Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms: Planar, Cylindrical, and Spherical Pores with Wall Relaxivity

A simple matrix formalism presented by Callaghan [J. Magn. Reson.129, 74–84 (1997)], and based on the multiple propagator approach of Caprihanet al.[J. Magn. Reson. A118, 94–102 (1996)], allows for the calculation of the echo attenuation,E(q), in spin echo diffusion experiments, for practically all gradient waveforms. We have extended the method to the treatment of restricted diffusion in parallel plate, cylindrical, and spherical geometries, including the effects of fluid–surface interactions. In particular, theq-space coherence curves are presented for the finite-width gradient pulse PGSE experiment and the results of the matrix calculations compare precisely with published computer simulations. It is shown that the use of long gradient pulses (δ a²/D) create the illusion of smaller pores if a narrow pulse approximation is assumed, while ignoring the presence of significant wall relaxation can lead to both an underestimation of the pore dimensions and a misidentification of the pore geometry.     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

A Pulsed Field Gradient Spin-Echo Method for Diffusion Measurements in the Presence of Internal Gradients

Over the past decade several pulsed field gradient stimulated-echo methods have been presented for diffusion measurements in heterogeneous media. These methods have reduced or eliminated the coupling between the applied magnetic field gradient and a constant internal magnetic field gradient caused by susceptibility changes throughout the sample. For many research purposes thez-storage delay between the second and third π/2 RF pulse has been included in order to increase the decay of the echo attenuation to an appropriate level and to increase the signal-to-noise ratio by avoidingT₂relaxation of the magnetization in parts of the pulse sequence. For these reasons a stimulated-echo method has been applied instead of a spin-echo method. When studying systems where it is necessary to keep the duration of the pulse sequence at a minimum, and one is not dependent on usingz-storage time to increase the echo attenuation or to study diffusion as a function of observation time, a spin-echo method should be chosen. Here we propose a bipolar pulsed field gradient spin-echo method which is well suited to this purpose, and preliminary diffusion measurements are presented as illustration.     

Accurate Measurement of Small Spin–Spin Couplings in Partially Aligned Molecules Using a Novel J-Mismatch Compensated Spin-State-Selection Filter

The accurate measurement of small spin–spin coupling constants in macromolecules dissolved in a liquid crystalline phase is important in the context of molecular structure investigation by modern liquid state NMR. A new spin-state-selection filter, DIPSAP, is presented with significantly reduced sensitivity to J-mismatch of the filter delays compared to previously proposed pulse sequences. DIPSAP presents an attractive new approach for the accurate measurement of small spin–spin coupling constants in molecules dissolved in anisotropic solution. Application to the measurement of ¹⁵N–¹³C′ and ¹H^N–¹³C′ coupling constants in the peptide planes of ¹³C, ¹⁵N labeled proteins demonstrates the high accuracy obtained by a DIPSAP-based experiment.     

C-NOESY-HSQC with Split Carbon Evolution for Increased Resolution with Uniformly Labeled Proteins

Two new pulse sequences are presented for the recording of 2D¹³C-HSQC and 3D¹³C-NOESY-HSQC experiments, containing two consecutive carbon evolution periods. The two periods are separated by az-filter which creates a clean C_xH_z-quantum state for evolution in the second period. Each period is incremented (in anon-constant-time fashion) only to the extent that the defocusing of carbon inphase magnetization throughJ-coupling with neighboring carbons remains insignificant. Therefore,¹³C homonuclearJ-couplings are rendered ineffective, reducing the loss of signal and peak splitting commonly associated with long¹³C evolution times. The two periods are incremented according to a special acquisition protocol employing a¹³C–¹³C gradient echo to yield a data set analogous to one obtained by evolution over the added duration of both periods. The spectra recorded with the new technique on uniformly¹³C-labeled proteins at twice the evolution time of the standard¹³C-HSQC experiment display a nearly twofold enhancement of resolution in the carbon domain, while maintaining a good sensitivity even in the case of large proteins. Applied to the IIA^Manprotein ofE. coli(31 kDa), the¹³C-HSQC experiment recorded with a carbon evolution time of 2 × 8 ms showed a 36% decrease in linewidths compared to the standard¹³C-HSQC experiment, and theS/Nratio of representative cross-peaks was reduced to 40%. This reduction reflects mostly the typical loss of intensity observed when recording with an increased resolution. The¹³C-NOESY-HSQC experiment derived from the¹³C-HSQC experiment yielded additional NOE restraints between resonances which previously had been unresolved.     

In Vivo3D LocalizedC Spectroscopy Using Modified INEPT and DEPT

The 3D localized¹³C spectroscopy methods LINEPT and LODEPT, which are modifications of INEPT and DEPT, are proposed. As long as a¹³C inversion pulse (180-degree pulse) is applied at 1/(4J) before the proton echo time in LINEPT and a¹³C excitation pulse (90-degree pulse) is applied at 1/(2J) before the proton echo time in LODEPT, the proton echo time can be set to any value longer than 1/(2J) in LINEPT and longer than 1/Jin LODEPT. As a result, the proton and the¹³C pulses can be applied separately and these proton pulses can be made slice-selective pulses. These localization features of LINEPT and LODEPT were evaluated using a phantom consisting of a cylinder filled with ethanol placed inside another cylinder filled with oil, and localized ethanol spectra could be obtained.In vivo3D localized¹³C spectra from the brain of a monkey could be obtained using decoupled LINEPT, and glutamate C-4 appeared directly after the administration of glucose C-1, followed by the appearance of glutamate C-2, C-3 and glutamine C-2, C-3, C-4.     

More line narrowing in TROSY by decoupling of long-range couplings: shift correlation and JNC′ coupling constant measurements

Since the introduction of RDCs in high-resolution NMR studies of macromolecules, there is a growing interest in the development of accurate, and sensitive methods for determining coupling constants. Most methods for extracting these couplings are based on the measurement of the splitting between multiplet components in J-coupled spectra. However, these methods are often unreliable since undesired multiple-bond couplings can considerably broaden the multiplet components and consequently make accurate determination of their position difficult. To demonstrate one approach to this problem, G-BIRD^(r) decoupled TROSY sequences are proposed for the measurement of ¹J_NH and ¹J_NC′ coupling constants. Resolved or unresolved splittings due to remote protons are removed by a G-BIRD^(r) module employed during t₁ and as a result, spectra with narrow, well-resolved peaks are obtained from which heteronuclear one-bond couplings can be accurately measured. Moreover, introduction of a spin-state-selective α/β-filter in the TROSY sequence allows the separation of the ¹J_NC′ doublet components into two subspectra which contain the same number of peaks as the regular TROSY spectrum. The ¹J_NC′ couplings are obtained from the displacement between the corresponding peaks in the subspectra.     

A k-Space Analysis of MR Tagging

We present a k-space approximation that directly relates a pulse sequence to its residual pattern of z-directed magnetization M_z, in a manner akin to the k-space approximation for small tip-angle excitation. Our approximation is particularly useful for the analysis and design of tagging sequences, in which M_z is the important quantity—as opposed to the transverse magnetization components M_x and M_y considered in selective excitation. We demonstrate that our approximation provides new insights into tagging, can be used to design novel tag patterns, and, more generally, may be applied to selective presaturation sequences for purposes other than tagging.     

Contributions of Spin–Lattice Relaxation to the Echo Decay of Planar Cu in High-Temperature Superconductors

Measurement ofT_2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT_2Gand show thatT_2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa₂Cu₄O₈, we find a correction on the order of 10% inT_2Gand using the corrected values we find that the isotope ratio⁶³T_2G/⁶⁵T_2Gagrees with theory.     

Rotating-Frame-Imaging Technique for Spatially Resolved Diffusion and Flow Studies in the Fringe Field of RF Probe Coils

A method for rotating-frame NMR diffusometry in the fringe-fieldB₁gradients of solenoid RF coils in standard probeheads is described. A 5 mm RF solenoid coil, for instance, producesB₁gradients of up to 3.3 T/m. The gradients can be enhanced by so-called flux concentrators so that values comparable to those common in laboratory-frame PGSE experiments should be feasible. The principle of the technique is to produce azmagnetization grid with the aid of aB₁gradient pulse. The wavenumber of the grid is varied by the length of the preparation pulse. After a certain diffusion delay, the grid is rendered as an image using a rapid rotating-frame-imaging technique. TheB₁gradient need not be constant. Diffusion coefficients are rather evaluated locally based on the localB₁gradients. Single-transient diffusion experiments in toroid resonators, and the employment of theB₁gradients produced by the skin effect of conducting materials are suggested.     

Determination of NMR cogwheel phase cycle with XML

The selection of correct coherence transfer pathways is an essential component of an NMR pulse sequence. This article describes a new method based on the use of web tools (eXtensible Markup Language and eXtensible Stylesheet Language Transformation) to generate a cogwheel phase cycle for selecting coherence transfer pathways. We illustrate this method with the three-pulse phase-modulated shifted-echo or split-t₁ MQMAS sequences for triple-quantum spin-3/2 systems. After generalization to the different half-integer quadrupole spins, we use the SIMPSON program to confirm our results. Finally, we apply our method to the case of the z-filter 3QMAS sequence for I=3/2 systems.     

Proton Diffusion andT1Relaxation in Polyacrylamide Gels: A Unified Approach Using Volume Averaging

The structure of polyacrylamide gels was studied using proton spin–lattice relaxation and PFG diffusion methods. Polyacrylamide gels, with total polymer concentrations ranging from 0.25 to 0.35 g/ml and crosslinker concentrations from 0 to 10% by weight, were studied. The data showed no effect of the crosslinker concentration on the diffusion of water molecules. The Ogston–Morris and Mackie–Meares models fit the general trends observed for water diffusion in gels. The diffusion coefficients from the volume averaging method also fit the data, and this theory was able to account for the effects of water-gel interactions that are not accounted for in the other two theories. The averaging theory also did not require the physically unrealistic assumption, required in the other two theories, that the acrylamide fibers are of similar size to water molecules. Contrary to the diffusion data,T₁relaxation measurements showed a significant effect of crosslinker concentration on the relaxation of water in gels. The model developed using the Bloch equations and the volume averaging method described the effects of water adsorption on the gel medium on both the diffusion coefficients and the relaxation measurements. In the proposed model the gel medium was assumed to consist of three phases (i.e., bulk water, uncrosslinked acrylamide fibers, and a bisacrylamide crosslinker phase). The effects of the crosslinker concentration were accounted for by introducing the proton partition coefficient,K^eq, between the bulk water and crosslinker phase. The derived relaxation equations were successful in fitting the experimental data. The partition coefficient,K^eq, decreased significantly as the crosslinker concentration increased from 5 to 10% by weight. This trend is consistent with the idea that bisacrylamide tends to form hydrophobic regions with increasing crosslinker concentration.     

29Si NMR in solid state with CPMG acquisition under MAS

A remarkable enhancement of sensitivity can be often achieved in ²⁹Si solid-state NMR by applying the well-known Carr–Purcell–Meiboom–Gill (CPMG) train of rotor-synchronized π pulses during the detection of silicon magnetization. Here, several one- and two-dimensional (1D and 2D) techniques are used to demonstrate the capabilities of this approach. Examples include 1D ²⁹Si{X} CPMAS spectra and 2D ²⁹Si{X} HETCOR spectra of mesoporous silicas, zeolites and minerals, where X = ¹H or ²⁷Al. Data processing methods, experimental strategies and sensitivity limits are discussed and illustrated by experiments. The mechanisms of transverse dephasing of ²⁹Si nuclei in solids are analyzed. Fast magic angle spinning, at rates between 25 and 40 kHz, is instrumental in achieving the highest sensitivity gain in some of these experiments. In the case of ²⁹Si–²⁹Si double-quantum techniques, CPMG detection can be exploited to measure homonuclear J-couplings.     

Erratum to: Hydrodynamic dispersion in $ \beta$-lactoglobulin gels measured by PGSE NMR

The displacement scale dependent molecular dynamics of solvent water molecules flowing through b \beta -lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.     

The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: experiments and simulations

q-Space diffusion MRI (QSI) provides a means of obtaining microstructural information about porous materials and neuronal tissues from diffusion data. However, the accuracy of this structural information depends on experimental parameters used to collect the MR data. q-Space diffusion MR performed on clinical scanners is generally collected with relatively long diffusion gradient pulses, in which the gradient pulse duration, δ, is comparable to the diffusion time, Δ. In this study, we used phantoms, consisting of ensembles of microtubes, and mathematical models to assess the effect of the ratio of the diffusion time and the duration of the diffusion pulse gradient, i.e., Δ/δ, on the MR signal attenuation vs. q, and on the measured structural information extracted therefrom. We found that for Δ/δ  1, the diffraction pattern obtained from q-space MR data are shallower than when the short gradient pulse (SGP) approximation is satisfied. For long δ the estimated compartment size is, as expected, smaller than the real size. Interestingly, for Δ/δ  1 the diffraction peaks are shifted to even higher q-values, even when δ is kept constant, giving the impression that the restricted compartments are even smaller than they are. When phantoms composed of microtubes of different diameters are used, it is more difficult to estimate the diameter distribution in this regime. Excellent agreement is found between the experimental results and simulations that explicitly account for the use of long duration gradient pulses. Using such experimental data and this mathematical framework, one can estimate the true compartment dimensions when long and finite gradient pulses are used even when Δ/δ  1.     

Hydrodynamic dispersion in $ \beta$ -lactoglobulin gels measured by PGSE NMR

The displacement scale dependent molecular dynamics of solvent water molecules flowing through b \beta -lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.     

Iterative Lineshape Fitting of MAS NMR Spectra: A Tool to Investigate HomonuclearJCoupling in Isolated Spin Pairs

Possibilities and limitations of iterative lineshape fitting procedures of MAS NMR spectra of isolated homonuclear spin pairs, aiming at determination of magnitudes and orientations of the various interaction tensors, are explored. Requirements regarding experimental MAS NMR spectra as well as simulation and fitting procedures are discussed. Our examples chosen are the isolated³¹P spin pairs in solid Na₄P₂O₇· 10H₂O, (1), and Cd(NO₃)₂· 2PPh₃, (2). In both cases the two³¹P chemical shielding tensors in the molecular unit are related byC₂symmetry, and determination of the orientations of these two tensors in the molecular frame is possible. In addition, aspects of homonuclearJcoupling will be addressed. For 1, both magnitude and sign of²J_iso(³¹P,³¹P) (J_iso= −19.5 ± 2.5 Hz) are obtained; for 2, (J_iso= +139 ± 3 Hz) anisotropy ofJwith an orientation of theJ-coupling tensor collinear, or nearly collinear, with the dipolar coupling tensor can be excluded, while absence or presence of anisotropy ofJwith any other relative orientation of theJ-coupling tensor cannot be determined.