Dynamic NMR q-space studies of microstructure with the multigrade CPMG sequence

A new approach to q-space studies of microstructure is proposed, which exploits the combined information contained in the water proton transverse relaxation time distribution and the frequency dependence of the apparent water diffusivity in heterogeneous systems. Using an automated two-dimensional multigrade CPMG sequence, both the pulse spacing and the amplitude of the applied field gradient are varied systematically and used to measure the frequency and wave vector dependence of the multiple exponential echo decay constants and amplitudes. Undesirable crossterms in the applied and background field gradients are eliminated by a simple procedure involving a sign reversal in the applied gradient. Nonlinear, local susceptibility-induced field gradients are shown to lead to enhanced, frequency-dependent apparent water diffusivities that are sensitive to the local microstructure.     

CAGEBIRD: improving the GBIRD filter with a CPMG sequence

An improvement of the GBIRD-filter is presented. The current approach utilizes Carr-Purcell-Meiboom-Gill type pulse train during the BIRD delay. The method enables recording of purely absorptive 1D spectrum using only one isotope editing element. In the current method, the parent signal leakage due to JHH evolution during the BIRD delay is considerably smaller than in the conventional approach. As a consequence, the t1-noise is smaller also in 2D applications, such as GBIRD-filtered HSQC.     

Multiple-quantum polarization-transfer coherence pathways in liquids

Polarization-transfer processes in liquid-state NMR are discussed in terms of a simplified operator formalism. The operator model is introduced and the various transformation rules are tabulated. The idea of a coherence pathway is also introduced and the various coherence pathways for the SPT, INEPT, and DEPT polarization-transfer experiments are discussed briefly. The bulk of the paper is devoted to the POMMIE family of pulse sequences and a detailed analysis is made of the extensive phase cycling possible with this pulse train. General expressions are derived for the signal acquired as the phase of the various pulses is changed. Subspectral editing using the POMMIE procedure is discussed in detail and it is shown to be superior to all other polarization-transfer techniques. Edited proton-decoupled carbon-13 spectra of cholesterol are generated using the POMMIE procedure.     

Spectral characterization of diffusion in porous media by the modulated gradient spin echo with CPMG sequence

Carr-Purcell-Meiboom-Gill train of radiofrequency pulses applied to spins in the constant magnetic field gradient is an efficient variant of the modulated magnetic field gradient spin echo method, which provides information about molecular diffusion in the frequency-domain instead in the time-domain as with the two-pulse gradient spin echo. The frequency range of novel technique is broad enough to sample the power spectrum of displacement fluctuation in water-saturated pulverized silica (SiO(2)) and provides comprehensive information about the molecular restricted motion as well as about the structure of medium.     

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.     

Velocity autocorrelation spectra of fluid in porous media measured by the CPMG sequence and constant magnetic field gradient

Carr-Purcell-Meiboom-Gill (CPMG) train of radiofrequency pulses applied to spins in the constant magnetic field gradient is an efficient variant of the modulated magnetic field gradient spin echo method, which provides information about molecular diffusion in the frequency domain instead of in the time domain as with the two-pulse gradient spin echo. The frequency range of this novel technique is broad enough to sample the power spectrum of displacement fluctuation in water-saturated pulverized silica (SiO2) and provides comprehensive information about the molecular restricted motion as well as about the structure of the medium.     

基于改进非局部均值的CPMG信号去噪算法

采用低场核磁共振技术进行检测时,接收到的回波信号微弱且信噪比低,真实的信号容易淹没在背景噪声中,严重影响到后续的反演等操作的准确性．针对这一问题,提出利用非局部均值滤波算法对CPMG(Carr Purcell Meiboom Gill)回波信号进行降噪的方法．首先,对算法中至关重要的参数选择的方法进行分析,提出了利用Stein无偏风险估计的自适应参数选取方法;然后,根据回波信号的特性对算法进行改进,即利用信号点数据方差的不同,自适应地求取各点进行非局部均值滤波时的相似窗宽度;最后,求取利用最优参数进行降噪后的CPMG回波信号．对仿真数据和真实数据的反演结果对比分析表明,该改进的非局部均值滤波算法能够取得更好的滤波效果,能够获得较优的反演谱．     

Enhancing MQMAS sensitivity using signals from multiple coherence transfer pathways

Multiple-quantum magic-angle spinning experiment removes second-order quadrupolar broadening from the central-transition of half-integer quadrupolar nuclei. This paper presents a novel scheme to enhance the sensitivity of MQMAS using signals from multiple coherence transfer pathways. The enhancement can be obtained in two ways. The first method uses the multiplex phase cycling to acquire MQMAS spectra from various coherence transfer pathways simultaneously. An addition of spectra collected with no extra time enhances the efficiency of the experiment. The second method, soft-pulse-added-mixing, is designed based on a complete alias of coherence transfer pathways. By properly fixing the soft-pulse phase, signals from various coherence transfer pathways can add constructively resulting higher signal intensities. The two methods are demonstrated for sensitivity enhancement with samples of spin-3/2 and 5/2.     

Sensitivity gain by simultaneous acquisition of two coherence pathways: the HNCA(+) experiment

In most multidimensional nuclear magnetic resonance experiments a single and distinct coherence transfer pathway is selected by phase cycling or by pulsed field gradients. It was shown that simultaneously exploiting more than one coherence transfer pathway could increase the overall sensitivity of NMR experiments. However, sensitivity enhancement schemes described to date introduce additional delays in the pulse schemes, resulting in considerable decrease of the expected sensitivity gain when applied to biomolecules due their fast transverse relaxation. A novel sensitivity enhancement principle which increases sensitivity of an experiment by simultaneously exploiting two completely independent coherence pathways in a single NMR pulse scheme is presented in this paper. As an example an improved HNCA experiment, the HNCA(+), is presented, which combines the "out-and-back" coherence transfer pathway used in HNCA with an "out-and-stay" experiment, analogous to HCANH, without adding any time periods compared to the conventional HNCA pulse sequence. The applicability of the HNCA(+) was theoretically evaluated with regard to different sizes of peptides or proteins, which showed that the experimental time can be reduced twofold in ideal cases. The application of this novel experiment to a 7-kDa protein showed a 20% sensitivity gain of HNCA(+) when compared to conventional HNCA.     

Short-time restricted diffusion in a static gradient and the attenuation of individual coherence pathways

We experimentally explore some of the implications of a recent theoretical study [J. Magn. Reson. 64 (2003) 145] for the measurement of restricted diffusion in connected porous media in a static gradient. In particular, we examine how restriction affects the short-time attenuation of different coherence pathways, all excited with the same sequence of slice-selective radiofrequency (RF) pulses, and how the various pathways make the transition to the long-time or tortuosity regime. We confirm that every pathway contains equivalent diffusional information and, for short times, yields the surface-to-volume ratio (S/V) of the confining space. We find also, in agreement with the theoretical predictions, that different pathways are controlled by different time scales and, thus, exhibit different sensitivity to restriction. This property might be exploited when designing optimal sequences to study restricted motion.     

High-resolution NMR spectra in inhomogeneous fields utilizing the CRAZED sequence without coherence selection gradients

Coherence selection gradients have been considered as indispensable for high-resolution NMR spectroscopy in inhomogeneous fields utilizing the CRAZED-type sequences. However, our experimental results demonstrate that these gradients can be omitted if an appropriate phase cycling is applied. The measured linewidth of reconstructing 1D high-resolution spectral peaks does not depend on the dipolar correlation distance determined by the coherence selection gradients, but is only affected by diffusion and T(2) relaxation. This finding suggests the need to reconsider the mechanism for the iMQC-based high-resolution spectroscopy.     

Application of optimal control to CPMG refocusing pulse design

We apply optimal control theory (OCT) to the design of refocusing pulses suitable for the CPMG sequence that are robust over a wide range of B(0) and B(1) offsets. We also introduce a model, based on recent progress in the analysis of unitary dynamics in the field of quantum information processing (QIP), that describes the multiple refocusing dynamics of the CPMG sequence as a dephasing Pauli channel. This model provides a compact characterization of the consequences and severity of residual pulse errors. We illustrate the methods by considering a specific example of designing and analyzing broadband OCT refocusing pulses of length 10t(180) that are constrained by the maximum instantaneous pulse power. We show that with this refocusing pulse, the CPMG sequence can refocus over 98% of magnetization for resonance offsets up to 3.2 times the maximum RF amplitude, even in the presence of ±10% RF inhomogeneity.     

Multiexponential attenuation of the CPMG spin echoes due to a geometrical confinement

The CPMG multi-echo technique is often used to investigate the translational motion of diffusing nuclei in a confining medium. Henceforth, periodically repeated RF pulses with a diffusion-sensitizing gradient yield a formation of spin echoes of gradually decreasing amplitudes. The parameters of their exponential fits may characterize the structure of porous materials or biological tissue. In this paper, a multiexponential character of the CPMG measurements is rigorously demonstrated, once a geometrical confinement is present. Based on the multiple propagator approach, we derived a spectral representation for the echo amplitudes under external magnetic field of an arbitrary gradient profile. The multiple relaxation times and their spectral weights were found in a general form. The study of simple restrictive media allowed to obtain a quantitative condition under which the multiexponential attenuation is reduced to a monoexponential one.     

Diffusion effects on the CPMG relaxation rate in a dipolar field

The diffusion in the magnetic dipolar field around a sphere is considered. The diffusion is restricted to the space between two concentric spheres, where the inner sphere is the source of the magnetic dipolar field. Analytical expressions for the CPMG transverse relaxation rate as well as the free induction decay and the spin echo time evolution are given in the Gaussian approximation. The influence of the inter-echo time is analyzed. The limiting cases of small and large inter-echo times as well as the short and long time behavior are evaluated.     

Faithful estimation of dynamics parameters from CPMG relaxation dispersion measurements

This work examines the robustness of fitting of parameters describing conformational exchange (k(ex), p(a/b), and Deltaomega) processes from CPMG relaxation dispersion data. We have analyzed the equations describing conformational exchange processes for the intrinsic inter-dependence of their parameters that leads to the existence of multiple equivalent solutions, which equally satisfy the experimental data. We have used Monte-Carlo simulations and fitting to the synthetic data sets as well as the direct 3-D mapping of the parameter space of k(ex), p(a/b), and Deltaomega to quantitatively assess the degree of the parameter inter-dependence. The demonstrated high correlation between parameters can preclude accurate dynamics parameter estimation from NMR spin-relaxation data obtained at a single static magnetic field. The strong parameter inter-dependence can readily be overcome through acquisition of spin-relaxation data at more than one static magnetic field thereby allowing accurate assessment of conformational exchange properties.     

A new approach for simultaneous measurement of ADC and T2 from echoes generated via multiple coherence transfer pathways

The study of rotational and translational diffusion requires the measurement of both T2 and apparent diffusion coefficient (ADC), quantities that are typically measured in separate experiments. The exploitation of echoes generated via multiple coherence transfer pathways offers an opportunity for measuring T2 and ADC values simultaneously in a single experiment. A series of RF pulses can generate multiple echoes via different coherence pathways with each one being uniquely encoded. Here, we demonstrate one pulse sequence that uses an initial theta; RF pulse to generate three coherence orders (C = 0, -1, +1). In the particular version of the method discussed here only two are used (C = 0, +1). Each order is encoded with a different b value from which the ADC is derived. The coherence order echo C = 0 is refocused to quantify T2. The performance of the method--dubbed simultaneous measurement of ADC and relaxation time (SMART)--is demonstrated on a set of samples differing in T2 and ADC achieved by varying the relative volume fractions in mixtures of gadolinium-doped H2O and D2O. The regional SMART derived T2 and ADC agree well with those obtained with conventional double-spin-echo and pulsed gradient spin-echo methods.     

Comparison of TSE, TGSE, and CPMG measurement techniques for MR polymer gel dosimetry

A radiation dose distribution that optimally conforms to the target volume is of major interest for stereotactic radiotherapy. For this purpose treatment plans have to be verified experimentally before transferring to the patient. The requirements regarding dose accuracy and spatial resolution can be fulfilled with tissue equivalent polymer gel dosimeters which offer the possibility to visualize 3D dose distributions. Herewith, dosimetry can be performed by the spin-spin relaxation rate R2 which varies with the absorbed dose. In this work, different MR measurement techniques were evaluated: The standard Carr-Purcell-Meiboom-Gill (CPMG) method, a modified Turbo-Spin-Echo (TSE) sequence, and a modified Turbo-Gradient-Spin-Echo (TGSE) sequence. Experiments were performed both with a homogeneous water phantom and an irradiated polymer gel. The results show that TGSE and especially TSE are suited well for MR polymer gel dosimetry: The acquisition time of both techniques can be reduced in comparison to CPMG by a factor of 5. The accuracy of dose determination for doses between 2 Gy and 13 Gy lies between 5.6% and 2.0% (TSE), 9.0% and 3.2% (TGSE), and 7.9% and 2.7% (CPMG). These investigations show that especially TSE can be handled as a substitute or at least an alternative to CPMG for the verification of treatment plans in stereotactic radiotherapy.     

Quantum Subgroups of the Haagerup Fusion Categories

We answer three related questions concerning the Haagerup subfactor and its even parts, the Haagerup fusion categories. Namely we find all simple module categories over each of the Haagerup fusion categories (in other words, we find the “quantum subgroups” in the sense of Ocneanu), we find all irreducible subfactors whose principal even part is one of the Haagerup fusion categories, and we compute the Brauer-Picard groupoid of Morita equivalences of the Haagerup fusion categories. In addition to the two even parts of the Haagerup subfactor, there is exactly one more fusion category which is Morita equivalent to each of them. This third fusion category has six simple objects and the same fusion rules as one of the even parts of the Haagerup subfactor, but has not previously appeared in the literature. We also find the full lattice of intermediate subfactors for every irreducible subfactor whose even part is one of these three fusion categories, and we discuss how our results generalize to Izumi subfactors.     

通过高斯加权的1H CPMG弛豫曲线测定橡胶交联密度

CPMG（Carr-Purcell-Meiboom-Gill）回波法是测量橡胶交联密度[常用交联点之间的分子量（M_c）表示]的一种常用核磁共振（NMR）技术,但实验发现通过该技术获得的M_c对于CPMG序列中脉冲间隔时间具有较强的依赖性,导致交联密度NMR测量值与橡胶材料硬度的相关性低.为了克服这一缺点,本文对不同脉冲间隔时间下CPMG实验测得的质子横向驰豫曲线进行高斯加权.通过对高斯加权求和后的质子横向驰豫曲线进行处理分析,实现了对橡胶交联密度更加准确地测量,大幅提升了天然橡胶交联密度NMR测量值与材料硬度的相关性.本文方案测量能获得与¹H DQ NMR方法相当,或比之更佳的交联密度-硬度相关性.同时,本文方案比¹H DQ NMR方法更为高效,整体测量时间缩短为¹H DQ NMR实验时间的1/10.