Optimized pulse parameters for reducing quantitation errors due to saturation factor changes in magnetic resonance spectroscopy

We present an analysis of the effects of chemical exchange and changes in T(1) on metabolite quantitation for heart, skeletal muscle, and brain using the one-pulse experiment for a sample which is subject to temporal variation. We use an optimization algorithm to calculate interpulse delay times, TRs, and flip angles, theta, resulting in maximal root-mean-squared signal-to-noise per unit time (S/N) for all exchanging species under 5 and 10% constraints on quantitation errors. The optimization yields TR and theta pairs giving signal-to-noise per unit time close or superior to typical literature values. Additional simulations were performed to demonstrate explicitly the dependence of the quantitation errors on pulse parameters and variations in the properties of the sample, such as may occur after an intervention. We find that (i) correction for partial saturation in accordance with the usual analysis neglecting variations in metabolite concentrations and rate constants may readily result in quantitation errors of 15% or more; the exact degree of error depends upon the details of the system under consideration; (ii) if T(1)'s vary as well, significantly larger quantitation errors may occur; and (iii) optimal values of pulse parameters may minimize errors in quantitation with minimal S/N loss.     

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.     

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.     

Pitfalls in the measurement of metabolite concentrations using the one-pulse experiment in in Vivo NMR: commentary on "On neglecting chemical exchange effects when correcting in vivo (31)P MRS data for partial saturation"

In an article in a previous issue of the Journal of Magnetic Resonance, Ouwerkerk and Bottomley (J. Magn. Reson. 148, pp. 425--435, 2001) show that even in the presence of chemical exchange, the dependence of saturation factors on repetition time in the one-pulse experiment is approximately monoexponential. They conclude from this fact that the effect of chemical exchange on the use of saturation factors when correcting for partial saturation is negligible. We take issue with this conclusion and demonstrate that because saturation factors in the presence of chemical exchange are strongly dependent upon all of the chemical parameters of the system, that is, upon all T(1)'s and M(0)'s of resonances in the exchange network and upon the reaction rates themselves, it is problematic to apply saturation factor corrections in situations in which any of these parameters may change. The error criterion we establish reflects actual errors in quantitation, rather than departures from monoexponentiality.     

Pitfalls in the Measurement of Metabolite Concentrations Using the One-Pulse Experiment in in Vivo NMR: Commentary on “On Neglecting Chemical Exchange Effects When Correcting in VivoP MRS Data for Partial Saturation”

In an article in a previous issue of the Journal of Magnetic Resonance, Ouwerkerk and Bottomley (J. Magn. Reson.148, pp. 425–435, 2001) show that even in the presence of chemical exchange, the dependence of saturation factors on repetition time in the one-pulse experiment is approximately monoexponential. They conclude from this fact that the effect of chemical exchange on the use of saturation factors when correcting for partial saturation is negligible. We take issue with this conclusion and demonstrate that because saturation factors in the presence of chemical exchange are strongly dependent upon all of the chemical parameters of the system, that is, upon all T₁'s and M₀'s of resonances in the exchange network and upon the reaction rates themselves, it is problematic to apply saturation factor corrections in situations in which any of these parameters may change. The error criterion we establish reflects actual errors in quantitation, rather than departures from monoexponentiality.     

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.     

On neglecting chemical exchange when correcting in vivo (31)P MRS data for partial saturation: commentary on: "Pitfalls in the measurement of metabolite concentrations using the one-pulse experiment in in Vivo NMR"

This article replies to Spencer et al. (J. Magn. Reson. 149, 251--257, 2001) concerning the degree to which chemical exchange affects partial saturation corrections using saturation factors. Considering the important case of in vivo (31)P NMR, we employ differential analysis to demonstrate a broad range of experimental conditions over which chemical exchange minimally affects saturation factors, and near-optimum signal-to-noise ratio is preserved. The analysis contradicts Spencer et al.'s broad claim that chemical exchange results in a strong dependence of saturation factors upon M(0)'s and T(1) and exchange parameters. For Spencer et al.'s example of a dynamic (31)P NMR experiment in which phosphocreatine varies 20-fold, we show that our strategy of measuring saturation factors at the start and end of the study reduces errors in saturation corrections to 2% for the high-energy phosphates.     

Structure of the two-dimensional relaxation spectra seen within the eigenmode perturbation theory and the two-site exchange model

The form of the two-dimensional (2D) NMR-relaxation spectra--which allow to study interstitial fluid dynamics in diffusive systems by correlating spin-lattice (T(1)) and spin-spin (T(2)) relaxation times--has given rise to numerous conjectures. Herein we find analytically a number of fundamental structural properties of the spectra: within the eigen-modes formalism, we establish relationships between the signs and intensities of the diagonal and cross-peaks in spectra obtained by various 1 and 2D NMR-relaxation techniques, reveal symmetries of the spectra and uncover interdependence between them. We investigate more specifically a practically important case of porous system that has sets of T(1)- and T(2)-eigenmodes and eigentimes similar to each other by applying the perturbation theory. Furthermore we provide a comparative analysis of the application of the, mathematically more rigorous, eigen-modes formalism and the, rather more phenomenological, first-order two-site exchange model to diffusive systems. Finally we put the results that we could formulate analytically to the test by comparing them with computer-simulations for 2D porous model systems. The structural properties, in general, are to provide useful clues for assignment and analysis of relaxation spectra. The most striking of them--the presence of negative peaks--underlines an urgent need for improvement of the current 2D Inverse Laplace Transform (ILT) algorithm used for calculation of relaxation spectra from NMR raw data.     

Band-selective chemical exchange saturation transfer imaging with hyperpolarized xenon-based molecular sensors

Molecular imaging based on saturation transfer in exchanging systems is a tool for amplified and chemically specific magnetic resonance imaging. Xenon-based molecular sensors are a promising category of molecular imaging agents in which chemical exchange of dissolved xenon between its bulk and agent-bound phases has been use to achieve sub-picomolar detection sensitivity. Control over the saturation transfer dynamics, particularly when multiple exchanging resonances are present in the spectra, requires saturation fields of limited bandwidth and is generally accomplished by continuous wave irradiation. We demonstrate instead how band-selective saturation sequences based on multiple pulse inversion elements can yield saturation bandwidth tuneable over a wide range, while depositing less RF power in the sample. We show how these sequences can be used in imaging experiments that require spatial-spectral and multispectral saturation. The results should be applicable to all CEST experiments and, in particular, will provide the spectroscopic control required for applications of arrays of xenon chemical sensors in microfluidic chemical analysis devices.     

Optimizing tissue contrast in magnetic resonance imaging

Magnetic resonance imaging demands that tissue contrast and signal-to-noise advantages be sought in each component of the imaging system. One component of magnetic resonance imaging in which contrast and signal-to-noise ratios are easily manipulated is in the choice of pulse sequences and interpulse delay times. This article provides a general method for determining the best choices of interpulse delay times in pulse sequences and applies that method to saturation recovery, inversion recovery, and spin-echo sequences. Saturation recovery and inversion recovery sequences with rephasing pulses, and tissues with unequal hydrogen densities are considered. Optimization of pulse sequences is carried out for the two distinct cases of (a) a fixed number of sequence repetitions and (b) a fixed total imaging time. Analytic expressions are derived or approximate expressions are provided for the interpulse delay times that optimize contrast-to-noise ratios in each pulse sequence. The acceptable range of interpulse delay times to obtain reasonable contrast using each pulse sequence is discussed.     

Selection of pulse sequences producing maximum tissue contrast in magnetic resonance imaging

The importance of spin density [N(H)] and spin-lattice (T₁) and spin-spin (T₂) relaxation in the characterization of tissue by nuclear magnetic resonance (NMR) is clearly recognized. This work considers which optimized pulse sequences provide the best tissue discrimination between a given pair of tissues. The effects of tissue spin density and machine-imposed minimum rephasing echo times (TE_MIN) for achieving maximum signal tissue contrast are discussed. A long TE_MIN sacrifices T₁-dependent contrast in saturation recovery (SR) and inversion recovery (IR) pulse sequences so that spin-echo (SE) becomes the optimum sequence to provide tissue contrast, due to T₂ relaxation. Pulse sequences providing superior performance may be selected based on spin density and T₁ and T₂ ratios for a given pair of tissues. Selection of the preferred pulse sequence and interpulse delay times to produce maximum tissue contrast is strongly dependent on knowledge of tissue spin densities as well as T₁ and T₂ characteristics. As the spin density ratio increases, IR replaces SR as the preferred sequence and SE replaces IR and SR as the pulse sequence providing superior contrast. To select the optimal pulse sequence and interpulse delay times, an accurate knowledge of tissue spin density, T₁ and T₂ must be known for each tissue.     

On Neglecting Chemical Exchange Effects When Correcting in VivoP MRS Data for Partial Saturation

This article replies to Spencer et al. (J. Magn. Reson.149, 251–257, 2001) concerning the degree to which chemical exchange affects partial saturation corrections using saturation factors. Considering the important case of in vivo³¹P NMR, we employ differential analysis to demonstrate a broad range of experimental conditions over which chemical exchange minimally affects saturation factors, and near-optimum signal-to-noise ratio is preserved. The analysis contradicts Spencer et al.'s broad claim that chemical exchange results in a strong dependence of saturation factors upon M₀'s and T₁ and exchange parameters. For Spencer et al.'s example of a dynamic ³¹P NMR experiment in which phosphocreatine varies 20-fold, we show that our strategy of measuring saturation factors at the start and end of the study reduces errors in saturation corrections to 2% for the high-energy phosphates.     

Effects of the Fluctuations on Thermodynamic Properties of the Mixed Valence Compounds

Based on the SU(Nd) Anderson lattice mode1 in the slave boson formalism, westudy the effect of fluctuations around the saddle-point approximation on the thermodynamic properties for mixed valence lattice systems. The fluctuation component of slave boson field is explicitly introduced and its interactions with electrons are studied. By using the Green's function technique we obtain modified self-consistent equations of mean-field parameters and free energy. The fluctuation correction to the pseudophase transition temperature is obtained, and the validity of the mean-field approximation is examined. In the limit of low energy and small moment um transfer, a fluctuation correction to the specific heat proportional to T3 lnT at low temperature is extracted. The chemical potential shift is also studied. In order to describe the thermodynamic properties correctly, it is important to determine the chemical potential shift properly.     

Magnetization transfer of water T(2) relaxation components in human brain: implications for T(2)-based segmentation of spectroscopic volumes

Biexponential T(2) relaxation of the localized water signal can be used for segmentation of spectroscopic volumes. To assess the specificity of the components an iterative relaxation measurement of the localized water signal (STEAM, 12 echo times, geometric spacing from 30 ms to 2000 ms) was combined with magnetization transfer (MT) saturation (40 single lobe pulses, 12 ms duration, 1440 degrees nominal flip angle, 1 kHz offset, repeated every 30 ms). Voxels including CSF were examined in parietal cortex and periventricular parietal white matter (10 each), as well as 13 voxels in central white matter and 16 T(1)-hypointense non-enhancing multiple sclerosis lesions without CSF inclusion. Biexponential models (excluding myelin water) were fitted to the relaxation data. In periventricular VOIs the component of long T(2) (1736 +/- 168 ms) that is attributed to CSF was not affected by MT. In cortical VOIs this component had markedly shorter T(2)'s (961 +/- 239 ms) and showed both attenuation and prolongation with MT, indicating contributions from tissue. MS lesions and central WM showed a second tissue component of intermediate T(2) (160-410 ms). In white matter similar MT attenuation indicated strong exchange between the two tissue components, prohibiting segmentation. In MS lesions, however, markedly less MT of the intermediate component was found, which is consistent with decreased cellularity and exchange in a region that is large compared to diffusion motion.     

1.5 T磁共振化学交换饱和转移成像的影响因素分析

本文探讨1.5 T磁共振化学交换饱和转移（Chemical Exchange Saturation Transfer,CEST）成像的影响因素.通过试管模型和临床病例,采用GE Signa HDe 1.5 T磁共振成像（Magnetic Resonance Imaging,MRI）扫描仪分别进行不同矩阵、激励次数、翻转角、磁化传递翻转角的CEST成像对比分析,以及不同激励次数、磁化传递翻转角的Z谱分析,并从成像组织、成像设备、成像技术等方面对原始图信号、酰胺质子转移（Amide Proton Transfer,APT）信号及Z谱进行分析研究.实验结果表明1.5 T MRI扫描仪的CEST图像信噪比相对较低,且磁场稳定性及均匀度影响了CEST成像的效果.在其他参数不变的情况下,降低采集矩阵和增加激励次数与翻转角可以增加原始图像信噪比.磁化传递翻转角为105°时,CEST成像效果最好.激励次数为2、磁化传递翻转角为105°时,所得数据符合组织Z谱情况.模型Z谱在磁化传递频率为-294~-194 Hz范围可显示30%谷氨酸（Glu）、碘剂（I₃₂₀）、纯水（H₂O）、肌酸（Cr）的信号差异,与H₂O差异最大处在-244~-214 Hz.原始图像信号30% I₃₂₀明显高于Glu、H₂O、Cr,Cr略低于Glu,APT图Cr略低于Glu.25例脑肿瘤的APT图呈高信号、12例脑梗塞的APT图呈低信号,CEST原始图像均可区分病变区域.有12例因采集时间、患者配合情况、环境及室温等影响导致CEST成像的失败.由此得出1.5 T场强下,CEST技术受到成像组织、设备、技术等因素的影响,需要进行多方面优化.在保证磁场稳定性及均匀度的情况下,优化参数的CEST成像和Z谱成像可以区分代谢物及其浓度.     

The time-dependence of exchange-induced relaxation during modulated radio frequency pulses

The problem of the relaxation of identical spins 1/2 induced by chemical exchange between spins with different chemical shifts in the presence of time-dependent RF irradiation (in the first rotating frame) is considered for the fast exchange regime. The solution for the time evolution under the chemical exchange Hamiltonian in the tilted doubly rotating frame (TDRF) is presented. Detailed derivation is specified to the case of a two-site chemical exchange system with complete randomization between jumps of the exchanging spins. The derived theory can be applied to describe the modulation of the chemical exchange relaxation rate constants when using a train of adiabatic pulses, such as the hyperbolic secant pulse. Theory presented is valid for quantification of the exchange-induced time-dependent rotating frame longitudinal T1rho,ex and transverse T2rho,ex relaxations in the fast chemical exchange regime.     

Transverse relaxation in the rotating frame induced by chemical exchange

In the presence of radiofrequency irradiation, relaxation of magnetization aligned with the effective magnetic field is characterized by the time constant T1rho. On the other hand, the time constant T2rho characterizes the relaxation of magnetization that is perpendicular to the effective field. Here, it is shown that T2rho can be measured directly with Carr-Purcell sequences composed of a train of adiabatic full-passage (AFP) pulses. During adiabatic rotation, T2rho characterizes the relaxation of the magnetization, which under adiabatic conditions remains approximately perpendicular to the time-dependent effective field. Theory is derived to describe the influence of chemical exchange on T2rho relaxation in the fast-exchange regime, with time constant defined as T2rho,ex. The derived theory predicts the rate constant R2rho,ex (= 1/T2rho,ex) to be dependent on the choice of amplitude- and frequency-modulation functions used in the AFP pulses. Measurements of R2rho,ex of the water/ethanol exchanging system confirm the predicted dependence on modulation functions. The described theoretical framework and adiabatic methods represent new tools to probe exchanging systems.     

Correcting for incomplete saturation and off-resonance effects in multiple-site saturation-transfer kinetic measurements

The effects of incomplete saturation and off-resonance irradiation on nuclear magnetic resonance saturation-transfer measurements of three-site chemical-exchange rates are discussed. A new method that uses double-saturation measurements is compared with two published methods, one that uses single-saturation measurements and one that uses a single-saturation measurement and a double-saturation measurement. Several formulas are compared for measuring the exchange rate constant k(DE) for exchange from a detected spin D to an exchanging spin E in the presence of exchange from spin D to a competing spin C. For each method, formulas are derived with corrections for incomplete saturation or off-resonance effects, with both corrections, and with neither correction. Exact formulas are available for three exchanging sites with incomplete saturation if there are no off-resonance effects. Off-resonance corrections are imperfect even with complete saturation.     

串型耦合双量子点处于自旋阻塞区时磁输运性质的研究

使用双杂质安德森模型的哈密顿量,从理论上研究了串型耦合双量子点系统处于自旋阻塞区时的磁输运性质,并用主方程近似方法求解了哈密顿量.结果表明,自旋轨道耦合作用导致的双量子点间的自旋反转隧穿能够解除系统的自旋阻塞.同时也研究了超精细相互作用导致的在量子点内自旋反转和双量子点之间的自旋关联对系统的磁输运性质的影响,取得了一些有价值的结果,并对相关的物理问题进行了讨论.     

Quantitative magnetization transfer by trains of radio frequency pulses in human brain: extension of a free evolution model to continuous-wave-like conditions

A theoretical model of free evolution between repeated magnetic transfer (MT) pulses was extended to continuous-wave (CW)-like conditions showing that only the repetitive "direct" saturation of bulk water changes the transient and stationary behavior. The influence of the pulse repetition period (PR) on progressive saturation was studied in cortical gray matter (GM) and central white matter (WM) under conditions of short periods of free evolution and strong macromolecular saturation. Interpulse delays of 3 ms were achieved in vivo on a 1.5-T MR system with bell-shaped MT pulses of 12-ms duration and nominal flip angles of up to 1440 degrees and single-shot readout by a stimulated echo acquisition mode localization sequence. The frequency offset was chosen between 1 and 3 kHz to avoid excessive direct saturation. The stationary MT ratio (MTR) followed an inverse linear PR dependence, showing a consistent partial saturation of about 90% at zero PR for both WM and GM. Comparison to a relaxation-matched liquid indicated the presence of MT, but not necessarily of direct saturation. The transient behavior indicated considerable direct saturation, but this could also be explained by MT. These inconsistencies showed that the intervals of time evolution in our experiments were too long to be modeled by CW-like conditions. Free evolution takes place during the whole PR rather than during the interpulse delay only. Quantification using the rates of free evolution theory yielded the saturations and rate constants necessary to explain the observed behavior. The theory of rapid CW-like pulsing provides an upper limit for the rate of progressive saturation. This limit is approached at PR below an estimated value of 5 ms. The phenomenological PR dependence of the steady-state MTR may indicate that MT exceeded the direct saturation. Unlike to an idealized CW experiment, the extrapolated value at zero PR is subject to direct effects and not a physically meaningful constant.