechanism of injury. Then we employ 2D diffusion correlation imaging (DCI) to improve discrimination of different water microenvironments by measuring and mapping the joint water mobility distributions perpendicular and parallel to the spinal cord axis. We determine six distinct diffusion spectral components that differ according to their microscopic anisotropy and mobility. We show that at the injury site a highly anisotropic diffusion component completely disappears and instead becomes more isotropic. Based on these findings, an injury-specific MR image of the spinal cord was generated, and a radiological-pathological correlation with histological silver staining % area was performed. The resulting strong and significant correlation (r = 0.70, p < 0.0001) indicates the high specificity with which DCI detects injury-induced tissue alterations. We predict that the ability to selectively image microstructural changes following axonal injury in the spinal cord can be useful in clinical and research applications by enabling specific detection and increased sensitivity to injury-induced microstructural alterations. These results also encourage us to translate DCI to higher spatial dimensions to enable assessment of traumatic axonal injury, and possibly other diseases and disorders in the brain.

JEDI: Joint Estimation Diffusion Imaging of macroscopic and microscopic tissue properties

PURPOSE

A new method for enhancing the sensitivity of diffusion MRI (dMRI) by combining the data from single (sPFG) and double (dPFG) pulsed field gradient experiments is presented.

METHODS

This method uses our JESTER framework to combine microscopic anisotropy information from dFPG experiments using a new method called diffusion tensor subspace imaging (DiTSI) to augment the macroscopic anisotropy information from sPFG data analyzed using our guided by entropy spectrum pathways method. This new method, called joint estimation diffusion imaging (JEDI), combines the sensitivity to macroscopic diffusion anisotropy of sPFG with the sensitivity to microscopic diffusion anisotropy of dPFG methods.

RESULTS

Its ability to produce significantly more detailed anisotropy maps and more complete fiber tracts than existing methods within both brain white matter (WM) and gray matter (GM) is demonstrated on normal human subjects on data collected using a novel fast, robust, and clinically feasible sPFG/dPFG acquisition.

CONCLUSIONS

The potential utility of this method is suggested by an initial demonstration of its ability to mitigate the problem of gyral bias. The capability of more completely characterizing the tissue structure and connectivity throughout the entire brain has broad implications for the utility and scope of dMRI in a wide range of research and clinical applications.

Magnetic resonance measurements of cellular and sub-cellular membrane structures in live and fixed neural tissue

We develop magnetic resonance (MR) methods for real-time measurement of tissue microstructure and membrane permeability of live and fixed excised neonatal mouse spinal cords. Diffusion and exchange MR measurements are performed using the strong static gradient produced by a single-sided permanent magnet. Using tissue delipidation methods, we show that water diffusion is restricted solely by lipid membranes. Most of the diffusion signal can be assigned to water in tissue which is far from membranes. The remaining 25% can be assigned to water restricted on length scales of roughly a micron or less, near or within membrane structures at the cellular, organelle, and vesicle levels. Diffusion exchange spectroscopy measures water exchanging between membrane structures and free environments at 100 s^-1.

Diffusion MRI in the brain - Theory and concepts

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

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.

In vivo microscopic diffusional kurtosis imaging with symmetrized double diffusion encoding EPI

PURPOSE

Diffusional kurtosis imaging (DKI) measures the deviation of the displacement probability from a normal distribution, complementing the data commonly acquired by diffusion MRI. It is important to elucidate the sources of kurtosis contrast, particularly in biological tissues where microscopic kurtosis (intrinsic kurtosis) and diffusional heterogeneity may co-exist.

METHODS

We have developed a technique for microscopic kurtosis MRI, dubbed microscopic diffusional kurtosis imaging (µDKI), using a symmetrized double diffusion encoding (s-DDE) EPI sequence. We compared this newly developed µDKI to conventional DKI methods in both a triple compartment phantom and in vivo.

RESULTS

Our results showed that whereas conventional DKI and µDKI provided similar measurements in a compartment of monosphere beads, kurtosis measured by µDKI was significantly less than that measured by conventional DKI in a compartment of mixed Gaussian pools. For in vivo brain imaging, µDKI showed small yet significantly lower kurtosis measurement in regions of the cortex, CSF, and internal capsule compared to the conventional DKI approach.

CONCLUSIONS

Our study showed that µDKI is less susceptible than conventional DKI to sub-voxel diffusional heterogeneity. Our study also provided important preliminary demonstration of our technique in vivo, warranting future studies to investigate its diagnostic use in examining neurological disorders.

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.

Liquid crystal phantom for validation of microscopic diffusion anisotropy measurements on clinical MRI systems

PURPOSE

To develop a phantom for validating MRI pulse sequences and data processing methods to quantify microscopic diffusion anisotropy in the human brain.

METHODS

Using a liquid crystal consisting of water, detergent, and hydrocarbon, we designed a 0.5-L spherical phantom showing the theoretically highest possible degree of microscopic anisotropy. Data were acquired on the Connectome scanner using echo-planar imaging signal readout and diffusion encoding with axisymmetric b-tensors of varying magnitude, anisotropy, and orientation. The mean diffusivity, fractional anisotropy (FA), and microscopic FA (µFA) parameters were estimated.

RESULTS

The phantom was observed to have values of mean diffusivity similar to brain tissue, and relaxation times compatible with echo-planar imaging echo times on the order of 100 ms. The estimated values of µFA were at the theoretical maximum of 1.0, whereas the values of FA spanned the interval from 0.0 to 0.8 as a result of varying orientational order of the anisotropic domains within each voxel.

CONCLUSIONS

The proposed phantom can be manufactured by mixing three widely available chemicals in volumes comparable to a human head. The acquired data are in excellent agreement with theoretical predictions, showing that the phantom is ideal for validating methods for measuring microscopic diffusion anisotropy on clinical MRI systems. Magn Reson Med 79:1817-1828, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

Determining mean fractional anisotropy using DDCOSY: preliminary results in biological tissues

Complex materials are ubiquitous in science, engineering and nature. One important parameter for characterising their morphology is the degree of anisotropy. Magnetic resonance imaging offers non-invasive methods for quantitative measurements of the materials anisotropy, most commonly via diffusion tensor imaging and the subsequent extraction of the spatially resolved fractional anisotropy (FA) value. Here, we propose an alternative way of determining the FA as a sample average for cases where spatially resolved methods are not needed or not applicable. It is based on a particular diffusion-diffusion correlation spectroscopy protocol, allowing for the extraction of the mean (i.e. sample averaged) FA value. We demonstrate that mean FA values obtained from three anisotropic biological tissues are consistent with those extracted using diffusion tensor imaging. Moreover, we show that differences of mean FA values in healthy and tumour-bearing mouse brains allow to distinguish these tissue types. We anticipate that the proposed method will be beneficial in the wider context of medical and material science. Copyright © 2016 John Wiley & Sons, Ltd.

Anisotropic phantom to calibrate high-q diffusion MRI methods

A silicon oil-filled glass capillary array is proposed as an anisotropic diffusion MRI phantom. Together with a computational/theoretical pipeline these provide a gold standard for calibrating and validating high-q diffusion MRI experiments. The phantom was used to test high angular resolution diffusion imaging (HARDI) and double pulsed-field gradient (d-PFG) MRI acquisition schemes. MRI-based predictions of microcapillary diameter using both acquisition schemes were compared with results from optical microscopy. This phantom design can be used for quality control and quality assurance purposes and for testing and validating proposed microstructure imaging experiments and the processing pipelines used to analyze them.

Analyzing the tradeoff between electrical complexity and accuracy in patient-specific computational models of deep brain stimulation

OBJECTIVE

Deep brain stimulation (DBS) is an adjunctive therapy that is effective in treating movement disorders and shows promise for treating psychiatric disorders. Computational models of DBS have begun to be utilized as tools to optimize the therapy. Despite advancements in the anatomical accuracy of these models, there is still uncertainty as to what level of electrical complexity is adequate for modeling the electric field in the brain and the subsequent neural response to the stimulation.

APPROACH

We used magnetic resonance images to create an image-based computational model of subthalamic DBS. The complexity of the volume conductor model was increased by incrementally including heterogeneity, anisotropy, and dielectric dispersion in the electrical properties of the brain. We quantified changes in the load of the electrode, the electric potential distribution, and stimulation thresholds of descending corticofugal (DCF) axon models.

MAIN RESULTS

Incorporation of heterogeneity altered the electric potentials and subsequent stimulation thresholds, but to a lesser degree than incorporation of anisotropy. Additionally, the results were sensitive to the choice of method for defining anisotropy, with stimulation thresholds of DCF axons changing by as much as 190%. Typical approaches for defining anisotropy underestimate the expected load of the stimulation electrode, which led to underestimation of the extent of stimulation. More accurate predictions of the electrode load were achieved with alternative approaches for defining anisotropy. The effects of dielectric dispersion were small compared to the effects of heterogeneity and anisotropy.

SIGNIFICANCE

The results of this study help delineate the level of detail that is required to accurately model electric fields generated by DBS electrodes.

Cerebral Reorganization after Hemispherectomy: A DTI Study

BACKGROUND AND PURPOSE

Hemispherectomy is a neurosurgical procedure to treat children with intractable seizures. Postsurgical improvement of cognitive and behavioral functions is observed in children after hemispherectomy suggesting plastic reorganization of the brain. Our aim was to characterize changes in DTI scalars in WM tracts of the remaining hemisphere in children after hemispherectomy, assess the associations between WM DTI scalars and age at the operation and time since the operation, and evaluate the changes in GM fractional anisotropy values in patients compared with controls.

MATERIALS AND METHODS

Patients with congenital or acquired neurologic diseases who required hemispherectomy and had high-quality postsurgical DTI data available were included in this study. Atlas- and voxel-based analyses of DTI raw data of the remaining hemisphere were performed. Fractional anisotropy and mean, axial, and radial diffusivity values were calculated for WM and GM regions. A linear regression model was used for correlation between DTI scalars and age at and time since the operation.

RESULTS

Nineteen patients after hemispherectomy and 21 controls were included. In patients, a decrease in fractional anisotropy and axial diffusivity values and an increase in mean diffusivity and radial diffusivity values of WM regions were observed compared with controls (P < .05, corrected for multiple comparisons). In patients with acquired pathologies, time since the operation had a significant positive correlation with white matter fractional anisotropy values. In all patients, an increase in cortical GM fractional anisotropy values was found compared with controls (P < .05).

CONCLUSIONS

Changes in DTI metrics likely reflect Wallerian and/or transneuronal degeneration of the WM tracts within the remaining hemisphere. In patients with acquired pathologies, postsurgical fractional anisotropy values correlated positively with elapsed time since the operation, suggesting a higher ability to recover compared with patients with congenital pathologies leading to hemispherectomy.

Microscopic diffusion anisotropy in the human brain: reproducibility, normal values, and comparison with the fractional anisotropy

Human neuroimaging of tissue microstructure, such as axonal density and integrity, is key in clinical and neuroscience research. Most studies rely on diffusion tensor imaging (DTI) and the measures derived from it, most prominently fractional anisotropy (FA). However, FA also depends on fiber orientation distribution, a more macroscopic tissue property. Recently introduced measures of so-called microscopic diffusion anisotropy, diffusion anisotropy on a cellular or microscopic level, overcome this limitation because they are independent of the orientation distributions of axons and fibers. In this study, we evaluate the feasibility of two measures of microscopic diffusion anisotropy I(MA) and MA indices, for human neuroscience and clinical research. Both indices reflect the eccentricity of the cells but while I(MA) also depends on the cell size, MA is independent of the cell size and, like FA, scaled between 0 and 1. In whole-brain measurements of a group of 19 healthy volunteers, we measured average values and variability, evaluated their reproducibility, both within and between sessions, and compared MA to FA values in selected regions-of-interest (ROIs). The within- and between-session comparison did not show substantial differences but the reproducibility was much better for the MA than I(MA) (coefficient of variation between sessions 10.5% vs. 28.9%). The reproducibility was less for MA than FA overall, but comparable in the defined ROIs and the average group sizes required for between-group comparisons was similar (about 60 participants for a relative difference of 5%). Group-averaged values of MA index were generally larger and showed less variation across white-matter brain ROIs than FA (mean ± standard deviation of seven ROIs 0.83 ± 0.10 vs. 0.58 ± 0.13). Even in some gray-matter ROIs, MA values comparable to those of white matter ROIs were observed. Furthermore, the within-group variation of the values in white matter ROIs was lower for the MA compared to the FA (mean standard deviation over volunteers 0.038 vs. 0.049) which could be due to significant variability in the distribution of fiber orientation contributing to FA. These results indicate that MA (i) should be preferred to I(MA), (ii) has a reproducibility and group-size requirements comparable to those of FA; (iii) is less sensitive to the fiber orientation distribution than FA; and (iv) could be more sensitive to differences or changes of the tissue microstructure than FA. R1.1.

Orientationally invariant metrics of apparent compartment eccentricity from double pulsed field gradient diffusion experiments

Pulsed field gradient diffusion sequences (PFG) with multiple diffusion encoding blocks have been indicated to offer new microstructural tissue information, such as the ability to detect nonspherical compartment shapes in macroscopically isotropic samples, i.e. samples with negligible directional signal dependence on diffusion gradients in standard diffusion experiments. However, current acquisition schemes are not rotationally invariant in the sense that the derived metrics depend on the orientation of the sample, and are affected by the interplay of sampling directions and compartment orientation dispersion when applied to macroscopically anisotropic systems. Here we propose a new framework, the d-PFG 5-design, to enable rotationally invariant estimation of double wave vector diffusion metrics (d-PFG). The method is based on the idea that an appropriate orientational average of the signal emulates the signal from a powder preparation of the same sample, where macroscopic anisotropy is absent by construction. Our approach exploits the theory of exact numerical integration (quadrature) of polynomials on the rotation group, and we exemplify the general procedure with a set consisting of 60 pairs of diffusion wave vectors (the d-PFG 5-design) facilitating a theoretically exact determination of the fourth order Taylor or cumulant expansion of the orientationally averaged signal. The d-PFG 5-design is evaluated with numerical simulations and ex vivo high field diffusion MRI experiments in a nonhuman primate brain. Specifically, we demonstrate rotational invariance when estimating compartment eccentricity, which we show offers new microstructural information, complementary to that of fractional anisotropy (FA) from diffusion tensor imaging (DTI). The imaging observations are supported by a new theoretical result, directly relating compartment eccentricity to FA of individual pores.

Assessment of electric field distribution in anisotropic cortical and subcortical regions under the influence of tDCS

The focus of this study is to estimate the contribution of regional anisotropic conductivity on the spatial distribution of an induced electric field across gray matter (GM), white matter (WM), and subcortical regions under transcranial direct current stimulation (tDCS). The assessment was conducted using a passive high-resolution finite element head model with inhomogeneous and variable anisotropic conductivities derived from the diffusion tensor data. Electric field distribution was evaluated across different cortical as well as subcortical regions under four bicephalic electrode configurations. Results indicate that regional tissue heterogeneity and anisotropy cause the pattern of induced fields to vary in orientation and strength when compared to the isotropic scenario. Different electrode montages resulted in distinct distribution patterns with noticeable variations in field strengths. The effect of anisotropy is highly montage dependent and directional conductivity has a more profound effect in defining the strength of the induced field. The inclusion of anisotropy in the GM and subcortical regions has a significant effect on the strength and spatial distribution of the induced electric field. Under the (C3-Fp2) montage, the inclusion of GM and subcortical anisotropy increased the average percentage difference in the electric field strength of brain from 5% to 34% (WM anisotropy only). In terms of patterns distribution, the topographic errors increased from 9.9% to 40% (WM anisotropy only) across the brain.

The CONNECT project: Combining macro- and micro-structure

In recent years, diffusion MRI has become an extremely important tool for studying the morphology of living brain tissue, as it provides unique insights into both its macrostructure and microstructure. Recent applications of diffusion MRI aimed to characterize the structural connectome using tractography to infer connectivity between brain regions. In parallel to the development of tractography, additional diffusion MRI based frameworks (CHARMED, AxCaliber, ActiveAx) were developed enabling the extraction of a multitude of micro-structural parameters (axon diameter distribution, mean axonal diameter and axonal density). This unique insight into both tissue microstructure and connectivity has enormous potential value in understanding the structure and organization of the brain as well as providing unique insights to abnormalities that underpin disease states. The CONNECT (Consortium Of Neuroimagers for the Non-invasive Exploration of brain Connectivity and Tracts) project aimed to combine tractography and micro-structural measures of the living human brain in order to obtain a better estimate of the connectome, while also striving to extend validation of these measurements. This paper summarizes the project and describes the perspective of using micro-structural measures to study the connectome.

Estimation of pore size distribution using concentric double pulsed-field gradient NMR

Estimation of pore size distribution of well calibrated phantoms using NMR is demonstrated here for the first time. Porous materials are a central constituent in fields as diverse as biology, geology, and oil drilling. Noninvasive characterization of monodisperse porous samples using conventional pulsed-field gradient (PFG) NMR is a well-established method. However, estimation of pore size distribution of heterogeneous polydisperse systems, which comprise most of the materials found in nature, remains extremely challenging. Concentric double pulsed-field gradient (CDPFG) is a 2-D technique where both q (the amplitude of the diffusion gradient) and φ (the relative angle between the gradient pairs) are varied. A recent prediction indicates this method should produce a more accurate and robust estimation of pore size distribution than its conventional 1-D versions. Five well defined size distribution phantoms, consisting of 1-5 different pore sizes in the range of 5-25 μm were used. The estimated pore size distributions were all in good agreement with the known theoretical size distributions, and were obtained without any a priori assumption on the size distribution model. These findings support that in addition to its theoretical benefits, the CDPFG method is experimentally reliable. Furthermore, by adding the angle parameter, sensitivity to small compartment sizes is increased without the use of strong gradients, thus making CDPFG safe for biological applications.

Mapping average axon diameters in porcine spinal cord white matter and rat corpus callosum using d-PFG MRI

Knowledge of microstructural features of nerve fascicles, such as their axon diameter, is crucial for understanding normal function in the central and peripheral nervous systems as well as assessing changes due to pathologies. In this study double-pulsed field gradient (d-PFG) filtered MRI was used to map the average axon diameter (AAD) in porcine spinal cord, which was then compared to AADs measured with optical microscopy of the same specimen, as a way to further validate this new MRI method. A novel 3D d-PFG acquisition scheme was used to obtain AADs in each voxel of a coronal slice of rat brain corpus callosum. AAD measurements were also acquired using optical microscopy performed on histological sections and validated using a glass capillary array phantom.

The role of tissue microstructure and water exchange in biophysical modelling of diffusion in white matter

Biophysical models that describe the outcome of white matter diffusion MRI experiments have various degrees of complexity. While the simplest models assume equal-sized and parallel axons, more elaborate ones may include distributions of axon diameters and axonal orientation dispersions. These microstructural features can be inferred from diffusion-weighted signal attenuation curves by solving an inverse problem, validated in several Monte Carlo simulation studies. Model development has been paralleled by microscopy studies of the microstructure of excised and fixed nerves, confirming that axon diameter estimates from diffusion measurements agree with those from microscopy. However, results obtained in vivo are less conclusive. For example, the amount of slowly diffusing water is lower than expected, and the diffusion-encoded signal is apparently insensitive to diffusion time variations, contrary to what may be expected. Recent understandings of the resolution limit in diffusion MRI, the rate of water exchange, and the presence of microscopic axonal undulation and axonal orientation dispersions may, however, explain such apparent contradictions. Knowledge of the effects of biophysical mechanisms on water diffusion in tissue can be used to predict the outcome of diffusion tensor imaging (DTI) and of diffusion kurtosis imaging (DKI) studies. Alterations of DTI or DKI parameters found in studies of pathologies such as ischemic stroke can thus be compared with those predicted by modelling. Observations in agreement with the predictions strengthen the credibility of biophysical models; those in disagreement could provide clues of how to improve them. DKI is particularly suited for this purpose; it is performed using higher b-values than DTI, and thus carries more information about the tissue microstructure. The purpose of this review is to provide an update on the current understanding of how various properties of the tissue microstructure and the rate of water exchange between microenvironments are reflected in diffusion MRI measurements. We focus on the use of biophysical models for extracting tissue-specific parameters from data obtained with single PGSE sequences on clinical MRI scanners, but results obtained with animal MRI scanners are also considered. While modelling of white matter is the central theme, experiments on model systems that highlight important aspects of the biophysical models are also reviewed.

fMRI and DTI assessment of patients undergoing radical epilepsy surgery

Hemispherectomy is effective for young patients suffered from unilateral cortical disease and severe drug-resistant epilepsy, but a major concern for hemispherectomy is the remaining brain functions and function recovery in patients after such surgery. In this study, seven patients were evaluated with clinical and imaging assessment pre- and post-surgery. Among them, four underwent anatomic hemispherectomy (AH) and three underwent subtotal hemispherectomy (functional hemispherectomy, FH). After the surgery, 71.4% (5/7) patients [(4/4) with AH and (1/3) with FH] became seizure free (Engel class I). Motor function of the paretic upper extremity unchanged in 4 patients and deteriorated in 3. Functional imaging results indicated that relocation of hand motor function (to the ipsilateral hemisphere) could take place before or after the surgery, or did not occur. Similar observations were made in the motor cortex activation on the paretic foot movement. In addition, both the affected and unaffected hemispheres underwent post-surgical changes in the corticospinal tracks (CST) in various degrees, but significant reinforcement of the CST in the remaining unaffected hemisphere was not evident. Further research is needed to reveal the true functional and structural changes of the remaining brain after surgery and to explore the mechanisms of such functional relocation and reorganization in patients underwent hemispherectomy.

Isotropic diffusion weighting in PGSE NMR by magic-angle spinning of the q-vector

When PGSE NMR is applied to water in microheterogeneous materials such as liquid crystals, foodstuffs, porous rocks, and biological tissues, the signal attenuation is often multi-exponential, indicating the presence of pores having a range of sizes or anisotropic domains having a spread of orientations. Here we modify the standard PGSE experiment by introducing low-amplitude harmonically modulated gradients, which effectively make the q-vector perform magic-angle spinning (MAS) about an axis fixed in the laboratory frame. With this new technique, denoted q-MAS PGSE, the signal attenuation depends on the isotropic average of the local diffusion tensor. The capability of q-MAS PGSE to distinguish between pore size and domain orientation dispersion is demonstrated by experiments on a yeast cell suspension and a polydomain anisotropic liquid crystal. In the latter case, the broad distribution of apparent diffusivities observed with PGSE is narrowed to its isotropic average with q-MAS PGSE in a manner that is analogous to the narrowing of chemical shift anisotropy powder patterns using magic-angle sample spinning in solid-state NMR. The new q-MAS PGSE technique could be useful for resolving size/orientation ambiguities in the interpretation of PGSE data from, e.g., water confined within the axons of human brain tissue.

In vivo detection of microscopic anisotropy using quadruple pulsed-field gradient (qPFG) diffusion MRI on a clinical scanner

We report our design and implementation of a quadruple pulsed-field gradient (qPFG) diffusion MRI pulse sequence on a whole-body clinical scanner and demonstrate its ability to non-invasively detect restriction-induced microscopic anisotropy in human brain tissue. The microstructural information measured using qPFG diffusion MRI in white matter complements that provided by diffusion tensor imaging (DTI) and exclusively characterizes diffusion of water trapped in microscopic compartments with unique measures of average cell geometry. We describe the effect of white matter fiber orientation on the expected MR signal and highlight the importance of incorporating such information in the axon diameter measurement using a suitable mathematical framework. Integration of qPFG diffusion-weighted images (DWI) with fiber orientations measured using high-resolution DTI allows the estimation of average axon diameters in the corpus callosum of healthy human volunteers. Maps of inter-hemispheric average axon diameters reveal an anterior-posterior variation in good topographical agreement with anatomical measurements reported in previous post-mortem studies. With further technical refinements and additional clinical validation, qPFG diffusion MRI could provide a quantitative whole-brain histological assessment of white and gray matter, enabling a wide range of neuroimaging applications for improved diagnosis of neurodegenerative pathologies, monitoring neurodevelopmental processes, and mapping brain connectivity.

A spin echo sequence with a single-sided bipolar diffusion gradient pulse to obtain snapshot diffusion weighted images in moving media

In vivo MRI data can be corrupted by motion. Motion artifacts are particularly troublesome in Diffusion Weighted MRI (DWI), since the MR signal attenuation due to Brownian motion can be much less than the signal loss due to dephasing from other types of complex tissue motion, which can significantly degrade the estimation of self-diffusion coefficients, diffusion tensors, etc. This paper describes a snapshot DWI sequence, which utilizes a novel single-sided bipolar diffusion sensitizing gradient pulse within a spin echo sequence. The proposed method shortens the diffusion time by applying a single refocused bipolar diffusion gradient on one side of a refocusing RF pulse, instead of a set of diffusion sensitizing gradients, separated by a refocusing RF pulse, while reducing the impact of magnetic field inhomogeneity by using a spin echo sequence. A novel MRI phantom that can exhibit a range of complex motions was designed to demonstrate the robustness of the proposed DWI sequence.