Removal of J-coupling peak distortion in PGSE experiments

Peak distortion caused by homonuclear J-coupling is a major problem that limits the utility of the pulsed-field gradient spin–echo (PGSE) method for studying translational diffusion. This unwanted effect can be removed by incorporation of anti-phase magnetization purging pulse elements at the end of the spin–echo sequence. Three methods, namely, trim-pulse, homospoil pulse gradient and chirp based z-filter were evaluated as potential candidates for an improved NMR diffusion method that is less sensitive to J-coupling peak distortion. The chirp based z-filter was found to be excellent in suppressing anti-phase magnetization while leaving the in-phase magnetization basically intact in spin–echo and stimulated-echo based experiments. The incorporation of chirp based z-filter into PGSE could allow diffusion analysis that would otherwise be impossible by conventional means.     

Cross-Relaxation Effects in Pulsed-Field-Gradient Stimulated-Echo Measurements on Water in a Macromolecular Matrix

Water diffusion in poly[2-hydroxyethyl-methacrylate] hydrogels has been measured by PFG NMR techniques, using both spin-echo and stimulated-echo methods. It is found that the results differ when evaluated using the standard equations for the echo attenuation. Furthermore, an apparent dependence of the diffusion coefficient on the diffusion time was found in stimulated-echo experiments. This effect is shown to be caused by cross relaxation between the protons of the water and those on the polymer matrix. An equation is derived describing the attenuation of a stimulated echo in the presence of cross relaxation. This equation shows that the additional damping due to cross relaxation depends on the gradient amplitude. If this equation is used with the measured cross-relaxation parameters, both methods are found to agree within experimental error, and no diffusion-time dependence is found for the stimulated-echo experiments. The equation predicts the effect of replacing part of the H₂O by D₂O; this has been experimentally verified. It is concluded that macromolecular systems should be checked for cross relaxation when stimulated-echo methods will be used for self-diffusion measurements.     

MQ-PGSTE: A new multi-quantum STE-based PGSE NMR sequence

A new multi-quantum stimulated echo based pulsed gradient spin-echo sequence, MQ-PGSTE, has been developed for measuring translational diffusion. The new sequence provides a higher signal-to-noise ratio than the (Hahn spin-echo based) MAXY-D sequence at long diffusion times, and thus potentially affords better diffusion measurements on macromolecule samples. Based on multi-quantum coherence encoding, the MQ-PGSTE sequence needs considerably lower gradient strengths for diffusion characterization compared to standard single quantum pulsed gradient spin-echo sequences. By using the new sequence, the diffusion coefficient of l-[3-¹³C]-alanine was found to be 8.1 ± 0.1 × 10⁻¹⁰ m² s⁻¹, which is in line with the value obtained by the use of the standard stimulated echo based pulsed gradient spin-echo sequence.     

Improved convection compensating pulsed field gradient spin-echo and stimulated-echo methods

The need for convection compensating methods in NMR has been manifested through an increasing number of publications related to the subject over the past few years (J. Magn. Reson. 125, 372 (1997); 132, 13 (1998); 131, 126 (1998); 118, 50 (1996); 133, 379 (1998)). When performing measurements at elevated temperature, small convection currents may give rise to erroneous values of the diffusion coefficient. In work with high resolution NMR spectroscopy, the application of magnetic field gradients also introduces an eddy-current magnetic field which may result in errors in phase and baseline in the FFT-spectra. The eddy current field has been greatly suppressed by the application of bipolar magnetic field gradients. However, when introducing bipolar magnetic field gradients, the pulse sequence is lengthened significantly. This has recently been pointed out as a major drawback because of the loss of coherence and of NMR-signal due to transverse relaxation processes. Here we present modified convection compensating pulsed field gradient double spin echo and double stimulated echo sequences which suppress the eddy-current magnetic field without increasing the duration of the pulse sequences.     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.     

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.     

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.     

Probing short length scales with restricted diffusion in a static gradient using the CPMG sequence

We experimentally verify a new method of extracting the surface-to-volume ratio (S/V) of porous media with diffusion NMR. In contrast to the widely used pulsed field gradient (PFG) technique, which employs the stimulated echo coherence pathway, we use here the direct Carr-Purcell-Meiboom-Gill (CPMG) path. Even for high echoes, which exhibit ample attenuation due to diffusion in the field gradient, the relevant ruler length for the direct pathway is fixed by the diffusion length during a single inter-pulse spacing. The direct path, therefore, is well suited for probing shorter length scales than is possible with the conventional approach. In our experiments in a low-field static-gradient system, the direct CPMG pathway was found to be sensitive to structure an order of magnitude smaller than accessible with the stimulated-echo pathway.     

Emulation of petroleum well-logging D-T2 correlations on a standard benchtop spectrometer

An experimental protocol is described that allows two-dimensional (2D) nuclear magnetic resonance (NMR) correlations of apparent diffusion coefficient D_app and effective transverse relaxation time T_2,eff to be acquired on a bench-top spectrometer using pulsed field gradients (PFG) in such a manner as to emulate D_app − T_2,eff correlations acquired using a well-logging tool with a fixed field gradient (FFG). This technique allows laboratory-scale NMR measurements of liquid-saturated cored rock to be compared directly to logging data obtained from the well by virtue of providing a comparable acquisition protocol and data format, and hence consistent data processing. This direct comparison supports the interpretation of the well-logging data, including a quantitative determination of the oil/brine saturation. The D − T₂ pulse sequence described here uses two spin echoes (2SE) with a variable echo time to encode for diffusion. The diffusion and relaxation contributions to the signal decay are then deconvolved using a 2D numerical inversion. This measurement allows shorter relaxation time components to be probed than in conventional diffusion measurements. A brief discussion of the numerical inversion algorithms available for inverting these non-rectangular data is included. The PFG-2SE sequence described is well suited to laboratory-scale studies of porous media and short T₂ samples in general.     

A modified PGSE for measuring diffusion in the presence of static magnetic field gradients

With a proper timing of pi pulses, it is possible to reduce the effect of the static internal magnetic field gradient on the measurement of diffusion with the pulsed gradient spin echo (PGSE). A pulse sequence that in the first order eliminates the effect of weak internal static gradients in a standard PGSE experiment is introduced. The method should be applied in the cases, where strong and short magnetic gradient pulses are used to investigate the motion of liquid in heterogeneous samples with large susceptibility differences such as porous media.     

Constant gradient stimulated echo studies of diffusion in porous materials at high spectrometer fields

A high field strength, constant gradient stimulated-echo pulse sequence is applied to a model heterogeneous system consisting of randomly packed beds of glass microspheres. A multiple exponential analysis of the dependence of the stimulated echo amplitude on diffusion time, Δ, yields coefficients that depend explicitly on both the wavevector, q and on the time delay, δ. The wavevector and δ-dependence of the coefficients is analyzed both theoretically and experimentally and shown to be sensitive to the effects of coupled relaxation and diffusion. It is proposed that these effects could be exploited as a new probe of microstructure.     

PGSTE-WATERGATE: an STE-based PGSE NMR sequence with excellent solvent suppression

A new stimulated-echo based pulsed gradient spin-echo NMR diffusion sequence incorporating WATERGATE solvent suppression, PGSTE-WATERGATE, is presented. The sequence provides superb solvent suppression without any phase distortions. The sequence is simple to set up and particularly suited to measuring diffusion coefficients in aqueous solution such as is commonly required in pharmaceutical and combinatorial applications. The utility of the sequence is demonstrated on samples containing lysozyme and sucrose. Importantly, the high degree of phase-distortion suppression allows more complicated selective pi pulses to be used to enhance the selectivity of solvent suppression.     

1H NMR signal broadening in spectra of alkane molecules adsorbed on MFI-type zeolites

The anisotropic behavior of C1-C6 alkane molecules adsorbed in MFI zeolite was studied by 1H nuclear magnetic resonance (NMR) using single-pulse excitation, Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence, Hahn echo (HE) pulse sequence, and magic-angle spinning. The molecular order parameter was obtained by both static 2H NMR spectroscopy and molecular simulations. This yields an order parameter in the range of 0.28-0.42 for linear alkanes in MFI zeolite, whereas the parameter equals zero for FAU zeolite with a cubic symmetry. Thus, in the case of a zeolite with a non-cubic symmetry like MFI, the mobility of the molecules in one crystallite cannot fully average the dipolar interaction. As a consequence, transverse nuclear magnetization as revealed in the echo attenuation notably deviates from a mono-exponential decay. This information is of particular relevance for the performance of pulsed field gradient (PFG) NMR diffusion experiments, since the occurrence of non-exponential magnetization attenuation could be taken as an indication of the existence of different molecules or of molecules in different states of mobility.     

Diffusion measurements using the nonlinear stimulated echo

The nonlinear stimulated echo that is generated by a sequence of three radiofrequency pulses, 90 degrees-tau(1)-90 degrees-tau(2)-45 degrees, in high magnetic fields (or at low temperatures) in the presence of pulsed or steady field gradients can be applied for measurements of the diffusion coefficient. Corresponding test experiments are reported. Steady gradients can be used without knowledge of the relaxation times. Remarkably the attenuation of the nonlinear stimulated echo by diffusion is substantially stronger than in the case of the ordinary stimulated echo.     

D-T2二维核磁共振脉冲序列及反演方法改进设计

面对日益复杂的勘探对象, D-T₂二维核磁共振技术在实际应用中面临无法兼顾扩散系数测量范围和横向弛豫分辨率的困境. 脉冲序列作为D-T₂二维核磁共振数据采集的核心技术, 其性能优劣直接影响应用效果, 在综合对比PFG, STE-PFG, BP-PFG、改良式CPMG, 扩散编程, 多回波间隔CPMG脉冲序列性能的基础上, 有效融合脉冲梯度场、恒定梯度场D-T₂脉冲序列的优点, 本文提出一种基于脉冲梯度场的双变量、两窗口D-T₂脉冲序列改进设计. 针对两个窗口的D-T₂二维核磁共振数据反演, 为突破现有反演方法无法兼顾反演精度和解谱效率的瓶颈, 本着第二个窗口回波信号为主、第一个窗口回波信号为辅的原则, 本文提出一种同时使用两个窗口数据参与解谱的联合TSVD反演方法. 气水、油水、稠油、油气水模型不同信噪比条件下的数值模拟结果表明, 本文提供的D-T₂改进脉冲序列达到了平衡扩散系数测量范围和横向弛豫分辨率的设计要求, 本文提供的联合TSVD反演方法也有效平衡了反演精度要求和解谱效率. 文中的D-T₂改进脉冲序列及联合TSVD反演方法在复杂油气藏流体识别和产能预测中具有广泛的应用前景, 可为促进国内D-T₂二维核磁共振岩心分析技术的发展提供有利条件.     

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.     

A mixed basis approach in the SGP-limit

A perturbation method for computing quick estimates of the echo decay in pulsed spin echo gradient NMR diffusion experiments in the short gradient pulse limit is presented. The perturbation basis involves (relatively few) dipole distributions on the boundaries generating a small perturbation matrix in O(s²) time, where s denotes the number of boundary elements. Several approximate eigenvalues and eigenfunctions to the diffusion operator are retrieved. The method is applied to 1D and 2D systems with Neumann boundary conditions.     

Determination of water self-diffusion coefficient in complex food products by low field 1H PFG-NMR: comparison between the standard spin-echo sequence and the T1-weighted spin-echo sequence

In 1990, Van Den Enden et al. proposed a method for the determination of water droplet size distributions in emulsions using a pulsed-field-gradient nuclear magnetic resonance (PFG-NMR) T1-weighted stimulated-echo technique. This paper describes both the T1-weighted spin-echo sequence, an improved method based on this earlier work, and, the standard PFG spin-echo sequence. These two methods were compared for water self-diffusion coefficient measurement in the fatty protein concentrate sample used as a 'cheese model.' The transversal and longitudinal relaxation parameters T1 and T2 were determined according to the temperature and investigated for each sample; fat-free protein concentrate sample, pure anhydrous milk fat, and fatty protein concentrate sample. The water self-diffusion in fat-free protein concentrate samples followed a linear behavior. Consequently, the water self-diffusion coefficient could be easily characterized for fat-free protein concentrate samples. However, it seemed more complicated to obtain accurate water self-diffusion in fatty protein concentrate samples since the diffusion-attenuation data were fitted by a bi-exponential function. This paper demonstrates that the implementation of the T1-weighted spin-echo sequence, using the different T1 properties of water and fat phases, allows the accurate determination of water self-diffusion coefficient in a food product. To minimize the contribution of the 1H nuclei in the fat phase on the NMR echo signal, the fat protons were selectively eliminated by an additional 180 degrees pulse. This new method reduces the standard errors of diffusion data obtained with a basic spin-echo technique, by a factor of 10. The effectiveness of the use of the T1-weighted spin-echo sequence to perform accurate water self-diffusion coefficients measurement in fatty products is thus demonstrated.     

Microscopic displacement imaging with pulsed field gradient turbo spin-echo NMR

We present a pulse sequence that enables the accurate and spatially resolved measurements of the displacements of spins in a variety of (biological) systems. The pulse sequence combines pulsed field gradient (PFG) NMR with turbo spin-echo (TSE) imaging. It is shown here that by ensuring that the phase of the echoes within a normal spin-echo train is constant, displacement propagators can be generated on a pixel-by-pixel basis. These propagators accurately describe the distribution of displacements, while imaging time is decreased by using separate phase encoding for every echo in a TSE train. Measurements at 0.47 T on two phantoms and the stem of an intact tomato plant demonstrate the capability of the sequence to measure complete and accurate propagators, encoded with 16 PFG steps, for each pixel in a 128 x 128 image (resolution 117 x 117 x 3,000 microm) within 17 min. Dynamic displacement studies on a physiologically relevant time resolution for plants are now within reach.     

Accurate measurement of translational diffusion coefficients: a practical method to account for nonlinear gradients

For NMR probes equipped with pulsed field gradient coils, which are not optimized for gradient linearity, the precision and accuracy of experimentally measured translational diffusion coefficients are limited by the linearity of the gradient pulses over the sample volume. This study shows that the accuracy and precision of measured diffusion coefficients by the Stejskal--Tanner spin-echo pulsed field gradient experiment can be significantly improved by mapping the gradient z-profile and by using the mapped calibration parameters in the data analysis. For practical applications the gradient distribution may be approximated by a truncated linear distribution defined by minimum and maximum values of the gradient. By including the truncated linear gradient distribution function in the Stejskal--Tanner equation, the systematic deviation between the fitted curve and the experimental attenuation curve decreases by an order of magnitude. The gradient distribution may be calibrated using an intense NMR signal from a sample with a known diffusion coefficient. The diffusion coefficient of an unknown sample may then be determined from a two-parameter fit, using the known gradient distribution function.