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 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.     

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 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.     

Measurement of spin-lattice relaxation times and concentrations in systems with chemical exchange using the one-pulse sequence: breakdown of the Ernst model for partial saturation in nuclear magnetic resonance spectroscopy

A fundamental problem in Fourier transform NMR spectroscopy is the calculation of observed resonance amplitudes for a repetitively pulsed sample, as first analyzed by Ernst and Anderson in 1966. Applications include determination of spin-lattice relaxation times (T(1)'s) by progressive saturation and correction for partial saturation in order to determine the concentrations of the chemical constituents of a spectrum. Accordingly, the Ernst and Anderson formalism has been used in innumerable studies of chemical and, more recently, physiological systems. However, that formalism implicitly assumes that no chemical exchange occurs. Here, we present an analysis of N sites in an arbitrary chemical exchange network, explicitly focusing on the intermediate exchange rate regime in which the spin-lattice relaxation rates and the chemical exchange rates are comparable in magnitude. As a special case of particular importance, detailed results are provided for a system with three sites undergoing mutual exchange. Specific properties of the N-site network are then detailed. We find that (i) the Ernst and Anderson analysis describing the response of a system to repetitive pulsing is inapplicable to systems with chemical exchange and can result in large errors in T(1) and concentration measurements; (ii) T(1)'s for systems with arbitrary exchange networks may still be correctly determined from a one-pulse experiment using the Ernst formula, provided that a short interpulse delay time and a large flip angle are used; (iii) chemical concentrations for exchanging systems may be correctly determined from a one-pulse experiment either by using a short interpulse delay time with a large flip angle, as for measuring T(1)'s, and correcting for partial saturation by use of the Ernst formula, or directly by using a long interpulse delay time to avoid saturation; (iv) there is a significant signal-to-noise penalty for performing one-pulse experiments under conditions which permit accurate measurements of T(1)'s and chemical concentrations. The present results are analogous to but are much more general than those that we have previously derived for systems with two exchanging sites. These considerations have implications for the design and interpretation of one-pulse experiments for all systems exhibiting chemical exchange in the intermediate exchange regime, including virtually all physiologic samples.     

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.     

Spin-wave spectrum of an ideal multilayer magnet upon modulation of all parameters of the Landau-Lifshitz equation

The spectrum of exchange spin waves in a multilayer magnet is theoretically investigated without regard for dissipation upon periodic modulation of all magnetic material parameters (uniaxial anisotropy constant, exchange interaction constant, saturation magnetization, gyromagnetic ratio) entering into the Landau-Lifshitz equation. A graphical method is proposed for analyzing the dependence of the propagation of spin waves on the depth of modulation of the material parameters. Practical application of the results obtained and the effect of dissipation on the propagation of spin waves in the system are discussed.     

A new class of contrast agents for MRI based on proton chemical exchange dependent saturation transfer (CEST)

It has been previously shown that intrinsic metabolites can be imaged based on their water proton exchange rates using saturation transfer techniques. The goal of this study was to identify an appropriate chemical exchange site that could be developed for use as an exogenous chemical exchange dependent saturation transfer (CEST) contrast agent under physiological conditions. These agents would function by reducing the water proton signal through a chemical exchange site on the agent via saturation transfer. The ideal chemical exchange site would have a large chemical shift from water. This permits a high exchange rate without approaching the fast exchange limit at physiological pH (6.5-7.6) and temperature (37 degrees C), as well as minimizing problems associated with magnetic field susceptibility. Numerous candidate chemicals (amino acids, sugars, nucleotides, heterocyclic ring chemicals) were evaluated in this preliminary study. Of these, barbituric acid and 5, 6-dihydrouracil were more fully characterized with regard to pH, temperature, and concentration CEST effects. The best chemical exchange site found was the 5.33-ppm indole ring -NH site of 5-hydroxytryptophan. These data demonstrate that a CEST-based exogenous contrast agent for MRI is feasible.     

Improved measurement of (15)N-[(1)H] NOEs in the presence of H(N)-water proton chemical exchange.

A simple method is presented to accurately determine (15)N-[(1)H] NOEs in biomolecules in the presence of H(N)-water proton chemical exchange. Three measurements are required: one with nonselective proton saturation and two with different water saturation conditions to determine the equilibrium value of the (15)N signal. This approach is exemplified with data on two peptides, one helix-forming 17-mer and one compactly folded 56-mer. Results indicate that (15)N-[(1)H] NOEs determined using the standard approach with short recycle times (3 to 4 s) can be significantly in error when H(N)-water proton chemical exchange is relatively rapid, water proton relaxation is relatively slow, and (15)N-[(1)H] NOEs are away from the value of -1. This new method avoids such inaccuracies resulting from the use of short recycle times.     

Optimization of the irradiation power in chemical exchange dependent saturation transfer experiments

In chemical exchange dependent saturation transfer imaging experiments, exchangeable solute protons are saturated and the transfer of saturation to water is subsequently detected. When the applied irradiation power is comparable to the resonance frequency difference between the water protons and saturated solute protons, the proton transfer (PT) efficiency is reduced due to concomitant direct saturation effects. In this study, the PT process is modeled using a two-pool system. An empirical general proton transfer ratio (PTR) equation for arbitrary RF irradiation power is derived, and its optimal power to maximize the PTR is analyzed. The results are confirmed experimentally on 4.7 T using a poly-L-lysine solution. The theory provides a useful tool for optimizing the irradiation power of the PT sequences in the presence of direct saturation effects.     

19F double resonance in the presence of chemical exchange

The ¹⁹F N.M.R. spectra of CF₂BrCClBr₂ in CS₂ from 20°c to -80°c are reported. Computer-fitting of the experimental spectra using the density matrix formalism of Alexander yields the chemical exchange correlation times and produces a computed internal rotation barrier for trans →gauche of 39·7 ± 0·5 kJ mol^-1 (9·5±0·1 kcal/mole). Results of double resonance studies on the -80°c spectrum upon irradiation of the various peaks with a strong r.f. field are presented. The density matrix equations in the presence of chemical exchange and several relaxation mechanisms were solved to obtain theoretical changes in peak intensities on irradiation. The indirect spin saturation data and their relation to the rate of internal rotation and the relaxation mechanism are discussed. Random field relaxation is shown to be the important relaxation mechanism in the system. The strong irradiation of one component of a strongly coupled spin multiplet with intramolecular exchange causes indirect saturation of the transitions connecting energy levels that have the same m _I values as the one being irradiated whereas the intensities of other transitions are only slightly affected. It appears therefore to be an important complement to the spin-tickling technique in determining energy level diagrams and relative signs of coupling constants.     

Measurement of APT using a combined CERT-AREX approach with varying duty cycles

The goal is to develop an imaging method where contrast reflects amide-water magnetization exchange, with minimal signal contributions from other sources. Conventional chemical exchange saturation transfer (CEST) imaging of amides (often called amide proton transfer, or APT, and quantified by the metric MTR_asym) is confounded by several factors unrelated to amides, such as aliphatic protons, water relaxation, and macromolecular magnetization transfer. In this work, we examined the effects of combining our previous chemical exchange rotation (CERT) approach with the non-linear AREX method while using different duty cycles (DC) for the label and reference scans. The dependencies of this approach, named AREX_double,vdc, on tissue parameters, including T₁, T₂, semi-solid component concentration (f_m), relayed nuclear Overhauser enhancement (rNOE), and nearby amines, were studied through numerical simulations and control sample experiments at 9.4 T and 1 μT irradiation. Simulations and experiments show that AREX_double,vdc is sensitive to amide-water exchange effects, but is relatively insensitive to T₁, T₂, f_m, nearby amine, and distant aliphatic protons, while the conventional metric MTR_asym, as well as several other APT imaging methods, are significantly affected by at least some of these confounding factors.     

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.     

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.     

Reflection of spin waves from a ferromagnetic multilayer with interfacial coupling of finite strength (reflection of spin waves from multilayer)

The reflection coefficient of bulk spin waves from a ferromagnetic multilayer with periodically modulated parameters of the exchange interaction, the uniaxial magnetic anisotropy and the saturation magnetization (a magnonic crystal) is calculated. The dependence of the reflection coefficient upon the spin wave frequency and the values of the bias magnetic field, the parameter of interfacial coupling, and the internal structure of the unit cell are investigated.      

Near-unity quantum yields of biexciton emission from CdSe/CdS nanocrystals measured using single-particle spectroscopy

Biexciton photoluminescence (PL) quantum yields (Q(2X)) of individual CdSe/CdS core-shell nanocrystal quantum dots with various shell thicknesses are derived from independent PL saturation and two-photon correlation measurements. We observe a near-unity Q(2X) for some nanocrystals with an ultrathick 19-monolayer shell. High Q(2X)'s are, however, not universal and vary widely among nominally identical nanocrystals indicating a significant dependence of Q(2X) upon subtle structural differences. Interestingly, our measurements indicate that high Q(2X)'s are not required to achieve complete suppression of PL intensity fluctuations in individual nanocrystals.     

Complete relaxation and conformational exchange matrix (CORCEMA) analysis of intermolecular saturation transfer effects in reversibly forming ligand-receptor complexes

A couple of recent applications of intermolecular NOE (INOE) experiments as applied to biomolecular systems involve the (i) saturation transfer difference NMR (STD-NMR) method and (ii) the intermolecular cross-saturation NMR (ICS-NMR) experiment. STD-NMR is a promising tool for rapid screening of a large library of compounds to identify bioactive ligands binding to a target protein. Additionally, it is also useful in mapping the binding epitopes presented by a bioactive ligand to its target protein. In this latter application, the STD-NMR technique is essentially similar to the ICS-NMR experiment, which is used to map protein-protein or protein-nucleic acid contact surfaces in complexes. In this work, we present a complete relaxation and conformational exchange matrix (CORCEMA) theory (H. N. B. Moseley et al., J. Magn. Reson. B 108, 243-261 (1995)) applicable for these two closely related experiments. As in our previous work, we show that when exchange is fast on the relaxation rate scale, a simplified CORCEMA theory can be formulated using a generalized average relaxation rate matrix. Its range of validity is established by comparing its predictions with those of the exact CORCEMA theory which is valid for all exchange rates. Using some ideal model systems we have analyzed the factors that influence the ligand proton intensity changes when the resonances from some protons on the receptor protein are saturated. The results show that the intensity changes in the ligand signals in an intermolecular NOE experiment are very much dependent upon: (1) the saturation time, (2) the location of the saturated receptor protons with respect to the ligand protons, (3) the conformation of the ligand-receptor interface, (4) the rotational correlation times for the molecular species, (5) the kinetics of the reversibly forming complex, and (6) the ligand/receptor ratio. As an example of a typical application of the STD-NMR experiment we have also simulated the STD effects for a hypothetical trisaccharide bound to a protein. The CORCEMA theory for INOE and the associated algorithm are useful in a quantitative interpretation of the intensity changes in the ligand in both the STD-NMR and ICS-NMR, provided the identity of the receptor protons experiencing direct RF saturation is known. The formalism presented here is likely to be useful in the design of bioactive ligands to a specific target protein and in the quantitative mapping of binding epitopes and interfaces between molecules in complexes.     

7 T 下脂肪对基于 NOE 的磁共振对比成像的影响

核 Overhauser 增强(NOE)效应在高场下的化学交换饱和转移中会造成 Z 谱高场位置的负背景信号,有望成为一种新的磁共振成像(MRI)对比机制．然而,研究指出, NOE信号的发生区域与主要的脂肪信号的频率位置有重叠,因此 MRI 中观察到的 NOE 信号有可能混合了脂肪信号．该文通过鸡蛋的模型实验,初步分析了脂肪含量较高的组织内脂肪信号对 NOE 效应的影响,并通过健康大鼠鼠脑及颅内肿瘤大鼠鼠脑实验,分析了脂肪对脑部 NOE 对比成像及基于 NOE 对比成像的疾病诊断的影响．结果表明,脂肪含量较高的组织内脂肪信号会引起伪 NOE 效应,并影响 NOE对比图像的准确性．
     

Effects of off-resonance irradiation, cross-relaxation, and chemical exchange on steady-state magnetization and effective spin-lattice relaxation times

In the presence of an off-resonance radiofrequency field, recovery of longitudinal magnetization to a steady state is not purely monoexponential. Under reasonable conditions with zero initial magnetization, recovery is nearly exponential and an effective relaxation rate constant R_1eff = 1/T_1eff can be obtained. Exact and approximate formulas for R_1eff and steady-state magnetization are derived from the Bloch equations for spins undergoing cross-relaxation and chemical exchange between two sites in the presence of an off-resonance radiofrequency field. The relaxation formulas require that the magnetization of one spin is constant, but not necessarily zero, while the other spin relaxes. Extension to three sites with one radiofrequency field is explained. The special cases of off-resonance effects alone and with cross-relaxation or chemical exchange, cross-relaxation alone, and chemical exchange alone are compared. The inaccuracy in saturation transfer measurements of exchange rate constants by published formulas is discussed for the creatine kinase reaction.     

Exchange-mediated contrast in CEST and spin-lock imaging

Purpose

Magnetic resonance images of biological media based on chemical exchange saturation transfer (CEST) show contrast that depends on chemical exchange between water and other protons. In addition, spin–lattice relaxation rates in the rotating frame (R_1ρ) are also affected by exchange, especially at high fields, and can be exploited to provide novel, exchange-dependent contrast. Here, we evaluate and compare the factors that modulate the exchange contrast for these methods using simulations and experiments on simple, biologically relevant samples.

Methods

Simulations and experimental measurements at 9.4 T of rotating frame relaxation rate dispersion and CEST contrast were performed on solutions of macromolecules containing amide and hydroxyl exchanging protons.

Results

The simulations and experimental measurements confirm that both CEST and R_1ρ measurements depend on similar exchange parameters, but they manifest themselves differently in their effects on contrast. CEST contrast may be larger in the slow and intermediate exchange regimes for protons with large resonant frequency offsets (e.g. > 2 ppm). Spin-locking techniques can produce larger contrast enhancement when resonant frequency offsets are small (< 2 ppm) and exchange is in the intermediate-to-fast regime. The image contrasts scale differently with field strength, exchange rate and concentration.

Conclusion

CEST and R_1ρ measurements provide different and somewhat complementary information about exchange in tissues. Whereas CEST can depict exchange of protons with specific chemical shifts, appropriate R_1ρ-dependent acquisitions can be employed to selectively portray protons of specific exchange rates.