Hard Pulse Sequences Research Articles

Damage threshold of LiF crystal irradiated by femtosecond hard XFEL pulse sequence.

Here we demonstrate the results of investigating the damage threshold of a LiF crystal after irradiating it with a sequence of coherent femtosecond pulses using the European X-ray Free Electron Laser (EuXFEL). The laser fluxes on the crystal surface varied in the range ∼ 0.015-13 kJ/cm2 per pulse when irradiated with a sequence of 1-100 pulses (tpulse ∼ 20 fs, Eph = 9 keV). Analysis of the surface of the irradiated crystal using different reading systems allowed the damage areas and the topology of the craters formed to be accurately determined. It was found that the ablation threshold decreases with increasing number of X-ray pulses, while the depth of the formed craters increases non-linearly and reaches several hundred nanometers. The obtained results have been compared with data already available in the literature for nano- and picosecond pulses from lasers in the soft X-ray/VUV and optical ranges. A failure model of lithium fluoride is developed and verified with simulation of material damage under single-pulse irradiation. The obtained damage threshold is in reasonably good agreement with the experimentally measured one.

Quadrupolar solid-state NMR and repetitive experiments: Some aspects in the Liouville space. Application to spins I=1

The aim of this work is to generalize the Ernst-Anderson model developed to account of the steady-state regime of isolated spins I=1/2 subject to a train of strictly identical pulse sequences separated by free evolution periods of same duration. We generalize this model to the general case of spins I≥1 and general pulse sequence within the framework of the Liouville space. In particular, it is proved that under reasonable assumptions, a well defined steady-state regime is reached which is independent of the initial conditions. The general formal expressions obeyed by the steady-state density operator are given as a function of pulse propagators and relaxation operator for single and two-pulse sequences. In solid-state NMR where recycle time can be made, at the same time, much longer than typical coherence relaxation times and smaller than typical population relaxation times, further simplification leads to more tractable formula. As an example, the formalism is applied to I=1 spins with hard and soft single pulse sequence, or to the solid echo sequence. In particular, we were able to generalize the Ernst-Anderson formula to spins I=1. The pertinence of the theory is verified by comparing the theoretical and numerical simulations outputs to 2H single crystal experiments performed on nonadecane/urea C19D40/urea−H4 compound.

Robust INEPT and refocused INEPT transfer with compensation of a wide range of couplings, offsets, and B1-field inhomogeneities (COB3)

Following the two-step optimization procedure previously introduced with the COB-INEPT (Ehni and Luy, 2012), a corresponding inphase-to-antiphase transfer element with close to optimal transfer efficiencies over a coupling range comprising approximately J−6J has been derived. The hard pulse sequence length is only 5.5ms for coupling constants within 125–750Hz. Robustness with respect to an offset range of 37.5kHz on carbon (corresponding to 250ppm on a 600MHz spectrometer) and 10kHz on protons (16.6ppm at 600MHz) is achieved with corresponding BUBI and BURBOP broadband pulses. As the sequence achieves a three times higher upper limit of J-compensation compared to the COB-INEPT, we name the transfer element COB3-INEPT. Next to the description of optimization and pulse sequence details, the performance of the resulting element is demonstrated on a test sample and partially aligned sample with actual total couplings in the range of 134Hz⩽1TCH⩽391Hz. The sequence can also be used for inphase-to-antiphase transfer starting from carbon, where the upper limit of J-compensation is 6J for CH-groups, 3J for CH2-groups, and slightly less than 2J for CH3. Theoretical transfers and experimental verification for the different multiplicities in an refocused INEPT are given.

The Fantastic Four: A plug ‘n’ play set of optimal control pulses for enhancing NMR spectroscopy

We present highly robust, optimal control-based shaped pulses designed to replace all 90° and 180° hard pulses in a given pulse sequence for improved performance. Special attention was devoted to ensuring that the pulses can be simply substituted in a one-to-one fashion for the original hard pulses without any additional modification of the existing sequence. The set of four pulses for each nucleus therefore consists of 90° and 180° point-to-point (PP) and universal rotation (UR) pulses of identical duration. These 1ms pulses provide uniform performance over resonance offsets of 20kHz (1H) and 35kHz (13C) and tolerate reasonably large radio frequency (RF) inhomogeneity/miscalibration of ±15% (1H) and ±10% (13C), making them especially suitable for NMR of small-to-medium-sized molecules (for which relaxation effects during the pulse are negligible) at an accessible and widely utilized spectrometer field strength of 600MHz. The experimental performance of conventional hard-pulse sequences is shown to be greatly improved by incorporating the new pulses, each set referred to as the Fantastic Four (Fanta4).

High‐Pressure Synthesis and Structural Investigation of H3P8O8N9: A New Phosphorus(V) Oxonitride Imide with an Interrupted Framework Structure

The first crystalline phosphorus oxonitride imide H(3)P(8)O(8)N(9) (=P(8)O(8)N(6)(NH)(3)) has been synthesized under high-pressure and high-temperature conditions. To this end, a new, highly reactive phosphorus oxonitride imide precursor compound was prepared and treated at 12 GPa and 750 °C by using a multianvil assembly. H(3)P(8)O(8)N(9) was obtained as a colorless, microcrystalline solid. The crystal structure of H(3)P(8)O(8)N(9) was solved ab initio by powder X-ray diffraction analysis, applying the charge-flipping algorithm, and refined by the Rietveld method (C2/c (no. 15), a=1352.11(7), b=479.83(3), c=1820.42(9) pm, β=96.955(4)°, Z=4). H(3)P(8)O(8)N(9) exhibits a highly condensed (κ=0.47), 3D, but interrupted network that is composed of all-side vertex-sharing (Q(4)) and only threefold-linking (Q(3)) P(O,N)(4) tetrahedra in a Q(4)/Q(3) ratio of 3:1. The structure, which includes 4-ring assemblies as the smallest ring size, can be subdivided into alternating open-branched zweier double layers {oB,2(2)(∞)}[(2)P(3)(O,N)(7)] and layers containing pairwise-linked Q(3) tetrahedra parallel (001). Information on the hydrogen atoms in H(3)P(8)O(8)N(9) was obtained by 1D (1)H MAS, 2D homo- and heteronuclear (together with (31)P) correlation NMR spectroscopy, and a (1)H spin-diffusion experiment with a hard-pulse sequence designed for selective excitation of a single peak. Two hydrogen sites with a multiplicity ratio of 2:1 were identified and thus the formula of H(3)P(8)O(8)N(9) was unambiguously determined. The protons were assigned to Wyckoff positions 8f and 4e, the latter located within the Q(3) tetrahedra layers.

Correcting slice selectivity in hard pulse sequences

Many MRI sequences use non-selective hard pulse excitation in the presence of imaging gradients. In this work, we investigate to which extent the sinc-shaped frequency excitation profiles of the pulse can be used for imaging without the generation of artefacts. A correction algorithm is proposed that eliminates the influence of the excitation profile. Phantom as well as in vivo measurements prove that enhanced image quality can be obtained as long as the first minimum of the excitation profile lies outside the imaged object.

Sodium inversion recovery MRI of the knee joint in vivo at 7T

The loss of proteoglycans (PG) in the articular cartilage is an early signature of osteoarthritis (OA). The ensuing changes in the fixed charge density in the cartilage can be directly linked to sodium concentration via charge balance. Sodium ions in the knee joint appear in two pools: in the synovial fluids or joint effusion where the ions are in free motion and bound within the cartilage tissue where the Na+ ions have a restricted motion. The ions in these two compartments have therefore different T1 and T2 relaxation times. The purpose of this study is to demonstrate the feasibility of a fluid-suppressed 3D ultrashort TE radial sodium sequence by implementing an inversion recovery (IR) preparation of the magnetization at 7T. This method could allow a more accurate and more sensitive quantification of loss of PG in patients with OA. It is shown that adiabatic pulses offer significantly improved performance in terms of robustness to B1 and B0 inhomogeneities when compared to the hard pulse sequence. Power deposition considerations further pose a limit to the RF inversion power, and we demonstrate in simulations and experiments how a practical compromise can be struck between clean suppression of fluid signals and power deposition levels. Two IR sequences with different types of inversion pulses (a rectangular pulse and an adiabatic pulse) were tested on a liquid phantom, ex vivo on a human knee cadaver and then in vivo on five healthy volunteers, with a (Nyquist) resolution of ∼3.6mm and a signal-to-noise ratio of ∼30 in cartilage without IR and ∼20 with IR. Due to specific absorption rate limitations, the total acquisition time was ∼17min for the 3D radial sequence without inversion or with the rectangular IR, and 24:30min for the adiabatic IR sequence. It is shown that the adiabatic IR sequence generates a more uniform fluid suppression over the whole sample than the rectangular IR sequence.

Pulsed magnetization transfer for imaging and spectroscopic applications on whole-body imagers

Magnetization transfer contrast is a tool to obtain additional information on tissue using standard whole-body magnetic resonance (MR) units without any hardware extension. Short hard pulse sequences with a total duration of about 1 ms can provide selective saturation of protons with very short relaxation timesT2 of 1–10 µs. Comparatively high amplitude of the radio-frequency field is advantageous; on the other hand, this amplitude is limited for whole-body units. The presented approach to achieve adapted hard pulse sequences is mainly based on maximum RF amplitudes corresponding with pulse angles per millisecond of 360 °, or 720°. The pulse sequences must not influence the magnetization of free protons with longer relaxation timesT2>10 ms in a frequency range that depends on the circumstances of the application. This frequency range has to be markedly broader for imaging techniques than for localized spectroscopy. The number of pulses, the pulse durations and pulse angles, and the interpulse delays were systematically varied. The time intervals between repetitions of the hard pulse sequences in order to obtain stronger magnetization transfer contrast were also optimized experimentally for human skeletal muscle and brain.

Numerically optimized hard pulse sequences for fast frequency selective excitation and inversion

Numerically optimized hard pulse sequences were developed providing a frequency selective response of the transverse and longitudinal magnetization for several applicationsin vivo. The sequences are based on pulse trains with binomial ratios of the pulse angles and constant time intervals between the pulses. These pulse trains were systematically optimized to obtain broad Larmor frequency ranges in which the magnetization is not markedly influenced by the pulse sequence. In addition, the sequences had to provide maximum transverse magnetization or complete inversion of the magnetization beside the suppression range. Such behaviour is needed for chemical shift selective imaging, pulsed magnetization transfer, and frequency selective spectroscopyin vivo. The phase of the magnetization response is shown and adequate rephasing conditions are discussed as well as the actual phase duration. Short optimized hard pulse sequences for water and fat-selective imaging provide lowT2-sensitivity of the resulting magnetization. The new optimized hard pulse sequences are suitable, if optimum suppression of signals at one single point in the Larmor frequency spectrum is less important than good suppression in a larger frequency range.

Improved hard-pulse sequences for frequency-selective presaturation in magnetic resonance

We have been investigating several fat-suppressing sequences compatible with mu ltislice “instant” (I, 2) (or echo planar) imaging. Wh ile lipid suppression may be used in conventional imaging both to reduce chemical-shift artifact and to improve visualization of body tissues embedded in fat, lipid suppression is crucial in instant imaging because of the extreme shift artifact. In one promising selective saturation technique (3-5) the lipid protons are excited selectively by a binomial series of hard pulses (6). A magnetic field gradient then dephases the resulting transverse magnetization prior to slice selection. The binomial sequences (and their variants, e.g., ( 7))) invented for solvent suppression, leave little transverse excitation in a broad frequency range near the species that is to be suppressed. However, in order to suppress fat by selective saturation, the remaining longitudinal magnetization determines the amount of suppression. Therefore, for MR imaging, a better strategy would be to make a sequence that produces or leaves m inimum longitudinal magnetization in a broad frequency range around the species to be suppressed. In this Note, we derive simple hard-pulse sequences using this strategy in order to reduce dramatically the sensitivity of selective saturation suppression to local BO inhomogeneity. We shall derive these new hard-pulse sequences in a manner inspired by Hore’s original paper, al though differing a bit in approach. We will examine how requirements on the excitation spectrum constrain the amp litude of the pulses that make up a sequence. Consider an excitation, A(t), composed of IZ + 1 hard pulses along one of the transverse axes (say 2;)) equally separated in time by half of the fat-water precession period, 7hv,

The application of spinors to pulse synthesis and analysis.

We show how spinors may be used to solve many problems in pulse synthesis and analysis. They provide an elegant simple notation for many problems. We show how one can specify the component of a spinor and then, by exactly solving the Bloch equations, synthesize a hard pulse sequence or a soft pulse which will yield the desired spinor. This is done by generalizing our previous approach to inverting the Bloch equations. This can be applied to synthesizing refocusing pulses. Finally, some simple consequences about symmetric pulses are derived. It is shown that given a symmetric inversion pulse, one can always synthesize an asymmetric inverting pulse of the same duration, which, as an inversion, is better.

The use of finite impulse response filters in pulse design.

We develop a new way of synthesizing pulse sequences with desirable frequency characteristics. By combining our previous results with techniques from the theory of finite impulse response filters, we can specify (1) the total duration of the pulse sequence, (2) the frequency ranges it is desired to perturb, (3) the desired perturbation, and (4) the frequency range it is desired not to perturb. We can then synthesize a hard pulse sequence which will yield that desired perturbation with the minimal possible error. The minimum error is global, in the sense that no pulse sequence can do better at achieving the specifications, and is not just a local minimum, around the pulse sequences close to the derived pulse.

The synthesis of soft pulses with a specified frequency response

We propose a new approach to synthesizing shaped pulses, by first synthesizing a hard pulse sequence and then converting it to a soft pulse. In previous papers, we developed a new approach to synthesizing hard pulse sequences by exactly inverting the Bloch equation, which yields the optimal frequency response. These results can now be applied to shaped pulses. Specifically, one can specify (1) the total duration of the pulse, (2) the frequency range it is desired to perturb, (3) the perturbation desired and, (4) the frequency range it is desired not to perturb. One can then synthesize a shaped pulse which has the desired effect with the least possible error. This enables us to obtain very sharp inversion and pi/2 pulses.

Irreducible tensor operators and weak, selective, and nonselective, RF fields

A general method, based on Newton's method of successive approximations, and irreducible tensor operators, is used to examine the effect of weak, selective, and nonselective, RF fields, in multiple-quantum NMR and NQR experiments. Results are given for an I = I ensemble, subject to a chemical shift, an axially symmetric quadrupole interaction, and a soft RF field directed along the x 1 axis in the rotating frame. Combined hard and soft RF pulse sequences are briefly examined, and the “Fano sum rule” is used to show that in certain cases 50% of the original multipolar NMR order oscillates at the double-quantum frequency of the order 2 ω Q , with the remainder at the slower frequency of √2 ω 1. The treatment is related to (i) the earlier work of S. Vega and A. Pines ( J. Chem. Phys. 66, 5624 (1977 ))and A. Wokaun and R. R. Ernst ( J. Chem. Phys. 67,1752 (1977)) and (ii) the “single-shot” Raman MQNMR experiment of C. S. Yannoni, R. D. Kendrick, and P. K. Wang ( Phys. Rev. Lett. 58, 345 (1987)). In addition, it is shown that the results presented in this paper can be used to describe NQR experiments using circularly polarized RF fields.

Hard-pulse sequences for solvent suppression which only need a zero-order phase correction

Among the various methods which have been proposed to achieve solvent suppression, the binomial hard-pulse sequences (1-8) are rather attractive. Their popularity in conventional NMR spectroscopy is undoubtedly due to several advantages. They produce little radiofrequency power dissipation in the sample, they lead to a water suppression factor which is insensitive to Bi inhomogeneities, and they can be easily implemented on most FT NMR spectrometers. Furthermore, the short total duration of binomial sequences allows the observation of slowly exchanging protons or of resonances with short T2. However, their main drawback is that, except for the jump and return sequence (i.e., 90°-T-900), they generally require a linearly frequencydependent (first-order) phase correction. In the case of a large residual solvent peak such a correction results in a rolling baseline (2, 3). Recently pulse sequences which only require a small frequency-dependent phase correction have been reported (9, HO). In this contribution we propose a new class of hard-pulse sequences which achieve good suppression of the solvent signal and which only require a frequency-independent (zero-order) phase correction. The basic concept is to exploit some interesting refocusing properties of phasecycled pulse sequences symmetrical or antisymmetrical in time (II). Let us consider the BX--7-8X binomial pulse sequence (2,5). Neglecting off-resonance effects during the pnlses and effects of spin-spin coupling, the corresponding propagator can be written as P = exp(+iU,)exp( iwTl,)exp( iU,). Cl

Water suppression using a combination of hard and soft pulses

Numerous methods are available for suppression of the Hz0 resonance in the NMR spectra of water-soluble compounds. These methods include presaturation (I, 2), excitation with a soft pulse (3) or a Redfield pulse (4), rapid scan correlation (5), binomial hard-pulse sequences (6-9), and methods that exploit the different relaxation characteristics of HZ0 and solute protons (10-13). In recent years, the binomial hard-pulse sequences and variations thereof (14, 15) have become most widely used. Morris and Smith (16) showed that the binomial sequences can be combined with a single nonselective 90” pulse to provide an excitation spectrum which has nearly maximal excitation over a wide frequency range except for a narrow region around the HZ0 resonance which has near-zero excitation. The phase distortions resulting from this type of excitation are severe which leads to problems when this type of composite pulse is used in phase-sensitive two-dimensional NMR experiments. Levitt and Roberts (I 7) very recently proposed a new hard-pulse sequence which has a much weaker phase dependence across the spectrum while still providing good water suppression. However, the remaining small phase distortions, which present no problem in 1D NMR, can present difficulties in 2D NMR spectra. For example, cross peaks in a NOESY spectrum are typically two orders of magnitude weaker than diagonal peaks and even small phase distortions of the diagonal resonances give rise to serious distortions in the 2D spectrum. A recently proposed echo scheme (18) yields pure absorptive resonances across the entire spectrum but gives poor excitation close to the water resonance. Here we demonstrate the use of a hard/soft pulse combination first suggested by Gupta and Redfield (I 9). In principle, this type of hard/soft pulse combination can solve both the excitation window and the phasing problems mentioned above. However, it should be noted that the hard/soft pulse combinations described below require very stable spectrometer hardware. Conceptually the method is extremely simple. With the carrier placed on the HZ0 resonance, a weak 90?, pulse of duration T (T = 5 ms) rotates the HZ0 magnetization from the z axis to the -y axis (Fig. la), while leaving all resonances more than about 50 Hz removed from the HZ0 resonance along the z axis. A subsequent nonselective 90,” pulse rotates the HZ0 magnetization back to the z axis and rotates the resonances

Improvements in 19F NMR imaging in perfluorocarbons

The application of an improved imaging sequence for 19F NMR imaging in perfluorotributylamine is discussed and the results of phantom studies are reported. Frequency-selective excitation by a 1-3-3-1 hard pulse sequence and a short echo time are used to increase the signal-to-noise ratio. In this way the influence of strong homonuclear spin coupling as well as flow and diffusion effects are reduced.

New hard pulse sequences for solvent signal suppression in fourier transform NMR. II

New hard pulse sequences for solvent signal suppression in fourier transform NMR. II

Bloch analysis and solvent suppression by soft pulses. Application to Proton NMR investigations of human hemoglobin in H 2O and in intact red blood cells

Bloch analysis of spin response to arbitrary pulse sequences is shown to be a powerful design technique that is very easy to implement and to apply, in particular, to the problem of solvent suppression in proton NMR. As a result of extensive experimenting with the technique, we conclude that soft pulse sequences are, in general, preferable to hard pulse sequences. Detailed comparison of soft and hard pulse sequences are made to show the practical advantages of the former. A number of NMR measurements, including T 1 and solvent saturation transfer, on samples of human hemoglobin both in water and inside intact red blood cells, are given as illustrations.

New hard pulse sequences for the solvent signal suppression in fourier-transform NMR. I

Des nouvelles sequences d'impulsions selectives ont ete suggerees pour surmonter les problemes du domaine dynamique dans la RMN par transformation de Fourier associes avec l'apparition de signaux de solvant intenses. Toutes ces nouvelles sequences d'impulsions utilisent des impulsions RF dures, non selectives separees par des retards relativement longs et sont caracterisees par des spectres d'excitation avec densite spectrale nulle a la position de resonance du solvant