Cross-relaxation effects in stimulated-echo-type PGSE NMR experiments by bipolar and monopolar gradient pulses

Exchange of longitudinal spin polarization by dipolar cross relaxation between nonequivalent spins results in a modulation of the stimulated echo signal on increasing the encoding/decoding delays and in a multiexponential decay on increasing the diffusion time. These artifacts are suppressed by 180° pulses inserted in the middle of the gradient encoding/decoding periods. The efficiency of the gradient encoding is preserved if bipolar gradient pulses are used instead of monopolar pulses. The behavior of the different pulse sequences is demonstrated by ¹⁹F PGSE NMR experiments in a lyotropic liquid crystal in both isotropic micellar and oriented nematic phases.     

Deuterium stimulated-echo-type PGSE NMR experiments for measuring diffusion: application to a liquid crystal.

The accessibility of molecular self-diffusion coefficients in anisotropic materials, such as liquid crystals or solids, by stimulated-echo-type (2)H PGSE NMR is examined. The amplitude and phase modulation of the signal in the stimulated-echo-type sequence by the static quadrupole coupling during the encoding/decoding delays is suppressed by adjusting the pulse flip angles and the phase cycle. For nuclei that experience both nonnegligible quadrupole and dipole couplings, the application of magic echoes during the evolution periods of stimulated echo is demonstrated as a helpful technique in the case of slow diffusion. These findings are demonstrated by experimental results in the thermotropic liquid crystal of partially deuterated 8CB. The obtained diffusion coefficients are also compared to data obtained by a (1)H homonuclear-decoupling-type PGSE NMR method in the same material.     

13C PGSE NMR experiment with heteronuclear dipolar decoupling to measure diffusion in liquid crystals and solids

A new PGSE NMR experiment, designed to measure molecular diffusion coefficients in systems with nonvanishing static dipolar coupling, is described. The fast static dipolar dephasing of the single-quantum (13)C coherences is removed by multiple-pulse heteronuclear decoupling. The resulting slow dephasing of the (13)C coherences allows for inserting appropriate gradient pulses into the pulse sequence. The presence of the large magnetic field gradient reduces the efficiency of the decoupling sequences which is compensated for by introducing a scheme of sequential slice selection across the sample. The method is demonstrated by (19)F-decoupled (13)C PGSE NMR experiments in a lyotropic nematic and lamellar liquid crystal.     

Investigating 3He diffusion NMR in the lungs using finite difference simulations and in vivo PGSE experiments

Finite difference simulations have been used to model (3)He gas diffusion in simulated lung tissue. The technique has the advantage that a wide range of structural models and diffusion-sensitizing gradient waveforms can be investigated, for which analytical methods would otherwise be virtually impossible. Results from simulations and in vivo pulsed-gradient-spin-echo (PGSE) experiments show that the apparent diffusion coefficient (ADC) is a function of diffusion time and gradient strength, and suggests diffusion is locally anisotropic. The simulations have been compared to recent work on an analytical model that characterizes lung tissue as a series of independent cylinders. The results presented may have clinical implications for (3)He ADC measurements in assessing lung diseases such as chronic-obstructive-pulmonary-disease.     

Some perspectives on dispersion and the use of ensemble-averaged PGSE NMR

Magnetic resonance methodology has made a significant impact in helping us understand the physics of porous media. Among an important class of experiments is that set of techniques designed to measure fluid dispersion. This paper provides some background on some of the underlying physics of dispersion, and outlines some of the NMR approaches that have proven successful. The local and nonlocal dispersion tensors are described and the prospects for future NMR advances considered.     

MAG-PGSTE: a new STE-based PGSE NMR sequence for the determination of diffusion in magnetically inhomogeneous samples

A new stimulated echo based pulsed gradient spin-echo sequence, MAG-PGSTE, has been developed for the determination of self-diffusion in magnetically inhomogeneous samples. The sequence was tested on two glass bead samples (i.e., 212-300 and <106 microm glass bead packs). The MAG-PGSTE sequence was compared to the MAGSTE (or MPFG) (P.Z. Sun, J.G. Seland, D. Cory, Background gradient suppression in pulsed gradient stimulated echo measurements, J. Magn. Reson. 161 (2003) 168-173; P.Z. Sun, S.A. Smith, J. Zhou, Analysis of the magic asymmetric gradient stimulated echo sequence with shaped gradients, J. Magn. Reson. 171 (2004) 324-329; P.Z. Sun, Improved diffusion measurement in heterogeneous systems using the magic asymmetric gradient stimulated echo (MAGSTE) technique, J. Magn. Reson. 187 (2007) 177-183; P. Galvosas, F. Stallmach, J. K?rger, Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios, J. Magn. Reson. 166 (2004) 164-173, P. Galvosas, PFG NMR-Diffusionsuntersuchungen mit ultra-hohen gepulsten magnetischen Feldgradienten an mikropor?sen Materialien, Ph.D. Thesis, Universit?t Leipzig, 2003, P.Z. Sun, Nuclear Magnetic Resonance Microscopy and Diffusion, Ph.D. Thesis, Massachusetts Institute of Technology, 2003] sequence and Cotts 13-interval [R.M. Cotts, M.J.R. Hoch, T. Sun, J.T. Marker, Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems, J. Magn. Reson. 83 (1989) 252-266] sequence using both glass bead samples. The MAG-PGSTE and MAGSTE (or MPFG) sequences outperformed the Cotts 13-interval sequence in the measurement of diffusion coefficients; more interestingly, for the sample with higher background gradients (i.e., the <106 microm glass bead sample), the MAG-PGSTE sequence provided higher signal-to-noise ratios and thus better diffusion measurements than the MAGSTE and Cotts 13-interval sequences. In addition, the MAG-PGSTE sequence provided good characterization of the surface-to-volume ratio for the glass bead samples.     

Analysis of protein/ligand interactions with NMR diffusion measurements: the importance of eliminating the protein background

Pulsed-field gradient nuclear magnetic resonance (PFG-NMR) is a well-established method for the determination of translational diffusion coefficients. Recently, this method has found applicability in the combinatorial arena with the introduction of affinity NMR for characterizing protein/ligand interactions. Although affinity NMR has been reported to be an effective method for the identification of active compounds in a complex mixture, there are limitations of this method. We have developed a simple mathematical model to predict optimum concentration ratios of the ligand and protein in order to observe maximum changes in the ligand diffusion coefficient upon protein binding. The ligand/protein systems of L-tryptophan and ibuprofen binding to human serum albumin were chosen to demonstrate the usefulness of this model. However, even when the conditions of the mathematical model are satisfied, the spectral background arising from the protein in proton-detected experiments can be problematic. To this end, we have employed spectral subtraction of the protein spectrum to yield ligand diffusion coefficients that are in agreement with those predicted by simulation.     

Formation of p-cresol:piperazine complex in solution monitored by spin-lattice relaxation times and pulsed field gradient NMR diffusion measurements

A study of the nature of the anthelmintic p-cresol:piperazine complex in chloroform solution has been conducted using different NMR techniques: self-diffusion coefficients using DOSY; NOE, NULL, and double-selective T1 measurements to determine inter-molecular distances; and selective and non-selective T1 measurements to determine correlation times. The experimental results in solution and CP-MAS were compared to literature X-ray diffraction data using molecular modeling. It was shown that the p-cresol:piperazine complex exists in solution in a very similar manner as it does in the solid state, with one p-cresol molecule hydrogen bonded through the hydroxyl hydrogen to each nitrogen atom of piperazine. The close correspondence between the X-ray diffraction data and the inter-proton distances obtained by NULL and double selective excitation techniques indicate that those methodologies can be used to determine inter-molecular distances in solution.     

Improved diffusion-weighting efficiency of pulsed gradient stimulated echo MR measurements with background gradient cross-term suppression

Accurate diffusion measurements with pulsed gradient NMR are hampered by cross-terms of the diffusion-weighting and background gradients. For experiments based on a stimulated echo pulse sequence, that is preferred for samples with a T2 short compared to the diffusion time, a diffusion-weighting scheme has been presented that avoids these cross-terms in each of the en- and decoding periods separately. However, this approach suffers from a reduced diffusion-weighting efficiency because the two gradients applied in each of the periods have effectively opposite polarities leading to a partial cancellation. An extension of this scheme is presented that involves an additional gradient pulse in each period and delivers an improved diffusion-weighting efficiency without sacrificing the cross-term compensation. Analytical expressions for the gradient pulse lengths and amplitudes are given for arbitrary timing parameters. MR measurements with artificial (switched) background gradients were performed to test the cross-term compensation capability of the proposed extension. The results show that considerably higher q and b values can be achieved with the extension without changing the timing parameters. The MR measurements yielded identical diffusion coefficients without, with the same, and with different background gradients in the en- and decoding periods demonstrating the cross-term compensation of the presented approach.     

Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios

By evaluating the spin echo attenuation for a generalized 13-interval PFG NMR sequence consisting of pulsed field gradients with four different effective intensities (F(p/r) and G(p/r)), magic pulsed field gradient (MPFG) ratios for the prepare (G(p)/F(p)) and the read (G(r)/F(r)) interval are derived, which suppress the cross term between background field gradients and the pulsed field gradients even in the cases where the background field gradients may change during the z-store interval of the pulse sequence. These MPFG ratios depend only on the timing of the pulsed gradients in the pulse sequence and allow a convenient experimental approach to background gradient suppression in NMR diffusion studies with heterogeneous systems, where the local properties of the (internal) background gradients are often unknown. If the pulsed field gradients are centered in the tau-intervals between the pi and pi/2 rf pulses, these two MPFG ratios coincide to eta=G(p/r)/F(p/r)=1-8/[1+(1/3)(delta/tau)(2)]. Since the width of the pulsed field gradients (delta) is bounded by 0< or =delta< or =tau, eta can only be in the range of 5< or =-eta< or =7. The predicted suppression of the unwanted cross terms is demonstrated experimentally using time-dependent external gradients which are controlled in the NMR experiment as well as spatially dependent internal background gradients generated by the magnetic properties of the sample itself. The theoretical and experimental results confirm and extend the approach of Sun et al. (J. Magn. Reson. 161 (2003) 168), who recently introduced a 13-interval type PFG NMR sequence with two asymmetric pulsed magnetic field gradients suitable to suppress unwanted cross terms with spatially dependent background field gradients.     

Influence of steady background gradients on the accuracy of molecular diffusion anisotropy measurements

Spatial susceptibility variations of body components lead to local gradients of the static magnetic field. Effects of such background gradients on fractional diffusion anisotropy (FA) measurements on whole-body magnetic resonance units operating at 1.5, 3.0 and 7.0 T were analyzed theoretically and experimentally. Analytical expressions were derived for the cases of diffusion occurring in isotropic media and in tissues with cylindrical symmetry (e.g., white matter tracts or skeletal musculature). Typical magnitudes of background gradient strengths were estimated from in vivo and in vitro measurements with B0 field mapping sequences. Additionally, numerical simulations of magnetic field distributions and resulting field gradients were performed considering tissue-air interfaces in simplified geometrical arrangements. For media with isotropic diffusion, both measurements and analytical calculations showed increasing FA inaccuracy with stronger coupling between diffusion-encoding and background gradients. For cylindrical symmetry, FA values were estimated for a standard diffusion tensor imaging protocol in a realistic scenario. At 1 mm distance from a water-air interface, susceptibility-related background gradients amount to approximately 9 mT/m at 7 T and lead to a relative error of the measured FA of up to 48%. The error in the anisotropy assessment rises considerably with increasing field strength and must be taken into account especially for experimental and clinical studies on modern high-field systems.     

A new type of magnetic field gradient coil for NMR measurements

General expressions for the components of magnetic field and magnetic field gradient are given for polygonal gradient coils of the point-group symmetry D_n. It is shown that triangular coils (n = 3) are particularly suitable for NMR applications and supply the high and uniform value of the gradient over relatively great volume. Moreover, for n > 3, it is found that at the magic angle between symmetry axis C_n and axis Z, of external magnetic field B₀, the gradient of B_z is perpendicular to B₀. This new feature may be very useful in NMR spin-echo measurements of anisotropic translational diffusion.     

Pulsed field gradient magic angle spinning NMR self-diffusion measurements in liquids

Several investigations have recently reported the combined use of pulsed field gradient (PFG) with magic angle spinning (MAS) for the analysis of molecular mobility in heterogeneous materials. In contrast, little attention has been devoted so far to delimiting the role of the extra force field induced by sample rotation on the significance and reliability of self-diffusivity measurements. The main purpose of this work is to examine this phenomenon by focusing on pure liquids for which its impact is expected to be largest. Specifically, we show that self-diffusion coefficients can be accurately determined by PFG MAS NMR diffusion measurements in liquids, provided that specific experimental conditions are met. First, the methodology to estimate the gradient uniformity and to properly calibrate its absolute strength is briefly reviewed and applied on a MAS probe equipped with a gradient coil aligned along the rotor spinning axis, the so-called 'magic angle gradient' coil. Second, the influence of MAS on the outcome of PFG MAS diffusion measurements in liquids is investigated for two distinct typical rotors of different active volumes, 12 and 50 microL. While the latter rotor led to totally unreliable results, especially for low viscosity compounds, the former allowed for the determination of accurate self-diffusion coefficients both for fast and slowly diffusing species. Potential implications of this work are the possibility to measure accurate self-diffusion coefficients of sample-limited mixtures or to avoid radiation damping interferences in NMR diffusion measurements. Overall, the outlined methodology should be of interest to anyone who strives to improve the reliability of MAS diffusion studies, both in homogeneous and heterogeneous media.     

Probing lateral diffusion in lipid membranes on nanoscale by PFG NMR with high gradient strength

This work demonstrates the feasibility of noninvasive studies of diffusion on a submicrometer length scale in aligned model lipid membranes using pulsed field gradient nuclear magnetic resonance with ultrahigh (up to 35 T/m) gradient strength. Application of such gradients allows the use of sufficiently small diffusion times under conditions of narrow-pulse approximation. As a result, monitoring anomalous or restricted diffusion in lipid membranes on a length scale in the range of 100 nm becomes possible. The ability to study diffusion in lipid membranes on this length scale is very important because it is comparable with the size of biologically relevant domains (i.e., rafts), which are believed to exist in biomembranes.     

Effects of radiation damping on Z-spectra

Radiation damping induced by the strong water magnetization in Z-spectroscopy experiments can be sufficient to perturb significantly the resultant Z-spectrum. With a probe tuned to exact electrical resonance the effects are relatively straightforward, narrowing the central feature of the Z-spectrum. Where, as is commonly the case, the probe is tuned sufficiently well to give optimum signal-to-noise ratio and radiofrequency field strength but is not at exact resonance, radiation damping introduces an unexpected asymmetry into the Z-spectrum. This has the potential to complicate the use of Z-spectrum asymmetry to study chemical exchange, for example in the estimation of pH in vivo.     

New method of 1H NMR diffusion measurements in chiral liquid crystals

A novel method for diffusion measurements in chiral liquid crystals by means of ¹H NMR is proposed. The proton NMR signal caused by a special preparation pulse sequence is computed. We determine the component of the diffusion tensor in the direction of the cholesteric helix by fitting the calculated to corresponding experimental lineshapes. A time-resolved study is possible.     

Self-diffusion measurements by a mobile single-sided NMR sensor with improved magnetic field gradient

A simple and fast method of measuring self-diffusion coefficients of protonated systems with a mobile single-sided NMR sensor is discussed. The NMR sensor uses a magnet geometry that generates a highly flat sensitive volume where a strong and highly uniform static magnetic field gradient is defined. Self-diffusion coefficients were measured by Hahn- and stimulated echoes detected in the presence of the uniform magnetic field gradient of the static field. To improve the sensitivity of these experiments, a Carr-Purcell-Meiboom-Gill pulse sequence was applied after the main diffusion-encoding period. By adding the echo train the experimental time was strongly shortened, allowing the measurement of complete diffusion curves in less than 1min. This method has been tested by measuring the self-diffusion coefficients D of various organic solvents and poly(dimethylsiloxane) samples with different molar masses. Diffusion coefficients were also measured for n-hexane absorbed at saturation in natural rubber with different cross-link densities. The results show a dependence on the concentration that is in good agreement with the theoretical prediction. Moreover, the stimulated-echo sequence was successfully used to measure the diffusion coefficient as a function of the evolution time in systems with restricted diffusion. This type of experiment proves the pore geometry and gives access to the surface-to-volume ratio. It was applied to measure the diffusion of water in sandstones and sheep Achilles tendon. Thanks to the strong static gradient G(0), all diffusion coefficients could be measured without having to account for relaxation during the pulse sequence.     

Macroscopic and Microscopic Fields in High-Resolution Liquid NMR

The microscopic magnetic-induction field “seen by each nucleus” in a material medium and which is generated by a rapidly time-dependent spin magnetization gives rise to surprising new features in high-resolution nuclear magnetic resonance experiments. The purpose of the present paper is to show how the relations between the macroscopic average fields, the magnetization, and the microscopic fields (which were studied and clarified long ago at thermal equilibrium) can be extended to the present NMR context in which the magnetization can become rapidly time dependent and unrelated to thermal equilibrium properties.