Solvent-suppression pulses. III. Design using simulated-annealing optimization with in vitro and in ivo testing

Pulses have been designed using a simulated-annealing optimization technique to overcome the problems associated with the observation of weak proton resonances in aqueous solution. As in a previous study (V. Smith, J. Kurhanewicz, and T. L. James, J. Magn. Reson. 95, 41 (1991), where optimization was accomplished using optimal control theory, pulses are tailored to provide null excitation at the water proton resonance frequency with uniform excitation and phasing of other proton resonance frequencies. The pulse duration is reasonable, easily enabling study of nuclei with spin-spin relaxation time ⩾ 10 ms. In general, effects from inhomogeneities in the stationary magnetic field and the radiofrequency field are minimal. The objectives were best achieved using a tailored 90° pulse in a Hahn spin-echo sequence with a long interpulse delay. Efficacy of some of the pulses was demonstrated with a solution containing a mixture of histidine, methionine, and threonine and in vivo with the kidney of an anesthetized rat utilizing a surface coil, in comparison with standard pulse sequences.     

Cross-correlated relaxation in NMR of macromolecules in the presence of fast and slow internal dynamics

In this paper we present an analysis of correlation and spectral density functions involved in autorelaxation and cross-correlated relaxation in the magnetic resonance of macromolecules. Internal dynamics of the macromolecule are described in terms of two distinct fluctuation processes with different, slow and fast, correlation times. The approach developed in this work takes into account the possible coupling between both fluctuating internal processes. To cite this article: L. Vugmeyster et al., C. R. Physique 5 (2004).     

Orientational dynamics of superfluid He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

Application of multiple inversion recovery for suppression of macromolecule resonances in short echo time (1)H NMR spectroscopy of human brain.

Macromolecules contribute broad "background" resonances to the (1)H NMR brain spectra at short echo times. The application of long echo times is the most widely used method for removing these resonances. Here, it is demonstrated that these background resonances may be suppressed at short echo times using multiple inversion recovery (MIR). In the technique presented, the MIR sequence consists of four adiabatic inversion pulses, applied preparatory to a 20-ms echo time stimulated echo localization sequence. The inversion times (359, 157, 69, and 20 ms) were selected to preferentially suppress macromolecules with longitudinal relaxation times between 38 and 300 ms. While the resulting spectra have lower overall signal-to-noise, baseline contributions from macromolecules are greatly reduced. Unlike the typical long TE acquisitions, the short TE MIR acquisition preserves the myo-inositol resonance.     

The matrix formalism for generalised gradients with time-varying orientation in diffusion NMR

Protein backbone 15N NMR spin relaxation rates are useful in characterizing the protein dynamics and structures. To observe the protein nuclear-spin resonances a pulse sequence has to include a water suppression scheme. There are two commonly employed methods, saturating or dephasing the water spins with pulse field gradients and keeping them unperturbed with flip-back pulses. Here different water suppression methods were incorporated into pulse sequences to measure 15N longitudinal T1 and transversal rotating-frame T1ρ spin relaxation. Unexpectedly the 15N T1 relaxation time constants varied significantly with the choice of water suppression method. For a 25-kDa Escherichiacoli. glutamine binding protein (GlnBP) the T1 values acquired with the pulse sequence containing a water dephasing gradient are on average 20% longer than the ones obtained using a pulse sequence containing the water flip-back pulse. In contrast the two T1ρ data sets are correlated without an apparent offset. The average T1 difference was reduced to 12% when the experimental recycle delay was doubled, while the average T1 values from the flip-back measurements were nearly unchanged. Analysis of spectral signal to noise ratios (s/n) showed the apparent slower 15N relaxation obtained with the water dephasing experiment originated from the differences in 1HN recovery for each relaxation time point. This in turn offset signal reduction from 15N relaxation decay. The artifact becomes noticeable when the measured 15N relaxation time constant is comparable to recycle delay, e.g., the 15N T1 of medium to large proteins. The 15N relaxation rates measured with either water suppression schemes yield reasonable fits to the structure. However, data from the saturated scheme results in significantly lower Model-Free order parameters (=0.81) than the non-saturated ones (=0.88), indicating such order parameters may be previously underestimated.     

A New Localization Method Using an Adiabatic Pulse,BIR-4

A new method is described for accomplishing localized spectroscopy with an adiabatic pulse, BIR-4. The method has advantages similar to previously described combinations of outer-volume suppression (OVS) and ISIS, with the additional advantages that localization is achieved with only three radiofrequency pulses and the localization remains accurate even in the presence of intense signals with short relaxation times. This new localization pulse sequence is referred to as integrated OVS-ISIS. Computer simulations, experimental images of the localized volumes, and in vivo¹H spectroscopy measurements demonstrate the high degree of localization achievable with integrated OVS-ISIS.     

Localized in vivo proton spectroscopy of the bone marrow in patients with leukemia

Volume selective magnetic resonance (MR) proton spectroscopy was used to investigate the haemopoietic (iliac bone) and fatty bone marrow (tibia) in patients with leukemia and polycythaemia vera. Selective measurements of the relaxation times T₁ and T₂ for the “water” and “fat” resonances in the bone marrow spectra were performed. Nine patients with acute leukemia and three patients with chronic leukemia were examined at diagnosis. Three patients with acute leukemia in remission were also examined. Five of the leukemic patients had follow-up examinations performed in relation to chemotherapeutic treatment. Nine patients with polycythaemia vera and 21 normal control subjects were examined with identical methods for comparison. All patients had bone marrow biopsies performed prior to every MR examination. Significant differences could be detected in the spectral patterns from iliac bone marrow in patients with leukemia at diagnosis compared to the healthy normal controls. The “relative water content” was increased in the iliac bone marrow spectra of the leukemic patients compared to the normal subjects, which indicates an increase in the amount of haemopoietic tissue and a corresponding decrease in marrow fat content. The T₁ relaxation times of the “water” resonance in the spectra from the iliac bone marrow of the leukemic patients were significantly prolonged at diagnosis, compared to the normal controls and the patients with polycythaemia vera. After chemotherapeutic induction of remission, the spectra from the iliac bone marrow in the patients with leukemia resembled normal spectra. Four leukemic patients had abnormal spectra from the tibial bone marrow and one patients showed early changes in tibial marrow during chemotherapeutic treatment, before any major changes could be detected in the iliac bone marrow.     

The spin dynamics of an anisotropic fermi supefluid (3He?)

In this paper we develop a general theory of the spin dynamics of anisotropic Fermi superfluids of the generalized BCS type, under conditions which should be realistic for any such phase of liquid ³He occurring below 3 mK. No restrictions are placed on the nature of the pairing configuration. The system is described in terms of the total spin vector S, and a vector T(n) which describes the amplitude and spin quantization axes of the pairs forming at a given point n on the Fermi surface; the kinematic relations between these quantities are emphasized. An approximation of the Born-Oppenheimer type is used to derive the general equations of motion of S and T; it is pointed out that relaxation of T due to collisions is inhibited by the coherent nature of the superfluid state. The equations of motion are solved for the particular case of unsaturated c.w. resonance, and it is shown that the nature of the transverse (usual) resonance spectrum is a strong function of the kind of configuration occurring; in particular, either one or two finite-frequency resonances may occur, depending on the configuration. A resonance is also predicted to occur when the r.f. field is polarized along the static external field. Specific predictions of the form of the transverse and “longitudinal” spectra are made for all the unitary l = 1 states, and it is shown that these predictions are unaffected by renormalization effects. The “Balian-Werthamer” state is predicted to show a longitudinal resonance but no transverse shift. The theory is compared with other approaches to the problem and its relevance to the anomalous low-temperature phases of liquid ³He is discussed.     

Temperature Characteristics of Vibrating Type Sensor Using Micromachined Optical Fiber-Tip

An optical sensor using a quartz core microcantilever was fabricated by etching clad layer from optical fiber. The temperature dependence of the resonance frequency of this sensor was measured in atmosphere and water. The temperature coefficient of the resonance frequency in water was 1.3×10⁻³/°C, which was about one order larger than that (2.3×10⁻⁴/°C) in atmosphere. This was caused by increase of additional mass due to temperature dependence of the viscosity of water, while, the increase of the resonance frequency in atmosphere was caused by temperature dependence of Young’s modulus of the quartz core. These results were evaluated theoretically using a “string-of-beads” model.     

Optimally chirped CARS using fiber stretchers

High spectral resolution coherent anti-Stokes Raman scattering (CARS) spectroscopy and microscopy are demonstrated with femtosecond laser systems. We perform optimal chirping in glass fibers and demonstrate a spectral resolution enhancement to better than 26 cm⁻¹, which is limited by the bandwidth of the measured resonances. Considering the convolution with the resonance bandwidth this corresponds to a spectral resolution of approximately 2.5 cm⁻¹, which is an enhancement by a factor of 165 with respect to the use of bandwidth-limited pulses. In microscopic imaging, a water background suppression of 81.5% is achieved.     

Measurement of Small One-Bond Proton–Carbon Residual Dipolar Coupling Constants in Partially Oriented C Natural Abundance Oligosaccharide Samples: Analysis of Heteronuclear JCH-Modulated Spectra with the BIRD Inversion Pulse

Two 2D J-modulated HSQC-based experiments were designed for precise determination of small residual dipolar one-bond carbon–proton coupling constants in ¹³C natural abundance carbohydrates. Crucial to the precision of a few hundredths of Hz achieved by these methods was the use of long modulation intervals and BIRD pulses, which acted as semiselective inversion pulses. The BIRD pulses eliminated effective evolution of all but ¹J_CH couplings, resulting in signal modulation that can be described by simple modulation functions. A thorough analysis of such modulation functions for a typical four-spin carbohydrate spin system was performed for both experiments. The results showed that the evolution of the ¹H–¹H and long-range ¹H–¹³C couplings during the BIRD pulses did not necessitate the introduction of more complicated modulation functions. The effects of pulse imperfections were also inspected. While weakly coupled spin systems can be analyzed by simple fitting of cross peak intensities, in strongly coupled spin systems the evolution of the density matrix needs to be considered in order to analyse data accurately. However, if strong coupling effects are modest the errors in coupling constants determined by the “weak coupling” analysis are of similar magnitudes in oriented and isotropic samples and are partially cancelled during dipolar coupling calculation. Simple criteria have been established as to when the strong coupling treatment needs to be invoked.     

Design of self-refocused pulses under short relaxation times

The effect of using self-refocused RF pulses of comparable duration to relaxation times is studied in detail using numerical simulation. Transverse magnetization decay caused by short T2 and longitudinal component distortion due to short T1 are consistent with other studies. In order to design new pulses to combat short T1 and T2 the relaxation terms are directly inserted into the Bloch equations. These equations are inverted by searching the RF solution space using simulated annealing global optimization technique. A new T2-decay efficient excitation pulse is created (SDETR: single delayed excursion T2 resistive) which is also energy efficient. Inversion pulses which improve the inverted magnetization profile and achieve better suppression of the remaining transverse magnetization are also created even when both T1 and T2 are short. This is achieved, however, on the expense of a more complex B1 shape of larger energy content.     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

Measurement of the Relaxation Rates ofH Longitudinal Modes

Accurate decay rate measurements for longitudinal modes are essential for many of the methods proposed for investigating molecular dynamics by NMR. However, the effects of cross relaxation often make it impossible to determine accurate values for these quantities. A method is presented that enables the effects of cross relaxation to be largely eliminated from such measurements. Its reliability is assessed by comparing the values for internuclear distances that can be determined from the resulting relaxation rates with values obtained using other methods. Other consequences of using this technique include an increased robustness of experiments to short (i.e., <5T₁) relaxation times and the ability to make multiple “selective” relaxation measurements simultaneously.     

互注入锁定产生双波长可调谐光脉冲的实验研究

报道了两个增益开关调制的法布里-珀罗半导体激光器互注入锁定实验方案,可产生双波长可调谐光脉冲。该装置对两个结构基本相同的法布里珀罗半导体激光器做增益开关调制,产生多模光脉冲输出;然后利用两个光纤光栅作为滤波元件,通过调节可调谐光延迟线(VODL2),可使得双波长光脉冲在两个法布里-珀罗激光器之间相互注入锁定．从而在输出端得到高边模抑制比的双波长光脉冲输出。然后再通过应力作用在两个光纤光栅上以改变它们的反射波长和适当调整另一个可调谐光延迟线(VODLI)长度．可得到不同的双波长的光脉冲输出,而重复频率保持524．6MHz不变。在13．2nm调谐范围内边模抑制比高于25dB．系统稳定且波长调节方便。     

H Spectroscopy without Solvent Suppression: Characterization of Signal Modulations at Short Echo Times

While most proton (¹H) spectra acquired in vivo utilize selective suppression of the solvent signal for more sensitive detection of signals from the dilute metabolites, recent reports have demonstrated the feasibility and advantages of collecting in vivo data without solvent attenuation. When these acquisitions are performed at short echo times, the presence of frequency modulations of the water resonance may become an obstacle to the identification and quantitation of metabolite resonances. The present report addresses the characteristics, origin, and elimination of these sidebands. Sideband amplitudes were measured as a function of delay time between gradient pulse and data collection, as a function of gradient pulse amplitude, and as a function of spatial location of the sample for each of the three orthogonal gradient sets. Acoustic acquisitions were performed to demonstrate the correlation between mechanical vibration resonances and the frequencies of MR sidebands. A mathematical framework is developed and compared with the experimental results. This derivation is based on the theory that these frequency modulations are induced by magnetic field fluctuations generated by the transient oscillations of gradient coils.     

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.     

Localized proton spectroscopy without water suppression: removal of gradient induced frequency modulations by modulus signal selection

Most Magnetic Resonance Spectroscopy (MRS) localization methods can generate gradient vibrations at acoustic frequencies and/or magnetic field oscillation, which can cause a time-varying magnetic field superimposed onto the static one. This effect can produce frequency modulations of the spectral resonances. When localized MRS data are acquired without water suppression, the associated frequency modulations are manifested as a manifold of spurious peaks, called sidebands, which occur symmetrically around the water resonance. These sidebands can be larger than the small metabolite resonances and can present a problem for the quantitation of the spectra, especially at short echo times. Furthermore, the resonance lineshapes may be distorted if any low frequency modulations are present. A simple solution is presented which consists of selecting the modulus of the acquired Free Induction Decay (FID) signal. Since the frequency modulations affect only the phase of the FID signal, the obtained real spectrum of the modulus is free from the spurious peaks where quantitative results may be directly obtained. Using this method, the distortions caused by the sidebands are removed. This is demonstrated by processing proton MRS spectra acquired without water suppression collected from a phantom containing metabolites at concentrations comparable to those in human brain and from a human subject using two different localization methods (PRESS and Chemical Shift Imaging PRESS-(CSI)). The results obtained illustrate the ability of this approach to remove the spurious peaks. The corrected spectra can then be fit accurately. This is confirmed by the results obtained from both the relative and the absolute metabolites concentrations in phantoms and in vivo.     

Generalized RF Pulse Train with Insensitivity to B 1 Inhomogeneity

Adiabatic inversion recovery radiofrequency (RF) pulse techniques are used to address B ₁ inhomogeneity; however, the specific absorption rates of these techniques are significantly higher than that of non-adiabatic RF pulse techniques. In addition, time efficiency is poorer because of the required longer inversion recovery time. Therefore, an RF pulse train with three subpulses was previously developed and reported. The purpose of this article was to generalize the RF pulse train for tissues with different T ₁ relaxation times and in a different application. The RF pulse train B ₁ insensitivities and frequency responses were calculated with different T ₁ relaxation times and different subpulse durations using the Bloch equation. The previously reported optimal flip angle (FA) combination was used. When using the optimal FA combination, the RF pulse train B ₁ insensitivity did not change even if the T ₁ relaxation times and the subpulse durations did change. In other words, the optimal FA combination does not require adjustments according to the T ₁ and subpulse duration. The RF pulse train frequency responses with these subpulses can be dramatically improved even if the inherent subpulse frequency response is poor. This finding will facilitate RF pulse train technique implementation on magnetic resonance imaging scanners.     

Guidelines for choosing the transition matrix in Monte Carlo methods using Markov chains

The sampling method proposed by Metropolis et al. (J. Chem. Phys. 21 (1953), 1087) requires the simulation of a Markov chain with a specified π as its stationary distribution. Hastings (Biometrika 57 (1970). 97) outlined a general procedure for constructing and simulating such a Markov chain. The matrix P = {p_ij} of transition probabilities is constructed using a defined symmetric function s and an arbitrary transition matrix Q. With respect to asymptotic variance reduction, Peskun (Biometrika 60 (1973), 607) determined, for a given Q, the optimum choice for s_ij. Here, guidelines are given for choosing Q so that the resulting Markov chain sampling method is as precise as is practically possible. Examples illustrating the use of the guidelines, including potential applications to problems in statistical mechanics and to the problem of estimating the probability of an simple event by “hit-ormiss” Monte Carlo in conjunction with Markov chain sampling, are discussed.