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

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.

MR Fingerprinting with b-Tensor Encoding for Simultaneous Quantification of Relaxation and Diffusion in a Single Scan

PURPOSE

Although both relaxation and diffusion imaging are sensitive to tissue microstructure, studies have reported limited sensitivity and robustness of using relaxation or conventional diffusion alone to characterize tissue microstructure. Recently, it has been shown that tensor-valued diffusion encoding and joint relaxation-diffusion quantification enable more reliable quantification of compartment-specific microstructural properties. However, scan times to acquire such data can be prohibitive. Here, we aim to simultaneously quantify relaxation and diffusion using MR fingerprinting (MRF) and b-tensor encoding in a clinically feasible time.

METHODS

We developed multidimensional MRF scans (mdMRF) with linear and spherical b-tensor encoding (LTE and STE) to simultaneously quantify T1, T2, and ADC maps from a single scan. The image quality, accuracy, and scan efficiency were compared between the mdMRF using LTE and STE. Moreover, we investigated the robustness of different sequence designs to signal errors and their impact on the maps.

RESULTS

T1 and T2 maps derived from the mdMRF scans have consistently high image quality, while ADC maps are sensitive to different sequence designs. Notably, the fast imaging steady state precession (FISP)-based mdMRF scan with peripheral pulse gating provides the best ADC maps that are free of image distortion and shading artifacts.

CONCLUSION

We demonstrated the feasibility of quantifying T1, T2, and ADC maps simultaneously from a single mdMRF scan in around 24 s/slice. The map quality and quantitative values are consistent with the reference scans.

Nonparametric 5D D-R2 distribution imaging with single-shot EPI at 21.1 T: Initial results for in vivo rat brain

In vivo human diffusion MRI is by default performed using single-shot EPI with greater than 50-ms echo times and associated signal loss from transverse relaxation. The individual benefits of the current trends of increasing B₀ to boost SNR and employing more advanced signal preparation schemes to improve the specificity for selected microstructural properties eventually may be cancelled by increased relaxation rates at high B₀ and echo times with advanced encoding. Here, initial attempts to translate state-of-the-art diffusion-relaxation correlation methods from 3 T to 21.1 T are made to identify hurdles that need to be overcome to fulfill the promises of both high SNR and readily interpretable microstructural information.

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.

Evidence for microscopic kurtosis in neural tissue revealed by correlation tensor MRI

PURPOSE

The impact of microscopic diffusional kurtosis (µK), arising from restricted diffusion and/or structural disorder, remains a controversial issue in contemporary diffusion MRI (dMRI). Recently, correlation tensor imaging (CTI) was introduced to disentangle the sources contributing to diffusional kurtosis, without relying on a-priori multi-gaussian component (MGC) or other microstructural assumptions. Here, we investigated µK in in vivo rat brains and assessed its impact on state-of-the-art methods ignoring µK.

THEORY AND METHODS

CTI harnesses double diffusion encoding (DDE) experiments, which were here improved for speed and minimal bias using four different sets of acquisition parameters. The robustness of the improved CTI protocol was assessed via simulations. In vivo CTI acquisitions were performed in healthy rat brains using a 9.4T pre-clinical scanner equipped with a cryogenic coil, and targeted the estimation of µK, anisotropic kurtosis, and isotropic kurtosis.

RESULTS

The improved CTI acquisition scheme substantially reduces scan time and importantly, also minimizes higher-order-term biases, thus enabling robust µK estimation, alongside K_aniso and K_iso metrics. Our CTI experiments revealed positive µK both in white and gray matter of the rat brain in vivo; µK is the dominant kurtosis source in healthy gray matter tissue. The non-negligible µK substantially were found to bias prior MGC analyses of K_iso and K_aniso .

CONCLUSIONS

Correlation Tensor MRI offers a more accurate and robust characterization of kurtosis sources than its predecessors. µK is non-negligible in vivo in healthy white and gray matter tissues and could be an important biomarker for future studies. Our findings thus have both theoretical and practical implications for future dMRI research.

Whole-Brain Imaging of Subvoxel T1-Diffusion Correlation Spectra in Human Subjects

T1 relaxation and water mobility generate eloquent MRI tissue contrasts with great diagnostic value in many neuroradiological applications. However, conventional methods do not adequately quantify the microscopic heterogeneity of these important biophysical properties within a voxel, and therefore have limited biological specificity. We describe a new correlation spectroscopic (CS) MRI method for measuring how T1 and mean diffusivity (MD) co-vary in microscopic tissue environments. We develop a clinical pulse sequence that combines inversion recovery (IR) with single-shot isotropic diffusion encoding (IDE) to efficiently acquire whole-brain MRIs with a wide range of joint T1-MD weightings. Unlike conventional diffusion encoding, the IDE preparation ensures that all subvoxel water pools are weighted by their MDs regardless of the sizes, shapes, and orientations of their corresponding microscopic diffusion tensors. Accordingly, IR-IDE measurements are well-suited for model-free, quantitative spectroscopic analysis of microscopic water pools. Using numerical simulations, phantom experiments, and data from healthy volunteers we demonstrate how IR-IDE MRIs can be processed to reconstruct maps of two-dimensional joint probability density functions, i.e., correlation spectra, of subvoxel T1-MD values. In vivo T1-MD spectra show distinct cerebrospinal fluid and parenchymal tissue components specific to white matter, cortical gray matter, basal ganglia, and myelinated fiber pathways, suggesting the potential for improved biological specificity. The one-dimensional marginal distributions derived from the T1-MD correlation spectra agree well with results from other relaxation spectroscopic and quantitative MRI studies, validating the T1-MD contrast encoding and the spectral reconstruction. Mapping subvoxel T1-diffusion correlations in patient populations may provide a more nuanced, comprehensive, sensitive, and specific neuroradiological assessment of the non-specific changes seen on fluid-attenuated inversion recovery (FLAIR) and diffusion-weighted MRIs (DWIs) in cancer, ischemic stroke, or brain injury.

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.

Challenges for biophysical modeling of microstructure

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

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.

Peripheral nerve magnetic resonance imaging

Magnetic resonance imaging (MRI) has been used extensively in revealing pathological changes in the central nervous system. However, to date, MRI is very much underutilized in evaluating the peripheral nervous system (PNS). This underutilization is generally due to two perceived weaknesses in MRI: first, the need for very high resolution to image the small structures within the peripheral nerves to visualize morphological changes; second, the lack of normative data in MRI of the PNS and this makes reliable interpretation of the data difficult. This article reviews current state-of-the-art capabilities in in vivo MRI of human peripheral nerves. It aims to identify areas where progress has been made and those that still require further improvement. In particular, with many new therapies on the horizon, this review addresses how MRI can be used to provide non-invasive and objective biomarkers in the evaluation of peripheral neuropathies. Although a number of techniques are available in diagnosing and tracking pathologies in the PNS, those techniques typically target the distal peripheral nerves, and distal nerves may be completely degenerated during the patient’s first clinic visit. These techniques may also not be able to access the proximal nerves deeply embedded in the tissue. Peripheral nerve MRI would be an alternative to circumvent these problems. In order to address the pressing clinical needs, this review closes with a clinical protocol at 3T that will allow high-resolution, high-contrast, quantitative MRI of the proximal peripheral nerves.

Maxwell-compensated design of asymmetric gradient waveforms for tensor-valued diffusion encoding

PURPOSE

Diffusion encoding with asymmetric gradient waveforms is appealing because the asymmetry provides superior efficiency. However, concomitant gradients may cause a residual gradient moment at the end of the waveform, which can cause significant signal error and image artifacts. The purpose of this study was to develop an asymmetric waveform designs for tensor-valued diffusion encoding that is not sensitive to concomitant gradients.

METHODS

The "Maxwell index" was proposed as a scalar invariant to capture the effect of concomitant gradients. Optimization of "Maxwell-compensated" waveforms was performed in which this index was constrained. Resulting waveforms were compared to waveforms from literature, in terms of the measured and predicted impact of concomitant gradients, by numerical analysis as well as experiments in a phantom and in a healthy human brain.

RESULTS

Maxwell-compensated waveforms with Maxwell indices below 100 (mT/m)2 ms showed negligible signal bias in both numerical analysis and experiments. By contrast, several waveforms from literature showed gross signal bias under the same conditions, leading to a signal bias that was large enough to markedly affect parameter maps. Experimental results were accurately predicted by theory.

CONCLUSION

Constraining the Maxwell index in the optimization of asymmetric gradient waveforms yields efficient diffusion encoding that negates the effects of concomitant fields while enabling arbitrary shapes of the b-tensor. This waveform design is especially useful in combination with strong gradients, long encoding times, thick slices, simultaneous multi-slice acquisition, and large FOVs.

In vivo magnetic resonance imaging and spectroscopy. Technological advances and opportunities for applications continue to abound

Over the past decades, the field of in vivo magnetic resonance (MR) has built up an impressive repertoire of data acquisition and analysis technologies for anatomical, functional, physiological, and molecular imaging, the description of which requires many book volumes. As such it is impossible for a few authors to have an authoritative overview of the field and for a brief article to be inclusive. We will therefore focus mainly on data acquisition and attempt to give some insight into the principles underlying current advanced methods in the field and the potential for further innovation. In our view, the foreseeable future is expected to show continued rapid progress, for instance in imaging of microscopic tissue properties in vivo, assessment of functional and anatomical connectivity, higher resolution physiologic and metabolic imaging, and even imaging of receptor binding. In addition, acquisition speed and information content will continue to increase due to the continuous development of approaches for parallel imaging (including simultaneous multi-slice imaging), compressed sensing, and MRI fingerprinting. Finally, artificial intelligence approaches are becoming more realistic and will have a tremendous effect on both acquisition and analysis strategies. Together, these developments will continue to provide opportunity for scientific discovery and, in combination with large data sets from other fields such as genomics, allow the ultimate realization of precision medicine in the clinic.

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

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

Tensor-valued diffusion encoding for diffusional variance decomposition (DIVIDE): Technical feasibility in clinical MRI systems

Microstructure imaging techniques based on tensor-valued diffusion encoding have gained popularity within the MRI research community. Unlike conventional diffusion encoding-applied along a single direction in each shot-tensor-valued encoding employs diffusion encoding along multiple directions within a single preparation of the signal. The benefit is that such encoding may probe tissue features that are not accessible by conventional encoding. For example, diffusional variance decomposition (DIVIDE) takes advantage of tensor-valued encoding to probe microscopic diffusion anisotropy independent of orientation coherence. The drawback is that tensor-valued encoding generally requires gradient waveforms that are more demanding on hardware; it has therefore been used primarily in MRI systems with relatively high performance. The purpose of this work was to explore tensor-valued diffusion encoding on clinical MRI systems with varying performance to test its technical feasibility within the context of DIVIDE. We performed whole-brain imaging with linear and spherical b-tensor encoding at field strengths between 1.5 and 7 T, and at maximal gradient amplitudes between 45 and 80 mT/m. Asymmetric gradient waveforms were optimized numerically to yield b-values up to 2 ms/μm2. Technical feasibility was assessed in terms of the repeatability, SNR, and quality of DIVIDE parameter maps. Variable system performance resulted in echo times between 83 to 115 ms and total acquisition times of 6 to 9 minutes when using 80 signal samples and resolution 2×2×4 mm3. As expected, the repeatability, signal-to-noise ratio and parameter map quality depended on hardware performance. We conclude that tensor-valued encoding is feasible for a wide range of MRI systems-even at 1.5 T with maximal gradient waveform amplitudes of 33 mT/m-and baseline experimental design and quality parameters for all included configurations. This demonstrates that tissue features, beyond those accessible by conventional diffusion encoding, can be explored on a wide range of MRI systems.

Microscopic anisotropy misestimation in spherical-mean single diffusion encoding MRI

Purpose

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

Methods

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

Results

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

Conclusion

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

Preliminary evaluation of accelerated microscopic diffusional kurtosis imaging (μDKI) in a rodent model of epilepsy

PURPOSE

Our study aimed to develop accelerated microscopic diffusional kurtosis imaging (μDKI) and preliminarily evaluated it in a rodent model of chronic epilepsy.

METHODS

We investigated two μDKI acceleration schemes of reduced sampling density and angular range in a phantom and wild-type rats, and further tested μDKI method in pilocarpine-induced epilepsy rats using a 4.7 Tesla MRI. Single slice average μD_app and μK_app maps were derived, and Nissl staining was obtained.

RESULTS

The kurtosis maps from two accelerated μDKI sampling schemes (sampling density and range) are very similar to that using fully sampled data (SSIM > 0.95). For the epileptic models, μDKI showed noticeably different contrast from those obtained with conventional DKI. Specifically, the average μK_app was significantly less than that of the average of K_app (0.15 ± 0.01 vs. 0.47 ± 0.02) in the ventricle.

CONCLUSIONS

Our study demonstrated the feasibility of accelerated in vivo μDKI. Our work revealed that μDKI provides complementary information to conventional DKI method, suggesting that advanced DKI sequences are promising to elucidate tissue microstructure in neurological diseases.

Using double pulsed-field gradient MRI to study tissue microstructure in traumatic brain injury (TBI)

Double pulsed-field gradient (dPFG) MRI is proposed as a new sensitive tool to detect and characterize tissue microstructure following diffuse axonal injury. In this study dPFG MRI was used to estimate apparent mean axon diameter in a diffuse axonal injury animal model and in healthy fixed mouse brain. Histological analysis was used to verify the presence of the injury detected by MRI.

Efficient experimental designs for isotropic generalized diffusion tensor MRI (IGDTI)

PURPOSE

We propose a new generalized diffusion tensor imaging (GDTI) experimental design and analysis framework for efficiently measuring orientationally averaged diffusion-weighted images (DWIs), which remove bulk signal modulations attributed to diffusion anisotropy and quantify isotropic higher-order diffusion tensors (HOT). We illustrate how this framework accelerates the clinical measurement of rotation-invariant tissue microstructural parameters derived from HOT, such as the HOT-Trace and the mean t-kurtosis.

THEORY AND METHODS

For a large range of b-values, we compare orientationally averaged DWIs measured with high angular resolution diffusion imaging to those obtained with the proposed isotropic GDTI (IGDTI) experimental design. We compare rotation-invariant microstructural parameters measured with IGDTI to those derived from HOTs measured explicitly with GDTI.

RESULTS

In both fixed-brain microimaging and in vivo clinical experiments, IGDTI accurately quantifies mean apparent diffusion coefficient (mADC)-weighted DWIs over a wide range of b-values and allows efficient computation of HOT-derived scalar tissue parameters from a small number of DWIs.

CONCLUSIONS

IGDTI provides direct and accurate estimates of orientationally averaged tissue water mobilities over a wide range of b-values. This efficient method may enable new, sensitive, and quantitative assessments for clinical applications in which changes in mADC can be observe,d such as detecting and characterizing stroke, cancers, and neurodegenerative diseases. Magn Reson Med 79:180-194, 2018. Published 2017. This article is a U.S. Government work and is in the public domain in the USA.

Double diffusion encoding MRI for the clinic

PURPOSE

The purpose of this study is to develop double diffusion encoding (DDE) MRI methods for clinical use. Microscopic diffusion anisotropy measurements from DDE promise greater specificity to changes in tissue microstructure compared with conventional diffusion tensor imaging, but implementation of DDE sequences on whole-body MRI scanners is challenging because of the limited gradient strengths and lengthy acquisition times.

METHODS

A custom single-refocused DDE sequence was implemented on a 3T whole-body scanner. The DDE gradient orientation scheme and sequence parameters were optimized based on a Gaussian diffusion assumption. Using an optimized 5-min DDE acquisition, microscopic fractional anisotropy (μFA) maps were acquired for the first time in multiple sclerosis patients.

RESULTS

Based on simulations and in vivo human measurements, six parallel and six orthogonal diffusion gradient pairs were found to be the minimum number of diffusion gradient pairs necessary to produce a rotationally invariant measurement of μFA. Simulations showed that optimal precision and accuracy of μFA measurements were obtained using b-values between 1500 and 3000 s/mm² . The μFA maps showed improved delineation of multiple sclerosis lesions compared with conventional fractional anisotropy and distinct contrast from T₂ -weighted fluid attenuated inversion recovery and T₁ -weighted imaging.

CONCLUSION

The μFA maps can be measured using DDE in a clinical setting and may provide new opportunities for characterizing multiple sclerosis lesions and other types of tissue degeneration. Magn Reson Med 80:507-520, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Promise and pitfalls of g-ratio estimation with MRI

The fiber g-ratio is the ratio of the inner to the outer diameter of the myelin sheath of a myelinated axon. It has a limited dynamic range in healthy white matter, as it is optimized for speed of signal conduction, cellular energetics, and spatial constraints. In vivo imaging of the g-ratio in health and disease would greatly increase our knowledge of the nervous system and our ability to diagnose, monitor, and treat disease. MRI based g-ratio imaging was first conceived in 2011, and expanded to be feasible in full brain white matter with preliminary results in 2013. This manuscript reviews the growing g-ratio imaging literature and speculates on future applications. It details the methodology for imaging the g-ratio with MRI, and describes the known pitfalls and challenges in doing so.

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.

Double oscillating diffusion encoding and sensitivity to microscopic anisotropy

Purpose

To introduce a novel diffusion pulse sequence, namely double oscillating diffusion encoding (DODE), and to investigate whether it adds sensitivity to microscopic diffusion anisotropy (µA) compared to the well‐established double diffusion encoding (DDE) methodology.

Methods

We simulate measurements from DODE and DDE sequences for different types of microstructures exhibiting restricted diffusion. First, we compare the effect of varying pulse sequence parameters on the DODE and DDE signal. Then, we analyse the sensitivity of the two sequences to the microstructural parameters (pore diameter and length) which determine µA. Finally, we investigate specificity of measurements to particular substrate configurations.

Results

Simulations show that DODE sequences exhibit similar signal dependence on the relative angle between the two gradients as DDE sequences, however, the effect of varying the mixing time is less pronounced. The sensitivity analysis shows that in substrates with elongated pores and various orientations, DODE sequences increase the sensitivity to pore diameter, while DDE sequences are more sensitive to pore length. Moreover, DDE and DODE sequence parameters can be tailored to enhance/suppress the signal from a particular range of substrates.

Conclusions

A combination of DODE and DDE sequences maximize sensitivity to µA, compared to using just the DDE method. Magn Reson Med 78:550–564, 2017. © 2016 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 License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

In vivo imaging of neuroinflammation in schizophrenia

In recent years evidence has accumulated to suggest that neuroinflammation might be an early pathology of schizophrenia that later leads to neurodegeneration, yet the exact role in the etiology, as well as the source of neuroinflammation, are still not known. The hypothesis of neuroinflammation involvement in schizophrenia is quickly gaining popularity, and thus it is imperative that we have reliable and reproducible tools and measures that are both sensitive, and, most importantly, specific to neuroinflammation. The development and use of appropriate human in vivo imaging methods can help in our understanding of the location and extent of neuroinflammation in different stages of the disorder, its natural time-course, and its relation to neurodegeneration. Thus far, there is little in vivo evidence derived from neuroimaging methods. This is likely the case because the methods that are specific and sensitive to neuroinflammation are relatively new or only just being developed. This paper provides a methodological review of both existing and emerging positron emission tomography and magnetic resonance imaging techniques that identify and characterize neuroinflammation. We describe \how these methods have been used in schizophrenia research. We also outline the shortcomings of existing methods, and we highlight promising future techniques that will likely improve state-of-the-art neuroimaging as a more refined approach for investigating neuroinflammation in schizophrenia.

Model-based estimation of microscopic anisotropy using diffusion MRI: a simulation study

Non-invasive estimation of cell size and shape is a key challenge in diffusion MRI. This article presents a model-based approach that provides independent estimates of pore size and eccentricity from diffusion MRI data. The technique uses a geometric model of finite cylinders with gamma-distributed radii to represent pores of various sizes and elongations. We consider both macroscopically isotropic substrates and substrates of semi-coherently oriented anisotropic pores and we use Monte Carlo simulations to generate synthetic data. We compare the sensitivity of single and double diffusion encoding (SDE and DDE) sequences to the size distribution and eccentricity, and further analyse different protocols of DDE sequences with parallel and/or perpendicular pairs of gradients. We show that explicitly accounting for size distribution is necessary for accurate microstructural parameter estimates, and a model that assumes a single size yields biased eccentricity values. We also find that SDE sequences support estimates, although DDE sequences with mixed parallel and perpendicular gradients enhance accuracy. In the case of macroscopically anisotropic substrates, this model-based approach can be extended to a rotationally invariant framework to provide features of pore shape (specifically eccentricity) in the presence of size distribution and orientation dispersion.

White matter microstructure from nonparametric axon diameter distribution mapping

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

Rapid in vivo detection of rat spinal cord injury with double-diffusion-encoded magnetic resonance spectroscopy

PURPOSE

Diffusion-weighted imaging is a common experimental tool for evaluating spinal cord injury (SCI), yet it suffers from complications that decrease its clinical effectiveness. The most commonly used technique, diffusion tensor imaging (DTI), is often confounded by effects of edema accompanying acute SCI, limiting its sensitivity to the important functional status marker of axonal integrity. The purpose of this study is to introduce a novel diffusion-acquisition method with the goal of overcoming these limitations.

METHODS

A double diffusion encoding (DDE) pulse sequence was implemented with a diffusion-weighted filter orthogonal to the spinal cord for suppressing nonneural signals prior to diffusion weighting parallel to the cord. A point-resolved spectroscopy readout (DDE-PRESS) was used for improved sensitivity and compared with DTI in a rat model of SCI with varying injury severities.

RESULTS

The DDE-PRESS parameter, restricted fraction, showed a strong relationship with injury severity (P < 0.001, R²  = 0.67). Although the whole-cord averaged DTI parameter values exhibited only minor injury relationships, a weighted region of interest (ROI) based DTI analysis improved sensitivity to injury (P < 0.001, R²  = 0.66).

CONCLUSIONS

In a rat model of SCI, DDE-PRESS demonstrated high sensitivity to injury with substantial decreases in acquisition time and data processing. This method shows promise for application in rapid evaluation of SCI severity. Magn Reson Med 77:1639-1649, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Estimation of Bounded and Unbounded Trajectories in Diffusion MRI

Disentangling the tissue microstructural information from the diffusion magnetic resonance imaging (dMRI) measurements is quite important for extracting brain tissue specific measures. The autocorrelation function of diffusing spins is key for understanding the relation between dMRI signals and the acquisition gradient sequences. In this paper, we demonstrate that the autocorrelation of diffusion in restricted or bounded spaces can be well approximated by exponential functions. To this end, we propose to use the multivariate Ornstein-Uhlenbeck (OU) process to model the matrix-valued exponential autocorrelation function of three-dimensional diffusion processes with bounded trajectories. We present detailed analysis on the relation between the model parameters and the time-dependent apparent axon radius and provide a general model for dMRI signals from the frequency domain perspective. For our experimental setup, we model the diffusion signal as a mixture of two compartments that correspond to diffusing spins with bounded and unbounded trajectories, and analyze the corpus-callosum in an ex-vivo data set of a monkey brain.

PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: Insight from a simulation study

PURPOSE

To identify optimal pulsed gradient spin-echo (PGSE) and oscillating gradient spin-echo (OGSE) sequence settings for maximizing sensitivity to axon diameter in idealized and practical conditions.

METHODS

Simulations on a simple two-compartment white matter model (with nonpermeable cylinders) are used to investigate a wide space of clinically plausible PGSE and OGSE sequence parameters with trapezoidal diffusion gradient waveforms. Signal sensitivity is measured as a derivative of the signal with respect to axon diameter. Models of parallel and dispersed fibers are investigated separately to represent idealized and practical conditions.

RESULTS

Simulations show that, for the simple case of gradients perfectly perpendicular to straight parallel fibers, PGSE always gives maximum sensitivity. However, in real-world scenarios where fibers have unknown and dispersed orientation, low-frequency OGSE provides higher sensitivity. Maximum sensitivity results show that on current clinical scanners (Gmax  = 60 mT/m, signal to noise ratio (SNR) = 20) axon diameters below 6 µm are indistinguishable from zero. Scanners with stronger gradient systems such as the Massachusetts General Hospital (MGH) Connectom scanner (Gmax  = 300 mT/m) can extend this sensitivity limit down to 2-3 µm, probing a much greater proportion of the underlying axon diameter distribution.

CONCLUSION

Low-frequency OGSE provides additional sensitivity to PGSE in practical situations. OGSE is particularly advantageous for systems with high performance gradients.

Eddy current compensated double diffusion encoded (DDE) MRI

PURPOSE

Eddy currents might lead to image distortions in diffusion-weighted echo planar imaging. A method is proposed to reduce their effects on double diffusion encoding (DDE) MRI experiments and the thereby derived microscopic fractional anisotropy (μFA).

METHODS

The twice-refocused spin echo scheme was adapted for DDE measurements. To assess the effect of individual diffusion encodings on the image distortions, measurements of a grid of plastic rods in water were performed. The effect of eddy current compensation on μFA measurements was evaluated in the brains of six healthy volunteers.

RESULTS

The use of an eddy current compensation reduced the signal variation. As expected, the distortions caused by the second encoding were larger than those of the first encoding, entailing a stronger need to compensate for them. For an optimal result, however, both encodings had to be compensated. The artifact reduction strongly improved the measurement of the μFA in ventricles and gray matter by reducing the overestimation. An effect of the compensation on absolute μFA values in white matter was not observed.

CONCLUSION

It is advisable to compensate both encodings in DDE measurements for eddy currents. Magn Reson Med 77:328-335, 2017. © 2015 Wiley Periodicals, Inc.

Clinical feasibility of using mean apparent propagator (MAP) MRI to characterize brain tissue microstructure

Diffusion tensor imaging (DTI) is the most widely used method for characterizing noninvasively structural and architectural features of brain tissues. However, the assumption of a Gaussian spin displacement distribution intrinsic to DTI weakens its ability to describe intricate tissue microanatomy. Consequently, the biological interpretation of microstructural parameters, such as fractional anisotropy or mean diffusivity, is often equivocal. We evaluate the clinical feasibility of assessing brain tissue microstructure with mean apparent propagator (MAP) MRI, a powerful analytical framework that efficiently measures the probability density function (PDF) of spin displacements and quantifies useful metrics of this PDF indicative of diffusion in complex microstructure (e.g., restrictions, multiple compartments). Rotation invariant and scalar parameters computed from the MAP show consistent variation across neuroanatomical brain regions and increased ability to differentiate tissues with distinct structural and architectural features compared with DTI-derived parameters. The return-to-origin probability (RTOP) appears to reflect cellularity and restrictions better than MD, while the non-Gaussianity (NG) measures diffusion heterogeneity by comprehensively quantifying the deviation between the spin displacement PDF and its Gaussian approximation. Both RTOP and NG can be decomposed in the local anatomical frame for reference determined by the orientation of the diffusion tensor and reveal additional information complementary to DTI. The propagator anisotropy (PA) shows high tissue contrast even in deep brain nuclei and cortical gray matter and is more uniform in white matter than the FA, which drops significantly in regions containing crossing fibers. Orientational profiles of the propagator computed analytically from the MAP MRI series coefficients allow separation of different fiber populations in regions of crossing white matter pathways, which in turn improves our ability to perform whole-brain fiber tractography. Reconstructions from subsampled data sets suggest that MAP MRI parameters can be computed from a relatively small number of DWIs acquired with high b-value and good signal-to-noise ratio in clinically achievable scan durations of less than 10min. The neuroanatomical consistency across healthy subjects and reproducibility in test-retest experiments of MAP MRI microstructural parameters further substantiate the robustness and clinical feasibility of this technique. The MAP MRI metrics could potentially provide more sensitive clinical biomarkers with increased pathophysiological specificity compared to microstructural measures derived using conventional diffusion MRI techniques.

Dynamic and inherent B0 correction for DTI using stimulated echo spiral imaging

PURPOSE

To present a novel technique for high-resolution stimulated echo diffusion tensor imaging with self-navigated interleaved spirals readout trajectories that can inherently and dynamically correct for image artifacts due to spatial and temporal variations in the static magnetic field (B0) resulting from eddy currents, tissue susceptibilities, subject/physiological motion, and hardware instabilities.

METHODS

The Hahn spin echo formed by the first two 90° radiofrequency pulses is balanced to consecutively acquire two additional images with different echo times and generate an inherent field map, while the diffusion-prepared stimulated echo signal remains unaffected. For every diffusion-encoding direction, an intrinsically registered field map is estimated dynamically and used to effectively and inherently correct for off-resonance artifacts in the reconstruction of the corresponding diffusion-weighted image.

RESULTS

After correction with the dynamically acquired field maps, local blurring artifacts are specifically removed from individual stimulated echo diffusion-weighted images and the estimated diffusion tensors have significantly improved spatial accuracy and larger fractional anisotropy.

CONCLUSION

Combined with the self-navigated interleaved spirals acquisition scheme, our new method provides an integrated high-resolution short-echo time diffusion tensor imaging solution with inherent and dynamic correction for both motion-induced phase errors and off-resonance effects.

Characterizing magnetic resonance signal decay due to Gaussian diffusion: the path integral approach and a convenient computational method

The influence of Gaussian diffusion on the magnetic resonance signal is determined by the apparent diffusion coefficient (ADC) and tensor (ADT) of the diffusing fluid as well as the gradient waveform applied to sensitize the signal to diffusion. Estimations of ADC and ADT from diffusion-weighted acquisitions necessitate computations of, respectively, the b-value and b-matrix associated with the employed pulse sequence. We establish the relationship between these quantities and the gradient waveform by expressing the problem as a path integral and explicitly evaluating it. Further, we show that these important quantities can be conveniently computed for any gradient waveform using a simple algorithm that requires a few lines of code. With this representation, our technique complements the multiple correlation function (MCF) method commonly used to compute the effects of restricted diffusion, and provides a consistent and convenient framework for studies that aim to infer the microstructural features of the specimen.

PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: Insight from a simulation study

Purpose

To identify optimal pulsed gradient spin‐echo (PGSE) and oscillating gradient spin‐echo (OGSE) sequence settings for maximizing sensitivity to axon diameter in idealized and practical conditions.

Methods

Simulations on a simple two‐compartment white matter model (with nonpermeable cylinders) are used to investigate a wide space of clinically plausible PGSE and OGSE sequence parameters with trapezoidal diffusion gradient waveforms. Signal sensitivity is measured as a derivative of the signal with respect to axon diameter. Models of parallel and dispersed fibers are investigated separately to represent idealized and practical conditions.

Results

Simulations show that, for the simple case of gradients perfectly perpendicular to straight parallel fibers, PGSE always gives maximum sensitivity. However, in real‐world scenarios where fibers have unknown and dispersed orientation, low‐frequency OGSE provides higher sensitivity. Maximum sensitivity results show that on current clinical scanners (G_max = 60 mT/m, signal to noise ratio (SNR) = 20) axon diameters below 6 µm are indistinguishable from zero. Scanners with stronger gradient systems such as the Massachusetts General Hospital (MGH) Connectom scanner (G_max = 300 mT/m) can extend this sensitivity limit down to 2–3 µm, probing a much greater proportion of the underlying axon diameter distribution.

Conclusion

Low‐frequency OGSE provides additional sensitivity to PGSE in practical situations. OGSE is particularly advantageous for systems with high performance gradients. Magn Reson Med 75:688–700, 2016. © 2015 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 License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Cerebral maturation in the early preterm period-A magnetization transfer and diffusion tensor imaging study using voxel-based analysis

The magnetization transfer ratio (MTR) and diffusion tensor imaging (DTI) correlates of early brain development were examined in cohort of 18 very preterm neonates (27-31 gestational weeks) presenting with normal radiological findings scanned within 2weeks after birth (28-32 gestational weeks). A combination of non-linear image registration, tissue segmentation, and voxel-wise regression was used to map the age dependent changes in MTR and DTI-derived parameters in 3D across the brain based on the cross-sectional in vivo preterm data. The regression coefficient maps obtained differed between brain regions and between the different quantitative MRI indices. Significant linear increases as well as decreases in MTR and DTI-derived parameters were observed throughout the preterm brain. In particular, the lamination pattern in the cerebral wall was evident on parametric and regression coefficient maps. The frontal white matter area (subplate and intermediate zone) demonstrated a linear decrease in MTR. While the intermediate zone showed an unexpected decrease in fractional anisotropy (FA) with age, with this decrease (and the increase in mean diffusivity (MD)) driven primarily by an increase in radial diffusivity (RD) values, the subplate showed no change in FA (and an increase in MD). The latter was the result of a concomitant similar increase in axial diffusivity (AD) and RD values. Interpreting the in vivo results in terms of available histological data, we present a biophysical model that describes the relation between various microstructural changes measured by complementary quantitative methods available on clinical scanners and a range of maturational processes in brain tissue.

A model for extra-axonal diffusion spectra with frequency-dependent restriction

PURPOSE

In the brain, there is growing interest in using the temporal diffusion spectrum to characterize axonal geometry in white matter because of the potential to be more sensitive to small pores compared to conventional time-dependent diffusion. However, analytical expressions for the diffusion spectrum of particles have only been derived for simple, restricting geometries such as cylinders, which are often used as a model for intra-axonal diffusion. The extra-axonal space is more complex, but the diffusion spectrum has largely not been modeled. We propose a model for the extra-axonal space, which can be used for interpretation of experimental data.

THEORY AND METHODS

An empirical model describing the extra-axonal space diffusion spectrum was compared with simulated spectra. Spectra were simulated using Monte Carlo methods for idealized, regularly and randomly packed axons over a wide range of packing densities and spatial scales. The model parameters are related to the microstructural properties of tortuosity, axonal radius, and separation for regularly packed axons and pore size for randomly packed axons.

RESULTS

Forward model predictions closely matched simulations. The model fitted the simulated spectra well and accurately estimated microstructural properties.

CONCLUSIONS

This simple model provides expressions that relate the diffusion spectrum to biologically relevant microstructural properties.

Double-pulsed diffusional kurtosis imaging

Diffusional kurtosis imaging (DKI) is extended to double-pulsed-field-gradient (d-PFG) diffusion MRI sequences. This gives a practical approach for acquiring and analyzing d-PFG data. In particular, the leading d-PFG effects, beyond what conventional single-pulsed field gradient (s-PFG) provides, are interpreted in terms of the kurtosis for a diffusion displacement probability density function (dPDF) in a six-dimensional (6D) space. The 6D diffusional kurtosis encodes the unique information provided by d-PFG sequences up to second order in the b-value. This observation leads to a compact expression for the signal magnitude, and it suggests novel data acquisition and analysis methods. Double-pulsed DKI (DP-DKI) is demonstrated for in vivo mouse brain with d-PFG data obtained at 7 T. Copyright © 2014 John Wiley & Sons, Ltd.

In vivo quantification of white matter microstructure for use in aging: a focus on two emerging techniques

Human brain imaging has seen many advances in the quantification of white matter in vivo. For example, these advances have revealed the association between white matter damage and vascular disease as well as their impact on risk for and development of dementia and depression in an aging population. Current neuroimaging methods to quantify white matter damage provide a foundation for understanding such age-related neuropathology; however, these methods are not as adept at determining the underlying microstructural abnormalities signaling at risk tissue or driving white matter damage in the aging brain. This review will begin with a brief overview of the use of diffusion tensor imaging (DTI) in understanding white matter alterations in aging before focusing in more detail on select advances in both diffusion-based methods and multi-component relaxometry techniques for imaging white matter microstructural integrity within myelin sheaths and the axons they encase. Although DTI greatly extended the field of white matter interrogation, these more recent technological advances will add clarity to the underlying microstructural mechanisms that contribute to white matter damage. More specifically, the methods highlighted in this review may prove more sensitive (and specific) for determining the contribution of myelin versus axonal integrity to the aging of white matter in brain.

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.