Nuclear Magnetic Resonance Relaxation Rates Research Articles

Simulation and analysis of 13C spin-rotation nuclear magnetic resonance relaxation rates of methyl groups

This work analyzes the nuclear spin–rotation contribution to the nuclear magnetic resonance relaxation of methyl groups from 10 rigid compounds (eight benzene derivatives with one, two, or three methyl groups and two bicyclic molecules) with internal rotation axes not aligned to the smallest molecular moment of inertia via molecular dynamics simulation and ab initio calculation. The molecular dynamics simulation and ab initio calculation of nuclear spin-rotation coupling constants reproduce the experimental behavior in selected systems. The presented methodology can help in the analysis and interpretation of experimental relaxation data.

Computing the frequency-dependent NMR relaxation of 1H nuclei in liquid water.

We present a computational framework for reliably determining the frequency-dependent intermolecular and intramolecular nuclear magnetic resonance (NMR) dipole-dipole relaxation rates of spin 1/2 nuclei from Molecular Dynamics (MD) simulations. This approach avoids the alterations caused by the well-known finite-size effects of translational diffusion. Moreover, a procedure is derived to control and correct for effects caused by fixed distance-sampling cutoffs and periodic boundary conditions. By construction, this approach is capable of accurately predicting the correct low-frequency scaling behavior of the intermolecular NMR dipole-dipole relaxation rate and thus allows for the reliable calculation of the frequency-dependent relaxation rate over many orders of magnitude. Our approach is based on the utilization of the theory of Hwang and Freed for the intermolecular dipole-dipole correlation function and its corresponding spectral density [L.-P. Hwang and J. H. Freed, J. Chem. Phys. 63, 4017-4025 (1975)] and its combination with data from MD simulations. The deviations from the Hwang and Freed theory caused by periodic boundary conditions and sampling distance cutoffs are quantified by means of random walker Monte Carlo simulations. An expression based on the Hwang and Freed theory is also suggested for correcting those effects. As a proof of principle, our approach is demonstrated by computing the frequency-dependent intermolecular and intramolecular dipolar NMR relaxation rates of 1H nuclei in liquid water at 273 and 298K based on the simulations of the TIP4P/2005 model. Our calculations are suggesting that the intermolecular contribution to the 1H NMR relaxation rate of the TIP4P/2005 model in the extreme narrowing limit has previously been substantially underestimated.

Ultrasound and magnetic resonance imaging–based investigation of the role of perfusion and oxygen availability in menstrual pain

BackgroundThe mechanisms responsible for menstrual pain are poorly understood. However, dynamic noninvasive pelvic imaging of menstrual pain sufferers could aid in identifying therapeutic targets and in testing novel treatments. ObjectiveTo study the mechanisms responsible for menstrual pain, we analyzed ultrasonographic and complementary functional Magnetic Resonance Imaging (fMRI) parameters in dysmenorrhea sufferers and pain-free controls under multiple conditions. Study DesignWe performed fMRI on participants with and without dysmenorrhea during menses and non-menses. To clarify whether regional changes in oxygen availability and perfusion occur, fMRI R2* measurements were made of the endometrium and myometrium. R2* measurements are calculated nuclear magnetic resonance relaxation rates sensitive to the paramagnetic properties of oxygenated and deoxygenated hemoglobin. We also compared parameters before and after an analgesic dose of naproxen sodium. In addition, we performed similar measurements with Doppler ultrasonography to identify whether changes in uterine arterial velocity occurred during menstrual cramping in real time. Mixed model statistics were performed to account for within-subject effects across conditions. Corrections for multiple comparisons were made with a false discovery rate adjustment. ResultsDuring menstruation, a notable increase in R2* values, indicative of tissue ischemia, was observed in both the myometrium (beta ± standard error of the mean: 15.74 ± 2.29 s-1, p = 0.001, q = 0.002) and the endometrium (26.37 ± 9.33 s-1, p = 0.005, q = 0.008) among participants experiencing dysmenorrhea. A similar increase was noted in the myometrium (28.89 ± 2.85 s-1, p = 0.001, q = 0.002) and endometrium (75.50 ± 2.57 s-1, p = 0.001, q = 0.003) among pain-free controls. Post-hoc analyses revealed that R2* values during menstruation were significantly higher than those in participants with dysmenorrhea (Myometrium: p = 0.008, Endometrium: p = 0.043). Whereas naproxen sodium increased endometrial R2* in participants with dysmenorrhea (48.29 ± 15.78 s-1,p = 0.005, q = 0.008), it decreased myometrial R2*in pain-free controls. Doppler findings were consistent with fMRI (-8.62 ± 3.25 s-1, p = 0.008, q = 0.011). The pulsatility index (-0.42 ± 0.14, p = 0.004, q = 0.004) and resistance index (-0.042 ± 0.012, p = 0.001, q = 0.001) decreased during menses compared with non-menses, and effects were significantly reversed by naproxen sodium. Naproxen sodium had the opposite effect in pain-free controls. There were no significant real-time changes in the pulsatility index, resistance index, peak systolic velocity, or minimum diastolic velocity during episodes of symptomatic menstrual cramping. ConclusionsfMRI and Doppler metrics suggest participants with dysmenorrhea have better perfusion and oxygen availability than pain-free controls. Naproxen sodium's therapeutic mechanism is associated with relative reductions in uterine perfusion and oxygen availability. An opposite pharmacological effect was observed in pain-free controls. During menstrual cramping, there is insufficient evidence of episodic impaired uterine perfusion. Thus, prostaglandins may have protective vasoconstrictive effects in pain-free controls and opposite effects among participants with dysmenorrhea.

Revealing the effect of phase and time coupling on NMR relaxation rate by random walks in phase space.

Phase-time coupling is a natural process in the phase random walks of a spin system; however, its effect on the nuclear magnetic resonance (NMR) relaxation is a challenge to the established theories such as the second-order quantum perturbation theory. This paper extends the recently developed phase diffusion method to treat the phase-time coupling effect, based on uncoupled phase diffusions, and coupled random walks. The instantaneous projection of the rotating random field is employed to get the accumulated phase of the NMR observable. In the static frame and the rotating frame, the phase diffusion coefficients are derived. The obtained theoretical results show that the phase-time coupling has a significant impact on the NMR relaxation rate: The angular frequency ω in the spectral density is modified to an apparent angular frequency ηω, where η is the phase-time coupling constant. The strongest coupling has η equaling 2, while η equaling 1 corresponds to the traditional results. As an example, the modified relaxation time expressions based on both monoexponential and nonmonoexponential functions can successfully fit the previously reported ^{13}CT_{1} NMR experimental data of polyisobutylene (PIB) in the blend of PIB and head-to-head poly(propylene). In contrast, the traditional relaxation rate expression based on the monoexponential time correlation function cannot fit such experimental data. With the phase-time coupling, the obtained characteristic time of the segmental motion is faster than that from conventional results.

Nuclear Magnetic Resonance Studies of Bicontinuous Liquid Crystalline Phases of Cubic Symmetry: Transport Properties from 2H Nuclear Magnetic Resonance Relaxation Rates.

The ternary system didodecyltrimethylammonium bromide, 1-decanol, and water forms an extended reversed continuous phase of cubic symmetry at 25 °C. The cubic phase belongs to the space group Im3m, as shown by small-angle X-ray experiments. We present extensive deuterium NMR relaxation data from this cubic phase for 1-decanol, deuterated at the carbon adjacent to the hydroxyl carbon position. 2H spin-lattice (R1) and spin-spin (R2) relaxation rates were measured over the existence region of the cubic phase, which extends from 0.2 to 0.6 in volume fraction of the dividing bilayer surface of the cubic phase. The data are interpreted with an existing theoretical framework for NMR spin relaxation in bicontinuous cubic phases, which takes its starting point in the description of bicontinuous phases using periodic minimal surfaces. Specifically, we obtain the self-diffusion coefficient over the minimal surface in one unit cell for 1-decanol. We also present pulsed field gradient NMR-derived self-diffusion data for didodecyltrimethylammonium bromide and compare the two sets of data. The diffusion data for both components show a mild, if any, dependence on the volume fraction of the bilayer surface. Furthermore, we present diffusion data for the water component in the cubic phase. Finally, we discuss the influences of the choice of the value of the product of the deuterium quadrupole constant and the order parameter S. Within the framework of the model used to analyze the relaxation data, a value for this parameter is required. As an initial value, we rely on measurements of deuterium quadrupolar splittings from deuterated decanol in an anisotropic phase.

NMR relaxation and diffusion studies to probe the motional dynamics of risperidone within PLGA microsphere

The present study aims to investigate the motional dynamics of risperidone within polylactic co-glycolic acid (PLGA) microsphere by employing solution state 1H and 19F nuclear magnetic resonance (NMR) measurements. Risperidone, a second-generation fluorinated antipsychotic drug used for the treatment of schizophrenia is commercially marketed as PLGA microsphere formulation resulting in prolonged release of the drug in solution. Although the current trend in the pharmaceutical market is to develop drug formulation with long-acting release (LAR) products, complete physicochemical characterization of such formulations are scarce. Especially the effects of microsphere encapsulation on the motional properties and diffusion behavior of the drugs are not discussed adequately in any of the earlier reports. We therefore, have employed NMR relaxation and diffusion measurements to decipher the interaction of PLGA cavity water with risperidone. A detailed analysis of NMR relaxation rates confirmed the event of encapsulation and the presence of local motion in the non-fluorinated end of risperidone. Further, the relaxation data indicated a significant alteration in 19F chemical shift anisotropy (CSA) and CSA/dipole-dipole (DD) cross-correlated relaxation mechanism and decreased effect of solvent relaxation pointing out reduced water concentration within the microsphere cavity. 1H and 19F diffusion coefficients of risperidone led to the information about hydrodynamic radius of risperidone in free and encapsulated states. Measurement of hydrodynamic radius supported the presence of limited water in PLGA cavity allowing higher translational mobility of risperidone after the encapsulation.

Electrical conductivity and nuclear magnetic resonance relaxation rate of Eliashberg superconductors in the weak-coupling limit

Electrical conductivity is an important transport response in superconductors, enabling clear signatures of dynamical interactions to be observed. Of primary interest in this paper is to study characteristics of the electron-phonon interaction in weak-coupling Eliashberg theory (Eth), and to note the distinctions with Bardeen-Cooper-Schrieffer (BCS) theory. Recent analysis of weak-coupling Eth has shown that while there are modifications from the BCS results, certain dimensionless ratios are in agreement. Here we show that the conductivities in BCS theory and Eth fundamentally differ, with the latter having an imaginary gap component that damps a divergence. We focus on the dirty limit, and for both BCS theory and Eth we derive expressions for the low-frequency limit of the real conductivity. For Eth specifically, there are two limits to consider, depending on the relative size of the frequency and the imaginary part of the gap. In the case of identically zero frequency, we derive an analytical expression for the nuclear magnetic resonance relaxation rate. Our analysis of the conductivity complements the previous study of the Meissner response and provides a thorough understanding of weak-coupling Eth.

DNA base order parameter determination without influence of chemical exchange.

Nuclear magnetic resonance (NMR) spectroscopy is a versatile tool used to investigate the dynamic properties of biological macromolecules and their complexes. NMR relaxation data can provide order parameters S2, which represent the mobility of bond vectors reorienting within a molecular frame. Determination of S2 parameters typically involves the use of transverse NMR relaxation rates. However, the accuracy in S2 determination can be diminished by elevation of the transverse relaxation rates through conformational or chemical exchange involving protonation/deprotonation or non-Watson-Crick base-pair states of nucleic acids. Here, we propose an approach for determination of S2 parameters without the influence of exchange processes. This approach utilizes transverse and longitudinal 13C chemical shift anisotropy (CSA) - dipole-dipole (DD) cross-correlation rates instead of 13C transverse relaxation rates. Anisotropy in rotational diffusion is taken into consideration. An application of this approach to nucleotide base CH groups of a uniformly 13C/15N-labeled DNA duplex is demonstrated.

Anomalously field-susceptible spin clusters emerging in the electric-dipole liquid candidate κ-(ET)2Hg(SCN)2Br.

Mutual interactions in many-body systems bring about various exotic phases, among which liquid-like states failing to order due to frustration are of keen interest. The organic system with an anisotropic triangular lattice of molecular dimers, κ-(ET)2Hg(SCN)2Br, has been suggested to host a dipole liquid arising from intradimer charge-imbalance instability, possibly offering an unprecedented stage for the spin degrees of freedom. Here, we show that an extraordinary unordered/unfrozen spin state having soft matter-like spatiotemporal characteristics emerges in this system. 1H nuclear magnetic resonance (NMR) spectra and magnetization measurements indicate that gigantic, staggered moments are nonlinearly and inhomogeneously induced by a magnetic field, whereas the moments vanish in the zero-field limit. The analysis of the NMR relaxation rate signifies that the moments fluctuate at a characteristic frequency slowing down to below megahertz at low temperatures. The inhomogeneity, local correlation, and slow dynamics indicative of middle-scale dynamical correlation length of several nanometers suggest novel frustration-driven spin clusterization.

Fully gapped superconducting state in interstitial-carbon-doped Zr5Pt3

We report a comprehensive study of the ${\mathrm{Zr}}_{5}{\mathrm{Pt}}_{3}{\mathrm{C}}_{x}$ superconductors, with interstitial carbon between 0 and 0.3. At a macroscopic level, their superconductivity, with ${T}_{c}$ ranging from 4.5 to 6.3 K, was investigated via electrical-resistivity, magnetic-susceptibility, and specific-heat measurements. The upper critical fields ${\ensuremath{\mu}}_{0}{H}_{\mathrm{c}2}\ensuremath{\sim}7$ T were determined mostly from measurements of the electrical resistivity in applied magnetic field. The microscopic electronic properties were investigated by means of muon-spin rotation and relaxation ($\ensuremath{\mu}\mathrm{SR}$) and nuclear magnetic resonance (NMR) techniques. In the normal state, NMR relaxation data indicate an almost ideal metallic behavior, confirmed by band-structure calculations, which suggest a relatively high electronic density of states at the Fermi level, dominated by the Zr $4d$ orbitals. The low-temperature superfluid density, obtained via transverse-field $\ensuremath{\mu}\mathrm{SR}$, suggests a fully gapped superconducting state in ${\mathrm{Zr}}_{5}{\mathrm{Pt}}_{3}$ and ${\mathrm{Zr}}_{5}{\mathrm{Pt}}_{3}{\mathrm{C}}_{0.3}$, with zero-temperature gap ${\mathrm{\ensuremath{\Delta}}}_{0}=1.20$ and 0.60 meV and magnetic penetration depth ${\ensuremath{\lambda}}_{0}$ = 333 and 493 nm, respectively. The exponential dependence of the NMR relaxation rates below ${T}_{c}$ further supports nodeless superconductivity. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined from zero-field $\ensuremath{\mu}\mathrm{SR}$ measurements, confirms the preserved time-reversal symmetry in the superconducting state of ${\mathrm{Zr}}_{5}{\mathrm{Pt}}_{3}{\mathrm{C}}_{x}$. In contrast to a previous study, our $\ensuremath{\mu}\mathrm{SR}$ and NMR results suggest conventional superconductivity in the ${\mathrm{Zr}}_{5}{\mathrm{Pt}}_{3}{\mathrm{C}}_{x}$ family, independent of the C content.

Learnings From a New Slimhole LWD NMR Technology

This paper presents recent results obtained from a new 4.75-in. logging-while-drilling (LWD) nuclear magnetic resonance (NMR) tool. Data from several wells provided real-time operational insight and new petrophysical learnings. The new LWD technology offers an innovative capability to simultaneously measure NMR T1 and T2 distributions with reduced sensitivity to drilling mud conductivity and a real-time sensor motion-warning system. The real-time T1 and T2 spectra compare favorably with the data set retrieved from the tool memory. The LWD NMR measurements were followed by wireline (WL) NMR logging for comparison in three wells. In carbonate reservoirs, the main objective was to evaluate the new NMR tool’s capability in resolving carbonate pore size with slow NMR relaxation rates. Another set of NMR logs contained time-lapse repeat passes in a well drilled with oil-based mud (OBM) that traversed a clastic reservoir. The sequence of measurements identified rock types and provided a unique insight into the mud filtrate invasion process. In a carbonate reservoir, the LWD NMR real-time partial porosity estimates were in excellent agreement with the core-calibrated WL micro-, meso-, and macropore volumes. Another carbonate formation contained high-permeability layers embedded in a microporous rock, where the real-time LWD NMR logs successfully located the high-quality rock zones, later verified by WL logging. In the clastic reservoir, the while-drilling LWD NMR data indicated native light hydrocarbons, whereas the subsequent LWD reaming and WL NMR passes showed a displacement of native hydrocarbons by oil-based mud filtrate (OBMF). The native hydrocarbon signature observed by the LWD NMR tool was in good agreement with the mud gas log. OBMF invasion occurred shortly after drilling, indicated by the differences observed in the LWD NMR relogged data acquired several hours after the while-drilling pass. The WL NMR data, logged about 4 days after drilling, showed advanced stages of OBMF invasion, including formation water displacement and wettability changes in intermediate and large pores. Finally, the environmental noise remained low in the LWD NMR data set acquired in a well in which the mud salinity changed by several folds, indicating that mud salinity had little effect on the quality of LWD NMR logs in slim holes. The new slimhole LWD NMR technology demonstrated its robust capability to provide T1 and T2 logs through several examples. For the first time, a time-lapse comparison of NMR logs showed that OBMF invasion could occur in silty sands with high capillary-bound fluid fractions.

S-wave superconductivity in the noncentrosymmetric W3Al2C superconductor: an NMR study

We report on a microscopic study of the noncentrosymmetric superconductor W3Al2C (with T c = 7.6 K), mostly by means of 27Al- and 13C nuclear magnetic resonance (NMR). Since in this material the density of states at the Fermi level is dominated by the tungsten’s 5d orbitals, we expect a sizeable spin–orbit coupling (SOC) effect. The normal-state electronic properties of W3Al2C resemble those of a standard metal, but with a Korringa product 1/(T 1 T) significantly smaller than that of metallic Al, reflecting the marginal role played by s-electrons. In the superconducting state, we observe a reduction of the Knight shift and an exponential decrease of the NMR relaxation rate 1/T 1, typical of s-wave superconductivity (SC). This is further supported by the observation of a small but distinct coherence peak just below T c in the 13C NMR relaxation-rate, in agreement with the fully-gapped superconducting state inferred from the electronic specific-heat data well below T c. The above features are compared to those of members of the same family, in particular, Mo3Al2C, often claimed to exhibit unconventional SC. We discuss why, despite the enhanced SOC, W3Al2C does not show spin-triplet features in its superconducting state and consider the broader consequences of our results for noncentrosymmetric superconductors in general.

1D magnetic resonance imaging and low-field nuclear magnetic resonance relaxometry of water-based silica nanofluids

The purpose of this research is to investigate 1-D Magnetic Resonance Imaging (MRI) and low-field Nuclear Magnetic Resonance (NMR) relaxation characteristics of silica nanofluids. The results show that presence of silica nanoparticles increases the MRI signal intensity and influences the NMR relaxation by shifting the relaxation peaks toward faster times compared to deionized water (DIW). Additionally, inversion recovery sequences show that nanoparticles reduce longitudinal relaxation time. For the tested nanofluid of EOR-12, signal intensity, longitudinal relaxation rate and transverse relaxation rate show a strong linear dependence on nanoparticle concentration with the highest enhancement of 1.75-fold, 2.57-fold and 3.20-fold, respectively compared to DIW. Additionally, investigation of the effect of nanoparticle size shows that below an optimal size, the MRI signal intensity and the NMR relaxation rates show a positive correlation with nanoparticle size but above the optimal size, the behavior reverses. For the nanoparticle with the optimal diameter, signal intensity, longitudinal relaxation rate and transverse relaxation rate enhancement was 2.21-fold, 4.44-fold and 4.45-fold, respectively compared to DIW. Application of the observed improvement in signal intensity to obtain the profile of the aqueous phase volume fraction in a Pickering emulsion shows a maximum error of 8% which indicates that the proposed technique can be applied for emulsion characterization with good accuracy.

NMR Relaxation Rates of Quadrupolar Aqueous Ions from Classical Molecular Dynamics Using Force-Field Specific Sternheimer Factors.

The nuclear magnetic resonance (NMR) relaxation of quadrupolar nuclei is governed by the electric field gradient (EFG) fluctuations at their position. In classical molecular dynamics (MD), the electron cloud contribution to the EFG can be included via the Sternheimer approximation, in which the full EFG at the nucleus that can be computed using quantum density functional theory (DFT) is considered to be proportional to that arising from the external, classical charge distribution. In this work, we systematically assess the quality of the Sternheimer approximation as well as the impact of the classical force field (FF) on the NMR relaxation rates of aqueous quadrupolar ions at infinite dilution. In particular, we compare the rates obtained using an ab initio parametrized polarizable FF, a recently developed empirical FF with scaled ionic charges and a simple empirical nonpolarizable FF with formal ionic charges. Surprisingly, all three FFs considered yield good values for the rates of smaller and less polarizable solutes (Li+, Na+, K+, Cl-), provided that a model-specific Sternheimer parametrization is employed. Yet, the polarizable and scaled charge FFs yield better estimates for divalent and more polarizable species (Mg2+, Ca2+, Cs+). We find that a linear relationship between the quantum and classical EFGs holds well in all of the cases considered; however, such an approximation often leads to quite large errors in the resulting EFG variance, which is directly proportional to the computed rate. We attempted to reduce the errors by including first order nonlinear corrections to the EFG, yet no clear improvement for the resulting variance has been found. The latter result indicates that more refined methods for determining the EFG at the ion position, in particular those that take into account the instantaneous atomic environment around an ion, might be necessary to systematically improve the NMR relaxation rate estimates in classical MD.

Rechargeable Thin‐Film Lithium Microbattery Using a Quasi‐Solid‐State Polymer Electrolyte

AbstractA thin‐film microbattery was designed after synthesizing a unique gel polymer electrolyte (GPE), using polyvinylidene fluoride‐co‐hexafluoropropylene (PVdF‐HFP) and cross‐linked poly(ethylene oxide) (PEO), with an ionic liquid and salt (LiTFSI) mixture. The polymers resulted in a semi‐interpenetrated polymer network (semi‐IPN), hosting an ionic liquid (IL)/salt mixture, and thus exhibited high ionic conductivity and excellent mechanical properties. Nuclear magnetic resonance (NMR) diffusion measurements and relaxation rates analysis highlighted the existence of interactions between Li+ ions and oxygen within the polymers, preventing electrolyte leakage and ensuring excellent mechanical strength which enabled a unique quasi‐solid electrolyte. Such mechanical strength and chemical stability made this electrolyte to be first ever reported GPE to withstand thermal evaporation deposition and hence direct deposition of lithium metal. The electrolyte could be shaped as self‐standing thin films, and thus worked as both separator and electrolyte in a thin‐film lithium microbattery. The thin‐film microbattery exhibited excellent performances showing no short‐circuit current, an open circuit voltage of ∼3.0 V, higher nominal voltage plateau, lower equivalent series resistance by comparison to a thin‐film microbattery designed in conventional way with a popular ceramic electrolyte LiPON.

23Na NMR T1 relaxation measurements as a probe for diffusion and dynamics of sodium ions in salt-glycerol mixtures.

Mixtures of sodium salts with oxygen-containing molecules are useful from the perspective of applications such as sodium ion batteries because they fill the gap between deep eutectic solvents and molten salt hydrates. In a previous work, the physical properties (such as diffusion coefficients, conductivity, viscosity, and glass transition temperature) of four salts, namely, Na2B4O7 · 10H2O, NaOAc · 3H2O, NaBr, and NaOAc, were measured with glycerol. Pulsed-field gradient (PFG) nuclear magnetic resonance (NMR) was also used to measure self-diffusion coefficients of 1H-bearing species. However, the technique was not able to measure diffusion of sodium ions due to the very fast NMR relaxation rate of such species, resulting in loss of the PFG NMR signal. In the current work, this study is expanded using 23Na T1 relaxation measurements which, under certain assumptions, can be translated into diffusion coefficients. Analysis of the physical properties is then correlated with self-diffusion coefficient measurements to elucidate information about structure and ionic mobility. It is shown that NaOAc · 3H2O, NaBr, and NaOAc fit models for ionic conductivity and diffusion, which are consistent with ionic liquids where charge transport is limited by ionic mobility rather than the number of charge carriers. The waters of hydration of NaOAc · 3H2O do not appear to form a separate phase but are instead strongly coordinated to the cation. In contrast, Na2B4O7 · 10H2O appears to form a water-rich phase with enhanced sodium mobility.

Describing NMR relaxation by effective phase diffusion equation

This paper proposes an effective diffusion equation method to analyze nuclear magnetic resonance (NMR) relaxation. NMR relaxation is a spin system recovery process, where the evolution of the spin system is affected by the random field due to Hamiltonians, such as dipolar couplings. The evolution of magnetization can be treated as a random walk in phase space described either by a normal or fractional phase diffusion equation. Based on these phase diffusion equations, the NMR relaxation rates and equations can be obtained, exemplified in the analysis of relaxations affected by an arbitrary random field, and by dipolar coupling for both like and unlike spins. The obtained theoretical results are consistent with the reported results in the literature. Additionally, the anomalous relaxation expression obtained from the Mittag-Leffler function based time correlation function can successfully fit the previously reported 13C T1 NMR experimental data of polyisobutylene (PIB) in the blend of PIB and head-to-head poly(propylene) (hhPP). Furthermore, the proposed phase diffusion approach provides an intuitive way to interpret NMR relaxation, particularly for the fractional NMR relaxation, which is still a challenge to explain by the available theoretical methods. The paper provides additional insights into NMR and magnetic resonance imaging (MRI) relaxation experiments.

Predicting NMR relaxation of proteins from molecular dynamics simulations with accurate methyl rotation barriers.

The internal dynamics of proteins occurring on time scales from picoseconds to nanoseconds can be sensitively probed by nuclear magnetic resonance (NMR) spin relaxation experiments, as well as by molecular dynamics (MD) simulations. This complementarity offers unique opportunities, provided that the two methods are compared at a suitable level. Recently, several groups have used MD simulations to compute the spectral density of backbone and side chain molecular motions and to predict NMR relaxation rates from these. Unfortunately, in the case of methyl groups in protein side chains, inaccurate energy barriers to methyl rotation were responsible for a systematic discrepancy in the computed relaxation rates, as demonstrated for the AMBER ff99SB*-ILDN force field (and related parameter sets), impairing quantitative agreement between simulations and experiments. However, correspondence could be regained by emending the MD force field with accurate coupled cluster quantum chemical calculations. Spurred by this positive result, we tested whether this approach could be generally applicable, in spite of the fact that different MD force fields employ different water models. Improved methyl group rotation barriers for the CHARMM36 and AMBER ff15ipq protein force fields were derived, such that the NMR relaxation data obtained from the MD simulations even now display very good agreement with the experiment. Results herein showcase the performance of present-day MD force fields and manifest their refined ability to accurately describe internal protein dynamics.

Design of a fast field-cycling magnetic resonance imaging system, characterization and methods for relaxation dispersion measurements around 1.5 T.

The dependence of the nuclear magnetic resonance relaxation rate on the magnetic field has been widely studied, in particular, in biomedical areas with the objectives to better understand the underlying microscopic mechanisms in tissues and provide biomarkers of diseases. By combining fast-field cycling (FFC) and magnetic resonance imaging (MRI), it is possible to provide localized relaxation dispersion measurements in heterogeneous systems with recent demonstrations in solutions, biological samples, human beings, and small animals. We report here the developments and performances of a device designed for small animal FFC-MRI comprising a resistive insert technology operating inside a 1.5 T MRI system. Specific measurement methods were developed to characterize the system efficiency, response time, homogeneity, stability, and compensation. By adding a non-linear element in the system and using a dual amplifier strategy, it is shown that large field offsets can be produced during relaxation periods while maintaining precise field control during detection periods. The measurement of longitudinal nuclear magnetic relaxation dispersion (NMRD) profiles in the range of 1.08 T-1.92 T is reported, essentially displaying a linear variation in this range for common MRI contrast agents. The slopes of both the longitudinal and transverse relaxation dispersion profiles at 1.5 T are measured and validated, extending the capabilities of previous approaches. The performances of a longitudinal relaxation dispersion mapping method are finally reported, opening the way to quantitative preclinical dispersion imaging studies at a high FFC-MRI field.

Enhancing 31P NMR relaxation rates with a kinetically inert gadolinium complex.

The kinetically stable heptadentate gadolinium complex Gd.pDO3A (1.Gd) demonstrates significant 31P nuclear magnetic resonance (NMR) relaxation enhancement of biologically relevant phosphate species; adenosine triphosphate (ATP), phosphocreatine (PCr) and inorganic phosphate. Gd.pDO3A (1.Gd) binds these species in fast exchange, enabling the relaxation of the bulk phosphate species in solution. This gives rise to 31P relaxation enhancements up to 250-fold higher than those observed for 31P relaxation enhancements with the commercial MRI contrast agent Gd.DOTA (DOTAREM), 2. Gd.pDO3A-like complexes may have potential applications as 31P magnetic resonance contrast agents, since shortening the T1 relaxation time of phosphate species would reduce the time needed to acquire 31P-MR spectra.