Tailored sinc pulses for uniform excitation and artifact-free radio frequency time-domain EPR imaging

A method to generate shaped radiofrequency pulses for uniform excitation of electron spins in time-domain radio frequency (RF) electron paramagnetic resonance (EPR) imaging is presented. A commercial waveform generator was integrated with the transmit arm of the existing time-domain RF-EPR spectrometer to generate tailored excitation pulses with sub-nano second resolution for excitation with a 90 degrees flip-angle. A truncated sinc [sin(x)/x] pulse, tailored to compensate for the Q-profile (RF frequency response) of the resonator, was shown to yield images from phantom objects as well as in vivo images, with minimal distortion. These studies point to the advantages in using shaped sinc pulses to achieve improved uniform excitation over a relatively wide bandwidth region in time-domain RF-EPR imaging (RF-FT-EPRI).     

A Near-Resonance Solution to the Bloch Equations and Its Application to RF Pulse Design

A near-resonance expansion of the solution to the Bloch equations in the presence of a radiofrequency (RF) pulse is presented in this paper. The first-order approximation explicitly demonstrates the nonlinear nature of the Bloch equations and precisely relates the excitation profile with the RF pulse when the flip angle is less than π/2. As an application of this solution, we present a procedure for designing RF pulses to generate symmetric excitation profiles with arbitrary shapes for new encoding approaches such as wavelet encoding.     

Design and optimization for variable rate selective excitation using an analytic RF scaling function

At higher B(0) fields, specific absorption rate (SAR) deposition increases. Due to maximum SAR limitation, slice coverage decreases and/or scan time increases. Conventional selective RF pulses are played out in conjunction with a time independent field gradient. Variable rate selective excitation (VERSE) is a technique that modifies the original RF and gradient waveforms such that slice profile is unchanged. The drawback is that the slice profile for off-resonance spins is distorted. A new VERSE algorithm based on modeling the scaled waveforms as a Fermi function is introduced. It ensures that system related constraints of maximum gradient amplitude and slew rate are not exceeded. The algorithm can be used to preserve the original RF pulse duration while minimizing SAR and peak b1 or to minimize the RF pulse duration. The design is general and can be applied to any symmetrical or asymmetrical RF waveform. The algorithm is demonstrated by using it to (a) minimize the SAR of a linear phase RF pulse, (b) minimize SAR of a hyperbolic secant RF pulse, and (c) minimize the duration of a linear phase RF pulse. Images with a T1-FLAIR (T1 FLuid Attenuated Inversion Recovery) sequence using a conventional and VERSE adiabatic inversion RF pulse are presented. Comparison of images and scan parameters for different anatomies and coils shows increased scan coverage and decreased SAR with the VERSE inversion RF pulse, while image quality is preserved.     

A chemical-shift-insensitive slice-selective RF pulse (CHISS)

In NMR imaging and in vivo spectroscopy, slice selection is usually achieved by applying a frequency-selective RF pulse in the presence of a magnetic field gradient. A serious limitation of this method of slice selection is that, in a system with many different chemical shifts, the selected slice is offset in space for each chemically shifted resonance. In the present study, a composite RF pulse that is insensitive to chemical-shift differences has been developed. The pulse involves applying a RF pulse of desired shape in the presence of an alternating magnetic field gradient, together with hard 180° pulses at each gradient transition. Calculations are presented to show that excitation with the proposed pulse averages the chemical-shift term to zero. An exact calculation for a rectangular RF excitation shape verifies this. Experiments based on observing the RF excitation profiles have been performed to demonstrate the validity of the proposed pulse.     

Reducing SAR in parallel excitation using variable-density spirals: a simulation-based study

Parallel excitation using multiple transmit channels has emerged as an effective method to shorten multidimensional spatially selective radiofrequency (RF) pulses, which have a number of important applications, including B1 field inhomogeneity correction in high-field MRI. The specific absorption rate (SAR) is a primary concern in high-field MRI, where wavelength effects can lead to local peaks in SAR. In parallel excitation, the subjects are exposed to RF pulses from multiple coils, which makes the SAR problem more complex to analyze, yet potentially enables greater freedom in designing RF pulses with lower SAR. Parallel-excitation techniques typically employ either Cartesian or constant-density (CD) spiral trajectories. In this article, variable-density (VD) spiral trajectories are explored as a means for SAR reduction in parallel-excitation pulse design. Numerical simulations were conducted to study the effects of CD and VD spirals on parallel excitation. Specifically, the electromagnetic fields of a four-channel transmit head coil with a three-dimensional head model at 4.7 T were simulated using a finite-difference time domain method. The parallel RF pulses were designed and the resulting excitation patterns were generated using a Bloch simulator. The SAR distributions due to CD and VD spirals were evaluated quantitatively. The simulation results show that, for the same pulse duration, parallel excitation with VD spirals can achieve a lower SAR compared to CD spirals for parallel excitation. VD spirals also resulted in reduced artifact power in the excitation patterns. This gain came with slight, but noticeable, degrading of the spatial resolution of the resulting excitation patterns.     

Pattern pulses: design of arbitrary excitation profiles as a function of pulse amplitude and offset

A novel class of pulses is presented which can be regarded as a generalization of both frequency-selective pulses and B1-selective pulses. The excitation profile of these pulses forms a pre-defined pattern in two dimensions, which are spanned by pulse offset and radio-frequency (RF) amplitude. The presented pulses were designed numerically based on principles of optimal control theory. For simple test patterns, we demonstrate the flexibility of this approach by simulations and experiments. This previously unknown flexibility may trigger novel applications in NMR spectroscopy and imaging. As a first practical application, we demonstrate a direct approach for calibrating RF pulses.     

Tailored slice selection in solid-state MRI by DANTE under magic-echo line narrowing

We propose a method of slice selection in solid-state MRI by combining DANTE selective excitation with magic-echo (ME) line narrowing. The DANTE RF pulses applied at the ME peaks practically do not interfere with the ME line narrowing in the combined ME DANTE sequence. This allows straightforward tailoring of the slice profile simply by introducing an appropriate modulation, such as a sinc modulation, into the flip angles of the applied DANTE RF pulses. The utility of the method has been demonstrated by preliminary experiments performed on a test sample of adamantane.     

Slice-selective J-coupled coherence transfer using symmetric linear phase pulses: applications to localized GABA spectroscopy

Symmetric, linear phase, slice-selective RF pulses were analyzed theoretically for performing slice-selective coherence transfer. It was shown using numerical simulations of product operators that, when a prefocusing gradient of the same area as that of the refocusing gradient is added, these pulses become slice-selective universal rotator pulses, therefore, capable of performing slice-selective coherence transfer. As an example, a slice-selective universal rotator pulse based on a seven-lobe hamming-filtered sinc pulse was applied to in vivo single-shot simultaneous spectral editing and spatial localization of neurotransmitter GABA in the human brain.     

Optimal control design of constant amplitude phase-modulated pulses: application to calibration-free broadband excitation

An optimal control algorithm for generating purely phase-modulated pulses is derived. The methodology is applied to obtain broadband excitation with unprecedented tolerance to RF inhomogeneity. Design criteria were transformation of Iz-->Ix over resonance offsets of +/-25 kHz for constant RF amplitude anywhere in the range 10-20 kHz, with a pulse length of 1 ms. Simulations transform Iz to greater than 0.99 Ix over the targetted ranges of resonance offset and RF variability. Phase deviations in the final magnetization are less than 2-3 degrees over almost the entire range, with sporadic deviations of 6-9 degrees at a few offsets for the lowest RF (10 kHz) in the optimized range. Experimental performance of the new pulse is in excellent agreement with the simulations, and the robustness of the excitation pulse and a derived refocusing pulse are demonstrated by insertion into conventional HSQC and HMBC-type experiments.     

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.     

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.     

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.     

Choice of soft pulse shapes for signal excitation in chemical shift selective imaging

The choice of soft pulse shapes for chemical shift selective excitation in chemical shift imaging is discussed. In the presence of inhomogeneities in the static magnetic field resulting from susceptibility anomalies, it is important to optimise pulse bandshape and frequency offset as well as bandwidth, in order to minimize artefacts arising from excitation of unwanted resonances. A comparison of the use of Gaussian and sinc shaped excitation pulses in the chemical shift micro-imaging of grapes serves to illustrate some of the effects that may be observed.     

Pure-phase selective excitation in fast-relaxing systems

Selective pulses have been used frequently for small molecules. However, their application to proteins and other macromolecules has been limited. The long duration of shaped-selective pulses and the short T(2) relaxation times in proteins often prohibited the use of highly selective pulses especially on larger biomolecules. A very selective excitation can be obtained within a short time by using the selective excitation sequence presented in this paper. Instead of using a shaped low-intensity radiofrequency pulse, a cluster of hard 90 degrees pulses, delays of free precession, and pulsed field gradients can be used to selectively excite a narrow chemical shift range within a relatively short time. Thereby, off-resonance magnetization, which is allowed to evolve freely during the free precession intervals, is destroyed by the gradient pulses. Off-resonance excitation artifacts can be removed by random variation of the interpulse delays. This leads to an excitation profile with selectivity as well as phase and relaxation behavior superior to that of commonly used shaped-selective pulses. Since the evolution of scalar coupling is inherently suppressed during the double-selective excitation of two different scalar-coupled nuclei, the presented pulse cluster is especially suited for simultaneous highly selective excitation of N-H and C-H fragments. Experimental examples are demonstrated on hen egg white lysozyme (14 kD) and the bacterial antidote ParD (19 kD).     

相位可控的核四极矩共振激励脉冲发生器设计

在核四极矩共振（NQR）领域,射频激励脉冲信号的优劣对NQR响应信号有重要影响.针对常规方法中射频激励脉冲参数不可控的问题,本文基于32位闪存微型控制器STM32和直接数字频率合成（DDS）芯片AD9910设计了一种相位可控激励脉冲发生器.采用STM32控制AD9910产生波形参数（脉冲宽度、脉冲间隔、脉冲个数和共振频率等）可控的射频激励脉冲,利用LabVIEW软件平台设计脉冲参数设置界面,并建立计算机与微控制器通信,实现波形参数的精确优化控制.实验结果表明,该方法实现了相位可控的NQR激励脉冲序列,可为后续NQR信号检测提供有效激励源.     

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.     

基于数字调制技术的核磁共振射频脉冲发生器

在核磁共振（NMR）领域,射频脉冲信号的质量、形状对NMR性能及应用有着重要影响.本文基于现场可编程门阵列（FPGA）和直接数字频率合成（DDS）芯片AD9910设计了一种硬件结构更为简单的NMR射频脉冲发生器,实现了射频脉冲各项参数的数字化调制.其频率、相位、振幅的控制精度分别达到了32位、16位和14位,脉冲调制的时间精度为0.01 μs,可灵活生成持续时间不小于0.1 μs、载波频率不高于400 MHz的各类软脉冲和硬脉冲.同时,针对脉冲序列的特点建立了"脉冲+延时"的基础模型,提出了一种通用性更强的列表式脉冲序列控制方案,精简了对上级控制单元的控制需求.此外,对射频脉冲信号的频谱特性进行了理论分析,并采用Hanning窗对软脉冲的包络波形进行了优化处理,仿真和实验结果表明,Hanning窗可以有效抑制软脉冲的频谱泄漏问题.     

Fat-water selective excitation in balanced steady-state free precession using short spatial-spectral RF pulses

Fat suppression is important but challenging in balanced steady-state free precession (bSSFP) acquisitions, for a number of clinical applications. In the present work, the practicality of performing fat-water selective excitations using spatial-spectral (SPSP) RF pulses in bSSFP sequence is examined. With careful pulse design, the overall duration of these SPSP pulses was kept short to minimize detrimental effects on TR, scan time and banding artifact content. Fat-water selective excitation using SPSP pulses was demonstrated in both phantom and human bSSFP imaging at 3T, and compared to results obtained using a two-point Dixon method. The sequence with SPSP pulses performed better than the two-point Dixon method, in terms of scan time and suppression performance. Overall, it is concluded here that SPSP RF pulses do represent a viable option for fat-suppressed bSSFP imaging.     

Four dimensional bolus tagging imaging of pulsatile flow

Inversion bolus tagging MR methods were used to provide a graphic depiction of the axial velocity in three spatial dimensions for pulsatile flow through complex geometries. Visualization of the flow field was readily apparent, and a train of tagged boli were depicted providing an immediate overview of the displacement of flowing fluid over the entire pulsatile cycle. Tagging efficiency obtained using adiabatic inversion pulses was improved compared to that with a windowed sinc pulse. Results from phantom experiments on steady flow were correlated with computational fluid dynamic (CFD) simulations. The use of 3D methods reduced spatial partial volume effects, and the displacement of boli in a steady flow experiment correlated well with CFD simulations. The use of adiabatic inversion pulses resulted in sharp edged inversion regions with good retention of longitudinal magnetization. However in order to keep the pulse duration short, of the order of 2-5 ms, a rather large RF amplitude had to be used. The inversion bolus tagging method is useful in visualizing the flow field in multiple levels for pulsatile fluid flowing through complex geometries, and may be useful in fluid dynamic applications.     

用于长脉冲多束团直线加速器的SLED系统

根据长脉冲多束团直线加速器对输入微波波形的要求,系统研究了带有SLED的微波系统,由SLED基本理论推导了输出RAMP波形和平顶波形脉冲时SLED所需的输入波形,给出SLED的参数优化方法.用冷测实验对所发展的理论进行了验证,第一次用SLED产生了RAMP波形和平顶波形的RF脉冲.