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.     

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.     

Design of phase-modulated broadband refocusing pulses

Broadband linear-phase refocusing pulses were designed with the Shinnar-Le Roux (SLR) transformation and verified experimentally. The design works in several steps: initially, a linear-phase B polynomial is created with the Parks-McClellan/Remez exchange algorithm. The complementary A polynomial required for the SLR transformation is generated with the Hilbert transformation, yielding the minimum-phase response. The phase response of the A polynomial is altered by zero-flipping, which changes the overall pulse shape while retaining its refocusing profile. Optimal pulses in terms of minimal B(1max) and hence broadest bandwidth were found with non-linear optimisation of the zero-flipping pattern. These pulses are generally phase modulated with a time-symmetric amplitude and anti-symmetric phase modulation. In this work, a whole range of pulses were designed to demonstrate the underlying relationships. Five exemplary pulses were implemented into a PRESS sequence and validated by acquiring images of a water-oil phantom and lactate spectra at TE = 144 ms.     

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.     

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.     

不同宽带脉冲在钕玻璃放大器中的幅频效应

宽带脉冲在钕玻璃放大器中传输时,由于受到增益窄化和增益饱和效应的影响,脉冲频谱将受到调制,从而产生边带丢失或者频谱两侧失衡,进而导致脉冲时间波形产生调制。针对不同的宽带光源模型,数值模拟了放大器输出波形的幅度调制,分析了增益带宽、输入脉冲带宽及增益曲线中心波长相对输入脉冲中心波长的偏差等因素对输出脉冲调制度的影响。结果表明：不同的宽带光源脉冲经过钕玻璃放大器后,均会产生不同程度的幅度调制;啁啾堆积脉冲比正弦相位调制脉冲产生的幅度调制小。     

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.     

Introduction to: A k-space analysis of small-tip-angle excitation

The article “A k-space analysis of small-tip-angle excitation” introduced a spatial frequency interpretation of the effect of RF excitation pulses. This introduction describes where the initial ideas for this paper came from, and traces out some of the applications that have been developed using this perspective.     

Optimal control in NMR spectroscopy: Numerical implementation in SIMPSON

We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.     

Tailoring the optimal control cost function to a desired output: application to minimizing phase errors in short broadband excitation pulses

The de facto standard cost function has been used heretofore to characterize the performance of pulses designed using optimal control theory. The freedom to choose new, creative quality factors designed for specific purposes is demonstrated. While the methodology has more general applicability, its utility is illustrated by comparison to a consistently chosen example--broadband excitation. The resulting pulses are limited to the same maximum RF amplitude used previously and tolerate the same variation in RF homogeneity deemed relevant for standard high-resolution NMR probes. Design criteria are unchanged: transformation of I(z)--> I(x) over resonance offsets of +/-20 kHz and RF variability of +/-5%, with a peak RF amplitude equal to 17.5 kHz. However, the new cost effectively trades a small increase in residual z magnetization for improved phase in the transverse plane. Compared to previous broadband excitation by optimized pulses (BEBOP), significantly shorter pulses are achievable, with only marginally reduced performance. Simulations transform I(z) to greater than 0.98 I(x), with phase deviations of the final magnetization less than 2 degrees, over the targeted ranges of resonance offset and RF variability. Experimental performance is in excellent agreement with the simulations.     

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.     

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

In this paper, we introduce optimal control algorithm for the design of pulse sequences in NMR spectroscopy. This methodology is used for designing pulse sequences that maximize the coherence transfer between coupled spins in a given specified time, minimize the relaxation effects in a given coherence transfer step or minimize the time required to produce a given unitary propagator, as desired. The application of these pulse engineering methods to design pulse sequences that are robust to experimentally important parameter variations, such as chemical shift dispersion or radiofrequency (rf) variations due to imperfections such as rf inhomogeneity is also explained.     

Bloch方程的精细时程积分及其在射频脉冲设计中的应用

射频脉冲的频率选择性直接影响磁共振成像的质量，而射频脉冲的优化设计又归结为对Bloch方程的求解.尽管在某些情况下Bloch方程存在解析解，但由于其缺乏通用性而且形式上过于复杂而难于得到实用.本文提出一种Bloch方程的精细时程积分算法，并结合全局优化算法给出一个完整的射频脉冲设计方案.精细积分算法具有高效、高精度的特点，对于射频脉冲的设计很有裨益.数值算例表明，设计所得的射频脉冲具有较好的频率选择性. 关键词： 磁共振成像 射频脉冲 Bloch方程 精细时程积分     

Phase and amplitude control of switching from positive to negative dispersion in superconducting quantum circuits

We study the absorption and dispersion properties of the three-level Δ$\Delta$-type superconducting fluxonium circuit, in which each atomic transition is respectively driven by a coherent classical field. The results show that the absorption and dispersion spectra depend strongly on the relative phase and intensities of the applied fields. When the relative phase is changed from π$\pi$/2 to 3π$\pi$/2, the switching from positive to negative dispersion arises, which can also be obtained via adjusting the relative intensities of the classical fields. Our scheme shows that the dispersion switching effect could be achievable for microwave pulse interacting with the superconducting fluxonium qubit.     

Infrared-laser-pulse control of bond- and state-selective excitation, dissociation and space quantization: application to a three-dimensional model of HONO2 in the ground electronic state

Selective control over the vibrational excitation and space quantization of the dissociation fragments by optimally designed linearly polarized and shaped infrared (IR) laser pulses of the picosecond (ps) and subpicosecond duration is demonstrated by means of quantum-dynamical simulations within the Schr?dinger wave-function formalism for a three-dimensional (3-D) model of HONO₂ in the ground electronic state, wherein the OH and the ON single-bond stretches are explicitly treated, together with the bending angle between them, on the basis of the ab initio defined 3-D potential-energy surface and dipole function. The high-lying zeroth-order vibrational states of the OH bond are prepared selectively both below and above the dissociation threshold of the ON single bond, and demonstrate a quasi-periodic oscillatory behaviour, manifesting intramolecular vibrational energy redistribution (IVR) on the picosecond timescale. Selective breakage of the ON single bond in HONO₂ with more than 97% probability is demonstrated, along with control of the space quantization of the dissociation fragments: the OH fragments rotating clockwise, OH(c), and anticlockwise, OH(a), are prepared selectively, with the OH(a)/OH(c) branching ratio being as high as 10.975. The results obtained show that optimally designed strong and short IR-laser pulses can compete against IVR and manipulate vibrational excitation and dissociation of polyatomic molecules. Received: 3 November 1999 / Published online: 13 July 2000     

Contribution and limits of a non‐intrusive Raman spectroscopic method compared with HPLC for routine application to pre‐delivery analytical control of two major camptothecin analogs: irinotecan and topotecan

The purpose of this study was to develop a Raman spectroscopy (RS) method as an effective tool for the non‐intrusive pre‐delivery analytical quality control (AQC) of two camptothecin analogs, i.e. irinotecan (IRI) and topotecan (TPT), which are prescribed and compounded at the hospital. Following a phase of analytical pre‐validation, based on the actual conditions of use of the analogs, the protocol was validated and compared with the reference high‐performance liquid chromatography (HPLC) method. For IRI, AQC by RS has been validated in ranges from 0.94 to 3.27 mg/ml in saline solutions and from 0.89 to 3.30 mg/ml in dextrose solutions. These ranges recover the entire therapeutic concentrations encountered in clinical practice, i.e. 1.08–2.8 mg/ml. The RS and HPLC methods were validated by calculating the accuracy profile and provided excellent results for the analytical validation key criteria. The Spearman and Kendall correlation tests (p‐value < 1.10⁻¹¹) and the statistical studies performed on the Bland and Altman graphs confirm a strong correlation between RS and HPLC results. However, we show that a routine apparatus is unable to quantify TPT therapeutic concentrations ranging between 25 and 50 µg/ml but that a sufficiently powerful RS bench is able to detect and quantify TPT. Overall, these results confirm the potential of the RS option for future innovative applications. Owing to its analytical and practical qualities, this promising method contributes to the improvement of the safety of the medication circuit at the hospital and to the protection of caregivers and their working environment. Copyright © 2015 John Wiley & Sons, Ltd.