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This chapter considers those contemporary methods of nuclear magnetic resonance (NMR) that are used in the study of molecular translational dynamics in the systems of different level of complexity including the porous heterogeneous systems of natural origin. The results of proton spin–lattice and spin–spin relaxations, cross-relaxation (CR), pulse field gradient NMR, and double-quantum-filtered (DQF) NMR technique in a study of slow molecular dynamics and diffusion properties in the systems with the anisotropic properties are reported. An anisotropic molecular tumbling does not average all dipolar interactions to zero. The residual dipolar interactions (RDI) between water protons and macromolecular protons result in second-rank tensor to be formed. The observed DQF NMR line shape may be due to the formation of second-rank tensor. The second-rank tensor is formed only in anisotropic phases. No DQF signal is expected for isotropic systems. The DQF spectrum of heterogeneous systems such as natural biomaterials may represent a sum of spectra arising from many different noninteracting sites. To characterize effectively the total water motion in each site that is anisotropic indeed, it is possible to consider local residual interaction at each site and orientation of local symmetry axis relative to the external field. In natural biopolymers, for example, collagens, the fibrils and microfibrils in fact cannot be perfectly oriented along the fiber axis. Therefore, the RDI may be of local or macroscopic nature. In macroscopic case, the effective director of the RDI is parallel to the natural fibers and DQF spectra will change when the sample is rotated. DQF NMR technique collects the information about local and macroscopic order in different systems. It is effectively applied in the systems with anisotropic motion of molecules. The apparent translational diffusion coefficients (Dapp) at two directions of applied gradient (along to the static magnetic field B0 and perpendicular to B0) in natural-oriented fibers are studied to clarify restriction diffusion and estimate the restricted distance and permeability coefficient. The results obtained reveal also the special features of the approaches of one-dimensional and two-dimensional NMR and show examples of the work of these methods in addition to the traditional methods of single-quantum NMR spectroscopy. The chapter presents also the data of two-dimensional correlation NMR spectroscopy as the distributions of diffusion coefficients in two orthogonal directions on the systems with anisotropic mobility. Simulations of two-dimensional NMR experiments have been done showing how it leads to the explanation of 2D experimental data on the anisotropy of diffusion coefficients. These NMR methods reveal the correlation of the diffusion motion of molecules along either collinear or orthogonal directions of applied pulse gradients of magnetic field. The results on some natural materials with anisotropic structure demonstrated how these methods reveal microscopic local anisotropy in the presence of global isotropy. This chapter presents the results of NMR studies of collagens, natural silk, and wood. Collagen is a natural biopolymer that is used extensively in nanoscaffolds fabrication for tissue engineering applications. Natural silk produced by silk worm Bombyx mori is known as one of the strong natural biomaterials. The natural polymers of collagen and silk fibroin are used in the creation of bioactive extracellular matrix.Wood, as a natural fiber composite, is one of the most important natural biomaterials.
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... As for moisturizing wood materials, these considered NMR parameters have not been studied properly to obtain the details on wood-water interaction in pieces of felled mature spruce in a wide range of water contents. However, some published data on spruce [7,8,18] showed that a cross-relaxation process between protons of solid surface and the ones of water can affect the behaviour of T 1 relaxation and should be considered for correct estimation of self-diffusion coefficients at various diffusion times with stimulated-echo pulse sequence [19,20]. Additionally, it was shown [18,21] that 2D correlation experiments with two pairs of gradient pulses applied in orthogonal directions to wood pieces can be valuable means to define an anisotropy of water self-diffusion. ...
... This point does mean such an amount of water in wood when only bound water is present in the spruce material, i.e., at FSP, there is no free water in the wood [8,21]. From the other side, if added water results in the range of moisture above the FSP, three T 2 components (two are between 0.1 and 10 ms, and third one is in a slow relaxing range of 20-140 ms) can be observed [7,8]. ...
... NMR methods. The spin-lattice relaxation times were measured using the inversion recovery pulse sequence (180 • -τ-90 • ) whereas T 2 measurements have been carried out using Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence [7,22,25]. The sample was placed within the volume of the probe coil to ensure RF field homogeneity. ...
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This paper examines how wetting the surface of wood affects characteristics of wood materials. An important question is how moisturizing wood has an effect on diffusion parameters of water, which will change conditions of the technological treatment of material. A fibrous structure of wood can result in different diffusivities of water in the perpendicular direction and along the wood fibers. The work explores how 1- and 2-dimensional NMR with pulsed field gradients (PFG) highlights an anisotropic diffusion of water when moisturizing spruce wood. The methods applied: T2-relaxation (CPMG) measurements with the application of inverse Laplace transform (ILT), cross-relaxation experiments (Goldman–Shen pulse sequence), 1D PFG NMR on oriented wood pieces or applying gradients in various orientation, and 2D diffusion-diffusion correlation spectroscopy (DDCOSY) with two pairs of colinear gradient pulses. The results showed anisotropic restricted diffusion correlating the size of tracheid cells. The experimental 2D diffusion-diffusion correlation maps were compared with model calculations based on parameters of 2D experiment on spruce and the theory of 2D DDCOSY with ILT. Moisturizing spruce wood resulted in anisotropic diffusion coefficient which can be monitored in 2D NMR to discover different diffusion coefficients of water along the axis of wood fibers and in orthogonal direction.
... After application of a radio frequency pulse, the receiver is unable to acquire a signal from the sample for a time of ~0.005 to 0.010 ms due to interfering signals from the electronic circuits and the probe material. Signal acquisition starts after a delay, the receiver dead time [16] [17]. This time is quite negligible in the quantitative measurements for polymer-water system because of the long T* 2 for liquid. ...
... For most cases NMR peaks are Lorentzian and/or Gaussian line shapes [13] [16] [17] [23]. If the line shape of the mobile protons is expected to be Lorentzian this gives for the FID the exponential function: ...
... Here P 1 is the signal intensity of the solid like part FID curve at t = 0. The parameters of a and b are used in the equation for the second moment М 2 = a 2 + b 2 /3 [16] [23]- [25]. ...
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V.Rodin, T.Cosgrove. (2016) Nuclear Magnetic Resonance Study of Water-Polymer Interactions and Self-Diffusion of Water in Polymer Films.// Open Access Library Journal: Chemistry and Materials Science, Fundamentals of Materials Sciences. Vol.3, Issue 10, pp.1-17. doi: 10.4236/oalib.1103018. ABSTRACT The diffusivity and distribution of water in the butyl methacrylate and methacrylic acid copolymer films swollen in water have been investigated using the NMR relaxation and pulse field gradient (PFG) NMR techniques. The contributions of polymer matrix protons, surface water and bound water have been determined from 1H NMR spectra and relaxation functions. PFG NMR experiments showed that the echo attenuation function depends on the diffusion time indicating that water inside the swollen film is trapped in restricted confinement. The data obtained have been discussed using published physical models for diffusion of water in polymeric materials. The sizes of pores inside the film were estimated using the published model approaches giving the range of 0.8-1.0 μm. Magnetization decays as well as the spin-spin relaxation times of water saturated polymer films were also determined in this study. NMR relaxation provided additional information on the water distribution in the porous microstructure. The volume-averaged water mobility decreased with increasing hydrophobic content of the polymers.
The chapter considers the achievements of NMR for biomedical engineering and estimates development of these methods to unveil the details of processes associated with recovering cells and tissues. NMR methods give the information about translational dynamics of molecules and macromolecules in complex systems including natural porous biosystems in different physicochemical environment. NMR relaxation, pulse field gradient (PFG) NMR in one- and two-dimensional realisations, and double-quantum-filtered (DQF) NMR techniques are analysed with brief theory and the examples in studying normal and disease state of cells and tissues, regulation of cell processes and monitoring changes in the cell/tissue microstructure. NMR & MRI methods are the leading non-invasive characterization tools, which can provide different MR parameters in studying the properties of tissue-engineered constructions. DQF NMR technique collects the information about local and macroscopic order in heterogeneous systems and it is effectively applied in the tissues with anisotropic motion of molecules. It is considered how DQF NMR has been applied to study collagen tissues with different quantity of covalent intermolecular cross-links. The apparent diffusion coefficient (Dapp) could be applied in studying biomedical engineering applications. The change in Dapp and NMR relaxation parameters (T1, T2) correlated well with the growth of engineered tissues. A restricted distance and permeability coefficient could be monitored as important MR parameters of fibers and tissue characteristics. Various classes of nanoparticles applied for drug delivery and other destinations in biotechnology have been studied effectively by NMR techniques on different nuclei. Hopefully the material of the chapter can help to establish a bridge between researchers specialised in particular MR techniques and cell and tissue engineers. Biological, Physical and Technical Basics of Cell Engineering pp 339-363 | Cite as Magnetic Resonance in Studying Cells, Biotechnology Dispersions, Fibers and Collagen Based Tissues for Biomedical Engineering Introduction Molecular, cellular and tissue engineering establishes the ways to improve the health of many people by restoring and maintaining cell and tissue functions [7, 13, 15, 23] as well as generating alternative tissues for reconstructive surgery. It is important to understand a mechanism of cellular interactions, a role of surface contacts and predict how cell growth, and how cell/tissue differentiation is affected by the environment [32, 34]. Cellular surroundings, both chemical and physical, can have strong effects on behavior, growth, differentiation and storage of cells [7, 32, 34, 37, 39, 54, 69]. The interdisciplinary approach of cell and tissue engineering provides a real basis for the investigation and fabrication of new biomedical devices with a broader perspective on quantifying efficacy and establishing clinical applications [7, 13, 23, 34, 37, 69]. Studying physical factors or creating special environmental conditions for the cells and tissues became very important. Many physical methods have been applied and developed to restore, maintain, and to supply the cell and tissue functions. Nuclear magnetic resonance (NMR) methods are also applied in this area [12, 15, 17, 20, 21, 26, 36, 38, 39, 42, 53, 54]. It is important to understand the NMR achievements, apply those for biomedical engineering and estimate development further to unveil the details of recovering cell and tissue functions [21, 38, 39, 42, 54, 69]. Nowadays the NMR methods study the processes inside living cells [12, 17, 26]. The techniques clarify the intracellular protein-protein interactions responsible for most biological functions [7, 26, 39, 54]. NMR now can analyze living prokaryotic cells in details [12, 17, 26, 54]. This chapter discusses mostly those NMR methods, which give the information about translational dynamics of molecules and macromolecules in complex systems including natural porous biomaterials. NMR relaxation, pulse field gradient (PFG) NMR, NMR imaging and multiple-quantum-filtered (MQF) NMR techniques are studying normal and disease cells and tissues, regulation of cell behaviour and fermentation processes resulting in special cell/tissue properties based on dynamics of molecules and diffusion characteristics [10, 16, 31, 38, 39, 41, 42, 51, 57]. Giving non-invasive characterization of engineered connective tissues, these tools consider a possibility to tabulate differences in the MR properties of tissue-engineered constructions [16, 21, 38, 57]. PFG NMR, NMR relaxation and MQF NMR methods are potential techniques in a study of molecular dynamics and diffusion properties in the anisotropic systems [31, 42]. An anisotropic molecular tumbling does not average all dipolar interactions to zero. The residual proton-proton dipolar interactions (RDIs) between macromolecular protons and water protons produce second-rank tensor that is responsible for the observed double-quantum-filtered (DQF) spectrum [16, 42, 51, 57]. There is no DQF signal in isotropic systems. The DQF spectra of connective tissues may represent a sum of spectra arising from a number of different non-interacting sites. If to consider local residual interaction at each site and orientation of local symmetry axis relative to the external field, this gives effective characterization of the total water motion in each site. DQF technique collects the information about local and macroscopic order in the systems with effective anisotropic motion of molecules [10, 31]. Proton and sodium MQF spectroscopy and proton spin-lattice (T1) and spin-spin (T2) relaxation times were used to study the chondrogenesis and osteogenesis of collagen contained tissues [21]. The apparent diffusion coefficient (Dapp) was also applied in studying tissue engineering materials [20, 21, 38]. PFG experiment can be carried out at different diffusion times or applying the gradients in two orthogonal directions to natural-oriented tissues. This can clarify anisotropy and restriction diffusion and estimate the restricted distance and permeability coefficient [42, 49]. Dapp values and NMR relaxation parameters (T1, T2) correlate well with the growth of engineered tissues and help to characterize the scaffolds [21]. MQF spectroscopy shows that the tissue-engineered cartilage has no order or preference in collagen orientation [21]. The chapter considers also two-dimensional correlation NMR spectroscopy as the distributions of diffusion coefficients in two orthogonal directions in the anisotropic systems. These 2D NMR methods can reveal the correlation of the diffusion motion of molecules along either collinear or orthogonal directions of applied pulse gradients of magnetic field. The approach is promising in studying tissues with anisotropic structure revealing microscopic local anisotropy in the presence of global isotropy. 2 Theory and Methods. Main NMR Techniques and Experiments In order to apply MR parameters for biomedical engineering properly, more MRS/MRI experiments with different combination of scaffolds and cells and understanding the details of measurements are needed [20, 21, 38]. The efforts to develop NMR tools to the tissue characterization are depending on how cell and tissue engineers are involved in MR experiments, as well as how deep is their understanding the basics of MR methods. As discussed in [21] and functional MRI/MRS for regenerative medicine meetings, the collaboration between MR community and regenerative medicine community is important for successful transfer of biomedical engineering achievements to practice. Therefore additional explanation of MR parameters and factors affected those should be presented in more details. This section introduces NMR methods and explains basic experimental approaches. Some models and experimental techniques are described to help in the realisation and interpretation of NMR relaxation and NMR diffusion experiments in one- and two-dimensions. A technique of double-quantum-filtered (DQF) NMR is presented for the study of molecular anisotropic motion. The magnetic properties of atomic nuclei, basic principles of NMR phenomenon and NMR applications in various fields are described in publications [1, 4, 5, 6, 11, 19, 40, 42]. Electrons, protons and neutrons in atoms can be imagined as spinning on their axes. In some atoms for example, 12C these spins are paired against each other and the nucleus of the atom has no overall spin. However, in other atoms, such as 1H, 13C, and 31P, the nucleus does possess an overall spin. The nuclei with spin experience NMR phenomenon, which occurs when the nuclei with nonzero spin are placed in a static magnetic field and a second oscillating magnetic field is orthogonally applied [1, 4, 11, 19]. According to quantum mechanics, this nuclear spin is characterised by a nuclear spin quantum number, I [1, 5, 6, 40]. A nucleus of spin I will have 2I + 1 possible orientations in magnetic field B0. For a spin-half nucleus (I = 1/2) an interaction with a magnetic field results in two energy levels [1, 5, 19, 40]. When external magnetic field B0 = 0 these orientations are of equal energy. In the case of nonzero B0, the energy levels split. Each level is given by a magnetic quantum number, m, which is restricted to the values from −I to I in integer steps. Thus, for a spin-half nucleus, there are only two values of magnetic quantum number m, +1/2 and −1/2 [11, 19, 40]. The energy state with m = +1/2 is denoted as α and is characterized with the lowest energy. This state is often described as ‘spin up’ notation. The state with m = −1/2 is denoted β, and it is described as ‘spin down’ notation. The m-values (+1/2, −1/2) express the parallel and antiparallel orientations of the nuclear spin with respect to the static magnetic field. The details of energy levels for two or more spins in molecule can be found elsewhere [4, 11, 19]. The initial populations of the energy levels of the nucleus in a magnetic field are determined by thermodynamics according to the Boltzmann distribution. The lower energy level will contain slightly more nuclei than the higher level when nuclei are in the state of equilibrium. With action of an electromagnetic radiation, it is possible to excite the nuclei from the low level into the higher level. The difference in energy between the energy levels ΔE = Eβ − Eα determines the frequency of radiation, which is needed for this excitation. When positive charged nucleus is spinning, this generates a small magnetic field. The nucleus therefore possesses a magnetic moment µ. This magnetic moment is proportional to its spin I, Planck’s constant h, and the constant γ, which is called the gyromagnetic ratio [1, 19]. γ for nucleus is a ratio of magnetic dipole moment to its angular momentum. γ is a fundamental nuclear constant which has a different value for every nucleus [4, 40]. The energy E m of each level m is proportional to the strength of the magnetic field at the nucleus B0, magnetic quantum number m and γh. The transition energy ΔE will be also proportional to B0. When the static magnetic field B0 is increased, the transition energy increases too. It is possible to imagine a nucleus (I = 1/2) in a magnetic field. This nucleus is in a base state. It is at the lower energy level and its magnetic moment does not oppose the applied field. The nucleus is spinning on its axis. In the presence of a magnetic field, this axis of rotation will precess around the magnetic field. The frequency of precession is called the Larmor frequency. The Larmor frequency is identical to the transition frequency. The angle of precession, φ, (the angle between the direction of the applied field and the axis of nuclear rotation) will change when energy is absorbed by the nucleus. The absorption of energy leads to a higher energy state. Due to the difference in population of levels in the state of equilibrium, there is a macroscopic magnetization M. It is oriented along the direction of the static magnetic field B0 (Z-axis). NMR-studies can be done in time-domain (for example, studying translational dynamics) and in frequency-domain using one-dimensional and two-dimensional NMR techniques (for example, studying structure of proteins) [5, 19, 40]. Fourier transformation is used to do transfer between time-domain and frequency-domain. The Fourier transform (FT) is a mathematical technique for converting data of time-domain to data in frequency-domain (giving a spectrum), and an inverse Fourier transform (IFT) converts data from the frequency-domain to the time-domain. The alternative magnetic field B1(t) = B1m.cos(ωt) is applied perpendicularly to constant magnetic field B0. Behaviour of the spin system in crossing magnetic fields is considered on the base of movement of magnetization vector M. Basic equations for the vector of the bulk magnetization M in outer magnetic field are the differential Bloch equations with the spin-lattice and spin-spin relaxation terms [5, 11, 19, 40]. These equations are much easier in a rotating coordinate system X′Y′Z′, which rotates with frequency ω around B0 (Z, Z′-axes) in the direction of nuclear precession [11, 40]. In rotation frame, vector M rotates around magnetic field B1 (X′-axis) with angle frequency ω = γB1. In the absence of magnetic field B1, magnetization M is along the direction of outer magnetic field B0. The angle θ for rotation of magnetization M during precession time tp is presented as θ = γB1tp [11]. During time tp, if vector M turns by θ = 90°, then this rotation is called as a 90°- or π/2-pulse (duration time tp is called the pulse length). When θ = 180° then this rotation is called as a π-pulse. An application of π/2-pulse to the magnetization M (using magnetic field B1) results in vector M being along the Y′-axis and the intensity of measurable signal (along Y′-axis) has maximal value. During the time (because of relaxation processes) a projection of magnetization vector M to the Y′-axis will decrease. This detected signal is called as a Free induction decay (FID). The signal intensity depends on the population difference between the two energy levels considered. The system is irradiated with a frequency, whose energy is equal to the difference in energy between these two energy levels. Upward transitions absorb energy and downward transitions release energy. The probability for transitions in either direction is the same. The number of transitions in either direction is determined by multiplying the initial level population by a probability. The nuclei, which are in a lower energy state can absorb radiation. At absorption of radiation, a nucleus jumps to the higher energy state. When the energy level populations are the same, the number of transitions in either direction will also be the same. When there is no further absorption of radiation, the spin system will be saturated. However, a possibility of saturation means that the relaxation processes would occur to return nuclei to the lower energy state. The sample in which the nuclei are held is called the lattice. All nuclei in the sample that are not observable are considered as lattice. Nuclei in the lattice are in vibrational and rotational motion, which creates a complex magnetic field. The magnetic field caused by motion of nuclei within the lattice is called the lattice field. The components of the lattice field, which are equal in frequency and phase to the Larmor frequency of the considered nuclei can interact with nuclei in the higher energy state, and cause them to lose energy and return back to the lower (equilibrium) state. The equilibrium is considered as a state of polarization with magnetization M0 directed along the longitudinal magnetic field B0. The restoration of the equilibrium is named longitudinal (spin-lattice) relaxation. The relaxation time constant, T1 describes the average lifetime of nuclei in the higher energy state. T1 is typically in the range of 0.1–20 s for protons in non-viscous liquids and other dielectric materials at room temperatures. A larger T1 indicates a slower or more inefficient spin relaxation [1, 4, 11]. The efficiency of spin-lattice relaxation depends on factors that influence molecular movement in the lattice, such as viscosity and temperature. The longitudinal relaxation times are often measured using the inversion recovery (IR) pulse sequence (180° − t − 90°) at repetition time ≥5T1 [40, 42, 47, 48, 52]. The period of 5T1 is waited in order to ensure that the fully recovered signal was acquired. When t is varied then experimental dependence of magnetization Mt = f (t) can be obtained and fitted by the law Mt = ∑M0i·[1–2·exp(−t/T1i)], where i is the number of relaxation component. An aim is to model experimental data as a sum of several relaxation components or distribution of NMR-relaxation times. To fit the data inverse Laplace transform (ILT) in one direction is applied [42, 53]. The kernel function in ILT is associated with Mt data from IR NMR experiments. Figure 1 shows T1 distributions obtained by one-dimensional ILT on the data sets of IR NMR experiments for bacterial suspension of E. coli and E. coli under xenon conditions. In original suspension, an exchange between intra- and extracellular water is too fast on NMR scale and gives one T1 component. The formation of xenon hydrates affected exchange dynamics of water between intra- and extracellular water compartments resulted in apparent two T1 components/peaks. Open image in new windowFig. 1 Fig. 1 T1 distribution of 1H in the suspension of E. coli with concentration of 0.07 g dry mass/g H2O (open circles) and in the same sample with xenon at 1.2 MPa (solid line) [53]. T = 280 K, ν = 90 MHz. All intensities have been normalized per maximal signal An interaction between neighbouring nuclei with identical frequencies but differing magnetic quantum states is described by spin-spin (transverse) relaxation. These nuclei can exchange quantum states. A nucleus in the lower energy level will be excited, while the excited nucleus relaxes to the lower energy state. The populations of the energy states do not change, but the average lifetime of a nucleus in the excited state will decrease. This can result in broadening resonance lines. More details are presented in publications [1, 4, 11, 19, 40]. Transverse relaxation is characterized by time constant T2. Spin-spin relaxation is a process whereby nuclear spins come to thermal equilibrium between themselves. At room temperatures, the T2 values for different materials are usually in the range from 10 µs to 10 s. It is always true for T2 ≤ T1. Transverse relaxation is unlike the longitudinal relaxation. It is sensitive to the interaction, which results in dephasing nuclear spins [39, 42]. For measurement of T2, it is possible to use Han pulse sequence (90° − τ − 180°). This sequence creates a signal of spin echo at t = 2τ [11, 19, 40]. When interval 2τ is varied, an experimental dependence M2τ = f(2τ) can be obtained and modelled to calculate the T2 [42]. The modification of Han method is Carr-Purcell (CP) pulse sequence (90° − τcp − 180° − 2τcp − 180° − 2τcp − 180° − …) which contains π-pulses train [11]. The Carr-Purcell-Meiboom-Gill (CPMG) sequence is the modification of CP-method: uses phase shift of π-pulses (by 90°) with respect to initial 90° pulse [40, 52]. CPMG decays are modelled by a sum of relaxation components [39, 43]. Alternatively, a distribution of T2 components, which could reconstruct spin-echo decay from CPMG experiment, should be found. To extract the function f(T2), the inverse Laplace transform is used. The probability density f(T2) is calculated from the Eq. (1) for the spin-echo signal M t presented according to Refs. [2, 6]:
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