Rapid encoding of T(1) with spectral resolution in n-dimensional relaxation correlations

A genetic optimisation and iterative reconstruction framework for sparse multi-dimensional diffusion-relaxation correlation MRI

Multi-dimensional diffusion-relaxation correlation (DRC) magnetic resonance imaging (MRI) techniques have recently been developed to investigate tissue microstructures. Sub-voxel tissue heterogeneity is resolved from the local correlation distributions of relaxation time and molecular diffusivity. However, the implementation of these techniques considerably increases the total acquisition time, and simply reducing the scan time may be at the expense of detailed structural resolution. To overcome these limitations, an optimised framework was proposed for acquiring microstructural maps of the human brain on a clinically feasible timescale. First, the acquisition parameters of the multi-dimensional DRC MRI method were sparsely optimised using a genetic algorithm with a fitness function according to the spectral resolution of the correlation map, hardware requirements, and total scan time. Next, the acquired DRC MRI data were processed using a proposed numerical algorithm based on the dynamic inverse Laplace transform (ILT). Prior knowledge from one-dimensional data was then utilised in the iterative procedure to improve the spectral resolution. Finally, the proposed framework was validated using Monte Carlo simulations and experimental data acquired from healthy participants on an MRI scanner. The results demonstrated that the suggested approach is feasible for offering high-resolution DRC maps that correspond to distinct microstructures with a limited amount of optimised acquisition data from two-dimensional DRC sampling space. By significantly reducing scan time while retaining structural resolution, this approach may enable multi-dimensional DRC MRI to be more widely used for quantitative evaluation in biological and medical settings.

Combined diffusion-relaxometry microstructure imaging: Current status and future prospects

Microstructure imaging seeks to noninvasively measure and map microscopic tissue features by pairing mathematical modeling with tailored MRI protocols. This article reviews an emerging paradigm that has the potential to provide a more detailed assessment of tissue microstructure-combined diffusion-relaxometry imaging. Combined diffusion-relaxometry acquisitions vary multiple MR contrast encodings-such as b-value, gradient direction, inversion time, and echo time-in a multidimensional acquisition space. When paired with suitable analysis techniques, this enables quantification of correlations and coupling between multiple MR parameters-such as diffusivity, T 1 , T 2 , and T 2 ∗ . This opens the possibility of disentangling multiple tissue compartments (within voxels) that are indistinguishable with single-contrast scans, enabling a new generation of microstructural maps with improved biological sensitivity and specificity.

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.

T1-T2* relaxation correlation measurements

The majority of low field Magnetic Resonance (MR) analyses rely on T₂ lifetime measurements. Modification of the T₂ measurement to include a T₁ dimension has made the T₁-T₂ measurement a very powerful analytical technique. The T₁-T₂ measurement is uniquely well suited to characterization of different spin populations in porous materials, such as fluid bearing reservoir rocks, and in soft biopolymer materials, for example foods. However, the T₁-T₂ measurement is challenging or impossible if the T₂ relaxation lifetime, or a component lifetime, is short-lived and the signal unobservable in an echo measurement. This occurs in many important classes of materials. A short lifetime T₂ will not however, in general, preclude observation of a free induction decay with signal decay governed by T₂*. As outlined in this paper a T₁-T₂* measurement is a useful analog to the T₁-T₂ experiment. T₁-T₂* measurement enables one to differentiate species as a function of T₂* in one dimension and T₁ in the other dimension. Monitoring changes of the T₁-T₂* coordinate, and associated signal intensity changes, has the potential to reveal structural changes in materials evolving in time. These methods may also be employed to discriminate and identify solid-like species present in static samples. The T₁-T₂* measurement is very general in application, but in this paper we focus on cement-based mortars to develop and illustrate the essential ideas. T₁-T₂* results show a multi-modal behaviour of the MR signal lifetimes, T₁ and T₂*, in mortar samples under study, indicating at least two different water populations. The short T₂* lifetime was assigned to interlayer water (water between C-S-H layers) where the associated T₁ is also short lived. The longer T₂* lifetime was assigned to water in the pore space, where T₁ is also longer lived. In addition to mortar samples we also show application of the method to a crystalline organic species, o-phenylenediamine, which features Sinc Gaussian and exponential decays of transverse magnetization.

New and rapid pulse sequences for two-dimensional D-T1 correlation measurements

Longitudinal relaxation time (T₁), transverse relaxation time (T₂) and diffusion coefficient (D) values have been widely used for the characterizations of materials using low field Time Domain Nuclear Magnetic Resonance (TD-NMR). Each parameter can be determined using one-dimensional techniques or their values and correlations by multi-dimensional experiments such as T₁-T₂, D-T₂, and T₁-D-T₂. In this work, we studied four D-T₁ sequences for TD-NMR combining Stejskal-Tanner Pulse Gradient Spin Echo (PGSE) diffusion measurement with Inversion-Recovery (IR), Saturation-Recovery (SR), Small-Angle Continuous Wave Free Precession (CWFP-T₁) and Small-Angle Flip-Flop (SAFF) for T₁ measurement. The results show that rapid D-T₁ measurements can be obtained with single shot CWFP-T₁ and SAFF sequences. The two sequences were two and eight time fast than sequences based on SR and IR, respectively. Although the two fast sequences yield low signal-to-noise ratio signal, they can be as fast as the traditional D-T₂ experiment, or even faster, because it is not necessary to wait a recycle delay of 5 T₁. Another advantage of the CWFP-T₁ and SAFF methods, when compared to the one based on SR or CPMG (for D-T₂) are the low specific absorption rate (SAR) of these sequences due the low flip angles in the sequences, that reduces the sample heating problem. These sequences were initially studied using phantom samples. They also were used to study plant tissues to observe the anisotropic diffusion in asparagus. Therefore, they can be useful methods for practical application in TD-NMR.

Using T1 as a direct detection dimension in two-dimensional time-domain NMR experiments using CWFP regime

The transverse relaxation time (T₂), measured with Carr-Purcell-Meiboom-Gill (CPMG) sequence, has been widely used to obtain the direct dimension data in two-dimension time domain NMR (2D TD-NMR). In this paper we are demonstrating that Continuous Wave Free Precession sequence, with low flip angle (CWFP-T₁), can be an alternative to CPMG as direct detection dimension. CWFP-T₁ is a fast single shot sequence, like CPMG, and yields an exponential signal governed predominantly by the longitudinal (T₁) relaxation time. To obtain the correlations between T₁ and T₂ (T₁-T₂ maps) we are proposing the use of CPMG-CWFP-T₁ pulse sequence. In this sequence CPMG encodes T₂ information (indirect dimension) that modulates the CWFP-T₁ (direct dimension) signal amplitudes. CPMG-CWFP-T₁ experiments were compared with classical 2D sequences such as Saturation-Recovery-CPMG (SR-CPMG) and Inversion-Recovery-CPMG (IR-CPMG) sequence and yields similar results in phantom sample. The experimental time for the 2D sequences, using single scan, shows that SR-CPMG ≤ CPMG-CWFP-T₁ < IR-CPMG. Experimental and simulated results demonstrated that 2D-CPMG-CWFP-T₁ maps have higher resolution in T₁ dimension than the techniques that uses CPMG as direct dimension. CPMG-CWFP-T₁ sequence was also applied to study beef samples, and 2D maps showed higher resolution in the two fat signals than the classical IR-CPMG method.

Single-shot measurement of solids and liquids T1 values by a small-angle flip-flop pulse sequence

We propose the small-angle flip-flop (SAFF) pulse sequence as an alternative procedure for the rapid measurement of the ¹ H spin-lattice relaxation time in the laboratory frame (T₁ ) of solid and liquid substances, in a time-domain NMR experiment. Based on the original flip-flop pulse sequence, this technique allows the fast estimation of T₁ values of samples that require minutes to hours of acquisition time if traditional pulse sequences are employed. We have applied SAFF to different substances, with T₁ ranging from microseconds up to seconds, including natural clays, polymers, and organic and inorganic solvents. We also demonstrate the potential of the pulse sequence in the real-time monitoring of dynamic processes, such as the conformational changes of polymeric materials during heating. The results we obtained with SAFF are comparable with those acquired with the inversion-recovery pulse sequence, with the addition of several benefits. This pulse sequence obeys steady-state and magnetization-conserving principles, making it possible to dismiss the need for relaxation delay times of the order of 5T₁ . SAFF has shown high sensitivity in the resolution of individual components of T₁ in multiexponential systems and can be easily integrated to well-established pulse sequences, such as Magic Sandwich Echo and Carr-Purcell-Meiboom-Gill, for the single-shot determination of T₁ and T₂ or T_2* .

A finite element approach to forward modeling of nuclear magnetic resonance measurements in coupled pore systems

Porous media characterized by a hierarchy of length scales are ubiquitous in industry and nature, and include carbonate rocks, cements, heterogeneous catalysts, and biological cells. Nuclear magnetic resonance (NMR) is a popular tool for studying liquid-saturated porous materials, where the spin relaxation rate is generally considered proportional to pore size. However, in porous granular media, the relaxation rate is modified by diffusion between the intraparticle and interparticle pores. The observed relaxation rates do not reflect the pore size under such conditions. Deconvolving the various contributions of surface relaxation, geometry, and diffusion is nontrivial, and forward models are a powerful technique for elucidating the underlying pore structure. Various forward models have been proposed previously, including analytic solutions and random walk simulations. Here, a finite element method is adopted to simulate the diffusion of nuclear magnetization in a coupled pore geometry. We validate our model against existing solutions and use the simulations to determine the surface relaxivity of powdered silica by matching experimental results. The finite element approach is more versatile than other modeling methods, allowing direct visualization of the diffusing magnetization and being trivially extensible to multidimensional NMR exchange experiments.

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.

Contributed review: nuclear magnetic resonance core analysis at 0.3 T

Nuclear magnetic resonance (NMR) provides a powerful toolbox for petrophysical characterization of reservoir core plugs and fluids in the laboratory. Previously, there has been considerable focus on low field magnet technology for well log calibration. Now there is renewed interest in the study of reservoir samples using stronger magnets to complement these standard NMR measurements. Here, the capabilities of an imaging magnet with a field strength of 0.3 T (corresponding to 12.9 MHz for proton) are reviewed in the context of reservoir core analysis. Quantitative estimates of porosity (saturation) and pore size distributions are obtained under favorable conditions (e.g., in carbonates), with the added advantage of multidimensional imaging, detection of lower gyromagnetic ratio nuclei, and short probe recovery times that make the system suitable for shale studies. Intermediate field instruments provide quantitative porosity maps of rock plugs that cannot be obtained using high field medical scanners due to the field-dependent susceptibility contrast in the porous medium. Example data are presented that highlight the potential applications of an intermediate field imaging instrument as a complement to low field instruments in core analysis and for materials science studies in general.

Rapid measurements of heterogeneity in sandstones using low-field nuclear magnetic resonance

Sandstone rocks can contain microscopic variations in composition that complicate interpretation of nuclear magnetic resonance (NMR) relaxation time measurements. In this work, methods for assessing the degree of sample heterogeneity are demonstrated in three sandstones. A two-dimensional T1-Δχapp correlation (where Δχapp is the apparent solid/liquid magnetic susceptibility contrast) reveals the microscopic heterogeneity in composition, whilst a spatially resolved T1 profile reveals the macroscopic structural heterogeneity. To perform these measurements efficiently, a rapid measure of longitudinal T1 relaxation time has been implemented on a low-field NMR spectrometer with a magnetic field strength B0=0.3 T. The "double-shot" T1 pulse sequence is appropriate for analysis of porous materials in general. Example relaxation time distributions are presented for doped water phantoms to validate the method. The acquisition time of the double-shot T1 sequence is equivalent to the single-shot Carr-Purcell Meiboom-Gill (CPMG) sequence used routinely in petrophysics to measure transverse T2 relaxation. Rapid T1 measurements enable practical studies of core plugs at magnetic field strengths previously considered inappropriate, as T1 is independent of molecular diffusion through pore-scale (internal) magnetic field gradients.

Low-field permanent magnets for industrial process and quality control

In this review we focus on the technology associated with low-field NMR. We present the current state-of-the-art in low-field NMR hardware and experiments, considering general magnet designs, rf performance, data processing and interpretation. We provide guidance on obtaining the optimum results from these instruments, along with an introduction for those new to low-field NMR. The applications of lowfield NMR are now many and diverse. Furthermore, niche applications have spawned unique magnet designs to accommodate the extremes of operating environment or sample geometry. Trying to capture all the applications, methods, and hardware encompassed by low-field NMR would be a daunting task and likely of little interest to researchers or industrialists working in specific subject areas. Instead we discuss only a few applications to highlight uses of the hardware and experiments in an industrial environment. For details on more particular methods and applications, we provide citations to specialized review articles.

Modeling two-dimensional magnetic resonance measurements in coupled pore systems

We present numerical simulations of a two-dimensional (2D) nuclear magnetic resonance process, T_{2}-storage-T_{2}, on a simple mixed porosity system, the micrograin consolidation (μGC) model. The results of these calculations are compared with predictions based on the analytic two-site exchange model, for which we have independently established numerical values for all the input parameters. Although there is qualitative and semiquantitative agreement between the two models, we identify specific instances where the two-site model fails to properly describe the combined effects of relaxation and diffusion. Generally, these instances occur when a gradient in magnetization within the large pores of the μGC model is established during the initial phase of the 2D process. The two-site model assumes that the magnetization is spatially uniform within each of its subpore systems and thus cannot describe such effects.

Structure of the two-dimensional relaxation spectra seen within the eigenmode perturbation theory and the two-site exchange model

The form of the two-dimensional (2D) NMR-relaxation spectra--which allow to study interstitial fluid dynamics in diffusive systems by correlating spin-lattice (T(1)) and spin-spin (T(2)) relaxation times--has given rise to numerous conjectures. Herein we find analytically a number of fundamental structural properties of the spectra: within the eigen-modes formalism, we establish relationships between the signs and intensities of the diagonal and cross-peaks in spectra obtained by various 1 and 2D NMR-relaxation techniques, reveal symmetries of the spectra and uncover interdependence between them. We investigate more specifically a practically important case of porous system that has sets of T(1)- and T(2)-eigenmodes and eigentimes similar to each other by applying the perturbation theory. Furthermore we provide a comparative analysis of the application of the, mathematically more rigorous, eigen-modes formalism and the, rather more phenomenological, first-order two-site exchange model to diffusive systems. Finally we put the results that we could formulate analytically to the test by comparing them with computer-simulations for 2D porous model systems. The structural properties, in general, are to provide useful clues for assignment and analysis of relaxation spectra. The most striking of them--the presence of negative peaks--underlines an urgent need for improvement of the current 2D Inverse Laplace Transform (ILT) algorithm used for calculation of relaxation spectra from NMR raw data.

AnalyzeNNLS: magnetic resonance multiexponential decay image analysis

Exponential decays are fundamental to magnetic resonance imaging, yet adequately sampling and analyzing multiexponential decays is rarely attempted. The advantage of multiexponential analysis is the quantification of sub-voxel structure caused by water compartmentalization, with application as a non-invasive imaging biomarker for myelin. We have developed AnalyzeNNLS, software designed specifically for multiexponential decay image analysis that has a user-friendly graphical user interface and can analyze data from many MR manufacturers. AnalyzeNNLS is a simple, platform independent analysis tool that was created using the extensive mathematical and visualization libraries in Matlab, and released as open source code allowing scientists to evaluate, scrutinize, improve, and expand.

Structural properties of 2D NMR relaxation spectra of diffusive systems

Much has been learnt and speculated about the form of 2D NMR relaxation spectra of diffusive systems. Herein we show that the eigen-modes formalism can help to establish a number of fundamental structural properties, i.e. symmetries, overall intensities, signs and relative intensities of the diagonal and cross components, of such spectra, on which one can safely rely in analysing experimental data. More specifically, we prove that the correlation T(1)-T(2) spectra will always have negative peaks, thus making questionable the nowadays wide spread strategy in developing inverse Laplace transformation algorithms.

A rapid measurement of T1/T2: the DECPMG sequence

The Driven-Equilibrium Carr-Purcell Meiboom-Gill (DECPMG) pulse sequence is a rapid method for obtaining the average ratio of longitudinal to transverse relaxation times (T(1)/T(2)) as a function of T(2). Since this is a one-dimensional experiment, the (T(1)/T(2))T(2) ratio can be acquired, potentially, in just two scans; the second scan being a reference CPMG measurement. Conventionally, T(1)/T(2) is determined from a two-dimensional T(1)-T(2) relaxation correlation experiment. The method described here offers a significant reduction in experimental time without a reduction in signal-to-noise. The (T(1)/T(2)) ratio is useful for comparing the behaviour of liquids in porous media. Here we demonstrate the application of the DECPMG sequence to the study of oil-bearing rocks by differentiating oil or water saturated rock cores, and by observing the relative strengths of surface interaction for water in two types of rock by measuring (T(1)/T(2)) as a function of magnetic field strength.