T2-Filtered T2 − T2 Exchange NMR

NMR Relaxation by Redfield equation in a spin system I=7/2

The Redfield master equation was solved analytically for a nuclear system with spin I=7/2. Using the irreducible tensor operator basis, the solutions of each density matrix element were computed. The experimental setup consisted of the ¹³³Cs nuclei of the cesium-pentadecafluorooctanoate molecule in a lyotropic liquid crystal sample in the nematic phase at room temperature. Experimental longitudinal and transverse magnetization dynamics of the ¹³³Cs nuclei were monitored, and the theoretical approach was used to generate valuable mathematical expressions with the highest accuracy through numerical procedures. This methodology can be extended to other nuclei with minimal difficulties.

Ultrafast transverse relaxation exchange NMR spectroscopy

Molecular exchange between different physical or chemical environments occurs due to either diffusion or chemical transformation. Nuclear magnetic resonance (NMR) spectroscopy provides a means of understanding the molecular exchange in a noninvasive way and without tracers. Here, we introduce a novel two dimensional, single-scan ultrafast Laplace NMR (UF LNMR) method to monitor molecular exchange using transverse relaxation as a contrast. The UF T2-T2 relaxation exchange spectroscopy (REXSY) method shortens the experiment time by one to two orders of magnitude compared to its conventional counterpart. Contrary to the conventional EXSY, the exchanging sites are distinguished based on T2 relaxation times instead of chemical shifts, making the method especially useful for systems including physical exchange of molecules. Therefore, the UF REXSY method offers an efficient means for quantification of exchange processes in various fields such as cellular metabolism and ion transport in electrolytes. As a proof of principle, we studied a halogen-free orthoborate based ionic liquid system and followed molecular exchange between molecular aggregates and free molecules. The results are in good agreement with the conventional exchange studies. Due to the single-scan nature, the method potentially significantly facilitates the use of modern hyperpolarization techniques to boost the sensitivity by several orders of magnitude.

A benchtop single-sided magnet with NMR well-logging tool specifications - Examples of application

This article was written in honor of Prof. Bernhard Blümich, who has heavily impacted many areas of Magnetic Resonance and, in particular, low-field and portable NMR with numerous advances, concepts, innovations, and applications of this impressive technology. Many years ago, we decided to research and develop single-sided magnets for the area of petroleum science and engineering to study oil reservoir rocks in the laboratory under well-logging conditions. The global urge to exploit oil reserves requires the analysis of reservoirs, intending to characterize the yields before starting the production. Thus, well-logging tools have been developed to estimate the quality of oil and reservoir productivity. NMR logging is included in these analytical tools, and numerous operations using this kind of device were performed since the early 1950s. To contribute to this vital research area, we show the development of a new benchtop single-sided NMR system, with well-logging tool characteristics, a cylindrical sweet spot with 4 cm of diameter and length, with magnetic field of 47 mT centered at 11 cm from the magnet's surface and a constant gradient of 35.7 G/cm along z. This system was used in self-diffusion, T₁-T₂, and D-T₂ measurements of standard liquids and rock cores, demonstrating its functionality.

Analysis of three-site T2-T2 exchange NMR

T₂-T₂ exchange NMR is a unique method to investigate the pore space and fluid dynamics in porous media. While two-site relaxation exchange is well understood, three-site exchange is not. We analyze the solutions for three-site T₂-T₂ exchange NMR analytically and by computer simulation. Three main results are obtained. First, the exchange map can be asymmetric in the case of microscale vortex motion in violation of the principle of detailed balance. Second, the apparent longitudinal relaxation times and/or apparent transverse relaxation times can be complex valued. In the case of complex apparent transverse relaxation times, the three-site exchange map coalesces to a two-site exchange map with characteristic oscillations in the time domain. As a result of the oscillations, the shorter relaxation time is less than expected. Third, there can be negative cross-peaks in the exchange map for certain combinations of longitudinal and transverse relaxation times or if the mixing period is shorter than the evolution and detection periods. In view of these results experimental exchange maps may need to be reevaluated.

Spatially-resolved 1H NMR relaxation-exchange measurements in heterogeneous media

In the last decades, the ¹H NMR T₂-T₂ relaxation-exchange (REXSY) technique has become an essential tool for the molecular investigation of simple and complex fluids in heterogeneous porous solids and soft matter, where the mixing-time-evolution of cross-correlated T₂-T₂ peaks enables a quantitative study of diffusive exchange kinetics in multi-component systems. Here, we present a spatially-resolved implementation of the T₂-T₂ correlation technique, named z-T₂-T₂, based on one-dimensional spatial mapping along z using a rapid frequency-encode imaging scheme. Compared to other phase-encoding methods, the adopted MRI technique has two distinct advantages: (i) is has the same experimental duration of a standard (bulk) T₂-T₂ measurement, and (ii) it provides a high spatial resolution. The proposed z-T₂-T₂ method is first validated against bulk T₂-T₂ measurements on homogeneous phantom consisting of cyclohexane uniformly imbibed in finely-sized α-Al₂O₃ particles at a spatial resolution of 0.47 mm; thereafter, its performance is demonstrated, on a layered bed of multi-sized α-Al₂O₃ particles, for revealing spatially-dependent molecular exchange kinetics properties of intra- and inter-particle cyclohexane as a function of particle size. It is found that localised z-T₂-T₂ spectra provide well resolved cross peaks whilst such resolution is lost in standard bulk T₂-T₂ data. Future prospective applications of the method lie, in particular, in the local characterisation of mass transport phenomena in multi-component porous media, such as rock cores and heterogeneous catalysts.

Computational approach to integrate 3D X-ray microtomography and NMR data

Nowadays, most of the efforts in NMR applied to porous media are dedicated to studying the molecular fluid dynamics within and among the pores. These analyses have a higher complexity due to morphology and chemical composition of rocks, besides dynamic effects as restricted diffusion, diffusional coupling, and exchange processes. Since the translational nuclear spin diffusion in a confined geometry (e.g. pores and fractures) requires specific boundary conditions, the theoretical solutions are restricted to some special problems and, in many cases, computational methods are required. The Random Walk Method is a classic way to simulate self-diffusion along a Digital Porous Medium. Bergman model considers the magnetic relaxation process of the fluid molecules by including a probability rate of magnetization survival under surface interactions. Here we propose a statistical approach to correlate surface magnetic relaxivity with the computational method applied to the NMR relaxation in order to elucidate the relationship between simulated relaxation time and pore size of the Digital Porous Medium. The proposed computational method simulates one- and two-dimensional NMR techniques reproducing, for example, longitudinal and transverse relaxation times (T₁ and T₂, respectively), diffusion coefficients (D), as well as their correlations. For a good approximation between the numerical and experimental results, it is necessary to preserve the complexity of translational diffusion through the microstructures in the digital rocks. Therefore, we use Digital Porous Media obtained by 3D X-ray microtomography. To validate the method, relaxation times of ideal spherical pores were obtained and compared with the previous determinations by the Brownstein-Tarr model, as well as the computational approach proposed by Bergman. Furthermore, simulated and experimental results of synthetic porous media are compared. These results make evident the potential of computational physics in the analysis of the NMR data for complex porous materials.

Simultaneous acquisition for T2-T2 Exchange and T1-T2 correlation NMR experiments

The NMR measurements of longitudinal and transverse relaxation times and its multidimensional correlations provide useful information about molecular dynamics. However, these experiments are very time-consuming, and many researchers proposed faster experiments to reduce this issue. This paper presents a new way to simultaneously perform T₂-T₂ Exchange and T₁-T₂ correlation experiments by taking the advantage of the storage time and the two steps phase cycling used for running the relaxation exchange experiment. The data corresponding to each step is either summed or subtracted to produce the T₂-T₂ and T₁-T₂ data, enhancing the information obtained while maintaining the experiment duration. Comparing the results from this technique with traditional NMR experiments it was possible to validate the method.

Probing numerical Laplace inversion methods for two and three-site molecular exchange between interconnected pore structures

Two-dimension (2D) Nuclear Magnetic Resonance relaxometry experiments are a powerful tool extensively used to probe the interaction among different pore structures, mostly in inorganic systems. The analysis of the collected experimental data generally consists of a 2D numerical inversion of time-domain data where T₂-T₂ maps are generated. Through the years, different algorithms for the numerical inversion have been proposed. In this paper, two different algorithms for numerical inversion are tested and compared under different conditions of exchange dynamics; the method based on Butler-Reeds-Dawson (BRD) algorithm and the fast-iterative shrinkage-thresholding algorithm (FISTA) method. By constructing a theoretical model, the algorithms were tested for a two- and three-site porous media, varying the exchange rates parameters, the pore sizes and the signal to noise ratio. In order to test the methods under realistic experimental conditions, a challenging organic system was chosen. The molecular exchange rates of water confined in hierarchical porous polymeric networks were obtained, for a two- and three-site porous media. Data processed with the BRD method was found to be accurate only under certain conditions of the exchange parameters, while data processed with the FISTA method is precise for all the studied parameters, except when SNR conditions are extreme.

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.