Relationships between diffusion tensor and q-space MRI

NVAM-Net: deep learning networks for reconstructing high-quality fiber orientation distributions

PURPOSE

Diffusion magnetic resonance imaging (dMRI) is a widely used non-invasive method for investigating brain anatomical structures. Conventional techniques for estimating fiber orientation distribution (FOD) from dMRI data often neglect voxel-level spatial relationships, leading to ambiguous associations between target voxels and their neighbors, which, in turn, adversely impacts FOD accuracy. This study aims to address this issue by introducing a novel neural network, the neighboring voxel attention mechanism network (NVAM-Net), designed to reconstruct high-quality FOD images.

METHODS

The NVAM-Net leverages a Transformer architecture and incorporates two innovative attention mechanisms: voxel attention and surface attention. These mechanisms are specifically designed to capture overlooked features among neighboring voxels. The processed features are subsequently passed through two fully connected layers, further enhancing FOD estimation accuracy by separately estimating spherical harmonics (SH) coefficients of varying orders.

RESULTS

The experimental findings, based on the Human Connectome Project (HCP) dataset, reveal that the reconstructed super-resolution FOD images achieve results comparable to those obtained through more advanced dMRI acquisition protocols. These results underscore the NVAM-Net's robust performance in reconstructing multi-shell multi-tissue constrained spherical deconvolution (MSMT-CSD).

CONCLUSION

In summary, this research underscores the NVAM-Net's advantages and practical feasibility in reconstructing high-quality FOD images. It provides a reliable reference point for clinical applications in the field of diffusion magnetic resonance imaging.

Clinical physiology: the crucial role of MRI in evaluation of peripheral artery disease

Peripheral artery disease (PAD) is a common vascular disease that primarily affects the lower limbs and is defined by the constriction or blockage of peripheral arteries and may involve microvascular dysfunction and tissue injury. Patients with diabetes have more prominent disease of microcirculation and develop peripheral neuropathy, autonomic dysfunction, and medial vascular calcification. Early and accurate diagnosis of PAD and disease characterization are essential for personalized management and therapy planning. Magnetic resonance imaging (MRI) provides excellent soft tissue contrast and multiplanar imaging capabilities and is useful as a noninvasive imaging tool in the comprehensive physiological assessment of PAD. This review provides an overview of the current state of the art of MRI in the evaluation and characterization of PAD, including an analysis of the many applicable MR imaging techniques, describing the advantages and disadvantages of each approach. We also present recent developments, future clinical applications, and future MRI directions in assessing PAD. The development of new MR imaging technologies and applications in preclinical models with translation to clinical research holds considerable potential for improving the understanding of the pathophysiology of PAD and clinical applications for improving diagnostic precision, risk stratification, and treatment outcomes in patients with PAD.

Optimal bi-planar gradient coil configurations for diamond nitrogen-vacancy based diffusion-weighted NMR experiments

INTRODUCTION

Diffusion weighting in optically detected magnetic resonance experiments involving diamond nitrogen-vacancy (NV) centers can provide valuable microstructural information. Bi-planar gradient coils employed for diffusion weighting afford excellent spatial access, essential for integrating the NV-NMR components. Nevertheless, owing to the polar tilt of roughly [Formula: see text] of the diamond NV center, the primary magnetic field direction must be taken into account accordingly.

METHODS

To determine the most effective bi-planar gradient coil configurations, we conducted an investigation into the impact of various factors, including the square side length, surface separation, and surface orientation. This was accomplished by generating over 500 bi-planar surface configurations using automated methods.

RESULTS

We successfully generated and evaluated coil layouts in terms of sensitivity and field accuracy. Interestingly, inclined bi-planar orientations close to the NV-NMR setup's requirement, showed higher sensitivity for the transverse gradient channels than horizontal or vertical orientations. We fabricated a suitable solution as a three-channel bi-planar double-layered PCB system and experimentally validated the sensitivities at [Formula: see text] and [Formula: see text] for the transverse [Formula: see text] and [Formula: see text] gradients, and [Formula: see text] for the [Formula: see text] gradient.

DISCUSSION

We found that the chosen relative bi-planar tilt of [Formula: see text] represents a reasonable compromise in terms of overall performance and allows for easier coil implementation with a straight, horizontal alignment within the overall experimental setup.

Validation of deep learning techniques for quality augmentation in diffusion MRI for clinical studies

The objective of this study is to evaluate the efficacy of deep learning (DL) techniques in improving the quality of diffusion MRI (dMRI) data in clinical applications. The study aims to determine whether the use of artificial intelligence (AI) methods in medical images may result in the loss of critical clinical information and/or the appearance of false information. To assess this, the focus was on the angular resolution of dMRI and a clinical trial was conducted on migraine, specifically between episodic and chronic migraine patients. The number of gradient directions had an impact on white matter analysis results, with statistically significant differences between groups being drastically reduced when using 21 gradient directions instead of the original 61. Fourteen teams from different institutions were tasked to use DL to enhance three diffusion metrics (FA, AD and MD) calculated from data acquired with 21 gradient directions and a b-value of 1000 s/mm2. The goal was to produce results that were comparable to those calculated from 61 gradient directions. The results were evaluated using both standard image quality metrics and Tract-Based Spatial Statistics (TBSS) to compare episodic and chronic migraine patients. The study results suggest that while most DL techniques improved the ability to detect statistical differences between groups, they also led to an increase in false positive. The results showed that there was a constant growth rate of false positives linearly proportional to the new true positives, which highlights the risk of generalization of AI-based tasks when assessing diverse clinical cohorts and training using data from a single group. The methods also showed divergent performance when replicating the original distribution of the data and some exhibited significant bias. In conclusion, extreme caution should be exercised when using AI methods for harmonization or synthesis in clinical studies when processing heterogeneous data in clinical studies, as important information may be altered, even when global metrics such as structural similarity or peak signal-to-noise ratio appear to suggest otherwise.

Cumulant expansion with localization: A new representation of the diffusion MRI signal

Diffusion MR is sensitive to the microstructural features of a sample. Fine-scale characteristics can be probed by employing strong diffusion gradients while the low b-value regime is determined by the cumulants of the distribution of particle displacements. A signal representation based on the cumulants, however, suffers from a finite convergence radius and cannot represent the 'localization regime' characterized by a stretched exponential decay that emerges at large gradient strengths. Here, we propose a new representation for the diffusion MR signal. Our method provides not only a robust estimate of the first three cumulants but also a meaningful extrapolation of the entire signal decay.

Nuclear Magnetic Resonance Diffusometry of Linear and Branched Wormlike Micelles

Diffusion studies using nuclear magnetic resonance (NMR) spectroscopy were conducted on two model surfactant solutions of cetyltrimethylammonium bromide/sodium salicylate (CTAB/NaSal) and cetylpyridinium chloride/sodium salicylate (CPCl/NaSal). By increasing the salt-to-surfactant concentration ratio, these systems display two peaks in the zero-shear viscosity and relaxation time, which are indicative of transitions from linear to branched micellar networks. The goal of this work is to assess the sensitivity of NMR diffusometry to different types of micellar microstructures and identify the mechanism(s) of surfactant self-diffusion in micellar solutions. At low salt-to-surfactant concentration ratios, for which wormlike micelles are linear, the surfactant self-diffusion is best described by a mean squared displacement, Z², that varies as Z² ∝ T_diff^0.5, where T_diff is the diffusion time. As the salt concentration increases to establish branched micelles, Z² ∝ T_diff, indicating a Brownian-like self-diffusion of surfactant molecules in branched micelles. This result indicates that NMR diffusometry is capable of differentiating various types of micellar microstructures. In addition, the self-diffusion coefficient of the surfactant molecules in linear and branched micelles are determined, for the first time, by comparing the existing restricted diffusion models and are shown to be much slower than the diffusion of proton molecules in the bulk. Moreover, in linear and moderately branched wormlike micelles, the dominant mechanism of surfactant self-diffusion is through the curvilinear diffusion of the surfactant molecules along the contour length of the micelles, whereas in the branched micelles, before the second viscosity maxima, the surfactant self-diffusion could arise from a combination of micellar breakage, exchange between micelles and/or the bulk.

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.

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.

Apparent propagator anisotropy from single-shell diffusion MRI acquisitions

PURPOSE

The apparent propagator anisotropy (APA) is a new diffusion MRI metric that, while drawing on the benefits of the ensemble averaged propagator anisotropy (PA) compared to the fractional anisotropy (FA), can be estimated from single-shell data.

THEORY AND METHODS

Computation of the full PA requires acquisition of large datasets with many diffusion directions and different b-values, and results in extremely long processing times. This has hindered adoption of the PA by the community, despite evidence that it provides meaningful information beyond the FA. Calculation of the complete propagator can be avoided under the hypothesis that a similar sensitivity/specificity may be achieved from apparent measurements at a given shell. Assuming that diffusion anisotropy (DiA) is nondependent on the b-value, a closed-form expression using information from one single shell (ie, b-value) is reported.

RESULTS

Publicly available databases with healthy and diseased subjects are used to compare the APA against other anisotropy measures. The structural information provided by the APA correlates with that provided by the PA for healthy subjects, while it also reveals statistically relevant differences in white matter regions for two pathologies, with a higher reliability than the FA. Additionally, APA has a computational complexity similar to the FA, with processing-times several orders of magnitude below the PA.

CONCLUSIONS

The APA can extract more relevant white matter information than the FA, without any additional demands on data acquisition. This makes APA an attractive option for adoption into existing diffusion MRI analysis pipelines.

Micro-structure diffusion scalar measures from reduced MRI acquisitions

In diffusion MRI, the Ensemble Average diffusion Propagator (EAP) provides relevant micro-structural information and meaningful descriptive maps of the white matter previously obscured by traditional techniques like Diffusion Tensor Imaging (DTI). The direct estimation of the EAP, however, requires a dense sampling of the Cartesian q-space involving a huge amount of samples (diffusion gradients) for proper reconstruction. A collection of more efficient techniques have been proposed in the last decade based on parametric representations of the EAP, but they still imply acquiring a large number of diffusion gradients with different b-values (shells). Paradoxically, this has come together with an effort to find scalar measures gathering all the q-space micro-structural information probed in one single index or set of indices. Among them, the return-to-origin (RTOP), return-to-plane (RTPP), and return-to-axis (RTAP) probabilities have rapidly gained popularity. In this work, we propose the so-called "Apparent Measures Using Reduced Acquisitions" (AMURA) aimed at computing scalar indices that can mimic the sensitivity of state of the art EAP-based measures to micro-structural changes. AMURA drastically reduces both the number of samples needed and the computational complexity of the estimation of diffusion properties by assuming the diffusion anisotropy is roughly independent from the radial direction. This simplification allows us to compute closed-form expressions from single-shell information, so that AMURA remains compatible with standard acquisition protocols commonly used even in clinical practice. Additionally, the analytical form of AMURA-based measures, as opposed to the iterative, non-linear reconstruction ubiquitous to full EAP techniques, turns the newly introduced apparent RTOP, RTPP, and RTAP both robust and efficient to compute.

Fast learning of fiber orientation distribution function for MR tractography using convolutional neural network

PURPOSE

In diffusion-weighted magnetic resonance imaging (DW-MRI), the fiber orientation distribution function (fODF) is of great importance for solving complex fiber configurations to achieve reliable tractography throughout the brain, which ultimately facilitates the understanding of brain connectivity and exploration of neurological dysfunction. Recently, multi-shell multi-tissue constrained spherical deconvolution (MSMT-CSD) method has been explored for reconstructing full fODFs. To achieve a reliable fitting, similar to other model-based approaches, a large number of diffusion measurements is typically required for MSMT-CSD method. The prolonged acquisition is, however, not feasible in practical clinical routine and is prone to motion artifacts. To accelerate the acquisition, we proposed a method to reconstruct the fODF from downsampled diffusion-weighted images (DWIs) by leveraging the strong inference ability of the deep convolutional neural network (CNN).

METHODS

The method treats spherical harmonics (SH)-represented DWI signals and fODF coefficients as inputs and outputs, respectively. To compensate for the reduced gradient directions with reduced number of DWIs in acquisition in each voxel, its surrounding voxels are incorporated by the network for exploiting their spatial continuity. The resulting fODF coefficients are fitted with applying the CNN in a multi-target regression model. The network is composed of two convolutional layers and three fully connected layers. To obtain an initial evaluation of the method, we quantitatively measured its performance on a simulated dataset. Then, for in vivo tests, we employed data from 24 subjects from the Human Connectome Project (HCP) as training set and six subjects as test set. The performance of the proposed method was primarily compared to the super-resolved MSMT-CSD with the decreasing number of DWIs. The fODFs reconstructed by MSMT-CSD from all available 288 DWIs were used as training labels and the reference standard. The performance was quantitatively measured by the angular correlation coefficient (ACC) and the mean angular error (MAE).

RESULTS

For the simulated dataset, the proposed method exhibited the potential advantage over the model reconstruction. For the in vivo dataset, it achieved superior results over the MSMT-CSD in all the investigated cases, with its advantage more obvious when a limited number of DWIs were used. As the number of DWIs was reduced from 95 to 25, the median ACC ranged from 0.96 to 0.91 for the CNN, but 0.93 to 0.77 for the MSMT-CSD (with perfect score of 1). The angular error in the typical regions of interest (ROIs) was also much lower, especially in multi-fiber regions. The average MAE for the CNN method in regions containing one, two, three fibers was, respectively, 1.09°, 2.75°, and 8.35° smaller than the MSMT-CSD method. The visual inception of the fODF further confirmed this superiority. Moreover, the tractography results validated the effectiveness of the learned fODF, in preserving known major branching fibers with only 25 DWIs.

CONCLUSION

Experiments on HCP datasets demonstrated the feasibility of the proposed method in recovering fODFs from up to 11-fold reduced number of DWIs. The proposed method offers a new streamlined reconstruction procedure and exhibits promising potential in acquisition acceleration for the reconstruction of fODFs with good accuracy.

Comparison of cumulant expansion and q-space imaging estimates for diffusional kurtosis in brain

PURPOSE

To compare estimates for the diffusional kurtosis in brain as obtained from a cumulant expansion (CE) of the diffusion MRI (dMRI) signal and from q-space (QS) imaging.

THEORY AND METHODS

For the CE estimates of the kurtosis, the CE was truncated to quadratic order in the b-value and fit to the dMRI signal for b-values from 0 up to 2000s/mm². For the QS estimates, b-values ranging from 0 up to 10,000s/mm² were used to determine the diffusion displacement probability density function (dPDF) via Stejskal's formula. The kurtosis was then calculated directly from the second and fourth order moments of the dPDF. These two approximations were studied for in vivo human data obtained on a 3T MRI scanner using three orthogonal diffusion encoding directions.

RESULTS

The whole brain mean values for the CE and QS kurtosis estimates differed by 16% or less in each of the considered diffusion encoding directions, and the Pearson correlation coefficients all exceeded 0.85. Nonetheless, there were large discrepancies in many voxels, particularly those with either very high or very low kurtoses relative to the mean values.

CONCLUSION

Estimates of the diffusional kurtosis in brain obtained using CE and QS approximations are strongly correlated, suggesting that they encode similar information. However, for the choice of b-values employed here, there may be substantial differences, depending on the properties of the diffusion microenvironment in each voxel.

A probabilistic atlas of fiber crossings for variability reduction of anisotropy measures

Diffusion imaging enables assessment of human brain white matter (WM) in vivo. WM microstructural integrity is routinely quantified via fractional anisotropy (FA). However, FA is also influenced by the number of differentially oriented fiber populations per voxel. To date, the precise statistical relationship between FA and fiber populations has not been characterized, complicating microstructural integrity assessment. Here, we used 630 state-of-the-art diffusion datasets from the Human Connectome Project, which allowed us to infer the number of fiber populations per voxel in a model-free fashion. Beyond the known impact on mean FA, variance of anisotropy distributions was drastically impacted, not only for FA, but also the more recent anisotropy indices generalized FA and multidimensional anisotropy. To ameliorate this bias, we introduce a probabilistic WM atlas delineating the number of distinctly oriented fiber populations per voxel. Our atlas shows that the majority of WM voxels features two differentially directed fiber populations (44.7%) rather than unidirectional fibers (32.9%) and identified WM regions with high numbers of crossing fibers, referred to as crossing pockets. Compartmentalizing anisotropy drastically reduced variance in group comparisons ranging from the whole brain to a few voxels in a single slice. In summary, we demonstrate a systematic effect of intra-voxel diffusion inhomogeneity on anisotropy. Moreover, we introduce a potential solution: The provided probabilistic WM atlas can easily be used with any given diffusion dataset to enhance the statistical robustness of anisotropy measures and increase their neurobiological utility.

Tensor estimation for double-pulsed diffusional kurtosis imaging

Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented.

Assessing the multiscale architecture of muscular tissue with Q-space magnetic resonance imaging: Review

Contraction of muscular tissue requires the synchronized shortening of myofibers arrayed in complex geometrical patterns. Imaging such myofiber patterns with diffusion-weighted MRI reveals architectural ensembles that underlie force generation at the organ scale. Restricted proton diffusion is a stochastic process resulting from random translational motion that may be used to probe the directionality of myofibers in whole tissue. During diffusion-weighted MRI, magnetic field gradients are applied to determine the directional dependence of proton diffusion through the analysis of a diffusional probability distribution function (PDF). The directions of principal (maximal) diffusion within the PDF are associated with similarly aligned diffusion maxima in adjacent voxels to derive multivoxel tracts. Diffusion-weighted MRI with tractography thus constitutes a multiscale method for depicting patterns of cellular organization within biological tissues. We provide in this review, details of the method by which generalized Q-space imaging is used to interrogate multidimensional diffusion space, and thereby to infer the organization of muscular tissue. Q-space imaging derives the lowest possible angular separation of diffusion maxima by optimizing the conditions by which magnetic field gradients are applied to a given tissue. To illustrate, we present the methods and applications associated with Q-space imaging of the multiscale myoarchitecture associated with the human and rodent tongues. These representations emphasize the intricate and continuous nature of muscle fiber organization and suggest a method to depict structural "blueprints" for skeletal and cardiac muscle tissue.

Diffusion Tractography in Deep Brain Stimulation Surgery: A Review

Deep brain stimulation (DBS) is believed to exert its therapeutic effects through modulation of brain circuitry, yet conventional preoperative planning does not allow direct targeting or visualization of white matter pathways. Diffusion MRI tractography (DT) is virtually the only non-invasive method of visualizing structural connectivity in the brain, leading many to suggest its use to guide DBS targeting. DT-guided DBS not only has the potential to allow direct white matter targeting for established applications [e.g., Parkinson’s disease (PD), essential tremor (ET), dystonia], but may also aid in the discovery of new therapeutic targets for a variety of other neurologic and psychiatric diseases. Despite these exciting opportunities, DT lacks standardization and rigorous anatomic validation, raising significant concern for the use of such data in stereotactic brain surgery. This review covers the technical details, proposed methods, and initial clinical data for the use of DT in DBS surgery. Rather than focusing on specific disease applications, this review focuses on methods that can be applied to virtually any DBS target.

MAPL: Tissue microstructure estimation using Laplacian-regularized MAP-MRI and its application to HCP data

The recovery of microstructure-related features of the brain's white matter is a current challenge in diffusion MRI. To robustly estimate these important features from multi-shell diffusion MRI data, we propose to analytically regularize the coefficient estimation of the Mean Apparent Propagator (MAP)-MRI method using the norm of the Laplacian of the reconstructed signal. We first compare our approach, which we call MAPL, with competing, state-of-the-art functional basis approaches. We show that it outperforms the original MAP-MRI implementation and the recently proposed modified Spherical Polar Fourier (mSPF) basis with respect to signal fitting and reconstruction of the Ensemble Average Propagator (EAP) and Orientation Distribution Function (ODF) in noisy, sparsely sampled data of a physical phantom with reference gold standard data. Then, to reduce the variance of parameter estimation using multi-compartment tissue models, we propose to use MAPL's signal fitting and extrapolation as a preprocessing step. We study the effect of MAPL on the estimation of axon diameter using a simplified Axcaliber model and axonal dispersion using the Neurite Orientation Dispersion and Density Imaging (NODDI) model. We show the positive effect of using it as a preprocessing step in estimating and reducing the variances of these parameters in the Corpus Callosum of six different subjects of the MGH Human Connectome Project. Finally, we correlate the estimated axon diameter, dispersion and restricted volume fractions with Fractional Anisotropy (FA) and clearly show that changes in FA significantly correlate with changes in all estimated parameters. Overall, we illustrate the potential of using a well-regularized functional basis together with multi-compartment approaches to recover important microstructure tissue parameters with much less variability, thus contributing to the challenge of better understanding microstructure-related features of the brain's white matter.

Patterns of intersecting fiber arrays revealed in whole muscle with generalized Q-space imaging

The multiscale attributes of mammalian muscle confer significant challenges for structural imaging in vivo. To achieve this, we employed a magnetic resonance method, termed "generalized Q-space imaging", that considers the effect of spatially distributed diffusion-weighted magnetic field gradients and diffusion sensitivities on the morphology of Q-space. This approach results in a subvoxel scaled probability distribution function whose shape correlates with local fiber orientation. The principal fiber populations identified within these probability distribution functions can then be associated by streamline methods to create multivoxel tractlike constructs that depict the macroscale orientation of myofiber arrays. We performed a simulation of Q-space input parameters, including magnetic field gradient strength and direction, diffusion sensitivity, and diffusional sampling to determine the optimal achievable fiber angle separation in the minimum scan time. We applied this approach to resolve intravoxel crossing myofiber arrays in the setting of the human tongue, an organ with anatomic complexity based on the presence of hierarchical arrays of intersecting myocytes. Using parameters defined by simulation, we imaged at 3T the fanlike configuration of the human genioglossus and the laterally positioned merging fibers of the styloglossus, inferior longitudinalis, chondroglossus, and verticalis. Comparative scans of the excised mouse tongue at 7T demonstrated similar midline and lateral crossing fiber patterns, whereas histological analysis confirmed the presence and distribution of these myofiber arrays at the microscopic scale. Our results demonstrate a magnetic resonance method for acquiring and displaying diffusional data that defines highly ordered myofiber patterns in architecturally complex tissue. Such patterns suggest inherent multiscale fiber organization and provide a basis for structure-function analyses in vivo and in model tissues.

Diffusion in realistic biophysical systems can lead to aliasing effects in diffusion spectrum imaging

PURPOSE

Diffusion spectrum imaging (DSI) is an imaging technique that has been successfully applied to resolve white matter crossings in the human brain. However, its accuracy in complex microstructure environments has not been well characterized.

THEORY AND METHODS

Here we have simulated different tissue configurations, sampling schemes, and processing steps to evaluate DSI performances' under realistic biophysical conditions. A novel approach to compute the orientation distribution function (ODF) has also been developed to include biophysical constraints, namely integration ranges compatible with axial fiber diffusivities.

RESULTS

Performed simulations identified several DSI configurations that consistently show aliasing artifacts caused by fast diffusion components for both isotropic diffusion and fiber configurations. The proposed method for ODF computation showed some improvement in reducing such artifacts and improving the ability to resolve crossings, while keeping the quantitative nature of the ODF.

CONCLUSION

In this study, we identified an important limitation of current DSI implementations, specifically the presence of aliasing due to fast diffusion components like those from pathological tissues, which are not well characterized, and can lead to artifactual fiber reconstructions. To minimize this issue, a new way of computing the ODF was introduced, which removes most of these artifacts and offers improved angular resolution. Magn Reson Med 76:1837-1847, 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.

A survey of current trends in diffusion MRI for structural brain connectivity

In this paper, we review the state of the art in diffusion magnetic resonance imaging (dMRI) and we present current trends in modelling the brain's tissue microstructure and the human connectome. dMRI is today the only tool that can probe the brain's axonal architecture in vivo and non-invasively, and has grown in leaps and bounds in the last two decades since its conception. A plethora of models with increasing complexity and better accuracy have been proposed to characterise the integrity of the cerebral tissue, to understand its microstructure and to infer its connectivity. Here, we discuss a wide range of the most popular, important and well-established local microstructure models and biomarkers that have been proposed from these models. Finally, we briefly present the state of the art in tractography techniques that allow us to understand the architecture of the brain's connectivity.

Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI): A framework for single-subject analysis in diffusion tensor imaging

The purpose of this work is to develop a framework for single-subject analysis of diffusion tensor imaging (DTI) data. This framework is termed Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI) because it is capable of testing whether an individual tract as represented by the major eigenvector of the diffusion tensor and its corresponding angular dispersion are significantly different from a group of tracts on a voxel-by-voxel basis. This work develops two complementary statistical tests based on the elliptical cone of uncertainty, which is a model of uncertainty or dispersion of the major eigenvector of the diffusion tensor. The orientation deviation test examines whether the major eigenvector from a single subject is within the average elliptical cone of uncertainty formed by a collection of elliptical cones of uncertainty. The shape deviation test is based on the two-tailed Wilcoxon-Mann-Whitney two-sample test between the normalized shape measures (area and circumference) of the elliptical cones of uncertainty of the single subject against a group of controls. The False Discovery Rate (FDR) and False Non-discovery Rate (FNR) were incorporated in the orientation deviation test. The shape deviation test uses FDR only. TOADDI was found to be numerically accurate and statistically effective. Clinical data from two Traumatic Brain Injury (TBI) patients and one non-TBI subject were tested against the data obtained from a group of 45 non-TBI controls to illustrate the application of the proposed framework in single-subject analysis. The frontal portion of the superior longitudinal fasciculus seemed to be implicated in both tests (orientation and shape) as significantly different from that of the control group. The TBI patients and the single non-TBI subject were well separated under the shape deviation test at the chosen FDR level of 0.0005. TOADDI is a simple but novel geometrically based statistical framework for analyzing DTI data. TOADDI may be found useful in single-subject, graph-theoretic and group analyses of DTI data or DTI-based tractography techniques.

Detecting compartmental non-Gaussian diffusion with symmetrized double-PFG MRI

Diffusion in tissue and porous media is known to be non-Gaussian and has been used for clinical indications of stroke and other tissue pathologies. However, when conventional NMR techniques are applied to biological tissues and other heterogeneous materials, the presence of multiple compartments (pores) with different Gaussian diffusivities will also contribute to the measurement of non-Gaussian behavior. Here we present symmetrized double PFG (sd-PFG), which can separate these two contributions to non-Gaussian signal decay as having distinct angular modulation frequencies. In contrast to prior angular d-PFG methods, sd-PFG can unambiguously extract kurtosis as an oscillation from samples with isotropic or uniformly oriented anisotropic pores, and can generally extract a combination of compartmental anisotropy and kurtosis. The method further fixes its sensitivity with respect to the time dependence of the apparent diffusion coefficient. We experimentally demonstrate the measurement of the fourth cumulant (kurtosis) of diffusion and find it consistent with theoretical predictions. By enabling the unambiguous identification of contributions of compartmental kurtosis to the signal, sd-PFG has the potential to help identify the underlying micro-structural changes corresponding to current kurtosis based diagnostics, and act as a novel source of contrast to better resolve tissue micro-structure.

What does diffusion tensor imaging (DTI) tell us about cognitive networks in temporal lobe epilepsy?

Diffusion tensor imaging (DTI) has provided considerable insight into our understanding of epilepsy as a network disorder, revealing subtle alterations in white matter microstructure both proximal and distal to the epileptic focus. These white matter changes have been shown to assist with lateralizing the seizure focus, as well as delineating the location/anatomy of key white matter tracts (i.e., optic radiations) for surgical planning. However, only recently have studies emerged describing the utility of DTI for probing cognitive networks in patients with epilepsy and for examining the structural plasticity within these networks both before and after epilepsy surgery. Here, we review the current literature describing the use of DTI for understanding language and memory networks in patients with temporal lobe epilepsy (TLE), as well as the extant literature on networks associated with executive functioning and global intelligence. Studies of memory and language reveal a complex network of frontotemporal fibers that contribute to naming and fluency performance in TLE, and demonstrate that these networks appear to undergo adaptive changes in response to surgical intervention. Although studies of executive functioning and global intelligence have been less conclusive, there is accumulating evidence that aberrant communication between frontoparietal and medial temporal networks may underlie working memory impairment in TLE. More recently, multimodal imaging studies have provided evidence that disruptions within these white matter networks co-localize with functional changes observed on functional MRI. However, structure-function associations are not entirely coherent and may breakdown in patients with TLE, especially those with a left-sided seizure focus. Although the reasons for discordant findings are unclear, small sample sizes, heterogeneity within patient populations and limitations of the current tensor model may account for contradictory and null findings. Improvements in imaging hardware and higher field strengths have now paved the way for the implementation of advanced diffusion techniques, and these advanced models show great promise for improving our understanding of how network dysfunction contributes to cognitive morbidity in TLE.

A model-based reconstruction for undersampled radial spin-echo DTI with variational penalties on the diffusion tensor

Radial spin-echo diffusion imaging allows motion-robust imaging of tissues with very low T2 values like articular cartilage with high spatial resolution and signal-to-noise ratio (SNR). However, in vivo measurements are challenging, due to the significantly slower data acquisition speed of spin-echo sequences and the less efficient k-space coverage of radial sampling, which raises the demand for accelerated protocols by means of undersampling. This work introduces a new reconstruction approach for undersampled diffusion-tensor imaging (DTI). A model-based reconstruction implicitly exploits redundancies in the diffusion-weighted images by reducing the number of unknowns in the optimization problem and compressed sensing is performed directly in the target quantitative domain by imposing a total variation (TV) constraint on the elements of the diffusion tensor. Experiments were performed for an anisotropic phantom and the knee and brain of healthy volunteers (three and two volunteers, respectively). Evaluation of the new approach was conducted by comparing the results with reconstructions performed with gridding, combined parallel imaging and compressed sensing and a recently proposed model-based approach. The experiments demonstrated improvements in terms of reduction of noise and streaking artifacts in the quantitative parameter maps, as well as a reduction of angular dispersion of the primary eigenvector when using the proposed method, without introducing systematic errors into the maps. This may enable an essential reduction of the acquisition time in radial spin-echo diffusion-tensor imaging without degrading parameter quantification and/or SNR.

A 4D hyperspherical interpretation of q-space

3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we derive several well-established q-space indices and numerically estimate the diffusion orientation distribution function (dODF). We also derive the integral transform describing the relationship between the diffusion signal and propagator on a hypersphere. Most importantly, we will demonstrate that for hybrid diffusion imaging (HYDI) acquisitions low order linear expansion of the HSH basis is sufficient to characterize diffusion in neural tissue. In fact, the HSH basis achieves comparable signal and better dODF reconstructions than other well-established methods, such as Bessel Fourier orientation reconstruction (BFOR), using fewer fitting parameters. All in all, this work provides a new way of looking at q-space.

Nonparametric pore size distribution using d-PFG: comparison to s-PFG and migration to MRI

Here we present the successful translation of a pore size distribution (PSD) estimation method from NMR to MRI. This approach is validated using a well-characterized MRI phantom consisting of stacked glass capillary arrays (GCA) having different diameters. By employing a double pulsed-field gradient (d-PFG) MRI sequence, this method overcomes several important theoretical and experimental limitations of previous single-PFG (s-PFG) based MRI methods by allowing the relative diffusion gradients' direction to vary. This feature adds an essential second dimension in the parameters space, which can potentially improve the reliability and stability of the PSD estimation. To infer PSDs from the MRI data in each voxel an inverse linear problem is solved in conjunction with the multiple correlation function (MCF) framework, which can account for arbitrary experimental parameters (e.g., long diffusion pulses). This scheme makes no a priori assumptions about the functional form of the underlying PSD. Creative use of region of interest (ROI) analysis allows us to create different underlying PSDs using the same GCA MRI phantom. We show that an s-PFG experiment on the GCA phantom fails to accurately reconstruct the size distribution, thus demonstrating the superiority of the d-PFG experiment. In addition, signal simulations corrupted by different noise levels were used to generate continuous and complex PSDs, which were then successfully reconstructed. Finally, owing to the reduced q- or b- values required to measure microscopic PSDs via d-PFG MRI, this method will be better suited to biomedical and clinical applications, in which gradient strength of scanners is limited.

Advanced diffusion MRI fiber tracking in neurosurgical and neurodegenerative disorders and neuroanatomical studies: A review

Diffusion MRI enabled in vivo microstructural imaging of the fiber tracts in the brain resulting in its application in a wide range of settings, including in neurological and neurosurgical disorders. Conventional approaches such as diffusion tensor imaging (DTI) have been shown to have limited applications due to the crossing fiber problem and the susceptibility of their quantitative indices to partial volume effects. To overcome these limitations, the recent focus has shifted to the advanced acquisition methods and their related analytical approaches. Advanced white matter imaging techniques provide superior qualitative data in terms of demonstration of multiple crossing fibers in their spatial orientation in a three dimensional manner in the brain. In this review paper, we discuss the advancements in diffusion MRI and introduce their roles. Using examples, we demonstrate the role of advanced diffusion MRI-based fiber tracking in neuroanatomical studies. Results from its preliminary application in the evaluation of intracranial space occupying lesions, including with respect to future directions for prognostication, are also presented. Building upon the previous DTI studies assessing white matter disease in Huntington's disease and Amyotrophic lateral sclerosis; we also discuss approaches which have led to encouraging preliminary results towards developing an imaging biomarker for these conditions.

Investigating the tradeoffs between spatial resolution and diffusion sampling for brain mapping with diffusion tractography: time well spent?

Interest in mapping white matter pathways in the brain has peaked with the recognition that altered brain connectivity may contribute to a variety of neurologic and psychiatric diseases. Diffusion tractography has emerged as a popular method for postmortem brain mapping initiatives, including the ex-vivo component of the human connectome project, yet it remains unclear to what extent computer-generated tracks fully reflect the actual underlying anatomy. Of particular concern is the fact that diffusion tractography results vary widely depending on the choice of acquisition protocol. The two major acquisition variables that consume scan time, spatial resolution, and diffusion sampling, can each have profound effects on the resulting tractography. In this analysis, we determined the effects of the temporal tradeoff between spatial resolution and diffusion sampling on tractography in the ex-vivo rhesus macaque brain, a close primate model for the human brain. We used the wealth of autoradiography-based connectivity data available for the rhesus macaque brain to assess the anatomic accuracy of six time-matched diffusion acquisition protocols with varying balance between spatial and diffusion sampling. We show that tractography results vary greatly, even when the subject and the total acquisition time are held constant. Further, we found that focusing on either spatial resolution or diffusion sampling at the expense of the other is counterproductive. A balanced consideration of both sampling domains produces the most anatomically accurate and consistent results.

Leading non-Gaussian corrections for diffusion orientation distribution function

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed from the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves on the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common.

Conceptual Foundations of Diffusion in Magnetic Resonance

A thorough review of the q-space technique is presented starting from a discussion of Fick's laws. The work presented here is primarily conceptual, theoretical and hopefully pedagogical. We offered the notion of molecular concentration to unify Fick's laws and diffusion MRI within a coherent conceptual framework. The fundamental relationship between diffusion MRI and the Fick's laws are carefully established. The conceptual and theoretical basis of the q-space technique is investigated from first principles.

Mean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure

Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in "q-space," and the corresponding "mean apparent propagator (MAP)" describing molecular displacements in "r-space." We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit "displacement" sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions-the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue.

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.

Bessel Fourier Orientation Reconstruction (BFOR): an analytical diffusion propagator reconstruction for hybrid diffusion imaging and computation of q-space indices

The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA).

Probing tissue microstructure with restriction spectrum imaging: Histological and theoretical validation

Water diffusion magnetic resonance imaging (dMRI) is a powerful tool for studying biological tissue microarchitectures in vivo. Recently, there has been increased effort to develop quantitative dMRI methods to probe both length scale and orientation information in diffusion media. Diffusion spectrum imaging (DSI) is one such approach that aims to resolve such information based on the three-dimensional diffusion propagator at each voxel. However, in practice, only the orientation component of the propagator function is preserved when deriving the orientation distribution function. Here, we demonstrate how a straightforward extension of the linear spherical deconvolution (SD) model can be used to probe tissue orientation structures over a range (or "spectrum") of length scales with minimal assumptions on the underlying microarchitecture. Using high b-value Cartesian q-space data on a rat brain tissue sample, we demonstrate how this "restriction spectrum imaging" (RSI) model allows for separating the volume fraction and orientation distribution of hindered and restricted diffusion, which we argue stems primarily from diffusion in the extraneurite and intraneurite water compartment, respectively. Moreover, we demonstrate how empirical RSI estimates of the neurite orientation distribution and volume fraction capture important additional structure not afforded by traditional DSI or fixed-scale SD-like reconstructions, particularly in gray matter. We conclude that incorporating length scale information in geometric models of diffusion offers promise for advancing state-of-the-art dMRI methods beyond white matter into gray matter structures while allowing more detailed quantitative characterization of water compartmentalization and histoarchitecture of healthy and diseased tissue.

The influence of complex white matter architecture on the mean diffusivity in diffusion tensor MRI of the human brain

In diffusion tensor magnetic resonance imaging (DT-MRI), limitations concerning complex fiber architecture (when an image voxel contains fiber populations with more than one dominant orientation) are well-known. Fractional anisotropy (FA) values are lower in such areas because of a lower directionality of diffusion on the voxel-scale, which makes the interpretation of FA less straightforward. Moreover, the interpretation of the axial and radial diffusivities is far from trivial when there is more than one dominant fiber orientation within a voxel. In this work, using (i) theoretical considerations, (ii) simulations, and (iii) experimental data, it is demonstrated that the mean diffusivity (or the trace of the diffusion tensor) is lower in complex white matter configurations, compared with tissue where there is a single dominant fiber orientation within the voxel. We show that the magnitude of this reduction depends on various factors, including configurational and microstructural properties (e.g., the relative contributions of different fiber populations) and acquisition settings (e.g., the b-value). These results increase our understanding of the quantitative metrics obtained from DT-MRI and, in particular, the effect of the microstructural architecture on the mean diffusivity. More importantly, they reinforce the growing awareness that differences in DT-MRI metrics need to be interpreted cautiously.

Diffusion MR imaging: basic principles

From their origin as simple techniques primarily used for detecting acute cerebral ischemia, diffusion MR imaging techniques have rapidly evolved into a versatile set of tools that provide the only noninvasive means of characterizing brain microstructure and connectivity, becoming a mainstay of both clinical and investigational brain MR imaging. In this article, the basic principles required for understanding diffusion MR imaging techniques are reviewed with clinical neuroradiologists in mind.

Diffusion tensor imaging of cerebral white matter integrity in cognitive aging

In this article we review recent research on diffusion tensor imaging (DTI) of white matter (WM) integrity and the implications for age-related differences in cognition. Neurobiological mechanisms defined from DTI analyses suggest that a primary dimension of age-related decline in WM is a decline in the structural integrity of myelin, particularly in brain regions that myelinate later developmentally. Research integrating behavioral measures with DTI indicates that WM integrity supports the communication among cortical networks, particularly those involving executive function, perceptual speed, and memory (i.e., fluid cognition). In the absence of significant disease, age shares a substantial portion of the variance associated with the relation between WM integrity and fluid cognition. Current data are consistent with one model in which age-related decline in WM integrity contributes to a decreased efficiency of communication among networks for fluid cognitive abilities. Neurocognitive disorders for which older adults are at risk, such as depression, further modulate the relation between WM and cognition, in ways that are not as yet entirely clear. Developments in DTI technology are providing a new insight into both the neurobiological mechanisms of aging WM and the potential contribution of DTI to understanding functional measures of brain activity. This article is part of a Special Issue entitled: Imaging Brain Aging and Neurodegenerative disease.

NTU-90: a high angular resolution brain atlas constructed by q-space diffeomorphic reconstruction

We present a high angular resolution brain atlas constructed by averaging 90 diffusion spectrum imaging (DSI) datasets in the ICBM-152 space. The spatial normalization of the diffusion information was conducted by a novel q-space diffeomorphic reconstruction method, which reconstructed the spin distribution function (SDF) in the ICBM-152 space from the diffusion MR signals. The performance of this method was examined by a simulation study modeling nonlinear transformation. The result showed that the reconstructed SDFs can resolve crossing fibers and that the accumulated quantitative anisotropy can reveal the relative ratio of the fiber populations. In the in vivo study, the SDF of the constructed atlas was shown to resolve crossing fiber orientations. Further, fiber tracking showed that the atlas can be used to present the pathways of fiber bundles, and the termination locations of the fibers can provide anatomical localization of the connected cortical regions. This high angular resolution brain atlas may facilitate future connectome research on the complex structure of the human brain.