Long repetition time experiments for measurement of concentrations in systems with chemical exchange and undergoing temporal variation-comparison of methods with and without correction for saturation

The purpose of this paper is to compare two methods for quantifying metabolite concentrations using the one-pulse experiment for a sample undergoing chemical exchange and subject to an intervention or other temporal variation. The methods, LATR-C (Long Acquisition TR (interpulse delay); Corrected for partial saturation) and LATR-NC (Long Acquisition TR; Not Corrected), are compared in terms of signal-to-noise ratio, SNR, per unit time and quantitation errors. Parameters relevant to the isolated perfused rat heart are used as a specific application, although the results are general. We assume throughout that spin-lattice relaxation times, T(1), do not change. For a given flip angle, theta, TR's are calculated which result in maximal SNR per unit time under 10%, 5%, and 1% constraints on quantitation errors. Additional simulations were performed to demonstrate explicitly the dependence of the quantitation errors on TR for a fixed theta. We find (i) if the allowed error is large, and when both metabolite concentrations and rate constants vary, LATR-C permits use of shorter TR, and hence yields greater SNR per unit time, than LATR-NC; (ii) for small allowed error, the two methods give similar TR's and SNR per unit time, so that the simpler LATR-NC experiment may be preferred; (iii) large values of theta result in similar constrained TR's and hence SNR per unit time for the two methods; (iv) the ratio of concentrations of metabolites with similar T(1) exhibit similar errors for the two methods.     

On neglecting chemical exchange effects when correcting in vivo (31)P MRS data for partial saturation

Signal acquisition in most MRS experiments requires a correction for partial saturation that is commonly based on a single exponential model for T(1) that ignores effects of chemical exchange. We evaluated the errors in (31)P MRS measurements introduced by this approximation in two-, three-, and four-site chemical exchange models under a range of flip-angles and pulse sequence repetition times (T(R)) that provide near-optimum signal-to-noise ratio (SNR). In two-site exchange, such as the creatine-kinase reaction involving phosphocreatine (PCr) and gamma-ATP in human skeletal and cardiac muscle, errors in saturation factors were determined for the progressive saturation method and the dual-angle method of measuring T(1). The analysis shows that these errors are negligible for the progressive saturation method if the observed T(1) is derived from a three-parameter fit of the data. When T(1) is measured with the dual-angle method, errors in saturation factors are less than 5% for all conceivable values of the chemical exchange rate and flip-angles that deliver useful SNR per unit time over the range T(1)/5 < or = T(R) < or = 2T(1). Errors are also less than 5% for three- and four-site exchange when T(R) > or = T(1)(*)/2, the so-called "intrinsic" T(1)'s of the metabolites. The effect of changing metabolite concentrations and chemical exchange rates on observed T(1)'s and saturation corrections was also examined with a three-site chemical exchange model involving ATP, PCr, and inorganic phosphate in skeletal muscle undergoing up to 95% PCr depletion. Although the observed T(1)'s were dependent on metabolite concentrations, errors in saturation corrections for T(R) = 2 s could be kept within 5% for all exchanging metabolites using a simple interpolation of two dual-angle T(1) measurements performed at the start and end of the experiment. Thus, the single-exponential model appears to be reasonably accurate for correcting (31)P MRS data for partial saturation in the presence of chemical exchange. Even in systems where metabolite concentrations change, accurate saturation corrections are possible without much loss in SNR.     

Denoising NMR time-domain signal by singular-value decomposition accelerated by graphics processing units

We present a post-processing method that decreases the NMR spectrum noise without line shape distortion. As a result the signal-to-noise (S/N) ratio of a spectrum increases. This method is called Cadzow enhancement procedure that is based on the singular-value decomposition of time-domain signal. We also provide software whose execution duration is a few seconds for typical data when it is executed in modern graphic-processing unit. We tested this procedure not only on low sensitive nucleus ²⁹Si in hybrid materials but also on low gyromagnetic ratio, quadrupole nucleus ⁸⁷Sr in reference sample Sr(NO₃)₂. Improving the spectrum S/N ratio facilitates the determination of T/Q ratio of hybrid materials. It is also applicable to simulated spectrum, resulting shorter simulation duration for powder averaging. An estimation of the number of singular values needed for denoising is also provided.     

Effects of apodization smoothing and denoising on spectral fitting

PurposeVisual review of individual spectra in magnetic resonance spectroscopic imaging (MRSI) data benefits from the application of spectral smoothing; however, if this processing step is applied prior to spectral analysis this can impact the accuracy of the quantitation. This study aims to analyze the effect of spectral denoising and apodization smoothing on the quantitation of whole-brain MRSI data obtained at short TE.MethodsShort-TE MRSI data obtained at 3 T were analyzed with no spectral smoothing, following (i) Gaussian apodization with values of 1, 2, 4, 6, and 8 Hz, and (ii) denoising using principal component analysis (dnPCA) with 3 different values for the number of retained principal components. The mean lobar white matter estimates for four metabolites, signal-to-noise ratio (SNR), spectral linewidth, and confidence intervals were compared to data reconstructed using no smoothing. Additionally, a voxel-wise comparison for N-acetylaspartate quantitation with different smoothing schemes was performed.ResultsSignificant pairwise differences were seen for all Gaussian smoothing methods as compared to no smoothing (p<0.001) in linewidth and metabolite estimates, whereas dnPCA methods showing no statistically significant differences in these measures. Confidence intervals decreased, and SNR increased with increasing levels of apodization smoothing or dnPCA denoising.ConclusionMild Gaussian apodization (≤2 Hz at 3 T) can be applied with minimal (1%) errors in quantitation; however, smoothing values greater than that can significantly affect metabolite quantification. In contrast, mild to moderate dnPCA based denoising provides quantitative results that are consistent with the analysis of unsmoothed data and this method is recommended for spectral denoising.     

Two-point method for T1 estimation with optimized gradient-echo sequence

Relaxation times estimation methods play a central role in various problems, such as magnetic resonance (MR) hardware calibration, tissue characterization, or temperature measurement. Previous studies have proposed optimization criteria to estimate the relaxation time T1 faster than with a multipoint method leading to two-point methods. In this paper, the class of optimized two-point methods is extended to gradient-echo (GE) sequence offering new advantages over spin-echo (SE) or inversion recovery (IR) sequences. Two GE acquisitions, with optimal flip angles theta1 and theta2 minimizing both the total scan time and the variance in the computed T1 image were applied to estimate T1, and the results were compared with those of SE sequence with optimized paired repetition times T(R1) and T(R2). First, phantom studies were carried out with five tissue-like samples on a 0.5T scanner. Then in vivo, human brain T1 image were calculated using both optimized GE and SE two-point methods. More precise T1 GE estimates than those for SE were found thanks to high signal-to-noise ratio (SNR) per unit of time, but with a small bias. These results also concern the temperature variation measurement methods, based on T1 estimation. Preliminary experimental data for temperature measurement are given.     

Spin-echoes in nitrogen-14 quadrupolar spin-system with axially symmetric electric field gradient tensor

The behaviour of the magnetisation in the spin-1 system with the axial symmetry of the electric field gradient (EFG) tensor was analysed theoretically. The behaviour of the NQR signals in hexamethylenetetramine (C6H12N4) was also studied experimentally using the pulse NQR technique and sensitive equipment. It was shown that the axial symmetry of the EFG in a sample could not be the reason why spin-echo signals were not observed in conventional pulse experiments for the same type of sample. A very short spin-spin relaxation time T2 seems to be the reason of that. The signal-to-noise ratio was sufficient for measuring T2 in C6H12N4, which had not been reported earlier. Experimental results of applying certain pulse sequences to the 14N NQR in a sample are also presented.     

Fluorine nuclear magnetic resonance: calibration and system optimization

Fluorine-19 magnetic resonance imaging (MRI) offers advantages for imaging organs and tissues. 19F is readily synthesized into a variety of compounds and offers the potential for in-vivo imaging as a complement to hydrogen MRI. The purpose of this work was to determine the minimum detection sensitivity for a fluorinated compound (CF3-CO2H) as a function of pulse sequence, interpulse times (TE, TI, and TR), gradient values and the number of data averages. CF3-CO2H was chosen because it has a single spectral line and exhibits a minimal frequency shift under the experimental conditions used for this experiment. A resistance MR scanner operating at a resonance frequency of 6.255 MHz was used for imaging both fluorine (.156 T) and hydrogen (.147 T). Critical factors determining the minimum detection sensitivity included system signal-to-noise ratio (S/N), acquisition time, relaxation times (T1, T2), and sample volume. Samples were measured over the range of 0.05 M to 20.0 M and showed a linear relationship between signal strength and concentration. The minimum detection sensitivity was 0.1 M. Use of higher static fields and optimized coils as well as improved system signal-to-noise ratios will improve detection sensitivity. We conclude that imaging of fluorine on low-field system is feasible, although it is necessary to optimize many parameters to maximize detection sensitivity.     

Maximizing signal-to-noise and contrast-to-noise ratios in FLASH imaging

This paper presents an analysis of signal-to-noise and contrast-to-noise ratios from small tip angle, gradient reversal (FLASH) imaging. Analytic and numerical techniques are used to determine the delay times and tip angles that maximize signal-to-noise per unit time from a single tissue. Similar procedures are used to determine the delay times and tip angles that maximize both T1-induced and T-2*-induced contrast-to-noise per unit time for a pair of tissues as a function of tissue characteristics and pulse sequence sampling times. The advantage of optimized FLASH imaging over optimized spin-echo imaging is quantitated by comparing signal-to-noise and contrast-to-noise ratios per unit time from the two sequences. Images are used to confirm these numerical results, to compare noise levels resulting from gradient reversals versus 180 degrees rephasing pulses and to assess the possible adverse effects of static magnetic field inhomogeneities on FLASH imaging.     

Experimental demonstration of quantitation errors in MR spectroscopy resulting from saturation corrections under changing conditions

Metabolite concentration measurements in in vivo NMR are generally performed under partially saturated conditions, with correction for partial saturation performed after data collection using a measured saturation factor. Here, we present an experimental test of the hypothesis that quantitation errors can occur due to application of such saturation factor corrections in changing systems. Thus, this extends our previous theoretical work on quantitation errors due to varying saturation factors. We obtained results for two systems frequently studied by 31P NMR, the ischemic rat heart and the electrically stimulated rat gastrocnemius muscle. The results are interpreted in light of previous theoretical work which defined the degree of saturation occurring in a one-pulse experiment for a system with given spin-lattice relaxation times, T(1)s, equilibrium magnetizations, M(0)s, and reaction rates. We found that (i) the assumption of constancy of saturation factors leads to quantitation errors on the order of 40% in inorganic phosphate; (ii) the dominant contributor to the quantitation errors in inorganic phosphate is most likely changes in T(1); (iii) T(1) and M(0) changes between control and intervention periods, and chemical exchange contribute to different extents to quantitation errors in phosphocreatine and gamma-ATP; (iv) relatively small increases in interpulse delay substantially decreased quantitation errors for metabolites in ischemic rat hearts; (v) random error due to finite SNR led to approximately 4% error in quantitation, and hence was a substantially smaller contributor than were changes in saturation factors.     

Surface coil depth measurement from steady-state free induction decays of partially relaxed spins

We propose improved protocols for depth measurement of underground liquids with a planar coil on the ground surface. The existing Earth’s field nuclear magnetic resonance (NMR) prospecting method uses radio-frequency pulses to accumulate free induction decays from fully recovered magnetization as a function of radio-frequency power per pulse, that is, the pulse moment. Our proposal is to accumulate free induction decays from partially relaxed spins, resulting in enhanced signal-to-noise ratio per unit time of measurement. First, we consider the consequences of simply shortening the interval between pulses in the traditional method. The maximum signal-to-noise ratio per unit time increases and, in addition, is reached at a smaller value of pulse moment to shorten the sequence. We also consider an alternative sequence wherein the pulse moment is kept fixed, while the pulse intervals are varied. Both methods require an increase in the average transmitter power but neither method requires any other modification in the basic NMR hardware. A time saving by a factor of at least 5 is possible with less than an order of magnitude increase in average power required. An added benefit of these approaches is its potential to measureT ₁ at the same time as the depth.     

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.     

Application of the time-variable feedback to the input amplifiers of pulse magnetic resonance spectrometers: Theoretical considerations

An analytical model for the optimization of the signal-to-noise (S/N) performance for the receiver with input resonance circuit and variable feedback is developed. It is shown that by varying the feedback type and depth optimization of the receiver the best S/N performance could be achieved. This approach is based upon a resonator-receiver model with lumped elements. These assumptions are relatively general for the model to be applicable for the design of both continuous and pulse receivers in radio-frequency and microwave bands. The overall S/N performance of the receiver upon the noise properties of its elements and the feedback settings in the input amplifier is studies for different parameter settings. It is shown that the separate optimization of individual elements does not necessarily lead to the best S/N performance of the receiver, especially when bandwidth properties and noise contribution of the elements are substantially different. It is shown that critical coupling of the amplifier to the resonance structure could be far from optimum. In some cases the optimum S/N performance could be achieved with coupling settings below the critical value. But under the assumptions made the coupling above the critical value does not correspond to be best receiver S/N performance. Suggestions on the optimum architecture of magnetic resonance spectrometer receivers with variable feedback are made.     

Comparative study of fast MR imaging: quantitative analysis on image quality and efficiency among various time frames and contrast behaviors

The purpose of this study is to quantitatively compare the image quality and efficiency provided by widely available fast MR imaging pulse sequences. A composite phantom with various T1 and T2 values and subjected to periodic motion was imaged at 1.5 T. The fast MRI sequences evaluated included fast spin-echo (FSE), single shot fast spin-echo (SSFSE), echo-planar imaging (EPI), multi-slice gradient recalled (MPGR), fast MPGR (FMPGR), and fast multi-slice spoiled gradient echo (FMPSPGR). T1-weighted (T1WI), T2-weighted (T2WI), proton-density-weighted (PDWI), and T2*-weighted (T2*WI) images were evaluated in breath-hold and non-breath-hold time frames. Analysis included measurement of image signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), nonuniformity, ghosting ratio, SNR per unit time and CNR per unit time. Among fast T2WI sequences, FSE with breath-hold time frame resulted in the highest image quality and in superior SNR and CNR efficiency by a factor of 5 or 6 as compared with conventional spin echo sequence. Among fast T1WI sequences, FMPGR and FMPSPGR both with non-breath-hold time frame produced the highest image quality and SNR and CNR efficiency by a factor of greater than 5 as compared with conventional spin echo. Among fast PDWI and T2*WI sequences, FSE produced the highest SNR and CNR, and was maximally efficient with a factors of greater than 6 as compared with conventional spin echo.     

MALDI-TOF MS对难溶聚芳酰胺PA6T的分析表征

选用五种样品试剂三氟乙酸、四氢呋喃、甲酸、乙腈、60%乙腈/5%三氟乙酸和两种不同的制样方法,采用基质辅助激光解吸电离飞行时间质谱(MALDI-TOF MS)表征难溶性聚合物聚对苯二甲酸己二酰胺(PA6T)的结构和分子量。发现以60%乙腈/5%三氟乙酸为样品试剂所得谱图的分子质量范围和信噪比最大,且溶剂法一步点样优于无溶剂法制样。获得了离子液体中合成产物PA6T的链结构,表明其主链为线性,未发现环状聚合物的存在,存在三种端基结构聚合体： 两端均为氨基或羧基、或一端为氨基另一端为羧基。采用MALDI-TOF MS和SEC两种方法对比测量了PA6T的平均分子量和分子量分布指数,表明MALDI-OF MS测得的平均分子量低于SEC法,分子量分布指数也低于SEC法,这是由于MS处理数据时忽略了低分子量部分,且高分子量部分因难以离子化而无法得到引起的。对于难溶的聚芳酰胺类聚合物的结构和分子量及其分布表征,MALDI-TOF MS仍不失为一个好方法。     

Fast T2-weighted MR imaging: impact of variation in pulse sequence parameters on image quality and artifacts

The purpose of this study was to quantitatively evaluate in a phantom model the practical impact of alteration of key imaging parameters on image quality and artifacts for the most commonly used fast T(2)-weighted MR sequences. These include fast spin-echo (FSE), single shot fast spin-echo (SSFSE), and spin-echo echo-planar imaging (EPI) pulse sequences. We developed a composite phantom with different T1 and T2 values, which was evaluated while stationary as well as during periodic motion. Experiments involved controlled variations in key parameters including effective TE, TR, echo spacing (ESP), receive bandwidth (BW), echo train length (ETL), and shot number (SN). Quantitative analysis consisted of signal-to-noise ratio (SNR), image nonuniformity, full-width-at-half-maximum (i.e., blurring or geometric distortion) and ghosting ratio. Among the fast T(2)-weighted sequences, EPI was most sensitive to alterations in imaging parameters. Among imaging parameters that we tested, effective TE, ETL, and shot number most prominently affected image quality and artifacts. Short T(2) objects were more sensitive to alterations in imaging parameters in terms of image quality and artifacts. Optimal clinical application of these fast T(2)-weighted imaging pulse sequences requires careful attention to selection of imaging parameters.     

Noise thermal impedance of a diffusive wire

The current noise density S2 of a conductor in equilibrium, the Johnson noise, is determined by its temperature T: S2 = 4k(B)TG, with G the conductance. The sample's noise temperature T(N) = S2/(4k(B)G) generalizes T for a system out of equilibrium. We introduce the "noise thermal impedance" of a sample as the ratio deltaT(N)omega/deltaP(J)omega of the amplitude deltaT(N)omega of the oscillation of T(N) when heated by an oscillating power deltaP(J)omega at frequency omega. For a macroscopic sample, it is the usual thermal impedance. We show for a diffusive wire how this (complex) frequency-dependent quantity gives access to the electron-phonon interaction time in a long wire and to the diffusion time in a shorter one, and how its real part may also give access to the electron-electron inelastic time. These times are not simply accessible from the frequency dependence of S2 itself.     

Multi-objective optimization of Nd:YAG laser cutting of nickel-based superalloy sheet using orthogonal array with principal component analysis

Laser cutting of nickel-based superalloy sheets, having wide applications in aircraft and rocket industries, is important from the quality of cut point of view. Keeping this in view, a hybrid approach of Taguchi method (TM) and principal component analysis (PCA) has been applied for multi-objective optimization (MOO) of pulsed Nd:YAG laser beam cutting (LBC) of nickel-based superalloy (SUPERNI 718) sheet to achieve better cut qualities within existing resources. The three-quality characteristics kerf width, kerf deviation (along the length of cut), and kerf taper have been considered for simultaneous optimization. The input parameters considered are assist gas pressure, pulse width, pulse frequency, and cutting speed. Initially, single-objective optimization has been performed using TM and then the signal-to-noise (S/N) ratios obtained from TM have been further used in PCA for multi-objective optimization. The results of MOO include the prediction of optimum input parameter level and their relative significance on multiple quality characteristics (MQC). The responses at predicted optimum parameter level are in good agreement with the results of confirmation experiments conducted for verification tests.     

Single-scan longitudinal relaxation measurements in high-resolution NMR spectroscopy

Several single-scan experiments for the measurement of the longitudinal relaxation time (T1) are proposed. These experiments result in fast and accurate determinations of the relaxation rate, are relatively robust to pulse imperfections, and preserve information about the chemical shift. The method used in these experiments is to first encode the T1 values as a spatial variation of the magnetization and then to read out this variation either by applying a weak gradient during acquisition or by sequentially observing different slices of the sample. As a result, it is possible to reduce the time necessary to determine the T1 values by one or two orders of magnitude. This time saving comes at the expense of the signal-to-noise level of the resulting spectrum and some chemical shift resolution.     

脉冲信号被噪声调制的单模激光随机共振

建立了一个脉冲信号受噪声调制的新型的单模激光随机共振模型, 采用线性化近似的方法计算了相应的光强关联函数和系统的输出信噪比, 并详细讨论了相应的随机共振现象. 研究结果表明: 由于噪声调制脉冲信号, 使得单模激光表现出崭新的随机共振现象, 即通过改变脉冲信号周期T来实现抑制或优化输出信噪比的目的.     

Fast fat-suppressed reduced field-of-view temperature mapping using 2DRF excitation pulses

The purpose of this study is to develop a fast and accurate temperature mapping method capable of both fat suppression and reduced field-of-view (rFOV) imaging, using a two-dimensional spatially-selective RF (2DRF) pulse. Temperature measurement errors caused by fat signals were assessed, through simulations. An 11×1140μs echo-planar 2DRF pulse was developed and incorporated into a gradient-echo sequence. Temperature measurements were obtained during focused ultrasound (FUS) heating of a fat-water phantom. Experiments both with and without the use of a 2DRF pulse were performed at 3T, and the accuracy of the resulting temperature measurements were compared over a range of TE values. Significant inconsistencies in terms of measured temperature values were observed when using a regular slice-selective RF excitation pulse. In contrast, the proposed 2DRF excitation pulse suppressed fat signals by more than 90%, allowing good temperature consistency regardless of TE settings. Temporal resolution was also improved, from 12 frames per minute (fpm) with the regular pulse to 28 frames per minute with the rFOV excitation. This technique appears promising toward the MR monitoring of temperature in moving adipose organs, during thermal therapies.