Relaxation Rate In Rotating Frame Research Articles

Whole-brain amide CEST imaging at 3T with a steady-state radial MRI acquisition.

To develop a steady-state saturation with radial readout chemical exchange saturation transfer (starCEST) for acquiring CEST images at 3 Tesla (T). The polynomial Lorentzian line-shape fitting approach was further developed for extracting amideCEST intensities at this field. StarCEST MRI using periodically rotated overlapping parallel lines with enhanced reconstruction-based spatial sampling was implemented to acquire Z-spectra that are robust to brain motion. Multi-linear singular value decomposition postprocessing was applied to enhance the CEST SNR. The egg white phantom studies were performed at 3T to reveal the contributions to the 3.5 ppm CEST signal. Based on the phantom validation, the amideCEST peak was quantified using the polynomial Lorentzian line-shape fitting, which exploits the inverse relationship between Z-spectral intensity and the longitudinal relaxation rate in the rotating frame. The 3D turbo spin echo CEST was also performed to compare with the starCEST method. The amideCEST peak showed a negligible peak B1 dependence between 1.2 µT and 2.4 µT. The amideCEST images acquired with starCEST showed much improved image quality, SNR, and motion robustness compared to the conventional 3D turbo spin echo CEST method with the same scan time. The amideCEST contrast extracted by the polynomial Lorentzian line-shape fitting method trended toward a stronger gray matter signal (1.32% ± 0.30%) than white matter (0.92% ± 0.08%; P = .02, n = 5). When calculating the magnetization transfer contrast and T1 -corrected rotating frame relaxation rate maps, amideCEST again was not significantly different for white matter and gray matter. Rapid multi-slice amideCEST mapping can be achieved by the starCEST method (< 5 min) at 3T by combing with the polynomial Lorentzian line-shape fitting method.

Deuterium solid-state NMR quadrupolar order rotating frame relaxation with applications to amyloid-β fibrils.

We describe a new method for measuring molecular dynamics based on the deuterium solid-state nuclear magnetic resonance (NMR) quadrupolar order rotating frame relaxation rateR1ρ,Q under static conditions. The observed quadrupolar order coherence is created using the broad-band Jeener-Broekaert excitation and is locked with a weak radio frequency (RF) field. We describe the experimental and theoretical approaches and show applications to a selectively deuterated valine side chain of the phosphorylated amyloid-β (1-40) fibrils phosphorylated at the serine-8 position. The R1ρ,Q rate is sensitive to the rotameric exchange mode. For biological samples, the low spin-lock field in the 5- to 10-kHz range has the advantage of avoiding sample heating and dehydration. Thus, it provides an alternative to approaches based on single-quantum coherence, which require larger spin-lock fields.

Proton dynamics in tetramethylammonium cadmium chloride (CH3)4NCdCl3 single crystal by using 1H NMR measurements

Tetramethylammonium (TMA) cadmium chloride (TMCC), (CH3)4NCdCl3, has four phases with first-order transition temperatures at 104 and 118 K. To investigate the proton dynamics, we performed 1H nuclear magnetic resonance spectroscopy on a single TMCC crystal and measured the spin–lattice relaxation rate 1/T1 and rotating frame relaxation rate 1/T1ρ in the range of 65−300 K at 206.4 MHz under ∼4.8 T. 1/T1 displays an abrupt increase at 111.5 K and 1/T1ρ exhibits a sudden jump between 110 and 120 K. The discontinuities of both 1/T1 and 1/T1ρ across the phase transitions are unique in TMCC and have not been observed in other TMA-based compounds. Above 118 K, the temperature dependence of both T1 and T1ρ is linear, which indicates Arrhenius behavior. Below 118 K, T1 has a single minimum, and both T1 and T1ρ are linear in the low temperature range. This behavior at 206.4 MHz is very different from the double minima observed in T1 at 14.7 MHz for powder TMCC samples and in both T1 and T1ρ for other TMA-based compounds. By fitting two different regimes to the Bloembergen-Purcell-Pound curves, we extract both Ea and τ0 above and below 118 K. By carefully analyzing the T1 and T1ρ data, we ascertain that the coexistence of CH3 and TMA motions displays the double minima, unlike the T1 and T1ρ data at 206.4 MHz. Therefore, we conclude that the only active proton dynamics of TMCC originate from the CH3 rotation, and there is no reorientation of TMA ions, unlike other TMA-based compounds. Both T1 and T1ρ data confirm that the proton dynamics of the CH3 groups suddenly switch from rapid rotation above 118 K to slow rotation below 118 K, with no TMA ion dynamics in TMCC.

Quantitative rotating frame relaxometry methods in MRI.

Macromolecular degeneration and biochemical changes in tissue can be quantified using rotating frame relaxometry in MRI. It has been shown in several studies that the rotating frame longitudinal relaxation rate constant (R1ρ ) and the rotating frame transverse relaxation rate constant (R2ρ ) are sensitive biomarkers of phenomena at the cellular level. In this comprehensive review, existing MRI methods for probing the biophysical mechanisms that affect the rotating frame relaxation rates of the tissue (i.e. R1ρ and R2ρ ) are presented. Long acquisition times and high radiofrequency (RF) energy deposition into tissue during the process of spin-locking in rotating frame relaxometry are the major barriers to the establishment of these relaxation contrasts at high magnetic fields. Therefore, clinical applications of R1ρ and R2ρ MRI using on- or off-resonance RF excitation methods remain challenging. Accordingly, this review describes the theoretical and experimental approaches to the design of hard RF pulse cluster- and adiabatic RF pulse-based excitation schemes for accurate and precise measurements of R1ρ and R2ρ . The merits and drawbacks of different MRI acquisition strategies for quantitative relaxation rate measurement in the rotating frame regime are reviewed. In addition, this review summarizes current clinical applications of rotating frame MRI sequences. Copyright © 2016 John Wiley & Sons, Ltd.

Lithium dynamics in carbon-rich polymer-derived SiCN ceramics probed by nuclear magnetic resonance

We report 7Li, 29Si, and 13C NMR studies of two different carbon-rich SiCN ceramics SiCN-1 and SiCN-3 derived from the preceramic polymers polyphenylvinylsilylcarbodiimide and polyphenylvinylsilazane, respectively. From the spectral analysis of the three nuclei, we find that only the 13C spectrum is strongly influenced by Li insertion/extraction, suggesting that carbon phases are the major electrochemically active sites for Li storage. Temperature (T) and Larmor frequency (ωL) dependences of the 7Li linewidth and spin-lattice relaxation rates T1−1 are described by an activated law with the activation energy EA of 0.31 eV and the correlation time τ0 in the high temperature limit of 1.3 ps. The 3/2 power law dependence of T1−1 on ωL which deviates from the standard Bloembergen, Purcell, and Pound (BPP) model implies that the Li motion on the μs timescale is governed by continuum diffusion mechanism rather than jump diffusion. On the other hand, the rotating frame relaxation rate T1ρ−1 results suggest that the slow motion of Li on the ms timescale may be affected by complex diffusion and/or non-diffusion processes.

Exchange-mediated contrast in CEST and spin-lock imaging

PurposeMagnetic resonance images of biological media based on chemical exchange saturation transfer (CEST) show contrast that depends on chemical exchange between water and other protons. In addition, spin–lattice relaxation rates in the rotating frame (R1ρ) are also affected by exchange, especially at high fields, and can be exploited to provide novel, exchange-dependent contrast. Here, we evaluate and compare the factors that modulate the exchange contrast for these methods using simulations and experiments on simple, biologically relevant samples. MethodsSimulations and experimental measurements at 9.4T of rotating frame relaxation rate dispersion and CEST contrast were performed on solutions of macromolecules containing amide and hydroxyl exchanging protons. ResultsThe simulations and experimental measurements confirm that both CEST and R1ρ measurements depend on similar exchange parameters, but they manifest themselves differently in their effects on contrast. CEST contrast may be larger in the slow and intermediate exchange regimes for protons with large resonant frequency offsets (e.g. >2ppm). Spin-locking techniques can produce larger contrast enhancement when resonant frequency offsets are small (<2ppm) and exchange is in the intermediate-to-fast regime. The image contrasts scale differently with field strength, exchange rate and concentration. ConclusionCEST and R1ρ measurements provide different and somewhat complementary information about exchange in tissues. Whereas CEST can depict exchange of protons with specific chemical shifts, appropriate R1ρ-dependent acquisitions can be employed to selectively portray protons of specific exchange rates.

An R1ρ expression for a spin in chemical exchange between two sites with unequal transverse relaxation rates

An analytical expression is derived for the rotating frame relaxation rate, R(1ρ), of a spin exchanging between two sites with different transverse relaxation times. A number of limiting cases are examined, with the equation reducing to formulae derived previously under the assumption of equivalent relaxation rates at each site. The measurement of a pair off-resonance R(1ρ) values, with the carrier displaced equally on either side of the observed correlation, forms the basis of one of the approaches for obtaining signs of chemical shift differences, Δω, of exchanging nuclei. The results presented here establish that this method is relatively insensitive to differential transverse relaxation rates between the exchaning states, greatly simplifying the calculation of optimal parameters in R(1ρ) based experiments that are used for measurement of signs of Δω.

1H NMR study of the hydrogen dynamics in the (NaS)xGe(OH)4 − x·yH2O ceramic proton conductors

1H NMR was performed on the ceramic proton conductor (NaS)xGe(OH)4−x·yH2O for x=2, 3 and y~1–4 over the temperature range of −100°C to 400°C. NMR spectra, nuclear spin–lattice relaxation rates (R1), spin–spin relaxation rates (R2), and rotating frame relaxation rates (R1ρ) were obtained for both hydrated and dehydrated samples. It was found that the low temperature NMR spectra were consistent with simulated H2O lineshapes, and the presence of H3O+ at low temperature was not detected within the experimental uncertainty. Short- and long-range hydrogen motion occurred together, a signature of Grotthuss conduction mechanisms. The long range motion was a combination of H+ and H2O diffusion, with H2O motion limiting H+ dynamics as the onset temperature was approached.

Heteronuclear Adiabatic Relaxation Dispersion (HARD) for quantitative analysis of conformational dynamics in proteins

NMR relaxation methods probe biomolecular motions over a wide range of timescales. In particular, the rotating frame spin-lock R1ρ and Carr–Purcell–Meiboom–Gill (CPMG) R2 experiments are commonly used to characterize μs to ms dynamics, which play a critical role in enzyme folding and catalysis. In an effort to complement these approaches, we introduced the Heteronuclear Adiabatic Relaxation Dispersion (HARD) method, where dispersion in rotating frame relaxation rate constants (longitudinal R1ρ and transverse R2ρ) is created by modulating the shape and duration of adiabatic full passage (AFP) pulses. Previously, we showed the ability of the HARD method to detect chemical exchange dynamics in the fast exchange regime (kex∼104–105s−1). In this article, we show the sensitivity of the HARD method to slower exchange processes by measuring R1ρ and R2ρ relaxation rates for two soluble proteins (ubiquitin and 10C RNA ligase). One advantage of the HARD method is its nominal dependence on the applied radio frequency field, which can be leveraged to modulate the dispersion in the relaxation rate constants. In addition, we also include product operator simulations to define the dynamic range of adiabatic R1ρ and R2ρ that is valid under all exchange regimes. We conclude from both experimental observations and simulations that this method is complementary to CPMG-based and rotating frame spin-lock R1ρ experiments to probe conformational exchange dynamics for biomolecules. Finally, this approach is germane to several NMR-active nuclei, where relaxation rates are frequency-offset independent.

Site-Specific Measurement of Slow Motions in Proteins

We demonstrate that a quantitative measure of slow molecular motions in solid proteins can be accessed by measuring site-specific (15)N rotating-frame relaxation rates at high magic-angle-spinning frequencies.

Relaxation dispersion in MRI induced by fictitious magnetic fields

A new method entitled Relaxation Along a Fictitious Field (RAFF) was recently introduced for investigating relaxations in rotating frames of rank ⩾2. RAFF generates a fictitious field ( E) by applying frequency-swept pulses with sine and cosine amplitude and frequency modulation operating in a sub-adiabatic regime. In the present work, MRI contrast is created by varying the orientation of E, i. e. the angle ε between E and the z″ axis of the second rotating frame. When ε > 45°, the amplitude of the fictitious field E generated during RAFF is significantly larger than the RF field amplitude used for transmitting the sine/ cosine pulses. Relaxation during RAFF was investigated using an invariant-trajectory approach and the Bloch–McConnell formalism. Dipole–dipole interactions between identical (like) spins and anisochronous exchange ( e. g., exchange between spins with different chemical shifts) in the fast exchange regime were considered. Experimental verifications were performed in vivo in human and mouse brain. Theoretical and experimental results demonstrated that changes in ε induced a dispersion of the relaxation rate constants. The fastest relaxation was achieved at ε ≈ 56°, where the averaged contributions from transverse components during the pulse are maximal and the contribution from longitudinal components are minimal. RAFF relaxation dispersion was compared with the relaxation dispersion achieved with off-resonance spin lock T 1ρ experiments. As compared with the off-resonance spin lock T 1ρ method, a slower rotating frame relaxation rate was observed with RAFF, which under certain experimental conditions is desirable.

Frequency offset dependence of adiabatic rotating frame relaxation rate constants: relevance to MRS investigations of metabolite dynamics in vivo

In this work, we investigated the frequency-offset dependence of the rotating frame longitudinal (R(1ρ)) and transverse (R(2ρ)) relaxation rate constants when using hyperbolic-secant adiabatic full passage pulses or continuous-wave spin-lock irradiation. Phantom and in vivo measurements were performed to validate theoretical predictions of the dominant relaxation mechanisms existing during adiabatic full passage pulses when using different settings of the frequency offset relative to the carrier. In addition, adiabatic R(1ρ) and R(2ρ) values of total creatine and N-acetylaspartate were measured in vivo from the human brain at 4 T. When the continuous-wave pulse power was limited to safe specific absorption rates for humans, simulations revealed a strong dependence of R(1ρ) and R(2ρ) values on the frequency offset for both dipolar interactions and anisochronous exchange mechanisms. By contrast, theoretical and experimental results showed adiabatic R(1ρ) and R(2ρ) values to be practically invariant within the large subregion of the bandwidth of the hyperbolic-secant pulse where complete inversion was achieved. However, adiabatic R(1ρ) and R(2ρ) values of the methyl protons of total creatine (at 3.03 ppm) were almost doubled when compared with those of the methyl protons of N-acetylaspartate (at 2.01 ppm) in spite of the fact that these resonances were in the flat region of the inversion band of the adiabatic full passage pulses. We conclude that differences in adiabatic R(1ρ) and R(2ρ) values of human brain metabolites are not a result of their chemical shifts, but instead reflect differences in dynamics.

Rotating frame relaxation during adiabatic pulses vs. conventional spin lock: simulations and experimental results at 4 T

Spin relaxation taking place during radiofrequency (RF) irradiation can be assessed by measuring the longitudinal and transverse rotating frame relaxation rate constants (R(1rho) and R(2rho)). These relaxation parameters can be altered by utilizing different settings of the RF irradiation, thus providing a useful tool to generate contrast in MRI. In this work, we investigate the dependencies of R(1rho) and R(2rho) due to dipolar interactions and anisochronous exchange (i.e., exchange between spins with different chemical shift deltaomega not equal0) on the properties of conventional spin-lock and adiabatic pulses, with particular emphasis on the latter ones which were not fully described previously. The results of simulations based on relaxation theory provide a foundation for formulating practical considerations for in vivo applications of rotating frame relaxation methods. Rotating frame relaxation measurements obtained from phantoms and from the human brain at 4 T are presented to confirm the theoretical predictions.

T2ρ and T1ρ Adiabatic Relaxations and Contrasts

Transverse relaxation in the rotating frame (T2ρ) is the dominant relaxation mechanism during a train of adiabatic full passage (AFP) radiofrequency (RF) pulses with no interpulse time intervals placed after the 90° excitation pulse. The magnetization components remain transverse to the time-dependent effective field and undergo relaxation with the time constant T2ρ. Longitudinal relaxation in the rotating frame (T1ρ) is the dominant relaxation mechanism during a train of AFP RF pulses placed prior to an excitation pulse. Here, magnetization is aligned along the time-dependent effective field during adiabatic rotation undergoes relaxation with the time constant T1ρ. A detailed description of rotating frame relaxations due to dipolar interactions and exchange during adiabatic pulses is presented herein. The exchange-induced and dipolar interaction contributions depend on the modulation functions of the adiabatic pulses used. The intrinsic rotating frame relaxation rate constant is sensitive to fluctuations at the effective frequencey (ωeff) in the rotating frame, and this is modulated differently during the two types of AFP pulses. This may lead to the possibility to assess T1ρ and T2ρ relaxation influenced by dipolar relaxation pathways and exchange in human brain tissue and provide a means to generate T1ρ and T2ρ contrasts in MRI.

Dynamics of paramagnetic agents by off-resonance rotating frame technique

Off-resonance rotating frame technique offers a novel tool to explore the dynamics of paramagnetic agents at high magnetic fields ( B 0 > 3 T). Based on the effect of paramagnetic relaxation enhancement in the off-resonance rotating frame, a new method is described here for determining the dynamics of paramagnetic ion chelates from the residual z-magnetizations of water protons. In this method, the dynamics of the chelates are identified by the difference magnetization profiles, which are the subtraction of the residual z-magnetization as a function of frequency offset obtained at two sets of RF amplitude ω 1 and pulse duration τ. The choices of ω 1 and τ are guided by a 2-D magnetization map that is created numerically by plotting the residual z-magnetization as a function of effective field angle θ and off-resonance pulse duration τ. From the region of magnetization map that is the most sensitive to the alteration of the paramagnetic relaxation enhancement efficiency R 1 ρ / R 1, the ratio of the off-resonance rotating frame relaxation rate constant R 1 ρ verse the laboratory frame relaxation rate constant R 1, three types of difference magnetization profiles can be generated. The magnetization map and the difference magnetization profiles are correlated with the rotational correlation time τ R of Gd-DTPA through numerical simulations, and further validated by the experimental data for a series of macromolecule conjugated Gd-DTPA in aqueous solutions. Effects of hydration water number q, diffusion coefficient D, magnetic field strength B 0 and multiple rotational correlation times are explored with the simulations of the magnetization map. This method not only provides a simple and reliable approach to determine the dynamics of paramagnetic labeling of molecular/cellular events at high magnetic fields, but also a new strategy for spectral editing in NMR/MRI based on the dynamics of paramagnetic labeling in vivo.

Practical Route to Relative Diffusion Coefficients and Electronic Relaxation Rates of Paramagnetic Metal Complexes in Solution by Model-Independent Outer-Sphere NMRD. Potentiality for MRI Contrast Agents

The relaxation of electronic spins S of paramagnetic species is studied by the field-dependence of the longitudinal, transverse, and longitudinal in the rotating frame relaxation rates R1, R2, and R1rho of nuclear spins I carried by dissolved probe solutes. The method rests on the model-independent low-frequency dispersions of the outer-sphere (OS) paramagnetic relaxation enhancement (PRE) of these rates due to the three-dimensional relative diffusion of the complex with respect to the probe solute. We propose simple analytical formulas to calculate these enhancements in terms of the relative diffusion coefficient D, the longitudinal electronic relaxation time T1e, and the time integral of the time correlation function of the I-S dipolar magnetic interaction. In the domain of vanishing magnetic field, these parameters can be derived from the low-frequency dispersion of R1 thanks to sensitivity improvements of fast field-cycling nuclear relaxometers. At medium field, we present various approaches to obtain these parameters by combining the rates R1, R2, and R1rho. The method is illustrated by a careful study of the proton PREs of deuterated water HOD, methanol CH3OD, and tert-butyl alcohol (CH3)3COD in heavy water in the presence of a recently reported nonacoordinate Gd(III) complex. The exceptionally slow electronic relaxation of the Gd(III) spin in this complex is confirmed and used to test the accuracy of the method through the self-consistency of the low- and medium-field results. The study of molecular diffusion at a few nanometer scale and of the electronic spin relaxation of other complexed metal ions is discussed.

NMR Methods for Studying the Structure and Dynamics of RNA

Proper functioning of RNAs requires the formation of complex three-dimensional structures combined with the ability to rapidly interconvert between multiple functional states. This review covers recent advances in isotope-labeling strategies and NMR experimental approaches that have promise for facilitating solution structure determinations and dynamics studies of biologically active RNAs. Improved methods for the production of isotopically labeled RNAs combined with new multidimensional heteronuclear NMR experiments make it possible to dramatically reduce spectral crowding and simplify resonance assignments for RNAs. Several novel applications of experiments that directly detect hydrogen-bonding interactions are discussed. These studies demonstrate how NMR spectroscopy can be used to distinguish between possible secondary structures and identify mechanisms of ligand binding in RNAs. A variety of recently developed methods for measuring base and sugar residual dipolar couplings are described. NMR residual dipolar coupling techniques provide valuable data for determining the long-range structure and orientation of helical regions in RNAs. A number of studies are also presented where residual dipolar coupling constraints are used to determine the global structure and dynamics of RNAs. NMR relaxation data can be used to probe the dynamics of macromolecules in solution. The power dependence of transverse rotating-frame relaxation rates was used here to study dynamics in the minimal hammerhead ribozyme. Improved methods for isotopically labeling RNAs combined with new types of structural data obtained from a growing repertoire of NMR experiments are facilitating structural and dynamic studies of larger RNAs.

Theoretical study of R1 ρ rotating-frame and R2 free-precession relaxation in the presence of n-site chemical exchange

The n-site Bloch–McConnell equations describe the evolution of nuclear spin magnetization in the laboratory or rotating frames of reference for molecules subject to chemical or conformational interconversions between n species with distinct NMR chemical shifts. Perturbation theory is used to approximate the largest eigenvalue of the Bloch–McConnell equations and obtain analytical expressions for the rotating-frame relaxation rate constant and for the laboratory frame resonance frequency and transverse relaxation rate constant. The perturbation treatment is valid whenever the population of one site is dominant. The new results are generally applicable to investigations of kinetic processes by NMR spectroscopy.

An NMR experiment for the accurate measurement of heteronuclear spin-lock relaxation rates.

Rotating-frame relaxation rates, R(1)(rho), are often measured in NMR studies of protein dynamics. We show here that large systematic errors can be introduced into measured values of heteronuclear R(1)(rho) rates using schemes which are usually employed to suppress cross-correlation between dipole-dipole and CSA relaxation mechanisms. For example, in a scalar-coupled two-spin X-H spin system the use of (1)H WALTZ16 decoupling or (1)H pulses applied at regularly spaced intervals leads to a significant overestimation of heteronuclear R(1)(rho) values. The problem is studied experimentally and theoretically for (15)N-(1)H and (13)C-(1)H spin pairs, and simple schemes are described which eliminate the artifacts. The approaches suggested are essential replacements of existing methodology if accurate dynamics parameters are to be extracted from spin-lock relaxation data sets.

Determination of T1 ρH Relaxation Rates in Charred and Uncharred Wood and Consequences for NMR Quantitation

The performance of three different techniques for determining proton rotating frame relaxation rates ( T 1 ρ H ) in charred and uncharred woods is compared. The variable contact time (VCT) experiment is shown to over-estimate T 1 ρH , particularly for the charred samples, due to the presence of slowly cross-polarizing 13C nuclei. The variable spin (VSL) or delayed contact experiment is shown to overcome these problems; however, care is needed in the analysis to ensure rapidly relaxing components are not overlooked. T 1 ρH is shown to be non-uniform for both charred and uncharred wood samples; a rapidly relaxing component ( T 1 ρH =0.46–1.07 ms) and a slowly relaxing component ( T 1 ρH =3.58–7.49) is detected in each sample. T 1 ρH for each component generally decreases with heating temperature (degree of charring) and the proportion of rapidly relaxing component increases. Direct T 1 ρH determination (via 1H detection) shows that all samples contain an even faster relaxing component (0.09–0.24 ms) that is virtually undetectable by the indirect (VCT and VSL) techniques. A new method for correcting for T 1 ρH signal losses in spin counting experiments is developed to deal with the rapidly relaxing component detected in the VSL experiment. Implementation of this correction increased the proportion of potential 13C CPMAS NMR signal that can be accounted for by up to 50% for the charred samples. An even greater proportion of potential signal can be accounted for if the very rapidly relaxing component detected in the direct T 1 ρH determination is included; however, it must be kept in mind that this experiment also detects 1H pools which may not be involved in 1H– 13C cross-polarization.