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.     

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.     

Novel Peak Assignments of in VivoC MRS in Human Brain at 1.5 T

¹³C MRS studies at natural abundance and after intravenous 1-¹³C glucose infusion were performed on a 1.5-T clinical scanner in four subjects. Localization to the occipital cortex was achieved by a surface coil. In natural abundance spectra glucose C_3β,5β, myo-inositol, glutamate C_1,2,5, glutamine C_1,2,5, N-acetyl-aspartate C_1-4,C=O, creatine CH₂, CH₃, and C_C=N, taurine C_2,3, bicarbonate HCO⁻₃ were identified. After glucose infusion ¹³C enrichment of glucose C_1α,1β, glutamate C_1-4, glutamine C_1-4, aspartate C_2,3, N-acetyl-aspartate C_2,3, lactate C₃, alanine C₃, and HCO⁻₃ were observed. The observation of ¹³C enrichment of resonances resonating at >150 ppm is an extension of previously published studies and will provide a more precise determination of metabolic rates and substrate decarboxylation in human brain.     

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.     

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.     

Anisotropy in Tendon Investigated in Vivo by a Portable NMR Scanner, the NMR-MOUSE

Ordered tissue like tendon is known to exhibit the magic-angle phenomenon in magnetic resonance investigations. Due to the anisotropic structure the transverse relaxation time T₂ depends on the orientation of the tendon in the magnetic field. In medical imaging, relaxation measurements of tendon orientation are restricted by the size of the object and the space available in the magnet. For humans, tendon orientation can only be varied within small limits. As a consequence, the magic-angle phenomenon may lead to a misjudgement of tendon condition. It is demonstrated that the NMR-MOUSE (mobile universal surface explorer), a hand-held NMR sensor, can be employed to investigate the anisotropy of T₂ in Achilles tendon in vivo. The NMR-MOUSE provides a convenient tool for analyzing the correlation of T₂ and the physical condition of tendon.     

A simple theory of spin-wave relaxation in ferromagnetic metals

The anisotropic exchange interaction between localized spins and conduction electrons is described by an appropriate spin hamiltonian. This is used to calculate the lifetime of magnons for arbitrary values of Λ_eq, where Λ_e is the electron mean free path and q the magnon wavevector. At Λ_eq ? 1, this lifetime depends on the angle between q and the saturation magnetization. The antisymmetric part of anisotropic exchange (Dzialoshinsky-Moriya interaction) may dominate the relaxation of spin-waves of large q. The complicated band structure of transition metals gives rise to a magnon lifetime independent of Λ_e. The contribution of isotropic exchange is also considered.     

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.     

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.     

The First in Vivo Observation of C–N Coupling in Mammalian Brain

[5-¹³C,¹⁵N]Glutamine, with ¹J(¹³C–¹⁵N) of 16 Hz, was observed in vivo in the brain of spontaneously breathing rats by ¹³C MRS at 4.7 T. The brain [5-¹³C]glutamine peak consisted of the doublet from [5-¹³C,¹⁵N]glutamine and the center [5-¹³C,¹⁴N]glutamine peak, resulting in an apparent triplet with a separation of 8 Hz. The time course of formation of brain [5-¹³C,¹⁵N]glutamine was monitored in vivo with a time resolution of 20–35 min. This [5-¹³C,¹⁵N]glutamine was formed by glial uptake of released neurotransmitter [5-¹³C]glutamate and its reaction with ¹⁵NH₃ catalyzed by the glia-specific glutamine synthetase. The neurotransmitter glutamate C5 was selectively¹³C-enriched by intravenous [2,5-¹³C]glucose infusion to ¹³C-label whole-brain glutamate C5, followed by [¹²C]glucose infusion to chase ¹³C from the small and rapidly turning-over glial glutamate pool, leaving ¹³C mainly in the neurotransmitter [5-¹³C]glutamate pool, which is sequestered in vesicles until release. Hence, the observed [5-¹³C,¹⁵N]glutamine arises from a coupling between ¹³C of neuronal origin and ¹⁵N of glial origin. Measurement of the rate of brain [5-¹³C,¹⁵N]glutamine formation provides a novel noninvasive method of studying the kinetics of neurotransmitter uptake into glia in vivo, a process that is crucial for protecting the brain from glutamate excitotoxicity.     

Neutron diffraction study of the U(Pd1−xFex)2Ge2 magnetic structure

The neutron diffraction and magnetic susceptibility studies have shown that the magnetic structure of UPd₂Ge₂ changes dramatically even under very low iron doping. Though the general magnetic structure of pure UPd₂Ge₂ and of 1%Fe-doped samples is the same, the temperature intervals of existence of different magnetic phases are different. The values of transition temperatures, where (i) the ‘square’ modulated longitudinal spin-density wave (LSDW) structure with the propagation vector k=(0; 0; ) starts to transform into the sinusoidal modulated LSDW structure and (ii) the commensurate phase transforms into incommensurate one, shift under the 1%Fe doping to the higher temperatures (from 50 to 65 K and from 80 to 90 K, respectively). In the pure and 1%Fe-doped UPd₂Ge₂, the magnetic transition from the commensurate to incommensurate phase is accompanied by the drastic decrease of the propagation vector k_z. In the 2%Fe-doped sample, besides the Néel point of T_N=135 K, we have found two additional characteristic temperatures of 65 and 93 K. Below 65 K, the material has a simple antiferromagnetic (AF) structure with the propagation vector k=(0; 0; 1) and, at 65 K<T<T_N, the magnetic structure is LSDW with sinusoidal modulation. Over almost the total region 65 K<T<T_N, the LSDW magnetic structure is incommensurate. Only at about 93 K, the propagation vector passes the commensurate value of , whereas at 65<T<93 K and at 93 K<T<T_N. We have found that the magnetic susceptibility and the uranium magnetic moment are sensitive to the transition. With increasing iron concentration to x0.15, the simple AF structure with k=(0; 0; 1) develops over all temperature region up to the Néel point. Below T_N, the uranium magnetic moments are always parallel to the tetragonal c-axis.     

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.     

Investigation of the magnetic properties and magnetic structure parameters of nanocrystalline Fe<Subscript>79</Subscript>Zr<Subscript>10</Subscript>N<Subscript>11</Subscript> films

The magnetic properties (magnetization curve, ferromagnetic resonance spectrum) of nanocrystalline Fe₇₉Zr₁₀N₁₁ films obtained by RF magnetron sputtering with subsequent annealing were studied experimentally, along with the fundamental magnetic constants of these films (saturation magnetization M _S, local magnetic anisotropy energy K, and the exchange coupling constant A). The magnetic properties are discussed within the random magnetic model, which determines the correlation of the magnetic properties with the fundamental magnetic constants and nanostructure parameters (grain size, magnetic anisotropy, and correlation radius R _C). The exchange correlation length 2R _L for the film magnetic microstructure was determined by correlation magnetometry.     

Substituent Dependent Optical Properties of <Emphasis Type="Italic">p</Emphasis>-phenyl Substituted ethenyl-<Emphasis Type="Italic">E</Emphasis>-thiophenes

Various electron donor and acceptor substituted (NO₂, CN, Cl, H, OCH₃, NH₂) p-phenyl ethenyl-E- thiophenes (1–6) were synthesized and substituent dependent optical properties (dipole moment, transition dipole moment, oscillator strength, optical band gap, hyperpolarizability) were studied using Solvatochromism and Density functional theory. It is shown that thiophene acts as a weak electron donor in presence of an electron withdrawing p-phenyl substituent (NO₂, CN, Cl), whereas thiophene acts as a weak electron acceptor in presence of an electron donating p-phenyl substituent (OCH₃, NH₂). In comparison to ethenyl thiophene 4, the HOMO-LUMO energy band gap is decreased upon increasing the electron donating or electron withdrawing capacity of p-phenyl substituent. From the excited state dipole moment calculation, it is shown that the excited state is highly dipolar for nitro and amino compounds 1 and 6, whereas compounds 2–5 show a non-polar excited state. As compared to the ethenyl thiophene 4, the first hyperpolarizability (β) increases upon substitution either with a strong electron withdrawing or strong electron donating p-phenyl substituent. A large β value is found for p-nitro phenyl ethenyl-E-thiophene and p-amino phenyl ethenyl-E- thiophene. Overall, these studies provide useful information in understanding the optical properties of phenyl and heterocyclic based ethenyl systems.     

An explicit derivation of a relation between magnetization M and saturation magnetization Ms

An explicit relationship between a magnetization vector M and its saturation magnetization M_s is derived using the definition of M along with assumptions of the continuum exchange theory. The obtained expression is found to be an extension of the commonly used fixed-length constraint and represents the continuous analog of it for the elementary moment per unit volume. The derivation of this relation is carried out in detail and important potential implications relating to equations for M are also highlighted.     

Giant Nernst effect in the pseudogap phase of high Tc superconductors

We have investigated theoretically the Nernst effect in unconventional (d-wave) charge and spin density waves (UDW). In the presence of magnetic field, Landau levels are formed, and the gapless behaviour of the low energy excitations change into gapped behaviour. When additional electric field is applied, the quasiparticles drift with a velocity of E × B/B², and carry entropy. From this, the Nernst coefficient can be calculated using the Kelvin relation. The present results account very nicely for the measured Nernst signal in the pseudogap phase of high T_c superconductor La_2−xSr_xCuO₄ and Bi₂Sr_2−yLa_yCuO₆. This indicates that the large Nernst effect is a clear signiture of UDW.     

Condition for adiabatic passage in the earth’s-field NMR technique

The equation of motion dM/dt=γ M×B(t) is solved for the case B(t)=jB_p(t)+kB_e. The field B_e is a small static field, typically the earth’s field. The field B_p(t) decays exponentially toward zero with time constant T. This decay is produced by an overdamped switching transient that occurs near the end of the rapid cutoff of the coil current used to polarize the sample. It is assumed that B_p is initially large compared to B_e, and that magnetization M is initially along the resultant field B. Exact solutions are obtained numerically for several decay time constants of B_p, and the motion of M is depicted graphically. It is found that for adiabatic passage, the final cone angle β of the precession in field B_e is related to the decay time constant of B_p by β=2e^{−(π/2)ω_eT}. This is confirmed by measurements of the amplitudes of the ensuing free-precession signals for various decay rates of B_p. Near-perfect adiabatic passage (magnetization aligned within 2° of the earth’s field) can be achieved for time constants T2.6/ω_e. For the case of sudden passage, an approximate analytic solution is developed by linearizing the equation of motion in the laboratory frame of reference. For the adiabatic case, an approximate analytic solution is obtained by linearizing the equation of motion in a rotating frame of reference that follows the resultant field B=B_p+B_e.     

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.     

Solvent-tuned ultrasonic synthesis of 2D coordination polymer nanostructures and flakes

Herein, a new 2-dimensional coordination polymer based on copper (II), {Cu₂(L)(DMF)₂}_n, where L stands for 1,2,4,5-benzenetetracarboxylate (complex 1) is synthesized. Interestingly, we demonstrate that both solvent and sonication are relevant in the top-down fabrication of nanostructures. Water molecules are intercalated in suspended crystals of complex 1 modifying not only the coordination sphere of Cu(II) ions but also the final chemical formula and crystalline structure obtaining {[Cu(L)(H₂O)₃]·H₂O}_n (complex 2). On the other hand, ultrasound is required to induce the nanostructuration. Remarkably, different morphologies are obtained using different solvents and interconversion from one morphology to another seems to occur upon solvent exchange. Both complexes 1 and 2, as well as the corresponding nanostructures, have been fully characterized by different means such as infrared spectroscopy, x-ray diffraction and microscopy.