Development, simulation, and validation of NMR relaxation-based exchange measurements

Molecular Dynamics and Nuclear Magnetic Resonance Studies of Supercritical CO2 Sorption in Poly(Methyl Methacrylate)

The study of supercritical carbon dioxide sorption processes is an important and urgent task in the field of "green" chemistry and for the selection of conditions for new polymer material formation. However, at the moment, the research of these processes is very limited, and it is necessary to select the methodology for each polymer material separately. In this paper, the principal possibility to study the powder sorption processes using ¹³C nuclear magnetic resonance spectroscopy, relaxation-relaxation correlation spectroscopy and molecular dynamic modeling methods will be demonstrated based on the example of polymethylmethacrylate and supercritical carbon dioxide. It was found that in the first nanoseconds and seconds during the sorption process, most of the carbon dioxide, about 75%, is sorbed into polymethylmethacrylate, while on the clock scale the remaining 25% is sorbed. The methodology presented in this paper makes it possible to select optimal conditions for technological processes associated with the production of new polymer materials based on supercritical fluids.

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.

Tracking oxidation-induced alterations in fibrin clot formation by NMR-based methods

Plasma fibrinogen is an important coagulation factor and susceptible to post-translational modification by oxidants. We have reported impairment of fibrin polymerization after exposure to hypochlorous acid (HOCl) and increased methionine oxidation of fibrinogen in severely injured trauma patients. Molecular dynamics suggests that methionine oxidation poses a mechanistic link between oxidative stress and coagulation through protofibril lateral aggregation by disruption of AαC domain structures. However, experimental evidence explaining how HOCl oxidation impairs fibrinogen structure and function has not been demonstrated. We utilized polymerization studies and two dimensional-nuclear magnetic resonance spectrometry (2D-NMR) to investigate the hypothesis that HOCl oxidation alters fibrinogen conformation and T₂ relaxation time of water protons in the fibrin gels. We have demonstrated that both HOCl oxidation of purified fibrinogen and addition of HOCl-oxidized fibrinogen to plasma fibrinogen solution disrupted lateral aggregation of protofibrils similarly to competitive inhibition of fibrin polymerization using a recombinant AαC fragment (AαC 419–502). DOSY NMR measurement of fibrinogen protons demonstrated that the diffusion coefficient of fibrinogen increased by 17.4%, suggesting the oxidized fibrinogen was more compact and fast motion in the prefibrillar state. 2D-NMR analysis reflected that water protons existed as bulk water (T₂) and intermediate water (T_2i) in the control plasma fibrin. Bulk water T₂ relaxation time was increased twofold and correlated positively with the level of HOCl oxidation. However, T₂ relaxation of the oxidized plasma fibrin gels was dominated by intermediate water. Oxidation induced thinner fibers, in which less water is released into the bulk and water fraction in the hydration shell was increased. We have confirmed that T₂ relaxation is affected by the self-assembly of fibers and stiffness of the plasma fibrin gel. We propose that water protons can serve as an NMR signature to probe oxidative rearrangement of the fibrin clot.

Multidimensional correlation spectroscopic imaging of exponential decays: From theoretical principles to in vivo human applications

Multiexponential modeling of relaxation or diffusion MR signal decays is a popular approach for estimating and spatially mapping different microstructural tissue compartments. While this approach can be quite powerful, it is also limited by the fact that one-dimensional multiexponential modeling is an ill-posed inverse problem with substantial ambiguities. In this article, we present an overview of a recent multidimensional correlation spectroscopic imaging approach to this problem. This approach helps to alleviate ill-posedness by making advantageous use of multidimensional contrast encoding (e.g., 2D diffusion-relaxation encoding or 2D relaxation-relaxation encoding) combined with a regularized spatial-spectral estimation procedure. Theoretical calculations, simulations, and experimental results are used to illustrate the benefits of this approach relative to classical methods. In addition, we demonstrate an initial proof-of-principle application of this kind of approach to in vivo human MRI experiments.

Machine learning assistive rapid, label-free molecular phenotyping of blood with two-dimensional NMR correlational spectroscopy

Translation of the findings in basic science and clinical research into routine practice is hampered by large variations in human phenotype. Developments in genotyping and phenotyping, such as proteomics and lipidomics, are beginning to address these limitations. In this work, we developed a new methodology for rapid, label-free molecular phenotyping of biological fluids (e.g., blood) by exploiting the recent advances in fast and highly efficient multidimensional inverse Laplace decomposition technique. We demonstrated that using two-dimensional T1-T2 correlational spectroscopy on a single drop of blood (<5 μL), a highly time- and patient-specific 'molecular fingerprint' can be obtained in minutes. Machine learning techniques were introduced to transform the NMR correlational map into user-friendly information for point-of-care disease diagnostic and monitoring. The clinical utilities of this technique were demonstrated through the direct analysis of human whole blood in various physiological (e.g., oxygenated/deoxygenated states) and pathological (e.g., blood oxidation, hemoglobinopathies) conditions.

Real-time measurement of diffusion exchange rate in biological tissue

Diffusion exchange spectroscopy (DEXSY) provides a means to isolate the signal attenuation associated with exchange from other sources of signal loss. With the total diffusion weighting b₁+b₂=b_s held constant, DEXSY signals acquired with b₁=0 or b₂=0 have no exchange weighting, while a DEXSY signal acquired with b₁=b₂ has maximal exchange weighting. The exchange rate can be estimated by fitting a diffusion exchange model to signals acquired with variable mixing times. Conventionally, acquired signals are normalized by a signal with b₁=0 and b₂=0 to remove the decay due to spin-lattice relaxation. Instead, division by a signal with equal b_s but b₁=0 or b₂=0 reduces spin-lattice relaxation weighting of the apparent exchange rate (AXR). Furthermore, apparent diffusion-weighted R₁ relaxation rates can be estimated from non-exchange-weighted DEXSY signals. Estimated R₁ values are utilized to remove signal decay due to spin-lattice relaxation from exchange-weighted signals, permitting a more precise estimate of AXR with less data. Data reduction methods are proposed and tested with regards to statistical accuracy and precision of AXR estimates on simulated and experimental data. Simulations show that the methods are capable of accurately measuring the ground-truth exchange rate. The methods remain accurate even when the assumption that DEXSY signals attenuate with b is violated, as occurs for restricted diffusion. Experimental data was collected from fixed neonatal mouse spinal cord samples at 25 and 7°C using the strong static magnetic field gradient produced by a single-sided permanent magnet (i.e., an NMR MOUSE). The most rapid method for exchange measurements requires only five data points (an 80 s experiment as implemented) and achieves a similar level of accuracy and precision to the baseline method using 44 data points. This represents a significant improvement in acquisition speed, overcoming a barrier which has limited the use of DEXSY on living specimen.

Ultrafast diffusion exchange nuclear magnetic resonance

The exchange of molecules between different physical or chemical environments due to diffusion or chemical transformations has a crucial role in a plethora of fundamental processes such as breathing, protein folding, chemical reactions and catalysis. Here, we introduce a method for a single-scan, ultrafast NMR analysis of molecular exchange based on the diffusion coefficient contrast. The method shortens the experiment time by one to four orders of magnitude. Consequently, it opens the way for high sensitivity quantification of important transient physical and chemical exchange processes such as in cellular metabolism. As a proof of principle, we demonstrate that the method reveals the structure of aggregates formed by surfactants relevant to aerosol research.

Analysis of exchange processes is time consuming by two-dimensional exchange NMR spectroscopy. Here the authors demonstrate a single-scan ultrafast Laplace NMR approach based on spatial encoding to measure molecular diffusion, with an increase by a factor six in the sensitivity per unit time.

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.

Saturation-recovery as a T1-filter for T2-T2 exchange NMR

The Inversion-Recovery (IR) technique has already been proposed to be used as a T₁-filter for T₂-T₂ Exchange experiments. However, when the Exchange experiments are employed for studying samples that show T₁ distributions, where the pools are defined by broad relaxation time distributions, e.g. porous media, IR might be difficult to be used as a filter. This paper presents the difficulties found when using IR and proposes the use of Saturation-Recovery (SR) technique as an alternative to T₁-filter.

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.

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.

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.

Quantifying NMR relaxation correlation and exchange in articular cartilage with time domain analysis

Measured nuclear magnetic resonance (NMR) transverse relaxation data in articular cartilage has been shown to be multi-exponential and correlated to the health of the tissue. The observed relaxation rates are dependent on experimental parameters such as solvent, data acquisition methods, data analysis methods, and alignment to the magnetic field. In this study, we show that diffusive exchange occurs in porcine articular cartilage and impacts the observed relaxation rates in T₁-T₂ correlation experiments. By using time domain analysis of T₂-T₂ exchange spectroscopy, the diffusive exchange time can be quantified by measurements that use a single mixing time. Measured characteristic times for exchange are commensurate with T₁ in this material and so impacts the observed T₁ behavior. The approach used here allows for reliable quantification of NMR relaxation behavior in cartilage in the presence of diffusive fluid exchange between two environments.

Inferring brain tissue composition and microstructure via MR relaxometry

MRI relaxometry is sensitive to a variety of tissue characteristics in a complex manner, which makes it both attractive and challenging for characterizing tissue. This article reviews the most common water proton relaxometry measures, T₁, T₂, and T₂^*, and reports on their development and current potential to probe the composition and microstructure of brain tissue. The development of these relaxometry measures is challenged by the need for suitably accurate tissue models, as well as robust acquisition and analysis methodologies. MRI relaxometry has been established as a tool for characterizing neural tissue, particular with respect to myelination, and the potential for further development exists.

Characterization of water in hydrated Bombyx mori silk fibroin fiber and films by 2H NMR relaxation and 13C solid state NMR

The mechanical properties of Bombyx mori silk fibroin (SF), such as elasticity and tensile strength, change remarkably upon hydration. However, the microscopic interaction with water is not currently well understood on a molecular level. In this work, the dynamics of water molecules interacting with SF was studied by ²H solution NMR relaxation and exchange measurements. Additionally, the conformations of hydrated [3-¹³C]Ala-, [3-¹³C]Ser-, and [3-¹³C]Tyr-SF fibers and films were investigated by ¹³C DD/MAS NMR. Using an inverse Laplace transform algorithm, we were able to identify four distinct components in the relaxation times for water in SF fiber. Namely, A: bulk water outside the fiber, B: water molecules trapped weakly on the surface of the fiber, C: bound water molecules located in the inner surface of the fiber, and D: bound water molecules located in the inner part of the fiber were distinguishable. In addition, four components were also observed for water in the SF film immersed in methanol for 30s, while only two components for the film immersed in methanol for 24h. The effects of hydration on the conformation of Ser and Tyr residues in the site-specific crystalline and non-crystalline domains of ¹³C selectively labeled SF, respectively, could be determined independently. Our measurements provide new insight relating the characteristics of water and the hydration structure of silk, which are relevant in light of current interest in the design of novel silk-based biomaterials.

STATEMENTS OF SIGNIFICANCE

The mechanical properties of Bombyx mori silk fibroin (SF) change remarkably upon hydration. However, the microscopic interaction between SF and water is not currently well understood on a molecular level. We were able to identify four distinct components in the relaxation times for water in SF fiber by ²H solution NMR relaxation and exchange measurements. In addition, the effects of hydration on the conformation of Ser and Tyr residues in the site-specific crystalline and non-crystalline domains of ¹³C selectively labeled SF, respectively, could be determined independently. Thus, our measurements provide new insight relating the characteristics of water and the hydration structure of silk, which are relevant in light of current interest in the design of novel silk-based biomaterials.

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.

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.

New insights on human skeletal muscle tissue compartments revealed by in vivo t2 NMR relaxometry

The spin-spin (T2) relaxation of (1)H-NMR signals in human skeletal muscle has been previously hypothesized to reveal information about myowater compartmentation. Although experimental support has been provided, no consensus has yet emerged concerning the attribution of specific anatomical compartments to the observed T2 components. Potential application of a noninvasive tool that might offer such information urges the quest for a definitive answer to this question. The purpose of this work was to obtain new information that might help elucidate the mechanism of T2 distribution in muscle. To do so, in vivo T2 relaxation data was acquired from the soleus of eight healthy volunteers using a localized Carr-Purcell-Meiboom-Gill technique. Each acquisition contained 1000 echoes with an interecho spacing of 1 ms. Data were acquired from each subject under different vascular filling preparations expected to change exclusively the extracellular water fraction. Two exponential components were systematically observed: an intermediate component (T2 ~ 32 ms) and a long component (100 < T2 < 210 ms). The relative fraction and T2 value characterizing the long component systematically increased after progressive augmentation of extracellular water volume. Characteristic relaxation behavior for each vascular filling condition was analyzed with a two-site exchange model and a three-site two-exchange model. We show that a two-site exchange model can only predict the observations for small exchange rates, much more representative of transendothelial than transcytolemmal exchange regimes. The three-site two-exchange model representing the intracellular, interstitial, and vascular spaces was capable of precisely predicting the observations for realistic transcytolemmal and transendothelial exchange rates. The estimated intrinsic relative fractions of each of these compartments corroborate with estimations from previous works and strongly suggest that the T2 relaxation from water within the intracellular and interstitial spaces is described by the intermediate component, whereas the long component represents water within the vascular space.

Characterizing inter-compartmental water exchange in myelinated tissue using relaxation exchange spectroscopy

PURPOSE

To investigate inter-compartmental water exchange in two model myelinated tissues ex vivo using relaxation exchange spectroscopy.

METHODS

Building upon a previously developed theoretical framework, a three-compartment (myelin, intra-axonal, and extra-axonal water) model of the inversion-recovery prepared relaxation exchange spectroscopy signal was applied in excised rat optic nerve and frog sciatic nerve samples to estimate the water residence time constants in myelin (τmyelin ).

RESULTS

In the rat optic nerve samples, τmyelin = 138 ± 15 ms (mean ± standard deviation) was estimated. In sciatic nerve, which possesses thicker myelin sheaths than optic nerve, a much longer τmyelin = 2046 ± 140 ms was observed.

CONCLUSION

Consistent with previous studies in rat spinal cord, the extrapolation of exchange rates in optic nerve to in vivo conditions indicates that τmyelin < 100 ms. This suggests that there is a significant effect of inter-compartmental water exchange on the transverse relaxation of water protons in white matter. The much longer τmyelin values in sciatic nerve supports the postulate that the inter-compartmental water exchange rate is mediated by myelin thickness. Together, these findings point to the potential for MRI methods to probe variations in myelin thickness in white matter.

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.