Determining the internal orientation, degree of ordering, and volume of elongated nanocavities by NMR: Application to studies of plant stem.

This study investigates the fibril nanostructure of fresh celery samples by modeling the anisotropic behavior of the transverse relaxation time (T2) in nuclear magnetic resonance (NMR). Experimental results are interpreted within the framework of a previously developed theory, which was successfully used to model the nanostructures of several biological tissues as a set of water filled nanocavities, hence explaining the anisotropy the T2 relaxation time in vivo. An important feature of this theory is to determine the degree of orientational ordering of the nanocavities, their characteristic volume, and their average direction with respect to the macroscopic sample. Results exhibit good agreement between theory and experimental data, which are, moreover, supported by optical microscopic resolution. The quantitative NMR approach presented herein can be potentially used to determine the internal ordering of biological tissues noninvasively.

Anisotropy of transverse and longitudinal relaxations in liquids entrapped in nano- and micro-cavities of a plant stem.

We studied the anisotropy of 1H NMR spin-lattice and spin-spin relaxations in a fresh celery stem experimentally and modeled the sample theoretically as the water-containing nano- and micro-cavities. The angular dependence of the spin-lattice and the spin-spin relaxation times was obtained, which clearly shows the presence of water-filled nano- and micro-cavities in the celery stem, which have elongated shapes and are related to non-spherical vascular cells in the stem. To explain the experimental data, we applied the relaxation theory developed by us and used previously to interpret similar effects in liquids in nanocavities located in biological tissues such as cartilages and tendons. Good agreement between the experimental data and theoretical results was obtained by adjusting the fitting parameters. The obtained values of standard deviations (0.33 for the mean polar angle and 0.1 for the mean azimuthal angle) indicate a noticeable ordering of the water-filled nano- and micro-cavities in the celery stem. Our approach allows the use of the NMR technique to experimentally determine the order parameters of the microscopic vascular structures in plants.

Dynamics of Zeeman and dipolar states in the spin locking in a liquid entrapped in nano-cavities: Application to study of biological systems.

We analyze the application of the spin locking method to study the spin dynamics and spin-lattice relaxation of nuclear spins-1/2 in liquids or gases enclosed in a nano-cavity. Two cases are considered: when the amplitude of the radio-frequency field is much greater than the local field acting the nucleus and when the amplitude of the radio-frequency field is comparable or even less than the local field. In these cases, temperatures of two spin reservoirs, the Zeeman and dipole ones, change in different ways: in the first case, temperatures of the Zeeman and dipolar reservoirs reach the common value relatively quickly, and then turn to the lattice temperature; in the second case, at the beginning of the process, these temperatures are equal, and then turn to the lattice temperature with different relaxation times. Good agreement between the obtained theoretical results and the experimental data is achieved by fitting the parameters of the distribution of the orientation of nanocavities. The parameters of this distribution can be used to characterize the fine structure of biological samples, potentially enabling the detection of degradative changes in connective tissues.

Anisotropy of Transverse Spin Relaxation in H2O-D2O Liquid Entrapped in Nanocavities: Application to Studies of Connective Tissues.

The spin-spin relaxation in connective tissues is simulated using a model in which a connective tissue is represented by a set of nanocavities containing H2O-D2O liquid. Collagen fibrils in connective tissues form ordered hierarchical long structures of hydrated nano-cavities with characteristic diameter from 1 nm to several tens of nanometers and length of about 100 nm. We consider influence of the restricted Brownian motion of molecules inside a nano-cavity on spin-spin relaxation. The analytical expression for the transverse time T 2 for H2O-D2O liquid in contained a nanocavity was obtained. We show that the angular dependence of the transverse relaxation rate does not depend on the concentration of D2O. The theoretical results could explain the experimentally observed dependence of the degree of deuteration on the relaxation time T 2. Accounting the orientation distribution of the nanocavities well agreement with the experimental dependence of the relaxation for articular cartilage on the deuteration degree was obtained.

Spin-lattice relaxation in liquid entrapped in a nanocavity.

We consider the spin lattice relaxation in bulk liquid and liquid entrapped in a nanocavity. The kinetic equation which describes the spin lattice relaxation is obtained by using the theory of the nonequilibrium state operator. A solution of the kinetic equation gives the quadrature expression for the relaxation time, T1. The calculated relaxation time agrees well with the experimental data. The spin-lattice relaxation time is calculated for nanocavities with a characteristic size much less than 700 nm, with the assumption that the spin-lattice relaxation mechanism is determined by nanocavity fluctuations. The resulting expression shows an explicit dependence of the relaxation time T1 on the volume, density of nuclear spins, and parameters of the cavity (shape and orientation relatively to the applied field). To compare with the experiment on the detection of the anisotropy of the relaxation time, we average the expression that describes the relaxation time over the orientation of the nanocavities relative to the applied magnetic field. The good agreement with the experimental data for fibril tissues was achieved by adjustment of few fitting parameters - the standard deviation, averaged fiber direction, and weight factors - which characterize the ordering of fibrils.

Spin locking in liquid entrapped in nanocavities: Application to study connective tissues.

Study of the spin-lattice relaxation in the spin-locking state offers important information about atomic and molecular motions, which cannot be obtained by spin lattice relaxation in strong external magnetic fields. The application of this technique for the investigation of the spin-lattice relaxation in biological samples with fibril structures reveals an anisotropy effect for the relaxation time under spin locking, T1ρ. To explain the anisotropy of the spin-lattice relaxation under spin-locking in connective tissue a model which represents a tissue by a set of nanocavities containing water is used. The developed model allows us to estimate the correlation time for water molecular motion in articular cartilage, τc=30µs and the averaged nanocavity volume, V≃5400nm3. Based on the developed model which represents a connective tissue by a set of nanocavities containing water, a good agreement with the experimental data from an articular cartilage and a tendon was demonstrated. The fitting parameters were obtained for each layer in each region of the articular cartilage. These parameters vary with the known anatomic microstructures of the tissue. Through Gaussian distributions to nanocavity directions, we have calculated the anisotropy of the relaxation time under spin locking T1ρ for a human Achilles tendon specimen and an articular cartilage. The value of the fitting parameters obtained at matching of calculation to experimental results can be used in future investigations for characterizing the fine fibril structure of biological samples.

Correlation of transverse relaxation time with structure of biological tissue.

Transverse spin-spin relaxation of liquids entrapped in nanocavities with different orientational order is theoretically investigated. Based on the bivariate normal distribution of nanocavities directions, we have calculated the anisotropy of the transverse relaxation time for biological systems, such as collagenous tissues, articular cartilage, and tendon. In the framework of the considered model, the dipole-dipole interaction is determined by a single coupling constant. The calculation results for the transverse relaxation time explain the angular dependence observed in MRI experiments with biological objects. The good agreement with the experimental data is obtained by adjustment of only one parameter which characterizes the disorder in fiber orientations. The relaxation time is correlated with the degree of ordering in biological tissues. Thus, microstructure of the tissues can be revealed from the measurement of relaxation time anisotropy. The clinical significance of the correlation, especially in the detection of damage must be evaluated in a large prospective clinical trials.

Anisotropy of spin-spin and spin-lattice relaxation times in liquids entrapped in nanocavities: Application to MRI study of biological systems.

Spin-spin and spin-lattice relaxations in liquid or gas entrapped in nanosized ellipsoidal cavities with different orientation ordering are theoretically investigated. The model is flexible in order to be applied to explain experimental results in cavities with various forms, from very prolate up to oblate ones, and different degree of ordering of nanocavities. In the framework of the considered model, the dipole-dipole interaction is determined by a single coupling constant, which depends on the form, size, and orientation of the cavity and number of nuclear spins in the cavity. It was shown that the transverse and longitudinal relaxation rates differently depend on the angle between the external magnetic field and cavity main axis. The calculation results for the local dipolar field, transverse and longitudinal relaxation times explain the angular dependencies observed in MRI experiments with biological objects: cartilage and tendon. Microstructure of these tissues can be characterized by the standard deviation of the Gaussian distribution of fibril orientations. The comparison of the theoretical and experimental results shows that the value of the standard deviation obtained at the matching of the calculation to experimental results can be used as a parameter characterizing the disorder in the biological sample.

Nuclear spin-lattice relaxation in nanofluids with paramagnetic impurities.

We study the spin-lattice relaxation of the nuclear spins in a liquid or a gas entrapped in nanosized ellipsoidal cavities with paramagnetic impurities. Two cases are considered where the major axes of cavities are in orientational order and isotropically disordered. The evolution equation and analytical expression for spin lattice relaxation time are obtained which give the dependence of the relaxation time on the structural parameters of a nanocavity and the characteristics of a gas or a liquid confined in nanocavities. For the case of orientationally ordered cavities, the relaxation process is exponential. When the nanocavities are isotropically disordered, the time dependence of the magnetization is significantly non-exponential. As shown for this case, the relaxation process is characterized by two time constants. The measurements of the relaxation time, along with the information about the cavity size, allow determining the shape and orientation of the nanocavity and concentration of the paramagnetic impurities.

NMR method for amplification of single-spin state.

Amplification of a single-spin state using nuclear magnetic resonance (NMR) techniques in a rotating frame is considered. The main aim is to investigate the efficiency of various schemes for quantum detection. Results of numerical simulation of the time dependence of individual and total nuclear polarizations for 1D, 2D, and 3D configurations of the spin systems are presented.

Competing reactions with initially separated components in the asymptotic time region.

Two competing irreversible reactions with initially separated components and with essentially different reaction constants are theoretically studied in the asymptotic time region. The description of the two simultaneous reactions is reduced to the consideration of two reactions separated in space. It is shown that the reaction rate profile can have two maxima and their ratio is independent of time. The location and relative value of the maxima are functions of the reaction constants and initial concentrations.