Exploring the limits of broadband excitation and inversion pulses

The design of broadband excitation and inversion pulses with compensation of B(1)-field inhomogeneity is a long standing goal in high resolution NMR spectroscopy. Most optimization procedures used so far have been restricted to particular pulse families to keep the scale of the problem within manageable limits. This restriction is unnecessary using efficient numerical algorithms based on optimal control theory. A systematic study of rf-limited broadband excitation by optimized pulses and broadband inversion by optimized pulses with respect to bandwidth and B(1)-field is presented. Upper limits on minimum pulse lengths are set for different degrees of pulse performance.     

Linear phase slope in pulse design: application to coherence transfer

Using optimal control methods, robust broadband excitation pulses can be designed with a defined linear phase dispersion. Applications include increased bandwidth for a given pulse length compared to equivalent pulses requiring no phase correction, selective pulses, and pulses that mitigate the effects of relaxation. This also makes it possible to create pulses that are equivalent to ideal hard pulses followed by an effective evolution period. For example, in applications, where the excitation pulse is followed by a constant delay, e.g. for the evolution of heteronuclear couplings, part of the pulse duration can be absorbed in existing delays, significantly reducing the time overhead of long, highly robust pulses. We refer to the class of such excitation pulses with a defined linear phase dispersion as ICEBERG pulses (Inherent Coherence Evolution optimized Broadband Excitation Resulting in constant phase Gradients). A systematic study of the dependence of the excitation efficiency on the phase dispersion of the excitation pulses is presented, which reveals surprising opportunities for improved pulse sequence performance.     

Velocity sensitivity of slice-selective excitation

The purpose of this study was to investigate how flow affects slice-selective excitation, particularly for radiofrequency (rf) pulses optimized for slice-selective excitation of stationary material. Simulation methods were used to calculate the slice profiles for material flowing at different velocities, using optimal flow compensation when appropriate. Four rf pulses of very different shapes were used in the simulation study: a 90° linear-phase Shinnar-LeRoux pulse; a 90° self-refocusing pulse; a minimum-phase Shinnar-LeRoux inversion pulse; and a SPINCALC inversion pulse. Slice profiles from simulations with a laminar flow model were compared with experimental studies for two different rf pulses using a clinical magnetic resonance imaging (MRI) system. We found that, for a given rf pulse, the effect of flow on slice-selective excitation depends on the product of the selection gradient amplitude, the component of velocity in the slice selection direction, and the square of the rf pulse duration. The shapes of the slice profiles from the Shinnar-LeRoux pulses were relatively insensitive to velocity. However, the slice profiles from the self-refocusing pulse and the SPINCALC pulse were significantly degraded by velocity. Experimental slice profiles showed excellent agreement with simulation. In conclusion, our study demonstrates that slice-selective excitation can be significantly degraded by flow depending on the velocity, the gradient amplitude, and characteristics of the rf excitation pulse used. The results can aid in the design of rf pulses for slice-selective excitation of flowing material.     

Design and application of robust rf pulses for toroid cavity NMR spectroscopy

We present robust radio frequency (rf) pulses that tolerate a factor of six inhomogeneity in the B? field, significantly enhancing the potential of toroid cavity resonators for NMR spectroscopic applications. Both point-to-point (PP) and unitary rotation (UR) pulses were optimized for excitation, inversion, and refocusing using the gradient ascent pulse engineering (GRAPE) algorithm based on optimal control theory. In addition, the optimized parameterization (OP) algorithm applied to the adiabatic BIR-4 UR pulse scheme enabled ultra-short (50 μs) pulses with acceptable performance compared to standard implementations. OP also discovered a new class of non-adiabatic pulse shapes with improved performance within the BIR-4 framework. However, none of the OP-BIR4 pulses are competitive with the more generally optimized UR pulses. The advantages of the new pulses are demonstrated in simulations and experiments. In particular, the DQF COSY result presented here represents the first implementation of 2D NMR spectroscopy using a toroid probe.     

Adjustable, broadband, selective excitation with uniform phase

An advance in the problem of achieving broadband, selective, and uniform-phase excitation in NMR spectroscopy of liquids is outlined. Broadband means that, neglecting relaxation, any frequency bandwidth may be excited even when the available radiofrequency (RF) field strength is strictly limited. Selective means that sharp transition edges can be created between pure-phase excitation and no excitation at all. Uniform phase means that, neglecting spin-spin coupling, all resonance lines have nearly the same phase. Conventional uniform-phase excitation pulses (e.g., E-BURP), mostly based on amplitude modulation of the RF field, are not broadband: they have an achievable bandwidth that is strictly limited by the peak power available. Other compensated pulses based on adiabatic half-passage, like BIR-4, are not selective. By contrast, inversion pulses based on adiabatic fast passage can be broadband (and selective) in the sense above. The advance outlined is a way to reformulate these frequency modulated (FM) pulses for excitation, rather than just inversion.     

Comparison of the Effects of Different <Superscript>19</Superscript>F <Emphasis Type="Italic">π</Emphasis> Pulses on the Sensitivity and Phaseability of the <Superscript>19</Superscript>F-<Superscript>13</Superscript>C HSQC

The ¹⁹F-¹³C heteronuclear single quantum coherence (HSQC) experiment is vital for the structural elucidation of polyfluorinated organic species, yet its sensitivity and phaseability are limited by difficulties in uniform excitation of the widely disperse ¹⁹F spectral window. Adiabatic pulses of different types have previously been employed to generate effective π pulses for inversion and refocussing, but a systematic comparison of various adiabatic and other inversion pulses has not been published. In this work, it was observed that the use of a broadband inversion pulse (BIP) during the t ₁ evolution period resulted in properly phaseable spectra for experiments optimized to detect ¹ J _CF, in contrast to CHIRP or WURST adiabatic pulses. For the INEPT and reverse-INEPT transfer segments of the HSQC, optimal sensitivity for resonances distant from the transmitter frequency was afforded by optimized universal rotation (BURBOP) or CHIRP pulses. In HSQC experiments with delays optimized for two-bond correlations, only the use of BURBOP pulses in INEPT and reverse-INEPT sequences afforded spectra cleanly phaseable across the F ₂ and F ₁ spectral windows. This observation is supported by off-resonance pulsed field gradient spin-echo experiments.     

Improved Broadband Inversion Performance for NMR in Liquids

New NMR broadband inversion pulses that compensate both for resonance offset and radiofrequency (RF) inhomogeneity are described. The approach described is a straightforward computer optimization of an initial digitized waveform generated from either a constant-amplitude frequency sweep or from an existing composite inversion pulse. Problems with convergence to local minima are alleviated by the way the optimization is carried out. For a given duration and maximum allowable RF field strength B₁ (but not necessarily given RMS power deposition), the resultant broadband inversion pulse (BIP) shows superior inversion compared to inversion pulses obtained from previous methods, including adiabatic inversion pulses. Any existing BIP can be systematically elaborated to build up longer inversion pulses that perform over larger and larger bandwidths. The resulting pulse need not be adiabatic throughout its duration or across the entire operational bandwidth.     

Varian系统所有通道上的整形脉冲

本文介绍了Varian系统所有通道上的整形脉冲;整形脉冲的形状;波形发生器的功率适中的脉冲整形以及应用"Tophat"的选择激发;整形脉冲与选择性反转;选择性反转或宽带反转,整形脉冲的宽带激发;以及多频率激发的移层式脉冲等.     

Asymmetric adiabatic pulses for NH selection.

Many types of NMR experiments demand the use of frequency-selective pulses to invert magnetization within discrete frequency limits. For certain experiments, only one side of the inversion band must be sharply demarcated, in which case this transition bandwidth can be narrowed when using an asymmetric adiabatic full passage. In the present study, a highly efficient asymmetric adiabatic full passage was created from a combination of two adiabatic half passages which used different modulation functions (HS12 and tanh/tan). Each adiabatic half passage occupied a different amount of time in the total pulse and performed one-half of the inversion. On one side, HS12 produced a sharp transition between inverted and noninverted states which was approximately 2.5 times narrower than the transition bandwidth afforded by a symmetric hyperbolic secant pulse of equal length. On the other side of the narrow transition band, the tanh/tan pulse achieved broadband inversion. These asymmetric pulses were applied to select NH groups immediately adjacent to the water signal in water-flip-back HSQC experiments using a double spin echo for the reverse INEPT step.     

Improved pulsed broadband ultrasonic spectroscopy for analysis of liquid-particle flow

The paper contains an investigation of broadband pulsed ultrasonic spectroscopy techniques, intended for testing of suspensions, such as a liquid-particle flow containing small diameter particles. Influence of traditional and novel broadband pulse shapes on quality of frequency spectra is analysed, as well as pulse design aspects leading to an optimal shape of an ultrasonic excitation wave. Effects that may influence signal quality and method reliability in a given setup, in particular resonances and noise are discussed. Solutions for signal acquisition and averaging techniques are presented, as well as results of testing of instrumentation limits and overall performance. Results of acoustic spectroscopy measurement of a concentrated liquid-particle flow are provided. A number of experimental and numerical examples, together with comprehensive explanations, show a potential for ultrasonic attenuation spectroscopy to be a successful methodology for an on-line measurement of fluid-particle suspensions and composite non-homogeneous materials in general.     

Reducing the duration of broadband excitation pulses using optimal control with limited RF amplitude

Combining optimal control theory with a new RF limiting step produces pulses with significantly reduced duration and improved performance for a given maximum RF amplitude compared to previous broadband excitation by optimized pulses (BEBOP). The resulting pulses tolerate variations in RF homogeneity relevant for standard high-resolution NMR probes. Design criteria were transformation of Iz-->Ix over resonance offsets of +/-20kHz and RF variability of +/-5%, with a pulse length of 500 micros and peak RF amplitude equal to 17.5 kHz. Simulations transform Iz to greater than 0.995 Ix, with phase deviations of the final magnetization less than 2 degrees, over ranges of resonance offset and RF variability that exceed the design targets. Experimental performance of the pulse is in excellent agreement with the simulations. Performance tradeoffs for yet shorter pulses or pulses with decreased digitization are also investigated.     

A simple scheme for the design of solvent-suppression pulses

Excitation sculpting was first introduced as a way to efficiently suppress solvent signals. It requires a pulse sequence that acts as a null pulse at the solvent-resonance frequency and as an inversion pulse everywhere else. In this article, it is shown that such a goal can be achieved starting with "top-hat" inversion shaped pulses such as I-BURP-2 or gaussian cascade G3. The result is a Globally Antisymmetric Selective Pulse, or GASP. Numerical optimization was used to extend the performance of such pulses. Multifrequency signal suppression was shown to be possible through application of successive excitation sculpting modules.     

针对限制幅值磁共振脉冲的优化设计

在磁共振脉冲优化领域,优化脉冲普遍存在幅值过大的问题,这极大地限制了优化脉冲的使用范围。为了限制优化脉冲的幅值,扩大其应用范围,提出了一种基于L-BFGS-B数值算法的脉冲优化设计方法。首先基于Liouville-von Neuman方程,使用最优控制思想构建优化模型;然后使用L-BFGS-B算法,在限制幅值的条件下对优化模型进行数值迭代求解;最后以脉冲的激发效率以及激发轮廓的均匀性作为衡量优化脉冲优劣的标准对该方法进行仿真和实验验证。结果表明,采用该方法获得的优化脉冲在幅值被限制的前提下,仍能获得较传统磁共振脉冲更好的共振激发效果,进而增强信号的灵敏度,提高图像的质量。     

Application of optimal control theory to the design of broadband excitation pulses for high-resolution NMR

Optimal control theory is considered as a methodology for pulse sequence design in NMR. It provides the flexibility for systematically imposing desirable constraints on spin system evolution and therefore has a wealth of applications. We have chosen an elementary example to illustrate the capabilities of the optimal control formalism: broadband, constant phase excitation which tolerates miscalibration of RF power and variations in RF homogeneity relevant for standard high-resolution probes. The chosen design criteria were transformation of I(z)-->I(x) over resonance offsets of +/- 20 kHz and RF variability of +/-5%, with a pulse length of 2 ms. Simulations of the resulting pulse transform I(z)-->0.995I(x) over the target ranges in resonance offset and RF variability. Acceptably uniform excitation is obtained over a much larger range of RF variability (approximately 45%) than the strict design limits. The pulse performs well in simulations that include homonuclear and heteronuclear J-couplings. Experimental spectra obtained from 100% 13C-labeled lysine show only minimal coupling effects, in excellent agreement with the simulations. By increasing pulse power and reducing pulse length, we demonstrate experimental excitation of 1H over +/-32 kHz, with phase variations in the spectra <8 degrees and peak amplitudes >93% of maximum. Further improvements in broadband excitation by optimized pulses (BEBOP) may be possible by applying more sophisticated implementations of the optimal control formalism.     

Phase‐shaping strategies for coherent anti‐Stokes Raman scattering

The identification of large molecules in complex environments requires probing of multiple vibrational resonances rather than a single resonance. Phase‐shaping the excitation pulses allows the coherent mixing of several resonances so that the presence of molecules can be inferred directly from the integrated output pulse energy. This avoids the need for the collection of spectra or multiple measurements. This article describes a particular implementation for coherent anti‐Stokes Raman scattering microscopy that uses a broadband pump and probe field in combination with a narrowband Stokes field. We numerically study the possibilities of optimizing selectivity, specificity, and sensitivity by precalculating pulse shapes using an evolutionary algorithm. Copyright © 2011 John Wiley & Sons, Ltd.     

用于同时多层MRI的选择性射频脉冲的优化设计

近年来,为提高磁共振成像（MRI）信号信噪比（SNR）、缩短成像时间,同时多层成像技术受到了极大的关注.为了实现同时多层的选择性激发,现有的多层成像序列大多使用组合射频（RF）脉冲,该脉冲可包含多个独立的幅值相同相位不同的简单脉冲,由于其采用简单的线性叠加方法,该类脉冲射频功率随脉冲数量呈现平方增长,因而应用受限.针对这一问题,基于自旋动力学和优化控制原理,本文提出了一种针对同时多层MRI的选择性射频脉冲的数值优化方法,该方法充分运用射频脉冲的调控机制,获得优化脉冲,并配合层选梯度,可实现任意层厚、层间距、层数的同时高效选择性激发.最后,通过数字模体的同时多层模拟成像实验验证了优化脉冲的有效性.     

RF pulse concatenation for spatially selective inversion

It is shown that spatially selective inversion and saturation can be achieved by concatenation of RF pulses with lower flip angles. A concatenation rule which enables global doubling of the flip angle of any given excitation pulse applied to initial z magnetization is proposed. In this fashion, the selectivity of the single pulse is preserved, making the high selectivity achievable in the low flip-angle regime available for inversion and large flip-angle saturation purposes. The profile quality achievable with exemplary concatenated pulses is investigated in comparison with adiabatic inversion. It is verified that by using concatenated inversion in the transfer insensitive labeling technique (TILT), the MT artifact is suppressed. Copyright 2000 Academic Press.     

Dispersion-based pulse shaping for multiplexed two-photon fluorescence microscopy

We demonstrate selective two-photon excited fluorescence microscopy with shaped pulses produced with a simple yet efficient scheme based on dispersive optical components. The pulse train from a broadband oscillator is split into two subtrains that are sent through different amounts of glass. Beam recombination results in pulse-shape switching at a rate of 150MHz. Time-resolved photon counting detection then provides two simultaneous images resulting from selective two-photon excitation, as demonstrated in a live embryo. Although less versatile than programmable pulse-shaping devices, this novel arrangement significantly improves the performance of selective microscopy using broadband shaped pulses while simplifying the experimental setup.     

Robust slice-selective broadband refocusing pulses

Slice-selective broadband refocusing pulses are of great interest in localized MR spectroscopy for improving spatial selectivity, reducing chemical-shift displacement errors, and reducing anomalous J modulation. In practice the bandwidth of RF pulses is limited by the maximum available B1 amplitude. The goal of the present work is to design slice-selective and broadband refocusing pulses which are tolerant against B1 deviations. Pulse design is performed by numerical optimization based on optimal control theory. A comprehensive study of different cost functions and their effect on the optimization is given. The optimized slice-selective broadband refocusing pulses are compared to conventional Shinnar-Le Roux (SLR), broadband SLR, and hyperbolic secant pulses. In simulations and experiments optimized pulses were shown to fulfill broadband slice specifications over a range of ±20% B1 scalings. Experimental validation showed a reduction of chemical-shift displacement error by a factor of 3 compared to conventional SLR pulses.     

Gapped pulses for frequency-swept MRI

A recently introduced method called SWIFT (SWeep Imaging with Fourier Transform) is a fundamentally different approach to MRI which is particularly well suited to imaging objects with extremely fast spin–spin relaxation rates. The method exploits a frequency-swept excitation pulse and virtually simultaneous signal acquisition in a time-shared mode. Correlation of the spin system response with the excitation pulse function is used to extract the signals of interest. With SWIFT, image quality is highly dependent on producing uniform and broadband spin excitation. These requirements are satisfied by using frequency-modulated pulses belonging to the hyperbolic secant family (HSn pulses). This article describes the experimental steps needed to properly implement HSn pulses in SWIFT. In addition, properties of HSn pulses in the rapid passage, linear region are investigated, followed by an analysis of the pulses after inserting the “gaps” needed for time-shared excitation and acquisition. Finally, compact expressions are presented to estimate the amplitude and flip angle of the HSn pulses, as well as the relative energy deposited by the SWIFT sequence.