Recent Fourier and Laplace perspectives for multidimensional NMR in porous media

Investigating the behaviour of NaCl brines and hydrocarbons in porous alumina using low-field NMR relaxation and diffusion methods

The behaviour of multiple fluid phases within a porous medium is hard to predict. NMR measurements offer an excellent tool to probe such systems in a fast and non-invasive way. Such systems can be relevant to hydrocarbon recovery, catalysis, and CO2 and H2 geo-storage, among others. Since electrolyte solutions are always present in subsurface reservoirs, understanding their behaviour within porous media is highly important. In this study, we use NMR relaxation and diffusion methods to investigate the diffusion coefficients and strength of interactions between alumina surfaces and brines at various NaCl concentrations, focusing on the effect of salt concentration on transport and interactions within the porous structure. Furthermore, we study the spontaneous displacement of dodecane, a model hydrocarbon, from the same alumina pellets using the same brine solutions. Results show that brines of lower salinity consistently displace more dodecane in total, after soaking dodecane-saturated pellets in a brine solution for several days. This indicates that increased salt concentrations can reduce wettability towards the aqueous phase in simple metal oxide surfaces and highlights the capabilities of NMR to efficiently study such systems.

Stabilization of parameter estimates from multiexponential decay through extension into higher dimensions

Analysis of multiexponential decay has remained a topic of active research for over 200 years. This attests to the widespread importance of this problem and to the profound difficulties in characterizing the underlying monoexponential decays. Here, we demonstrate the fundamental improvement in stability and conditioning of this classic problem through extension to a second dimension; we present statistical analysis, Monte-Carlo simulations, and experimental magnetic resonance relaxometry data to support this remarkable fact. Our results are readily generalizable to higher dimensions and provide a potential means of circumventing conventional limits on multiexponential parameter estimation.

Low-Field Functional Group Resolved Nuclear Spin Relaxation in Mesoporous Silica

Solid-fluid interactions underpin the efficacy of functional porous materials across a diverse array of chemical reaction and separation processes. However, detailed characterization of interfacial phenomena within such systems is hampered by their optically opaque nature. Motivated by the need to bridge this capability gap, we report low-magnetic-field two-dimensional (2D) ¹H nuclear spin relaxation measurements as a noninvasive probe of adsorbate identity and interfacial dynamics, exploring the relaxation characteristics exhibited by liquid hydrocarbon adsorbates confined to a model mesoporous silica. For the first time, we demonstrate the capacity of this approach in distinguishing functional group-specific relaxation phenomena across a diverse range of alcohols and carboxylic acids employed as solvents, reagents, and liquid hydrogen carriers, with distinct relaxation responses assigned to the alkyl and hydroxyl moieties of each confined liquid. Uniquely, this relaxation behavior is shown to correlate with adsorbate acidity, with the observed relationship rationalized on the basis of surface-adsorbate proton-exchange dynamics. Our results demonstrate that nuclear spin relaxation provides a molecular-level perspective on sorbent/sorbate interactions, motivating the exploration of such measurements as a unique probe of adsorbate identity within optically opaque porous media.

Perspectives in process analytics using low field NMR

Low field NMR is a powerful analytical tool which creates an enormous added value in process analytics. Based on specific applications in process analytics and perspectives for low field NMR in form of spectroscopy, relaxation, diffusion, and imaging in quality control, diverse applications and technical realizations like spectrometers, time domain NMR, mobile NMR sensors and MRI will be discussed.

A Tutorial Introduction to Inverse Problems in Magnetic Resonance

There has been a tremendous increase in applications of the inverse problem framework to parameter estimation in magnetic resonance. Attempting to capture both the basics of this formalism and modern developments would require an article of inordinate length. Therefore, in the following, we provide basic material as a practical introduction to the topic and an entree to the literature. First, we describe the formulation of linear and nonlinear inverse problems, with an emphasis on signal equations arising in magnetic resonance. We then describe the Fredholm equation of the first kind as a paradigm for these problems. This is followed by much more detailed considerations for determining solutions in the linear case, including central concepts such as condition number, regularization, and stability. Solution methods for nonlinear inverse problems are described next, followed by a treatment of their stability and regularization. Finally, we provide an introduction to compressed sensing, with signal reconstruction formulated as the solution to an inverse problem, making use of much of the previous material. Throughout, the emphasis is on outlines of the theory and on numerical examples, rather than on mathematical rigor and completeness.

Effect of pigment concentration on NMR relaxometry in acrylic paints

Acrylic emulsion paint is among the most common media employed by 20th century artists. Since early acrylic paintings have begun to require the attention of conservators, scientists are working to characterize the properties of these paints to facilitate conservation efforts. In this study, we report an investigation of the physical and chemical properties of acrylic emulsion paints using single-sided NMR in conjunction with gloss measurements and scanning electron microscopy-energy dispersive spectrometry. Combining the data from these techniques gives insight into pigment-base interactions and the acrylic curing process, showing that as pigment concentration is increased in paints, the amount of acrylic base adsorbed to pigment particles increases, resulting in films with differing relaxation times. This research both emphasizes and contextualizes the utility of NMR relaxometry in studying cultural heritage objects and prompts further study into the effects of pigment concentration on the curing and conservation of paint films.

NMR techniques in studying water in biotechnological systems

Different NMR methodologies have been considered in studying water as a part of the structure of heterogeneous biosystems. The current work mostly describes NMR techniques to investigate slow translational dynamics of molecules affecting anisotropic properties of polymers and biomaterials. With these approaches, information about organized structures and their stability could be obtained in conditions when external factors affect biomolecules. Such changes might include rearrangement of macromolecular conformations at fabrication of nano-scaffolds for tissue engineering applications. The changes in water-fiber interactions could be mirrored by the magnetic resonance methods in various relaxations, double-quantum filtered (DQF), 1D and 2D translational diffusion experiments. These findings effectively demonstrate the current state of NMR studies in applying these experiments to the various systems with the anisotropic properties. For fibrous materials, it is shown how NMR correlation experiments with two gradients (orthogonal or collinear) encode diffusion coefficients in anisotropic materials and how to estimate the permeability of cell walls. It is considered how the DQF NMR technique discovers anisotropic water in natural polymers with various cross-links. The findings clarify hydration sites, dynamic properties, and binding of macromolecules discovering the role of specific states in improving scaffold characteristics in tissue engineering processes. Showing the results in developing these NMR tools, this review focuses on the ways of extracting information about biophysical properties of biomaterials from the NMR data obtained.

In Situ Determination of Carbon Number Distributions of Mixtures of Linear Hydrocarbons Confined within Porous Media Using Pulsed Field Gradient NMR

Pulsed field gradient (PFG) NMR measurements, combined with a novel optimization method, are used to determine the composition of hydrocarbon mixtures of linear alkanes (C7-C16) in both the bulk liquid state and when imbibed within a porous medium of mean pore diameter 28.6 nm. The method predicts the average carbon number of a given mixture to an accuracy of ±1 carbon number and the mole fraction of a mixture component to within an average root-mean-square error of ±0.036 with just three calibration mixtures. Given that the method can be applied at any conditions of temperature and pressure at which the PFG NMR measurements are made, the method has the potential for application in characterizing hydrocarbon liquid mixtures inside porous media and at the operating conditions relevant to, for example, hydrocarbon recovery and heterogeneous catalysis.

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.

Dynamics of [Pyr13][Tf2N] ionic liquid confined to carbon black

The intrinsic ionic nature of room temperature ionic liquids (RTILs) bears the potential to replace classical aqueous electrolytes in electrochemical applications, for example in metal-air batteries. For a systematic adjustment of RTIL properties in porous cathodes, the ionic arrangement under confinement is of prime importance. Using spectrally resolved pulsed gradient stimulated echo nuclear magnetic resonance (PGSTE-NMR) and spin-lattice NMR relaxation time (T₁) distributions, the dynamics of 1-methyl-1-propylpyrrolidiniumbis(trifluoromethylsulfonyl)imide ([Pyr₁₃][Tf₂N]) confined to carbon black were investigated. A considerable dependence of the [PYR₁₃] mobility on the loading fraction of the carbon black pore space was found. There is evidence for a preferential layering of the RTIL adjacent to the carbon surface and a dependence of the ionic configuration on the local structure of the carbon surface. The inversion efficiency of inversion-recovery T₁ data indicates a quasi-stationary layer at the carbon surface with solid-like properties, where the bulk-like properties of the RTIL are adopted as the distance to the surface increases. From the NMR diffusion data an intermediate layer between the quasi-stationary and the bulk-like RTIL is evident. This layer shows a particularly strong pore space loading dependence. While it has an anisotropic, two-dimensional mobility with reduced diffusion perpendicular to the surface at any loading, when it interfaces a gas phase at low loading its mobility is higher than bulk diffusion by up to an order of magnitude and chemical exchange with other layers is low. This layer appears to be of particular importance for the ion exchange between RTIL environments with different spacing from the carbon surface and hence crucial for the overall dynamics of RTILs in the investigated porous environment.

Low-field NMR for quality control on oils

Oil is a prominent, but multifaceted material class with a wide variety of applications. Technical oils, crude oils as well as edibles are main subclasses. In this review, the question is addressed how low-field NMR can contribute in oil characterization as an analytical tool, mainly with respect to quality control. Prerequisite in the development of a quality control application, however, is a detailed understanding of the oils and of the measurement. Low-field NMR is known as a rich methodical toolbox that was and is explored and further developed to address questions about oils, their quality, and usability as raw materials, during production and formulation as well as in use.

Glass Dynamics and Domain Size in a Solvent-Polymer Weak Gel Measured by Multidimensional Magnetic Resonance Relaxometry and Diffusometry

Nuclear magnetic resonance measurements of rotational and translational molecular dynamics are applied to characterize the nanoscale dynamic heterogeneity of a physically cross-linked solvent-polymer system above and below the glass transition temperature. Measured rotational dynamics identify domains associated with regions of solidlike and liquidlike dynamics. Translational dynamics provide quantitative length and timescales of nanoscale heterogeneity due to polymer network cross-link density. Mean squared displacement measurements of the solvent provide microrheological characterization of the system and indicate glasslike caging dynamics both above and below the glass transition temperature.

Rapid detection of the presence of diffusion exchange

Diffusion exchange spectroscopy (DEXSY) provides a detailed picture of how fluids in different microenvironments communicate with one another but requires a large amount of data. For DEXSY MRI, a simple measure of apparent exchanging fractions may suffice to characterize and differentiate materials and tissues. Reparameterizing signal intensity from a PGSE-storage-PGSE experiment as a function of the sum, b_s=b₁+b₂, and difference b_d=b₂-b₁ of the diffusion encodings separates diffusion weighting from exchange weighting. Exchange leads to upward curvature along a slice of constant b_s. Exchanging fractions can be measured rapidly by a finite difference approximation of the curvature using four data points. The method is generalized for non-steady-state and multi-site exchange. We apply the method to image exchanging fractions and calculate exchange rates of water diffusing across the bulk water interface of a glass capillary array.

A diffusion model-free framework with echo time dependence for free-water elimination and brain tissue microstructure characterization

Purpose

The compartmental nature of brain tissue microstructure is typically studied by diffusion MRI, MR relaxometry or their correlation. Diffusion MRI relies on signal representations or biophysical models, while MR relaxometry and correlation studies are based on regularized inverse Laplace transforms (ILTs). Here we introduce a general framework for characterizing microstructure that does not depend on diffusion modeling and replaces ill‐posed ILTs with blind source separation (BSS). This framework yields proton density, relaxation times, volume fractions, and signal disentanglement, allowing for separation of the free‐water component.

Theory and Methods

Diffusion experiments repeated for several different echo times, contain entangled diffusion and relaxation compartmental information. These can be disentangled by BSS using a physically constrained nonnegative matrix factorization.

Results

Computer simulations, phantom studies, together with repeatability and reproducibility experiments demonstrated that BSS is capable of estimating proton density, compartmental volume fractions and transversal relaxations. In vivo results proved its potential to correct for free‐water contamination and to estimate tissue parameters.

Conclusion

Formulation of the diffusion‐relaxation dependence as a BSS problem introduces a new framework for studying microstructure compartmentalization, and a novel tool for free‐water elimination.

Observing different modes of mobility in lithium titanate spinel by nuclear magnetic resonance

Using a newly developed analysis method for SAE NMR andab initiocalculations we show the formation of localized high-mobility domains in lithium titanate that influence its global ion mobility.

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.

Obtaining T1-T2 distribution functions from 1-dimensional T1 and T2 measurements: The pseudo 2-D relaxation model

We present the pseudo 2-D relaxation model (P2DRM), a method to estimate multidimensional probability distributions of material parameters from independent 1-D measurements. We illustrate its use on 1-D T1 and T2 relaxation measurements of saturated rock and evaluate it on both simulated and experimental T1-T2 correlation measurement data sets. Results were in excellent agreement with the actual, known 2-D distribution in the case of the simulated data set. In both the simulated and experimental case, the functional relationships between T1 and T2 were in good agreement with the T1-T2 correlation maps from the 2-D inverse Laplace transform of the full 2-D data sets. When a 1-D CPMG experiment is combined with a rapid T1 measurement, the P2DRM provides a double-shot method for obtaining a T1-T2 relationship, with significantly decreased experimental time in comparison to the full T1-T2 correlation measurement.

The Power of Heterogeneity: Parameter Relationships from Distributions

Complex scientific data is becoming the norm, many disciplines are growing immensely data-rich, and higher-dimensional measurements are performed to resolve complex relationships between parameters. Inherently multi-dimensional measurements can directly provide information on both the distributions of individual parameters and the relationships between them, such as in nuclear magnetic resonance and optical spectroscopy. However, when data originates from different measurements and comes in different forms, resolving parameter relationships is a matter of data analysis rather than experiment. We present a method for resolving relationships between parameters that are distributed individually and also correlated. In two case studies, we model the relationships between diameter and luminescence properties of quantum dots and the relationship between molecular weight and diffusion coefficient for polymers. Although it is expected that resolving complicated correlated relationships require inherently multi-dimensional measurements, our method constitutes a useful contribution to the modelling of quantitative relationships between correlated parameters and measurements. We emphasise the general applicability of the method in fields where heterogeneity and complex distributions of parameters are obstacles to scientific insight.

Efficient 2D MRI relaxometry using compressed sensing

Potential applications of 2D relaxation spectrum NMR and MRI to characterize complex water dynamics (e.g., compartmental exchange) in biology and other disciplines have increased in recent years. However, the large amount of data and long MR acquisition times required for conventional 2D MR relaxometry limits its applicability for in vivo preclinical and clinical MRI. We present a new MR pipeline for 2D relaxometry that incorporates compressed sensing (CS) as a means to vastly reduce the amount of 2D relaxation data needed for material and tissue characterization without compromising data quality. Unlike the conventional CS reconstruction in the Fourier space (k-space), the proposed CS algorithm is directly applied onto the Laplace space (the joint 2D relaxation data) without compressing k-space to reduce the amount of data required for 2D relaxation spectra. This framework is validated using synthetic data, with NMR data acquired in a well-characterized urea/water phantom, and on fixed porcine spinal cord tissue. The quality of the CS-reconstructed spectra was comparable to that of the conventional 2D relaxation spectra, as assessed using global correlation, local contrast between peaks, peak amplitude and relaxation parameters, etc. This result brings this important type of contrast closer to being realized in preclinical, clinical, and other applications.

Determining pore length scales and pore surface relaxivity of rock cores by internal magnetic fields modulation at 2MHz NMR

Pore length scales and pore surface relaxivities of rock cores with different lithologies were studied on a 2MHz Rock Core Analyzer. To determine the pore length scales of the rock cores, the high eigenmodes of spin bearing molecules satisfying the diffusion equation were detected with optimized encoding periods in the presence of internal magnetic fields Bin. The results were confirmed using a 64MHz NMR system, which supports the feasibility of high eigenmode detection at fields as low as 2MHz. Furthermore, this methodology was combined with relaxometry measurements to a two-dimensional experiment, which provides correlation between pore length and relaxation time. This techniques also yields information on the surface relaxivity of the rock cores. The estimated surface relaxivities were then compared to the results using an independent NMR method.

A framework for accurate determination of the T₂ distribution from multiple echo magnitude MRI images

Measurement of the T2 distribution in tissues provides biologically relevant information about normal and abnormal microstructure and organization. Typically, the T2 distribution is obtained by fitting the magnitude MR images acquired by a multi-echo MRI pulse sequence using an inverse Laplace transform (ILT) algorithm. It is well known that the ideal magnitude MR signal follows a Rician distribution. Unfortunately, studies attempting to establish the validity and efficacy of the ILT algorithm assume that these input signals are Gaussian distributed. Violation of the normality (or Gaussian) assumption introduces unexpected artifacts, including spurious cerebrospinal fluid (CSF)-like long T2 components; bias of the true geometric mean T2 values and in the relative fractions of various components; and blurring of nearby T2 peaks in the T2 distribution. Here we apply and extend our previously proposed magnitude signal transformation framework to map noisy Rician-distributed magnitude multi-echo MRI signals into Gaussian-distributed signals with high accuracy and precision. We then perform an ILT on the transformed data to obtain an accurate T2 distribution. Additionally, we demonstrate, by simulations and experiments, that this approach corrects the aforementioned artifacts in magnitude multi-echo MR images over a large range of signal-to-noise ratios.

Solving 2D Fredholm Integral from Incomplete Measurements Using Compressive Sensing

We present an algorithm to solve the two-dimensional Fredholm integral of the first kind with tensor product structure from a limited number of measurements, with the goal of using this method to speed up nuclear magnetic resonance spectroscopy. This is done by incorporating compressive sensing-type arguments to fill in missing measurements, using a priori knowledge of the structure of the data. In the first step we recover a compressed data matrix from measurements that form a tight frame, and establish that these measurements satisfy the restricted isometry property. Recovery can be done from as few as 10% of the total measurements. In the second and third steps, we solve the zeroth-order regularization minimization problem using the Venkataramanan-Song-Hürlimann algorithm. We demonstrate the performance of this algorithm on simulated data and show that our approach is a realistic approach to speeding up the data acquisition.

Magnetic resonance of calcified tissues

MRI of the human body is largely made possible by the favorable relaxation properties of protons of water and triacyl glycerides prevalent in soft tissues. Hard tissues--key among them bone--are generally less amenable to measurement with in vivo MR imaging techniques, not so much as a result of the lower proton density but rather due to the extremely short life-times of the proton signal in water bound to solid-like entities, typically collagen, or being trapped in micro-pores. Either mechanism can enhance T2 relaxation by up to three orders of magnitude relative to their soft-tissue counterparts. Detection of these protons requires solid-state techniques that have emerged in recent years and that promise to add a new dimension to the study of hard tissues. Alternative approaches to probe calcified tissues exploit their characteristic magnetic properties. Bone, teeth and extra-osseous calcium-containing biomaterials are unique in that they are more diamagnetic than all other tissues and thus yield information indirectly by virtue of the induced magnetic fields present in their vicinity. Progress has also been made in methods allowing very high-resolution structural imaging of trabecular and cortical bone relying on detection of the surrounding soft-tissues. This brief review, much of it drawn from work conducted in the author's laboratory, seeks to highlight opportunities with focus on early-stage developments for image-based assessment of structure, function, physiology and mechanics of calcified tissues in humans via liquid and solid-state approaches, including proton, deuteron and phosphorus NMR and MRI.

Mapping molecular perturbations by a new form of two-dimensional spectroscopy

We propose a new general form of two-dimensional spectroscopy where the indirect "evolution" dimension is derived using the Radon transform. This idea is applicable to several types of spectroscopy but is illustrated here for the case of NMR spectroscopy. This "projection spectroscopy" displays characteristic correlation peaks that highlight perturbations of chemical shifts caused by temperature, pressure, solvent, molecular binding, chemical exchange, hydrogen bonding, pH variations, conformational changes, or paramagnetic agents. The results are displayed in a convenient format that allows the chemist to see all of the chemical shift perturbations at a glance and assess their rates of change and directions. As a proof of principle, we present two simple, practical examples that display two-dimensional representations of the effects of temperature and solvent on NMR spectra.

Development of miniaturized, portable magnetic resonance relaxometry system for point-of-care medical diagnosis

A novel, compact-sized (19 cm × 16 cm) and portable (500 g) magnetic resonance relaxometry system is designed and developed. We overcame several key engineering barriers so that magnetic resonance technology can be potentially used for disease diagnosis-monitoring in point-of-care settings, directly on biological cells and tissues. The whole system consists of a coin-sized permanent magnet (0.76 T), miniaturized radio-frequency microcoil probe, compact lumped-circuit duplexer, and single board 1-W power amplifier, in which a field programmable gate array -based spectrometer is used for pulse excitation, signal acquisition, and data processing. We show that by measuring the proton transverse relaxation rates from a large pool of natural abundance proton-nuclei presence in less than 1 μL of red blood cells, one can indirectly deduce the relative magnetic susceptibility of the bulk cells within a few minutes of signal acquisition time. Such rapid and sensitive blood screening system can be used to monitor the fluctuation of the bulk magnetic susceptibility of the biological cells (e.g., human blood cells), where unusual state of the bulk magnetic susceptibility is related to a number of diseases.

Origins of the ultrashort-T2 1H NMR signals in myelinated nerve: a direct measure of myelin content?

Recently developed MRI techniques have enabled clinical imaging of short-lived (1)H NMR signals with T(2) < 1 ms. Using these techniques, novel signal enhancement has been observed in myelinated tissues, although the source of this enhancement has not been identified. Herein, we report studies of the nature and origins of ultrashort T(2) (uT(2)) signals (50 μs < T(2) < 1 ms) from amphibian and mammalian myelinated nerves. NMR measurements and comparisons with myelin phantoms and expected myelin components indicate that these uT(2) signals arise predominantly from methylene (1)H on/in the myelin membranes, which suggests that direct measurement of uT(2) signals can be used as a new means for quantitative myelin mapping.

Characterization of 1H NMR signal in human cortical bone for magnetic resonance imaging

Recent advancements in MRI have enabled clinical imaging of human cortical bone, providing a potentially powerful new means for assessing bone health with molecular-scale sensitivities unavailable to conventional X-ray-based diagnostics. In human cortical bone, MRI is sensitive to populations of protons ((1)H) partitioned among water and protein sources, which may be differentiated according to intrinsic NMR properties such as chemical shift and transverse and longitudinal relaxation rates. Herein, these NMR properties were assessed in human cortical bone donors from a broad age range, and four distinct (1)H populations were consistently identified and attributed to five microanatomical sources. These findings show that modern human cortical bone MRI contrast will be dominated by collagen-bound water, which can also be exploited to study human cortical bone collagen via magnetization transfer.

Noninvasive bipolar double-pulsed-field-gradient NMR reveals signatures for pore size and shape in polydisperse, randomly oriented, inhomogeneous porous media

Noninvasive characterization of pore size and shape in opaque porous media is a formidable challenge. NMR diffusion-diffraction patterns were found to be exceptionally useful for obtaining such morphological features, but only when pores are monodisperse and coherently placed. When locally anisotropic pores are randomly oriented, conventional diffusion NMR methods fail. Here, we present a simple, direct, and general approach to obtain both compartment size and shape even in such settings and even when pores are characterized by internal field gradients. Using controlled porous media, we show that the bipolar-double-pulsed-field-gradient (bp-d-PFG) methodology yields diffusion-diffraction patterns from which pore size can be directly obtained. Moreover, we show that pore shape, which cannot be obtained by conventional methods, can be directly inferred from the modulation of the signal in angular bp-d-PFG experiments. This new methodology significantly broadens the types of porous media that can be studied using noninvasive diffusion-diffraction NMR.

From single-pulsed field gradient to double-pulsed field gradient MR: gleaning new microstructural information and developing new forms of contrast in MRI

One of the hallmarks of diffusion NMR and MRI is its ability to utilize restricted diffusion to probe compartments much smaller than the excited volume or the MRI voxel, respectively, and to extract microstructural information from them. Single-pulsed field gradient (s-PFG) MR methodologies have been employed with great success to probe microstructures in various disciplines, ranging from chemistry to neuroscience. However, s-PFG MR also suffers from inherent shortcomings, especially when specimens are characterized by orientation or size distributions: in such cases, the microstructural information available from s-PFG experiments is limited or lost. Double-pulsed field gradient (d-PFG) MR methodology, an extension of s-PFG MR, has attracted attention owing to recent theoretical studies predicting that it can overcome certain inherent limitations of s-PFG MR. In this review, we survey the microstructural features that can be obtained from conventional s-PFG methods in the different q regimes, and highlight its limitations. The experimental aspects of d-PFG methodology are then presented, together with an overview of its theoretical underpinnings and a general framework for relating the MR signal decay and material microstructure, affording new microstructural parameters. We then discuss recent studies that have validated the theory using phantoms in which the ground truth is well known a priori, a crucial step prior to the application of d-PFG methodology in neuronal tissue. The experimental findings are in excellent agreement with the theoretical predictions and reveal, inter alia, zero-crossings of the signal decay, robustness towards size distributions and angular dependences of the signal decay from which accurate microstructural parameters, such as compartment size and even shape, can be extracted. Finally, we show some initial findings in d-PFG MR imaging. This review lays the foundation for future studies, in which accurate and novel microstructural information could be extracted from complex biological specimens, eventually leading to new forms of contrast in MRI.

Noninvasive bipolar double-pulsed-field-gradient NMR reveals signatures for pore size and shape in polydisperse, randomly oriented, inhomogeneous porous media

Noninvasive characterization of pore size and shape in opaque porous media is a formidable challenge. NMR diffusion-diffraction patterns were found to be exceptionally useful for obtaining such morphological features, but only when pores are monodisperse and coherently placed. When locally anisotropic pores are randomly oriented, conventional diffusion NMR methods fail. Here, we present a simple, direct, and general approach to obtain both compartment size and shape even in such settings and even when pores are characterized by internal field gradients. Using controlled porous media, we show that the bipolar-double-pulsed-field-gradient (bp-d-PFG) methodology yields diffusion-diffraction patterns from which pore size can be directly obtained. Moreover, we show that pore shape, which cannot be obtained by conventional methods, can be directly inferred from the modulation of the signal in angular bp-d-PFG experiments. This new methodology significantly broadens the types of porous media that can be studied using noninvasive diffusion-diffraction NMR.

Observation of restricted diffusion in the presence of a free diffusion compartment: single- and double-PFG experiments

Theoretical and experimental studies of restricted diffusion have been conducted for decades using single pulsed field gradient (s-PFG) diffusion experiments. In homogenous samples, the diffusion-diffraction phenomenon arising from a single population of diffusing species has been observed experimentally and predicted theoretically. In this study, we introduce a composite bi-compartmental model which superposes restricted diffusion in microcapillaries with free diffusion in an unconfined compartment, leading to fast and slow diffusing components in the NMR signal decay. Although simplified (no exchange), the superposed diffusion modes in this model may exhibit features seen in more complex porous materials and biological tissues. We find that at low q-values the freely diffusing component masks the restricted diffusion component, and that prolongation of the diffusion time shifts the transition from free to restricted profiles to lower q-values. The effect of increasing the volume fraction of freely diffusing water was also studied; we find that the transition in the signal decay from the free mode to the restricted mode occurs at higher q-values when the volume fraction of the freely diffusing water is increased. These findings were then applied to a phantom consisting of crossing fibers, which demonstrated the same qualitative trends in the signal decay. The angular d-PGSE experiment, which has been recently shown to be able to measure small compartmental dimensions even at low q-values, revealed that microscopic anisotropy is lost at low q-values where the fast diffusing component is prominent. Our findings may be of importance in studying realistic systems which exhibit compartmentation.

Modeling of temperature-induced near-infrared and low-field time-domain nuclear magnetic resonance spectral variation: chemometric prediction of limonene and water content in spray-dried delivery systems

The influence of temperature on near-infrared (NIR) and nuclear magnetic resonance (NMR) spectroscopy complicates the industrial applications of both spectroscopic methods. The focus of this study is to analyze and model the effect of temperature variation on NIR spectra and NMR relaxation data. Different multivariate methods were tested for constructing robust prediction models based on NIR and NMR data acquired at various temperatures. Data were acquired on model spray-dried limonene systems at five temperatures in the range from 20 degrees C to 60 degrees C and partial least squares (PLS) regression models were computed for limonene and water predictions. The predictive ability of the models computed on the NIR spectra (acquired at various temperatures) improved significantly when data were preprocessed using extended inverted signal correction (EISC). The average PLS regression prediction error was reduced to 0.2%, corresponding to 1.9% and 3.4% of the full range of limonene and water reference values, respectively. The removal of variation induced by temperature prior to calibration, by direct orthogonalization (DO), slightly enhanced the predictive ability of the models based on NMR data. Bilinear PLS models, with implicit inclusion of the temperature, enabled limonene and water predictions by NMR with an error of 0.3% (corresponding to 2.8% and 7.0% of the full range of limonene and water). For NMR, and in contrast to the NIR results, modeling the data using multi-way N-PLS improved the models' performance. N-PLS models, in which temperature was included as an extra variable, enabled more accurate prediction, especially for limonene (prediction error was reduced to 0.2%). Overall, this study proved that it is possible to develop models for limonene and water content prediction based on NIR and NMR data, independent of the measurement temperature.