Longitudinal Magnetization Decay Research Articles

Study of the Variation of the Electronic Distribution and Motional Dynamics of Two Independent Molecules of an Asymmetric Unit of Atorvastatin Calcium by Solid-State NMR Measurements.

Significant changes in the spin-lattice time and chemical shift anisotropy (CSA) parameters are observed in two independent molecules of an asymmetric unit of atorvastatin calcium (ATC-I) (which is referred to as “a”- and “b”-type molecules by following Wang et al.). The longitudinal magnetization decay curve is fitted by two exponentials—one with longer relaxation time and another with shorter relaxation time for most of the carbon nuclei sites. The local correlation time also varies significantly. This is the experimental evidence of the coexistence of two different kinds of motional degrees of freedom within ATC-I molecule. The solubility and bioavailability of the drug molecule are enhanced due to the existence of two different kinds of dynamics. Hence, the macroscopic properties like solubility and bioavailability of a drug molecule are highly correlated with its microscopic properties. The motional degrees of freedom of “a”- and “b”-type molecules are also varied remarkably at certain carbon nuclei sites. This is the first time the change in the molecular dynamics of two independent molecules of an asymmetric unit of atorvastatin calcium is quantified using solid-state NMR methodology. These types of studies, in which the chemical shift anisotropy (CSA) parameters and spin-lattice relaxation time provide information about the change in electronic distribution and the spin dynamics at the various crystallographic location of the drug molecule, will enrich the field “NMR crystallography”. It will also help us to understand the electronic distribution around a nucleus and the nuclear spin dynamics at various parts of the molecule, which is essential to develop the strategies for the administration of the drug.

DANTE‐prepared pulse trains: A novel approach to motion‐sensitized and motion‐suppressed quantitative magnetic resonance imaging

Delay alternating with nutation for tailored excitation (DANTE) pulse trains are well appreciated as frequency-selective excitation methods in Fourier transform NMR and for spatial tagging in MRI. In this study, nonselective DANTE pulse trains are used in combination with gradient pulses and short repetition times as motion-sensitive preparation modules. We show that while the longitudinal magnetization of static tissue is mostly preserved, flowing spins are largely (or fully) attenuated as they fail to establish transverse steady state due to a spoiling effect caused by flow along the applied gradient. The attenuation of flowing spins is effectively insensitive to spin velocity (above a low threshold) and can be approximately quantified with a simple T₁ longitudinal magnetization decay model. The relevant analytical equations for moving spins and static spins during DANTE module application are derived for both transient and steady state epochs. The equations are validated by comparing analytical solutions and numerical Bloch equation simulations against experimental observations in phantoms and in vivo. Based on this contrast mechanism, the application of the DANTE preparation to black blood vessel imaging is proposed. A simple demonstration of DANTE black blood imaging modules shows that it provides excellent blood signal suppression and static tissue signal preservation.

Study of diffusion in erythrocyte suspension using internal magnetic field inhomogeneity

Transport of water and ions through cell membranes plays an important role in cell metabolism. We demonstrate a novel technique to measure water transport dynamics using erythrocyte suspensions as an example. This technique takes advantage of inhomogenous internal magnetic field created by the magnetic susceptibility contrast between the erythrocytes and plasma. The decay of longitudinal magnetization due to diffusion in this internal field reveals multi-exponential behavior, with one component corresponding to the diffusive exchange of water across erythrocyte membrane. The membrane permeability is obtained from the exchange time constant and is in good agreement with the literature values. As compared to the other methods, this technique does not require strong gradients of magnetic field or contrast agents and, potentially, can be applied in vivo.

NMR of multipolar spin states excitated in strongly inhomogeneous magnetic fields.

The possibility of exciting and filtering various multipolar spin states in proton NMR like dipolar encoded longitudinal magnetization (LM), double-quantum (DQ) coherences, and dipolar order (DO) in strongly inhomogeneous static and radio-frequency magnetic fields is investigated. For this purpose pulse sequences which label and manipulate the multipolar spin states in a specific way were implemented on the NMR-MOUSE (mobile universal surface explorer). The performance of the pulse sequences was also tested in homogeneous fields on a solid-state high-field NMR spectrometer. The theoretical justification of these procedures was shown for a rigid two-spin 1/2 system coupled by dipolar interactions. Dipolar encoded longitudinal magnetization decay curves, double-quantum and dipolar-order buildup curves, as well as double-quantum decay curves were recorded with the NMR-MOUSE for natural rubber samples with different crosslink density. The possibility of using these multipolar spin states for investigations of strained elastomers by NMR-MOUSE is also shown. These curves give access to quantitative values of the ratio of the total residual dipolar couplings of the protons in the series of samples which are in good agreement with those measured in homogeneous fields.

Deuteron spin diffusion and spin lattice relaxation in amorphous solids

The effect of spin diffusion on the decay of longitudinal magnetization in deuterated glassy systems is investigated. The decay of longitudinal magnetization was measured for different dilutions of amorphous deuterated toluene in protonated toluene. For increasing dilution the magnetization was found to decay more slowly, indicating the importance of spin diffusion also in deuteron spin systems. A strong correlation between the apparent width of the distribution of spin lattice relaxation times and the absolute value of the average spin lattice relaxation time was found. This correlation can be explained in terms of spin diffusion. A simple model is able to reproduce the main features of the observed phenomena. The initial decay rates are shown to be independent of spin diffusion. Conclusions concerning the frequency dependencies of observed average spin lattice relaxation times and width parameters are drawn.

Transient Decay of Longitudinal Magnetization in Heterogeneous Spin Systems under Selective Saturation. IV. Reformulation of the Spin-Bath-Model Equations by the Redfield-Provotorov Theory

Abstract Alternative formulations to the conventional Bloch equations for the RF saturation of the solid component in heterogeneous spin systems according to a spin-bath model are derived using the concept of spin temperature as suggested by Redfield and Provotorov. These formulations and the resulting equations derived by the projection-operator technique provide an analytical and explicit solution to the general problem of solid saturation under continuous RF irradiation. Using the Provotorov theory, a set of generalized (non-Markovian) equations of motions is derived. The solutions to these generalized equations approach those of the conventional Bloch formulation at one extreme when the applied RF is weak and the Redfield formulation at another when the applied RF is strong. In short, this development provides a simple alternative which removes the restriction of the lineshape function used to represent the solid component; the latter is well known to be non-Lorentzian, contrary to the tacit assumption made in the conventional Bloch formulation. Experimental verification of the generalized theory is provided by transient and steady-state longitudinal magnetization data acquired from cross-linked bovine serum albumin under selective saturation by continuous off-resonance RF irradiation.

Transient Decay of Longitudinal Magnetization in Heterogeneous Spin Systems Under Selective Saturation. III. Solution by Projection Operators

A general method of solving equations governing the transient response of heterogeneous spin systems to continuous and pulsed RF saturation using the projection-operator technique is outlined. An effective rate equation is derived in which there is natural separation of relaxation and source terms. Our previously derived implicit solution to the coupled Bloch equations is reformulated using this more general approach, which avoids some of the restrictive assumptions made earlier. With this formulation, we provide an analytical and explicit solution to the full set of coupled Bloch equations with no additional assumptions or restrictive conditions attached limiting their general validity. The results obtained with this new method of solution are compared with the results previously obtained by the Laplace-transform technique for heat-denatured albumin.

Transient decay of longitudinal magnetization in heterogeneous spin systems under selective saturation

The transient behavior of the longitudinal magnetization of the mobile protons in aqueous heterogeneous materials is investigated both theoretically and experimentally when selective saturation is applied by off resonance, RF irradiation to the homogeneously broadened, immobile protons which are coupled to the mobile protons through cross relaxation. Analytical solution of this problem is obtained by a generalization of H. C. Torrey's solution to the Bloch equations. Progressive (but indirect) saturation of the magnetization of the mobile protons under this RF irradiation is dynamically monitored using very-small-tip-angle sampling pulses. The apparent relaxation rate of heat-denatured egg albumin was measured as a function of frequency offset of the saturating RF with different amplitudes using a new dispersion method modified from a broadband technique recently invented for the rapid acquisition of a cross-relaxation z spectrum.

Molecular motion and nuclear magnetic relaxation in filled poly(vinyl acetate)

Molecular motion and nuclear magnetic relaxation were studied with samples of PVA filled with mica particles and fluoroplast-4, in the temperature range 25–150°C. By analysis of the shape of transversal and longitudinal magnetization decay curves it was found that segmental motion differs in the neighbourhood of the filler particles. It is assumed that the difference might be caused by interactions between the PVA macromolecules and fluoroplast-4. The non-exponential curves of the recovery of longitudinal and decay of transversal magnetization in samples filled with fluorplast and kica are described by the Bloembergen-Purcell-Pound theory of nuclear magnetic relaxation, with a log-normal distribution of the correlation times of segmental motion in macromolecules.

NMR relaxation studies of intracellular Na+ in red blood cells.

The state of intracellular Na+ in human and dog erythrocytes was characterized by 23Na-NMR using dysprosium complexes as shift reagents. Intracellular Na+ concentrations were determined using integration of the inner Na+ NMR signals and measurements of the intracellular volume using 59Co-NMR of extracellular Co(CN)3-6. T2 was found to be significantly shorter than T1, indicating some binding to macromolecules. While the longitudinal magnetization decay follows a single exponential, the transverse magnetization could be fitted with a double-exponential function. It was shown that neither the binding to the inner side of the membrane nor binding to hemoglobin contributes to the relaxation enhancement.

1H-NMR relaxation studies of native and thermally denatured lysozyme solutions : An isotope dilution experiment

1H-NMR relaxation times are reported for native and thermally denatured lysozyme aqueous solutions measured as the function of the proton mole fraction in the sample. A two-exponential character of proton longitudinal relaxation function was observed for native lysozyme solutions: the fast component was attributed to the non-exchangeable protein protons, the slow one to water protons. Purely exponential decay of longitudinal magnetization was observed for the thermally denatured samples. This has been explained in terms of a fast spin exchange model. The contributions of the protein protons to the water proton relaxation rate in native and thermally denatured samples were determined, too.

Oil and water determination in emulsions by pulsed low‐resolution NMR

AbstractA pulsed, low‐resolution nuclear magnetic resonance (NMR) technique has been used for the oil and water determination in O/W emulsions. The method is based on the analysis of the longitudinal magnetization decay curve, that, due to the different relaxation times of oil and water, consists of 2 recognizable components. Correlation of NMR results with fat content is described. A good correlation between the NMR response and fat content by weight has been found. The rapidity and accuracy of the measurements are comparable to those of other techniques.