Evaluation of non-selective refocusing pulses for 7 T MRI

There is a continuing need for improved RF pulses that achieve proper refocusing in the context of ultra-high field (≥ 7 T) human MRI. Simple block or sinc pulses are highly susceptible to RF field inhomogeneities, and adiabatic pulses are generally considered too SAR intensive for practical use at 7 T. The performance of the array of pulses falling between these extremes, however, has not been systematically evaluated. The aim of this work was to compare the performances of 21 non-selective refocusing pulses spanning a range of durations and SAR levels. The evaluation was based upon simulations and both phantom and in vivo human brain experiments conducted at 7 T. Tested refocusing designs included block, composite block, BIR-4, hyperbolic secant, and numerically optimized composite waveforms. These pulses were divided into three SAR classes and two duration categories, and, based on signal gain in a 3-D spin echo sequence, practical recommendations on usage are made within each category. All evaluated pulses were found to produce greater volume-averaged signals relative to a 180° block pulse. Although signal gains often come with the price of increased SAR or duration, some pulses were found to result in significant signal enhancement while also adhering to practical constraints. This work demonstrates the signal gains and losses realizable with single-channel refocusing pulse designs and should assist in the selection of suitable refocusing pulses for practical 3-D spin-echo imaging at 7 T. It further establishes a reference against which future pulses and multi-channel designs can be compared.     

Biselective refocusing pulses and the SERF experiment

The SERF experiment is a variant of the homonuclear J-resolved experiment, in which a single coupling constant is measured. It consists of a single chemical shift selective excitation that is followed by a biselective spin echo. Recent articles mention the existence of artefacts in SERF spectra that are supposedly related to pulse imperfections. This article presents a detailed study of the biselective refocusing pulses. It also reports a method for predicting the position and amplitude of the expected and unexpected 2D spectral peaks in SERF spectra. Artefacts can be partially eliminated by phase cycling or by the introduction of static field gradient pulses in the acquisition sequence. A procedure to obtain of pure absorption peaks in SERF spectra is proposed.     

The generating functions formalism for the analysis of spin response to the periodic trains of RF pulses. Echo sequences with arbitrary refocusing angles and resonance offsets

The generating functions (GF) formalism was applied for calculation of spin density matrix evolution under the influence of periodic trains of RF pulses. It was shown that in a general case, closed expression for the generating function can be found that allows in many cases to derive analytical expressions for the generating function of spin density matrix (magnetization, coherences). This approach was shown to be particularly efficient for the analysis of multi-echo sequences, where one has to average over various frequency isochromats. The explicit analytical expressions for the generating function for echo amplitudes in a Carr–Purcell–Meiboom–Gill (CPMG) echo sequence, a multiecho sequence with incremental phase of refocusing pulse, a gradient echo sequence including transient period were obtained for an arbitrary flip angle and an arbitrary resonance offset. Comparison of the theory and the spin-echo experiments was done, demonstrating a good agreement.     

Multiple-pulse coherence enhancement of solid state spin qubits

We describe how the spin coherence time of a localized electron spin in solids, i.e., a solid state spin qubit, can be prolonged by applying designed electron spin resonance pulse sequences. In particular, the spin echo decay due to the spectral diffusion of the electron spin resonance frequency induced by the non-Markovian temporal fluctuations of the nuclear spin flip-flop dynamics can be strongly suppressed using multiple-pulse sequences akin to the Carr-Purcell-Meiboom-Gill pulse sequence in nuclear magnetic resonance. Spin coherence time can be enhanced by factors of 4-10 in GaAs quantum-dot and Si:P quantum computer architectures using composite sequences with an even number of pulses.     

优化重聚脉冲提高梯度场核磁共振信号强度

缩短射频脉冲宽度, 有助于解决脉冲电力消耗大、样品吸收率高、信噪比低等极端条件核磁共振探测的关键问题. 本文首先分析射频脉冲角度对核磁共振自旋回波信号强度的影响机理, 基于Bloch方程推导了回波信号幅度与扳转角、重聚角的关系. 在特制核磁共振分析仪上采用变脉冲角度技术, 分别在均匀磁场和梯度磁场条件下实现对扳转角和重聚角与回波信号强度关系的数值模拟和实验测量. 结果表明, 梯度场中, 扳转角为90°、重聚角为140°的射频脉冲组合获得最大首波信号强度, 比180°脉冲对应的回波幅值提高13%, 能耗降低至78%. 选用该重聚角(140°) 优化设计饱和恢复脉冲序列探测流体的纵向弛豫时间T₁特性, 准确获得 T₁分布.该结果对于低电力供应、且对信噪比有较高要求的核磁共振测量, 如随钻核磁共振测井和在线核磁共振快速检测等, 具有重要意义. 关键词： 核磁共振 信号强度 重聚脉冲角度 Bloch方程     

Robust prescan calibration for multiple spin-echo sequences: application to FSE and b-SSFP

The collection of fast imaging techniques that use multiple spin-echo (MSE) sequences relies on a precise phase relationship between spin echoes and stimulated echoes that form along the radiofrequency refocusing pulse train. Failure to achieve this condition produces dark banding artifacts that result from destructive interference between signal coherence pathways. Satisfying this condition on the microsecond timescale required is technically challenging for conditions involving strong diffusion-weighted gradients, for arbitrary orientation acquisitions and at large field strengths with high-resolution acquisitions. Two clinically significant MSE sequences, fast spin echo (FSE) and balanced steady-state free precession (b-SSFP), are investigated in this work using a 4-T whole-body scanner. We developed a readout-projection-based prescan technique that ensures coherent signal formation by utilizing banding artifacts to automatically adjust gradient balance. Subsequent image acquisition using the results of this prescan permits the formation of coherent-echo images, which are robust under challenging imaging conditions. The robustness of this approach is demonstrated for FSE and b-SSFP images obtained from the knees of human volunteers. We believe that the use of this prescan calibration technique for the alignment of signal pools in MSE sequences is critical at high fields and will facilitate the implementation of high-quality clinically significant sequences such as FSE and b-SSFP.     

Compensation of refocusing inefficiency with synchronized inversion sweep (CRISIS) in multiplicity-edited HSQC

Use of adiabatic pulses in broadband inversion and decoupling is well known. Replacement of the rectangular pi pulses in the INEPT and rev-INEPT parts of the HSQC and gHSQC experiments with adiabatic pulses substantially improves the sensitivity of these experiments. However, modulation of cross peak intensity in multiplicity-edited HSQC or gHSQC experiments can be quite severe. These modulations arise during the multiplicity-editing periods due to the inefficient refocusing of the spin-echo caused by the mismatch of the echo delay with the one-bond coupling constant. These modulations (which we call echo modulations) are field strength (and hence spectral width) independent. Use of adiabatic pulses with the inversion sweep synchronized to the 1H-13C coupling constant range typically observed in a 13C spectrum will provide substantial improvement in sensitivity. The inversion profile problems associated with rectangular pi pulses can be moderately compensated by composite pulse schemes and these schemes could prove to be reasonable alternatives to adiabatic pulses. However, the adiabatic sweep provides a unique method to compensate the echo modulations for multiplicity-edited experiments. The origin and the compensation of refocusing inefficiency with synchronized inversion sweep (CRISIS) method to minimize these modulations is described.     

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.     

Application of double spin echo spiral chemical shift imaging to rapid metabolic mapping of hyperpolarized [1-¹³C]-pyruvate

Undersampled spiral CSI (spCSI) using a free induction decay (FID) acquisition allows sub-second metabolic imaging of hyperpolarized 13C. Phase correction of the FID acquisition can be difficult, especially with contributions from aliased out-of-phase peaks. This work extends the spCSI sequence by incorporating double spin echo radiofrequency (RF) pulses to eliminate the need for phase correction and obtain high quality spectra in magnitude mode. The sequence also provides an added benefit of attenuating signal from flowing spins, which can otherwise contaminate signal in the organ of interest. The refocusing pulses can potentially lead to a loss of hyperpolarized magnetization in dynamic imaging due to flow of spins through the fringe field of the RF coil, where the refocusing pulses fail to provide complete refocusing. Care must be taken for dynamic imaging to ensure that the spins remain within the B?-homogeneous sensitive volume of the RF coil.     

Multiple echoes, multiple quantum coherence, and the dipolar field: demonstrating the significance of higher order terms in the equilibrium density matrix.

It is well known that dipolar field effects lead to multiple spin echoes in a simple two-RF pulse experiment (the MSE experiment). We show here that coherence transfer echoes (which identify the existence of multiple quantum coherences in liquid NMR) and multiple spin echoes have a common origin. Using density matrix theory we have calculated the phase and timing of multiple spin echoes from all quadrature phase combinations of RF pulses. We show for the MSE experiment that there is a one-to-one correspondence between the time domain echo order and the multiple quantum coherence order. The experimental confirmation of these phase predictions shows that multiple spin echoes provide independent evidence for the breakdown of the high temperature approximation as proposed by Warren et al. (Science 262, 2005 (1993)).     

Radiofrequency pulse sequences which compensate their own imperfections. 1980

Radiofrequency pulse sequences are described which have the same overall effect as a single 90° or 180° pulse but which compensate the undesirable effects of resonance offset and spatial inhomogeneity of the radiofrequency field H₁. These “composite” pulses are built up from a small number of conventional pulses which rotate the nuclear magnetization vectors about different axes in the rotating frame, while in the intervals between pulses a limited amount of free precession may be allowed to occur. Insight into the way in which pulse imperfections are compensated is obtained by computer simulation of trajectories of families of nuclear spin “isochromats” representing a distribution of H₁ intensity or resonance offset. Composite 90° pulses are suggested as a method of reducing systematic errors in spin-lattice relaxation times derived from progressive saturation or saturation-recovery experiments, and as the preparation pulse of a spin-locking experiment. A test of the effectiveness of the composite 180° pulse sequence has been made by using it for population inversion in a spin-lattice relaxation measurement, where T₁ is derived from the null point in the recovery curve, a technique known to be very sensitive to pulse imperfections.     

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.     

Double spin-echo sequence for rapid spectroscopic imaging of hyperpolarized 13C

Dynamic nuclear polarization of metabolically active compounds labeled with (13)C has been introduced as a means for imaging metabolic processes in vivo. To differentiate between the injected compound and the various metabolic products, an imaging technique capable of separating the different chemical-shift species must be used. In this paper, the design and testing of a pulse sequence for rapid magnetic resonance spectroscopic imaging (MRSI) of hyperpolarized (13)C is presented. The pulse sequence consists of a small-tip excitation followed by a double spin echo using adiabatic refocusing pulses and a "flyback" echo-planar readout gradient. Key elements of the sequence are insensitivity to calibration of the transmit gain, the formation of a spin echo giving high-quality spectral information, and a small effective tip angle that preserves the magnetization for a sufficient duration. Experiments in vivo showed three-dimensional coverage with excellent spectral quality and SNR.     

Nuclear spin echo model based on Floquet–Lyapunov theory

The method of nuclear spin-echo amplitude calculation based on the density matrix technique is improved. The Floquet–Lyapunov theorem for a system of the ordinary differential equations with coefficients periodically dependent on time is used to find the solution of the Schrödinger equation for the time-evolution operator which describes behavior of a nuclear spin in the presence of a radiofrequency pulsed magnetic field. NQR spin echo for the case of nuclear spin I?=?1 and NMR spin echo for I?=?1/2 are considered as the simplest illustrations of the approach. The appearance of multiple spin echoes is predicted in the case of strong radiofrequency field.     

Constant time steady gradient NMR diffusometry using the secondary stimulated echo

A pulse sequence producing a second stimulated echo is suggested for the compensation of relaxation and residual dipolar interaction effects in steady gradient spin echo diffusometry. Steady field gradients of considerable strength exist in the fringe field of NMR magnets, for instance. While the absolute echo time of the second stimulated echo is kept constant throughout the experiment, the interval between the first two radiofrequency pulses is augmented leading to a modulation of the amplitude of that second stimulated echo by self-diffusion only. The unique feature of this technique is that it is of a single-scan/single-echo-signal nature. That is, no reference signals neither of the same pulse sequence nor of separate experiments are needed. The new method was tested with poly(ethylene oxide) melts and proved to provide reliable data for (time dependent) self-diffusion coefficients down to the physical limit (D approximately 10(-15)m(2)/s) when flip-flop spin diffusion starts to become effective.     

Paketimpulse in der magnetischen Kernresonanz

Composite Pulses in Nuclear Magnetic Resonance For the compensation of spatial inhomogeneity of the radiofrequency field and a resonance offset in NMR experiments, composite pulses are used instead of the conventional single pulses. In the present work the effect of a resonance offset on composite pulses is treated quantitatively. It will be shown also experimentally that the various constructions for \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{\pi }{2} $\end{document} composite pulses (contrary to π composite pulses) lead to only two different degrees of compensation depending on the choice of the phase of the pulses or the sign of the resonance offset.     

NMR spectroscopy in inhomogeneous B0 and B1 fields with non-linear correlation

Resolved NMR spectra from samples in inhomogeneous B0 and B1 fields can be obtained with the so-called "ex situ" methodology, employing a train of composite or adiabatic z-rotation RF pulses to periodically refocus the inhomogeneous broadening during the detection of the time-domain signal. Earlier schemes relied on a linear correlation between the inhomogeneous B0 and B1 fields. Here the pulse length, bandwidth, and amplitude of the adiabatic pulses of the hyperbolic secant type are adjusted to improve the refocusing for a setup with non-linear correlation. The field correlation is measured using a two-dimensional nutation experiment augmented with a third dimension with varying RF carrier frequency accounting for off-resonance effects. The pulse optimization is performed with a computer algorithm using the experimentally determined field correlation and a standard adiabatic z-rotation pulse as a starting point for the iterative optimization procedure. The shape of the z-rotation RF pulse is manipulated to provide refocusing for the conditions given by the sample-, magnet-, and RF-coil geometry.     

Theoretical studies of the effect of the dipolar field in multiple spin-echo sequences with refocusing pulses of finite duration

It has been observed recently that the finite duration of refocusing rf pulses in a multiecho acquisition of the signal formed under the influence of the dipolar field leads to significant signal attenuation [S. Kennedy, Z. Chen, C.K. Wong, E.W.-C. Kwok, J. Zhong, Investigation of multiple-echo spin-echo signal acquisition under distant dipole-dipole interactions, Proc. Int. Soc. Magn. Reson. Med. 13 (2005) 2288]. Hereto, we quantify the phenomenon by evaluating analytically the influences of both the distant dipolar field (DDF) and transverse relaxation T2 on the magnetization in a multiecho pulse sequence based on correlation spectroscopy revamped by asymmetric z-gradient echo detection (CRAZED). Analytic expressions for the magnetization were obtained, which demonstrate explicitly the origin of rephased signal in the presence of the finite pi pulses in the multiecho train. The expressions also explain the effects of the DDF and T2 during the refocusing pulses on the signal strength, and show the substantial signal dependence on the phase of the rf pulses. We show that when the DDF effect during the pulse is canceled, the signal rises primarily during the free evolution time in the acquisition period. This elucidates the signal attenuation when the rf pulses cover a significant proportion of time in the sequence. In addition, we performed an optimization on the number of refocusing pulses that maximizes the total acquired signal using parameters for water, brain white matter, and muscle. We found that maximal signal-to-noise ratio is obtained when the pulse duration approximately equals the free evolution time in the samples with a wide range of T2.     

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.