Determination of genuine diffusivities in heterogeneous media using stimulated echo pulsed field gradient NMR

Pulsed field gradient (PFG) NMR diffusion measurements in heterogeneous media may lead to erroneous results due to the disturbing influence of internal magnetic field gradients. Here, we present a simple theoretical model which allows one to interpret data obtained by stimulated spin echo PFG NMR in the presence of spatially varying internal field gradients. Using the results of this theory, the genuine self-diffusion coefficients in heterogeneous media may be extrapolated from the dependence of the apparent diffusivities on the dephasing time of the simulated echo PFG NMR sequence. Experimental evidence that such extrapolation yields satisfactory results for self-diffusion of hexadecane in natural sediments (sand) and of n-octanol in doped MgO pastes is provided.     

Nuclear magnetic resonance in inhomogeneous magnetic fields

The response of the spin system has been investigated by numerical simulations in the case of a nuclear magnetic resonance (NMR) experiment performed in inhomogeneous static and radiofrequency fields. The particular case of the NMR-MOUSE was considered. The static field and the component of the radiofrequency field perpendicular to the static field were evaluated as well as the spatial distribution of the maximum NMR signal detected by the surface coil. The NMR response to various pulse sequences was evaluated numerically for the case of an ensemble of isolated spins (1/2). The behavior of the echo train in Carr-Purcell-like pulse sequences used for measurements of transverse relaxation and self-diffusion was simulated and compared with the experiment. The echo train is shown to behave qualitatively differently depending on the particular phase schemes used in these pulse sequences. Different echo trains are obtained, because of the different superposition of Hahn and stimulated echoes forming mixed echoes as a result of the spatial distribution of pulse flip angles. The superposition of Hahn and stimulated echoes originating from different spatial regions leads to distortions of the mixed echoes in intensity, shape, and phase. The volume selection produced by Carr-Purcell-like pulse sequences is also investigated for the NMR-MOUSE. The developed numerical simulation procedure is useful for understanding a variety of experiments performed with the NMR-MOUSE and for improving its performance. Copyright 2000 Academic Press.     

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.     

The elimination of magnetic susceptibility artifacts in the micro-image of liquid-solid interfaces: internal gradient modulation by the CPMG RF train

Distortions of magnetic resonance images near solid-liquid interface appear as the result of the restriction to spin self-diffusion in the proximity of impermeable boundary as well as of a susceptibility difference. The spectral analysis of spin echo enables to resolve, in a simple way, how various RF-gradient pulse sequences reduce the effect of the internal magnetic field induced by the susceptibility difference at interfaces. The 1D diffusion-weighted imaging of water in the narrow notch tested efficiency of some sequence. The notch was milled in a piece of Plexiglas. The method can be used to distinguish the susceptibility effect from the effects of applied gradients when investigating the transport of fluid through a porous structure.     

Homonuclear vanadium-51 dipolar couplings in inorganic solids obtained via hahn spin echo decay NMR spectroscopy

Dipolar dephasing of the magnetization following a Hahn spin echo pulse sequence potentially provides a quantitative means for determining the dipolar second moment in solids. In this work, the possibility of employing Hahn spin echo decay spectroscopy to obtain quantitative ⁵¹V–⁵¹V dipolar second moments is explored. Theoretical spin echo response curves are compared to experimental ones for a collection of crystalline vanadium-containing compounds. This work suggests that ⁵¹V dipolar second moments can be obtained by selectively exciting the central m = 1/2 → −1/2 by a Hahn echo sequence for vanadate compounds with line broadening no greater than approximately 220 ppm. For vanadates with greater broadening of the central transition due to chemical shift, second-order quadrupolar, and dipolar interactions, off-resonance effects lead to an oscillatory time dependence of the spin echo. Experimentally determined second moments of the normalized echo decay intensities lie within 10–33% of the calculated values if the second moments are extrapolated to zero evolution time due to the time scale dependence of spin exchange among neighboring vanadium nuclei. Alternatively, the second moments can be obtained to within 10–25% of the calculated values if the broadening of the central transition due to chemical shift and second-order quadrupolar effects can be estimated.     

Applications of fast diffusion measurement using Difftrain

Novel applications of fast self-diffusion measurement are presented. Difftrain (Diffusion train), which uses successive stimulated echoes from a single excitation pulse where a portion of the available magnetisation is recovered for each echo, is used to measure self-diffusion by varying the observation time. It is applied to produce the droplet size distribution of an oil-in-water emulsion in less than 4s. This is verified by comparison with the droplet size distribution produced by a standard pulsed field gradient (PFG) technique. Difftrain is also extended to enable the application of incremental gradients, in addition to varying the observation time. This is used to produce propagators or displacement probabilities of water flowing through a packed bed for a range of 16 observation times in under 10 min. Again verification is provided by acquisition of the same propagators using a conventional PFG technique.     

Simple two-pulse time-reversal sequence for dipolar and quadrupolar-coupled spin systems

We demonstrate, both theoretically and experimentally, that two-pulse sequence (2n+1) X 90 degrees(Y) - 90 degrees(X) -Acq(t) without delay between pulses, yields the reverse of time evolution of spin system with dipolar and quadrupole interactions. This process results in refocusing of the spin magnetization into magic echo at te = t1/2 after the second pulse, where t1 is the length of the first pulse.     

Observation of a new coherent transient in NMR — Two-pulse nutational stimulated echo in the angular distribution of gamma-radiation from oriented nuclei

A new coherent transient in NMR, the two-pulse nutational stimulated echo is reported for the ferromagnetic system⁵⁰CoFe, observed by monitoring the nuclear spin dynamics as a function of the second pulse duration via anisotropic gamma quanta from thermally oriented radioactive nuclei,⁶⁰Co. The mechanism of echo formation under strong Larmor inhomogeneous broadening and the secondary but important role of inhomogeneity associated with the rf amplitude (Rabi freqeuncy) due to skin-effect are investigated via the method of concatenation of perturbation factors in the statistical tensor formalism. For those experiments performed on time scales short compared with irreversible relaxation the theoretical predictions and subsequent experimental time-domain signals are in excellent accord. Remarkable constancy of amplitude of the new gamma-detected two-pulse echo with increase of interpulse time interval is observed, the longitudinal relaxation being manifest in the off-echo signals. Comparisons are made with NMRON four-pulse stimulated off-echo decay (analogous with conventional NMR three pulse stimulated echo) which is also sensitive to longitudinal relaxation, and with three-pulse on-echo decay (analogous with conventional NMR two-pulse Hahn echo) which measures transverse relaxation.     

Semi-adiabatic Shinnar–Le Roux pulses and their application to diffusion tensor imaging of humans at 7T

The adiabatic Shinnar–Le Roux (SLR) algorithm for radiofrequency (RF) pulse design enables systematic control of pulse parameters such as bandwidth, RF energy distribution and duration. Some applications, such as diffusion-weighted imaging (DWI) at high magnetic fields, would benefit from RF pulses that can provide greater B₁ insensitivity while adhering to echo time and specific absorption rate (SAR) limits. In this study, the adiabatic SLR algorithm was employed to generate 6-ms and 4-ms 180° semi-adiabatic RF pulses which were used to replace the refocusing pulses in a twice-refocused spin echo (TRSE) diffusion-weighted echo planar imaging (DW-EPI) sequence to create two versions of a twice-refocused adiabatic spin echo (TRASE) sequence. The two versions were designed for different trade-offs between adiabaticity and echo time. Since a pair of identical refocusing pulses is applied, the quadratic phase imposed by the first is unwound by the second, preserving the linear phase created by the excitation pulse. In vivo images of the human brain obtained at 7 Testa (7 T) demonstrate that both versions of the TRASE sequence developed in this study achieve more homogeneous signal in the diffusion-weighted images than the conventional TRSE sequence. Semi-adiabatic SLR pulses offer a more B₁-insensitive solution for diffusion preparation at 7 T, while operating within SAR constraints. This method may be coupled with any EPI readout trajectory and parallel imaging scheme to provide more uniform coverage for diffusion tensor imaging at 7 T and 3 T.     

Electron spin-echo experiments in photo-excited triplet states in an external magnetic field

Electron spin-echo experiments in the photo-excited triplet states of quinoxaline-d₆ and naphthalene-d₈ at 1·2 K in an external magnetic field are presented. These include two-pulse Hahn echoes, three-pulse stimulated echoes and Carr-Purcell pulse-echo trains. The decay of the Hahn and stimulated echoes as a function of pulse interval yields measures of the spin relaxation times. Furthermore, the Hahn echo is used to obtain E.P.R. line shapes and the dynamics of the triplet sublevel populations. The angular dependence of the Hahn echo is also investigated. The Hahn echo decay time and decay modulation suggest the kind of role played by nuclear spins in the loss of electron spin phase coherence. Some promising characteristics of the pulse method are discussed.     

Application of biselective refocusing soft pulses to the simplification of heteronuclear correlation spectra

The biselective spin echo technique allows the signals of coupled proton pairs to be extracted from crowded liquid state proton NMR spectra. Its use as a preparation sequence in heteronuclear chemical shift correlation experiments requires the removal of the heteronuclear coupling interaction during the biselective echo time. The discrimination between coupled and uncoupled protons signals is achieved by double quantum filtration, which delivers antiphase magnetization states. The latter are not directly compatible with the design of an HSQC-like pulse sequence. The conversion of antiphase to in-phase magnetization states by a second biselective echo sequence solves this problem. The optimization of spin echo delays is also discussed. Lastly, the article presents modified HSQC and HMBC pulses sequences in which information is obtained solely for the biselectively selected proton pairs. A peracetylated trisaccharide was used as a test molecule.     

Translational free random walk of spins in the presence of a parabolic magnetic field

The free random walk approach has been used to analyze the attenuation of the NMR signal due to spin dephasing in the presence of a constant and pulsed parabolic magnetic field. The spin echo sequence was chosen to examine the attenuation of the NMR signal resulting from self-diffusion. In the framework of the gaussian approach, the long-time limit calculations predict more pronounced diffusion weighting for the parabolic field than for linear magnetic field. Analytical results were obtained and compared with those from other approaches based on a variety of different of approximations.     

核磁共振测井受激回波校正方法研究

核磁共振测井中,受激回波导致CPMG序列中前2个回波与期望值存在较大差异,严重影响仪器信噪比和储层评价效果. 为进一步改善核磁共振测井仪性能,通过探究受激回波产生机理,揭示其对CPMG回波串作用规律,提出了受激回波的校正方法. 同时针对仪器负载不同,相同发射功率产生射频场强度各异的特性,建立受激回波校正系数与射频场强的数学关系,在不同应用环境中实现对CPMG测量结果的校正. 实验表明,在信噪比较低的应用环境中,采用传统的舍去前2个回波的方法误差达24.58%,而该文设计的校正算法误差仅为4.9%.     

Electron dipole-dipole ESEEM in field-step ELDOR of nitroxide biradicals

The use of a rapid stepping of the magnetic field for investigation of electron dipole-dipole ESEEM in pulsed X-band ELDOR is described. The magnetic field jump, synchronized with a microwave pumping pulse, is positioned between the second and the third pulses of the stimulated echo pulse sequence. This echo is measured as a function of the delay between the first and the second pulses. The data are analyzed for a Fourier transform resulting in a Pake resonance pattern. To remove the electron-nuclear contributions to ESEEM, time traces with pumping were divided by those without. This resulted in complete elimination of electron-nuclear contributions, which is seen from the absence of peaks at nuclear frequencies and the similarity of results for protonated and deuterated solvents. For increasing the electron-electron modulation depth, a scanning of the magnetic field during the microwave pumping is proposed. The interspin distances and their distribution are determined for two long-chained (ca. 2 nm) nitroxide biradicals in glassy toluene and in frozen nematic liquid crystal 4-cyano-4'-pentyl-biphenyl. For the latter solvent, the alignment of the axis connecting two nitroxides in biradicals is quantitatively analyzed.     

NMR velocimetry with 13-interval stimulated echo multi-slice imaging in natural porous media under low flow rates

Characterization and quantification of root water uptake processes play a key role in understanding and managing the effects of global climate change on agricultural production and ecosystem dynamics. Part of this understanding is related to the flow of water towards plant roots in soils. In this study we demonstrate for the first time, to our knowledge, that fluid flow in the voids of the pore space of a model soil system (natural sand) can be detected and mapped to an NMR image for mean flows as low as 0.06 mm/s even under the influence of internal magnetic field gradients. To accomplish this we combined multi-slice imaging with a 13-interval pulse sequence to the NMR pulse sequence 13-interval stimulated echo multi-slice imaging (13-interval STEMSI). The result is a largely reduced influence of the internal magnetic field gradients, leading to an improved signal-to-noise ratio which in turn enables one to acquire velocity maps where conventional stimulated echo methods fail.     

A phase rotation scheme for achieving very short echo times with localized stimulated echo spectroscopy

In a single-voxel stimulated echo localization sequence in magnetic resonance spectroscopy, magnetic field gradients are inserted within the echo time (TE) to filter signals generated through coherence pathways other than that leading to the stimulated echo. There is a significant penalty for these gradients as they increase the minimum TE, thereby leading to significant signal loss from spin-spin relaxation and phase distortions in coupled spin systems. Here, an RF phase rotation technique is described for a stimulated echo localization sequence that allows removal of the gradients in the TE intervals and, subsequently, reduction of the minimum TE to only 6 ms. Experiments carried out on six healthy volunteers on a 1.5-T whole-body MR system show a significant signal increase in the metabolite concentrations when measured with a 6-ms TE (N-acetyl-aspartate, 12%, P=.002; creatine, 15%, P=.04; and glutamate+glutamine, 92%, P=.02) compared to concentrations measured with data collected at TEs of 15 and 20 ms.     

E-H-Zyklotronechos in Plasmen

A new echo type with free electrons in a slight inhomogeneous magnetic field excited by one electric and one magnetic pulse is calculated. Thus features of cyclotron echos and spin echoes are combined. The first electric pulse accelerates all (cold) particles to the same velocity as in the case of usual cyclotron echoes. The second magnetic pulse (at t = τ) rotates the plane of precession in phase space, quite in analogy to the motion of magnetic moments in the case of spin echoes. The echo arises at t = 2τ. The E-H echoes make relaxation and diffusion measurements in plasmas possible, using the methods proved useful in spin echo technique. There are no complications as in the case of E-E cyclotron echoes which are based on the fact that a velocity-dependent collision frequency is necessary for the nonlinearity of that echo mechanism.     

Flow compensation for the fast spin echo triple-echo Dixon sequence

The fast spin echo (FSE) triple-echo Dixon (FTED) sequence uses bipolar triple-echo readout during each echo-spacing period of FSE to collect all the images necessary for Dixon water and fat separation in a single scan. In comparison to other FSE implementations of the Dixon technique, the triple echo readout used in FTED incurs minimal deadtime in the pulse sequence design and thus greatly enhances the overall scan efficiency. A potential drawback of FTED is that the time dependence of the gradient moment along the frequency encode direction becomes more complicated than in FSE and flow compensation based on the gradient moment (GM) nulling is difficult to achieve. In this work, the first order GM along the frequency encode direction of FTED was examined and two different methods to minimize the GM were proposed. The first method nulls the GM at all the locations of the refocusing radiofrequency pulses so that the Carr-Purcell Meiboom-Gill condition is always maintained. The second method minimizes the GM of the spin echo component of the FSE signal at the echo locations. The efficacy of both methods in reducing the first order GM and flow-related artefacts was demonstrated both in phantom and in images in vivo.