Joint radius-length distribution as a measure of anisotropic pore eccentricity: an experimental and analytical framework

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

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

Ultrafast methods for relaxation and diffusion

Relaxation and diffusion NMR measurements offer an approach to studying rotational and translational motion of molecules non-invasively, and they also provide chemical resolution complementary to NMR spectra. Multidimensional experiments enable the correlation of relaxation and diffusion parameters as well as the observation of molecular exchange phenomena through relaxation or diffusion contrast. This review describes how to accelerate multidimensional relaxation and diffusion measurements significantly through spatial encoding. This so-called ultrafast Laplace NMR approach shortens the experiment time to a fraction and makes even single-scan experiments possible. Single-scan experiments, in turn, significantly facilitate the use of nuclear spin hyperpolarization methods to boost sensitivity. The ultrafast Laplace NMR method is also applicable with low-field, mobile NMR instruments, and it can be exploited in many disciplines. For example, it has been used in studies of the dynamics of fluids in porous materials, identification of intra- and extracellular metabolites in cancer cells, and elucidation of aggregation phenomena in atmospheric surfactant solutions.

Multidimensional correlation MRI

Multidimensional correlation spectroscopy is emerging as a novel MRI modality that is well suited for microstructure and microdynamic imaging studies, especially of biological specimens. Conventional MRI methods only provide voxel-averaged and mostly macroscopically averaged information; these methods cannot disentangle intra-voxel heterogeneity on the basis of both water mobility and local chemical interactions. By correlating multiple MR contrast mechanisms and processing the data in an integrated manner, correlation spectroscopy is able to resolve the distribution of water populations according to their chemical and physical interactions with the environment. The use of a non-parametric, phenomenological representation of the multidimensional MR signal makes no assumptions about tissue structure, thereby allowing the study of microscopic structure and composition of complex heterogeneous biological systems. However, until recently, vast data requirements have confined these types of measurement to non-localized NMR applications and prevented them from being widely and successfully used in conjunction with imaging. Recent groundbreaking advancements have allowed this powerful NMR methodology to be migrated to MRI, initiating its emergence as a promising imaging approach. This review is not intended to cover the entire field of multidimensional MR; instead, it focuses on pioneering imaging applications and the challenges involved. In addition, the background and motivation that have led to multidimensional correlation MR development are discussed, along with the basic underlying mathematical concepts. The goal of the present work is to provide the reader with a fundamental understanding of the techniques developed and their potential benefits, and to provide guidance to help refine future applications of this technology.

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

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

Retaining information from multidimensional correlation MRI using a spectral regions of interest generator

Multidimensional correlation magnetic resonance imaging (MRI) is an emerging imaging modality that is capable of disentangling highly heterogeneous and opaque systems according to chemical and physical interactions of water within them. Using this approach, the conventional three dimensional MR scalar images are replaced with spatially resolved multidimensional spectra. The ensuing abundance in microstructural and chemical information is a blessing that incorporates a real challenge: how does one distill and refine it into images while retaining its significant components? In this paper we introduce a general framework that preserves the spectral information from spatially resolved multidimensional data. Equal weight is given to significant spectral components at the single voxel level, resulting in a summarized image spectrum. This spectrum is then used to define spectral regions of interest that are utilized to reconstruct images of sub-voxel components. Using numerical simulations we first show that, contrary to the conventional approach, the proposed framework preserves spectral resolution, and in turn, sensitivity and specificity of the reconstructed images. The retained spectral resolution allows, for the first time, to observe an array of distinct [Formula: see text]-[Formula: see text]-[Formula: see text] components images of the human brain. The robustly generated images of sub-voxel components overcome the limited spatial resolution of MRI, thus advancing multidimensional correlation MRI to fulfilling its full potential.

Single- and double-Diffusion encoding MRI for studying ex vivo apparent axon diameter distribution in spinal cord white matter

Mapping average axon diameter (AAD) and axon diameter distribution (ADD) in neuronal tissues non-invasively is a challenging task that may have a tremendous effect on our understanding of the normal and diseased central nervous system (CNS). Water diffusion is used to probe microstructure in neuronal tissues, however, the different water populations and barriers that are present in these tissues turn this into a complex task. Therefore, it is not surprising that recently we have witnessed a burst in the development of new approaches and models that attempt to obtain, non-invasively, detailed microstructural information in the CNS. In this work, we aim at challenging and comparing the microstructural information obtained from single diffusion encoding (SDE) with double diffusion encoding (DDE) MRI. We first applied SDE and DDE MR spectroscopy (MRS) on microcapillary phantoms and then applied SDE and DDE MRI on an ex vivo porcine spinal cord (SC), using similar experimental conditions. The obtained diffusion MRI data were fitted by the same theoretical model, assuming that the signal in every voxel can be approximated as the superposition of a Gaussian-diffusing component and a series of restricted components having infinite cylindrical geometries. The diffusion MRI results were then compared with histological findings. We found a good agreement between the fittings and the experimental data in white matter (WM) voxels of the SC in both diffusion MRI methods. The microstructural information and apparent AADs extracted from SDE MRI were found to be similar or somewhat larger than those extracted from DDE MRI especially when the diffusion time was set to 40 ms. The apparent ADDs extracted from SDE and DDE MRI show reasonable agreement but somewhat weaker correspondence was observed between the diffusion MRI results and histology. The apparent subtle differences between the microstructural information obtained from SDE and DDE MRI are briefly discussed.

Water mobility spectral imaging of the spinal cord: Parametrization of model-free Laplace MRI

Diffusion magnetic resonance imaging (dMRI) of biological systems most often results in non-monoexponential signal, due to their complexity and heterogeneity. One approach to interpreting dMRI data without imposing tissue microstructural models is to fit the signal to a multiexponential function, which is sometimes referred to as an inverse Laplace transformation, and to display the coefficients as a distribution of the diffusivities, or water mobility spectra. Until recently, this method has not been used in a voxelwise manner, mainly because of heavy data requirements. With recent advancements in processing and experimental design, voxelwise Laplace MRI approaches are becoming feasible and attractive. The rich spectral information, combined with a three-dimensional image, presents a challenge because it tremendously increases the dimensionality of the data and requires a robust method for interpretation and analysis. In this work, we suggest parameterizing the empirically measured water mobility spectra using a bimodal lognormal function. This approach allows for a compact representation of the spectrum, and it also resolves overlapping spectral peaks, which allows for a robust extraction of their signal fraction. We apply the method on a fixed spinal cord sample and use it to generate robust intensity images of slow- and fast-diffusion components. Using the parametric variables, we create novel image contrasts, among them the information entropy of the water mobility spectrum, which pack unique features of the individual diffusion regimes in the investigated system.

Towards clinically feasible relaxation-diffusion correlation MRI using MADCO

Multidimensional relaxation-diffusion correlation (REDCO) NMR is an assumption-free method that measures how water is distributed within materials. Although highly informative, REDCO had never been used in clinical MRI applications because of the large amount of data it requires, leading to infeasible scan times. A recently suggested novel experimental design and processing framework, marginal distributions constrained optimization (MADCO), was used here to accelerate and improve the reconstruction of such MRI correlations. MADCO uses the 1D marginal distributions as a priori information, which provide powerful constraints when 2D spectra are reconstructed, while their estimation requires an order of magnitude less data than conventional 2D approaches. In this work we experimentally examined the impact the complexity of the correlation distribution has on the accuracy and robustness of the estimates. MADCO and a conventional method were compared using two T1-D phantoms that differ in the proximity of their peaks, leading to a relatively simple case as opposed to a more challenging one. The phantoms were used to vet the achievable data compression using MADCO under these conditions. MADCO required ~43 and ~30 less data than the conventional approach for the simple and complex spectra, respectively, making it potentially feasible for preclinical and even clinical applications.

Magnetic resonance microdynamic imaging reveals distinct tissue microenvironments

Magnetic resonance imaging (MRI) provides a powerful set of tools with which to investigate biological tissues noninvasively and in vivo. Tissues are heterogeneous in nature; an imaging voxel contains an ensemble of different cells and extracellular matrix components. A long-standing challenge has been to infer the content of and interactions among these microscopic tissue components within a macroscopic imaging voxel. Spatially resolved multidimensional relaxation-diffusion correlation (REDCO) spectroscopy holds the potential to deliver such microdynamic information. However, to date, vast data requirements have mostly relegated these type of measurements to nuclear magnetic resonance applications and prevented them from being widely and successfully used in conjunction with imaging. By using a novel data acquisition and processing strategy in this study, spatially resolved REDCO could be performed in reasonable scanning times with excellent prospects for clinical applications. This new MR imaging framework-which we term "magnetic resonance microdynamic imaging (MRMI)"-permits the simultaneous noninvasive and model-free quantification of multiple subcellular, cellular, and interstitial tissue microenvironments within a voxel. MRMI is demonstrated with a fixed spinal cord specimen, enabling the quantification of microscopic tissue components with unprecedented specificity. Tissue components, such as axons, neuronal and glial soma, and myelin were identified on the basis of their multispectral signature within individual imaging voxels. These tissue elements could then be composed into images and be correlated with immunohistochemistry findings. MRMI provides novel image contrasts of tissue components and a new family of microdynamic biomarkers that could lead to new diagnostic imaging approaches to probe biological tissue alterations accompanied by pathological or developmental changes.

Imaging Local Diffusive Dynamics Using Diffusion Exchange Spectroscopy MRI

The movement of water between microenvironments presents a central challenge in the physics of soft matter and porous media. Diffusion exchange spectroscopy (DEXSY) is a powerful 2D nuclear magnetic resonance method for measuring such exchange, yet it is rarely used because of its long scan time requirements. Moreover, it has never been combined with magnetic resonance imaging (MRI). Using probability theory, we vastly reduce the required data, making DEXSY MRI feasible for the first time. Experiments are performed on a composite nerve tissue phantom with restricted and free water-exchanging compartments.

Fast, accurate 2D-MR relaxation exchange spectroscopy (REXSY): Beyond compressed sensing

Previously, we showed that compressive or compressed sensing (CS) can be used to reduce significantly the data required to obtain 2D-NMR relaxation and diffusion spectra when they are sparse or well localized. In some cases, an order of magnitude fewer uniformly sampled data were required to reconstruct 2D-MR spectra of comparable quality. Nonetheless, this acceleration may still not be sufficient to make 2D-MR spectroscopy practicable for many important applications, such as studying time-varying exchange processes in swelling gels or drying paints, in living tissue in response to various biological or biochemical challenges, and particularly for in vivo MRI applications. A recently introduced framework, marginal distributions constrained optimization (MADCO), tremendously accelerates such 2D acquisitions by using a priori obtained 1D marginal distribution as powerful constraints when 2D spectra are reconstructed. Here we exploit one important intrinsic property of the 2D-MR relaxation exchange spectra: the fact that the 1D marginal distributions of each 2D-MR relaxation exchange spectrum in both dimensions are equal and can be rapidly estimated from a single Carr-Purcell-Meiboom-Gill (CPMG) or inversion recovery prepared CPMG measurement. We extend the MADCO framework by further proposing to use the 1D marginal distributions to inform the subsequent 2D data-sampling scheme, concentrating measurements where spectral peaks are present and reducing them where they are not. In this way we achieve compression or acceleration that is an order of magnitude greater than that in our previous CS method while providing data in reconstructed 2D-MR spectral maps of comparable quality, demonstrated using several simulated and real 2D T2 - T2 experimental data. This method, which can be called "informed compressed sensing," is extendable to other 2D- and even ND-MR exchange spectroscopy.

Use of marginal distributions constrained optimization (MADCO) for accelerated 2D MRI relaxometry and diffusometry

Measuring multidimensional (e.g., 2D) relaxation spectra in NMR and MRI clinical applications is a holy grail of the porous media and biomedical MR communities. The main bottleneck is the inversion of Fredholm integrals of the first kind, an ill-conditioned problem requiring large amounts of data to stabilize a solution. We suggest a novel experimental design and processing framework to accelerate and improve the reconstruction of such 2D spectra that uses a priori information from the 1D projections of spectra, or marginal distributions. These 1D marginal distributions provide powerful constraints when 2D spectra are reconstructed, and their estimation requires an order of magnitude less data than a conventional 2D approach. This marginal distributions constrained optimization (MADCO) methodology is demonstrated here with a polyvinylpyrrolidone-water phantom that has 3 distinct peaks in the 2D D-T1 space. The stability, sensitivity to experimental parameters, and accuracy of this new approach are compared with conventional methods by serially subsampling the full data set. While the conventional, unconstrained approach performed poorly, the new method had proven to be highly accurate and robust, only requiring a fraction of the data. Additionally, synthetic T1-T2 data are presented to explore the effects of noise on the estimations, and the performance of the proposed method with a smooth and realistic 2D spectrum. The proposed framework is quite general and can also be used with a variety of 2D MRI experiments (D-T2,T1-T2,D-D, etc.), making these potentially feasible for preclinical and even clinical applications for the first time.

NMR signal for particles diffusing under potentials: From path integrals and numerical methods to a model of diffusion anisotropy

We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using path integral methods. Explicit relationships are derived for commonly employed gradient waveforms involving pulsed and oscillating gradients. The Bloch-Torrey equation, describing the temporal evolution of magnetization, is modified by incorporating potentials. A general solution to this equation is obtained for the case of parabolic potential by adopting the multiple correlation function (MCF) formalism, which has been used in the past to quantify the effects of restricted diffusion. Both analytical and MCF results were found to be in agreement with random walk simulations. A multidimensional formulation of the problem is introduced that leads to a new characterization of diffusion anisotropy. Unlike the case of traditional methods that employ a diffusion tensor, anisotropy originates from the tensorial force constant, and bulk diffusivity is retained in the formulation. Our findings suggest that some features of the NMR signal that have traditionally been attributed to restricted diffusion are accommodated by the Hookean model. Under certain conditions, the formalism can be envisioned to provide a viable approximation to the mathematically more challenging restricted diffusion problems.

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.