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Furman G, Meerovich V, Sokolovsky V, Xia Y, Salem S, Shavit T, Blumenfeld-Katzir T, Ben-Eliezer N. Determining the internal orientation, degree of ordering, and volume of elongated nanocavities by NMR: Application to studies of plant stem. J Magn Reson 2022; 341:107258. [PMID: 35753185 PMCID: PMC9986720 DOI: 10.1016/j.jmr.2022.107258] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2022] [Revised: 06/12/2022] [Accepted: 06/13/2022] [Indexed: 05/05/2023]
Abstract
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.
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Affiliation(s)
- Gregory Furman
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel.
| | - Victor Meerovich
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel
| | | | - Yang Xia
- Physics Department, Oakland University, Rochester, MI, USA
| | - Sarah Salem
- Physics Department, Oakland University, Rochester, MI, USA
| | - Tamar Shavit
- Department of Biomedical Engineering, Tel Aviv University, Tel Aviv, Israel
| | | | - Noam Ben-Eliezer
- Department of Biomedical Engineering, Tel Aviv University, Tel Aviv, Israel; Sagol School of Neuroscience, Tel Aviv University, Israel; Center for Advanced Imaging Innovation and Research (CAI2R), New York University School of Medicine, NY, USA
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Furman G, Meerovich V, Petrov D, Sokolovsky V, Xia Y. Anisotropy of Transverse Spin Relaxation in H 2O-D 2O Liquid Entrapped in Nanocavities: Application to Studies of Connective Tissues. Hyperfine Interact 2021; 242:19. [PMID: 35990926 PMCID: PMC9390080 DOI: 10.1007/s10751-021-01731-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/21/2021] [Indexed: 06/15/2023]
Abstract
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.
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Affiliation(s)
- Gregory Furman
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel
| | - Victor Meerovich
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel
| | - Danil Petrov
- Physics of Phase Transitions Department, Perm State University, Perm, Russia
| | | | - Yang Xia
- Physics Department, Oakland University, Rochester, MI. US
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Furman G, Goren S, Meerovich V, Panich A, Sokolovsky V, Xia Y. Anisotropy of transverse and longitudinal relaxations in liquids entrapped in nano- and micro-cavities of a plant stem. J Magn Reson 2021; 331:107051. [PMID: 34455368 PMCID: PMC8842490 DOI: 10.1016/j.jmr.2021.107051] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Revised: 08/06/2021] [Accepted: 08/09/2021] [Indexed: 05/05/2023]
Abstract
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.
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Affiliation(s)
- Gregory Furman
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel.
| | - Shaul Goren
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel
| | - Victor Meerovich
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel
| | - Alexander Panich
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel
| | | | - Yang Xia
- Physics Department, Oakland University, Rochester, MI, US
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Furman G, Kozyrev A, Meerovich V, Sokolovsky V, Xia Y. Dynamics of Zeeman and dipolar states in the spin locking in a liquid entrapped in nano-cavities: Application to study of biological systems. J Magn Reson 2021; 325:106933. [PMID: 33636633 PMCID: PMC8889562 DOI: 10.1016/j.jmr.2021.106933] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2020] [Revised: 01/30/2021] [Accepted: 02/02/2021] [Indexed: 05/21/2023]
Abstract
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.
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Affiliation(s)
- Gregory Furman
- Physics Department, Ben Gurion University of the Negev, Beer Sheva 84105, Israel.
| | - Andrey Kozyrev
- Saint-Petersburg Electrotechnical University LETI, Saint-Petersburg, Russia
| | - Victor Meerovich
- Physics Department, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Vladimir Sokolovsky
- Physics Department, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Yang Xia
- Physics Department, Oakland University, Rochester, MI, USA
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Furman G, Meerovich V, Sokolovsky V, Xia Y. Spin-lattice relaxation in liquid entrapped in a nanocavity. J Magn Reson 2020; 311:106669. [PMID: 31881481 PMCID: PMC8829806 DOI: 10.1016/j.jmr.2019.106669] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2019] [Revised: 12/11/2019] [Accepted: 12/12/2019] [Indexed: 05/05/2023]
Abstract
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.
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Affiliation(s)
- Gregory Furman
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel; Physics Department, Oakland University, Rochester, MI, USA.
| | - Victor Meerovich
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel; Physics Department, Oakland University, Rochester, MI, USA
| | - Vladimir Sokolovsky
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel; Physics Department, Oakland University, Rochester, MI, USA
| | - Yang Xia
- Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel; Physics Department, Oakland University, Rochester, MI, USA
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Furman G, Meerovich V, Sokolovsky V, Xia Y. Spin locking in liquid entrapped in nanocavities: Application to study connective tissues. J Magn Reson 2019; 299:66-73. [PMID: 30580046 PMCID: PMC6942517 DOI: 10.1016/j.jmr.2018.12.012] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2018] [Revised: 12/12/2018] [Accepted: 12/13/2018] [Indexed: 05/05/2023]
Abstract
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.
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Affiliation(s)
- Gregory Furman
- Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel.
| | - Victor Meerovich
- Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel
| | - Vladimir Sokolovsky
- Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel
| | - Yang Xia
- Department of Physics, Oakland University, Rochester, MI 48309-4451, USA
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Sinder M, Pelleg J, Sokolovsky V, Meerovich V. Competing reactions with initially separated components in the asymptotic time region. Phys Rev E Stat Nonlin Soft Matter Phys 2003; 68:022101. [PMID: 14525025 DOI: 10.1103/physreve.68.022101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2003] [Indexed: 05/24/2023]
Abstract
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.
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Affiliation(s)
- Misha Sinder
- Department of Materials Engineering, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel
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