Theoretical treatment of volume localized NMR spectroscopy in weakly coupled spin systems

A pulse sequence is proposed for obtaining volume selective echoes with both chemical shift and homonuclear scalar coupling refocused. Theory, in terms of product operator formalism, is presented and the full response of the spin system is computed. The theoretical spatial dependence of the power signal given by spins localized in different planes (x=0,y=0, respectivez=0) is presented.     

The spin coherence relaxation in the rotating frame as a microscopy parameter for strongly coupled spin systems.

The transverse relaxation time in the rotating frame T2rho is proposed as an effective parameter to get specific contrast in solid state imaging. Several peculiarities make T2rho an interesting candidate to map dynamics and structure in solids: the effect of the secular spin interaction can be controlled by the experimenter and therefore the relaxation associated with the nonsecular terms, which is particularly sensitive to very slow dynamics, can be observed. In this paper we present preliminary results obtained on polymers and prove the capability of the MARF Imaging, enhanced by a filter based on rotary echo refocusing, to produce images of solids contrasted by T2rho.     

Picoliter (1)H NMR spectroscopy

In this study, a 267-microm-diameter solenoid transceiver is used to acquire localized (1)H NMR spectra and the measured signal-to-noise ratio (SNR) at 500 MHz is shown to be within 20--30% of theoretical limits formulated by considering only its resistive losses. This is illustrated using a 100-microm-diameter globule of triacylglycerols (approximately 900mM) that may be an oocyte precursor in young Xenopus laevis frogs and a water sample containing choline at a concentration often found in live mammalian cells (approximately 33 mM). In chemical shift imaging (CSI) experiments performed using a few thousand total scans, the choline methyl line is shown to have an acceptable SNR in resolved volume elements containing only 50 pL of sample, and localized spectra are resolved from just 5 pL in the Xenopus globule. These findings demonstrate the feasibility of performing (1)H NMR on picoliter-scale sample volumes in biological cells and tissues and illustrate how the achieved SNR in spectroscopic images can be predicted with reasonable accuracy at microscopic spatial resolutions.     

Analysis of longitudinal multispin orders in strongly coupled spin systems

Longitudinal multispin orders provide an effective way for measurement of scalar couplings and also to probe molecular interactions and dynamics. Analysis of longitudinal orders has been made in strongly coupled AB and ABX spin systems to determine the dependence of strong coupling parameter on these orders. Experimental and simulated spectra of various longitudinal orders are illustrated for these spin systems. This general procedure can be extended to broad range of spin systems to understand the influence of strong coupling on longitudinal orders.     

A model for strongly coupled spin waves

The connection between a model of coupled oscillators and the system of coupled spin waves is discussed. Also the region ofk-space is estimated in which the spin-wave amplitudes have appreciable magnitude when a normal mode of coupled spin waves is excited.     

Quantitative evaluation of the lactate signal loss and its spatial dependence in press localized (1)H NMR spectroscopy

Localized (1)H NMR spectroscopy using the 90 degrees -t(1)-180 degrees -t(1)+t(2)-180 degrees -t(2)-Acq. PRESS sequence can lead to a signal loss for the lactate doublet compared with signals from uncoupled nuclei which is dependent on the choice of t(1) and t(2). The most striking signal loss of up to 78% of the total signal occurs with the symmetrical PRESS sequence (t(1)=t(2)) at an echo time of 2/J (approximately 290 ms). Calculations have shown that this signal loss is related to the pulse angle distributions produced by the two refocusing pulses which leads to the creation of single quantum polarization transfer (PT) as well as to not directly observable states (NDOS) of the lactate AX(3) spin system: zero- and multiple-quantum coherences, and longitudinal spin orders. In addition, the chemical shift dependent voxel displacement (VOD) leads to further signal loss. By calculating the density operator for various of the echo times TE=n/J, n=1, 2, 3,..., we calculated quantitatively the contributions of these effects to the signal loss as well as their spatial distribution. A maximum signal loss of 75% can be expected from theory for the symmetrical PRESS sequence and TE=2/J for Hamming filtered sinc pulses, whereby 47% are due to the creation of NDOS and up to 28% arise from PT. Taking also the VOD effect into account (2 mT/m slice selection gradients, 20-mm slices) leads to 54% signal loss from NDOS and up to 24% from PT, leading to a maximum signal loss of 78%. Using RE-BURP pulses with their more rectangular pulse angle distributions reduces the maximum signal loss to 44%. Experiments at 1.5 T using a lactate solution demonstrated a maximum lactate signal loss for sinc pulses of 82% (52% NDOS, 30% PT) at TE=290 ms using the symmetrical PRESS sequence. The great signal loss and its spatial distribution is of importance for investigations using a symmetrical PRESS sequence at TE=2/J.     

High-field localized 1H NMR spectroscopy in the anesthetized and in the awake monkey

Localized cerebral in vivo ¹H NMR spectroscopy (MRS) was performed in the anesthetized as well as the awake monkey using a novel vertical 7 T/60 cm MR system. The increased sensitivity and spectral dispersion gained at high field enabled the quantification of up to 16 metabolites in 0.1- to 1-ml volumes. Quantification was accomplished by using simulations of 18 metabolite spectra and a macromolecule (MM) background spectrum consisting of 12 components. Major cerebral metabolites (concentrations >3 mM) such as glutamate (Glu), N-acetylaspartate (NAA), creatine (Cr)/phosphocreatine (PCr) and myo-inositol (Ins) were identified with an error below 3%; most other metabolites were quantified with errors in the order of 10%. Metabolite ratios were 1.39:1 for total NAA, 1.38:1 for glutamate (Glu)/glutamine (Gln) and 0.09:1 for cholines (Cho) relative to total Cr. Taurine (Tau) was detectable at concentrations lower than 1 mM, while lactate (Lac) remained below the detection limit. The spectral dispersion was sufficient to separate metabolites of similar spectral patterns, such as Gln and Glu, N-acetylaspartylglutamate (NAAG) and NAA, and PCr–Cr. MRS in the awake monkey required the development and refinement of acquisition and correction strategies to minimize magnetic susceptibility artifacts induced by respiration and movement of the mouth or body. Periods with major motion artifacts were rejected, while a frequency/phase correction was performed on the remaining single spectra before averaging. In resting periods, both spectral amplitude and line width, that is, the voxel shim, were unaffected permitting reliable measurements. The corrected spectra obtained from the awake monkey afforded the reliable detection of 6–10 cerebral metabolites of 1-ml volumes.     

Localized double-spin-echo proton spectroscopy of weakly coupled homonuclear spin systems

The effect of localized double-spin-echo spectroscopy (PRESS) on a homonuclear weakly coupled AX spin system was calculated by the use of the product-operator formalism. Due to flip-angle distributions within the excited slices, different unwanted coherences are created which give rise to signal losses after the second and third RF pulse. The amount of signal loss is dependent on the timing of the sequence; i.e., only a proper choice of the time intervals between the pulses results in a high signal strength for coupled spins. Experiments were carried out on a Siemens Magnetom 1.5 T whole-body imager to verify the theory. Signal gains of far more than 100% were obtained for the coupled spins of lactate.     

Triple resonance, triple-quantum NMR studies of dipolar coupled spin systems

Multiple quantum-single quantum correlation experiments are employed for spectral simplification and determination of the relative signs of the couplings. In this study, we have demonstrated the excitation of three nuclei, triple quantum coherences and discussed the information obtainable from such experiments. The experiments have been carried out on doubly labeled acetonitrile and fluoroacetonitrile aligned in liquid crystalline media. The experiment is advantageous in providing many spectral parameters from a single experiment. The coherence pathways involved in the pulse sequence are described using product operators.     

Two-Dimensional spin-echo multiple-quantum transitions in strongly coupled spin systems. Calculation of spectra

A general method for computation of two-dimensional spin-echo multiple-quantum spectra of strongly coupled spin systems is presented. It has been demonstrated that the 180° pulse can severely modify the multiple-quantum spectra of strongly coupled spins and explicit spectral details are given for the spin systems of types AB, ABX, and AB₂. In addition to the modified frequencies and additional transitions, it is found that such spectra possess additional frequency symmetry with respect to the center of each multiple-quantum order, even though the multiple-quantum spectrum without the 180° pulse may not be symmetric. The ABX spin system is treated in detail and the behavior of the homonuclear and heteronuclear multiple-quantum transitions in the presence of selective or nonselective 180° pulses is discussed. It has been demonstrated that strong coupling allows transfer of magnetization from abundant spins to a coupled rare spin even in the absence of excitation pulses on abundant spins. The amplitudes of various coherences created by selective and nonselective pulses and the nature of spin-echo zero-quantum transitions of strongly coupled spins are discussed in appendices.     

Empirical bridge function for strongly coupled yukawa systems

A simple bridge function for strongly coupled Yukawa systems is developed based upon a form previously extracted for a one-component plasma [H. Iyetomi, S. Ogata, and S. Ichimaru, Phys. Rev. A 46, 1051 (1992)]. Using the proposed bridge function in the modified hypernetted chain theory, excellent agreement is obtained with molecular dynamics simulations and the compressibility sum rule is satisfied to within a few percent. This result offers a simple and very accurate method to quickly compute correlation functions for Yukawa systems.     

The nutation spin echo and its use for localized NMR

A suitably matched combination of unidirectional gradient pulses of the radio frequency amplitude B(1) and of the main magnetic field B(0) produces an unconventional type of spin echo, the nutation echo. The echo signal becomes volume selective if the gradients to be matched are inhomogeneously distributed in space. An example is a combination of a constant B(0) gradient and the inhomogeneous B(1) gradient of a surface coil. We suggest a method for localized NMR on this basis. Nutation echoes can also be used to map the spatial distribution of B(1) gradients of an arbitrary radio frequency coil geometry with the aid of a small probe sample. Copyright 2000 Academic Press.     

FT NMR of nonequilibrium states of complex spin systems. II. Weakly coupled systems

Since the Fourier transform NMR spectrum of a nonequilibrium state may be different from the slow-passage spectrum, a theory is developed which describes the phenomenon in any weakly coupled system, including those with magnetic equivalence. Liouville space techniques are used to derive simple expressions for the line intensities as a function of flip angle, in terms of Legendre polynomials. The theory uses F² representations directly and is applicable to any weakly coupled system. The results are tabulated for A_mX_n systems, m,n = 1, 2, 3, and 6. The theory is still applicable when. the weak coupling approximation starts to break down and line intensities are perturbed. It is shown that if the nonequilibrium intensities are corrected by a simple factor, as in the equilibrium case, these systems may be treated as if they were weakly coupled. In practice, the theory may be used to extrapolate to the slow-passage, zero flip angle spectrum. Furthermore, different parts of a degenerate line may be separated by means of the flip angle dependence. As an illustration, a nonequilibrium state was created among the protons in ethyl acetate. The experimental flip angle dependence of its spectra is well represented by the theory.     

Quantitative 2H NMR spectroscopy with 1H lock extender

An inexpensive external unit that allows the use of the commercial high-resolution NMR spectrometer for (2)H observation with an (1)H lock system is described. The external unit does not require any tuning, is extremely easy to use, and could be a cheaper and more straightforward alternative to the more expensive (19)F lock configuration. An application for the quantitative determination of the natural isotopic ratio (2)H/(1)H of ethanol and acetic acid is reported.     

与XY双自旋链耦合的双量子比特系统的关联性与相干性

研究了双量子比特系统中在具有Dzyaloshinsky-Moriya相互作用的独立XY自旋链环境下的相干性与关联性动力学.推导出相干性与关联性的演化规律.发现在自旋链的临界点附近,当tt_0时,系统相干性的演化与经典关联完全相同;而在tt_0时,则与量子关联完全相同;在t_0时刻,量子关联突变为经典关联.     

Double quantum filtered (1)H NMR spectroscopy enables quantification of lactate in muscle

In this study we address the question of quantification of muscle lactate using double quantum filtered (DQF) (1)H NMR spectroscopy where dipolar and scalar coupled spectra are acquired. For this, lactate content in muscle samples was independently determined using a conventional enzymatic assay and DQF, (1)H NMR spectroscopy. NMR quantification of lactate relied on comparison of muscle spectra with similarly acquired spectra of standard lactate solutions. Transverse relaxation, T(2), and dipolar coupling effects were investigated at two different orientations of muscle fibers relative to B(o) and at various lactate concentrations. In all cases, we found a biexponential T(2) decay of the lactate methyl signal with a long T(2) of 142 ms (+/-8 ms, n=24) and a short T(2) of 37 ms (+/-6 ms, n=24). Lactate content of muscle determined by NMR spectroscopy agreed with the results obtained from enzymatic assays of the same samples provided that T(2) effects as well as the presence of both scalar and dipolar coupling interactions of lactate in muscle were taken into account.