Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities

A detailed theoretical analysis of the free induction decay (FID) and spin echo (SE) MR signal formation in the presence of mesoscopic structure-specific magnetic field inhomogeneities is developed in the framework of the Gaussian phase distribution approximation. The theory takes into account diffusion of nuclear spins in inhomogeneous magnetic fields created by arbitrarily shaped magnetized objects with permeable boundaries. In the short-time limit the FID signal decays quadratically with time and depends on the objects' geometry only through the volume fraction, whereas the SE signal decays as 5/2 power of time with the coefficient depending on both the volume fraction of the magnetized objects and their surface-to-volume ratio. In the motional narrowing regime, the FID and SE signals for objects of finite size decay mono-exponentially; a simple general expression is obtained for the relaxation rate constant deltaR2. In the case of infinitely long cylinders in the motional narrowing regime the theory predicts non-exponential signal decay lnS approximately -tlnt in accordance with previous results. For specific geometries of the objects (spheres and infinitely long cylinders) exact analytical expressions for the FID and SE signals are given. The theory can be applied, for instance, to biological systems where mesoscopic magnetic field inhomogeneities are induced by deoxygenated red blood cells, capillary network, contrast agents, etc.     

Three-dimensional numerical simulations of susceptibility-induced magnetic field inhomogeneities in the human head

Three-dimensional numerical simulations of the static magnetic field in the human head were carried out to assess the field inhomogeneity due to magnetic susceptibility differences at tissue interfaces. We used a finite difference method and magnetic permeability distributions obtained by segmentation of computed tomography images. Computations were carried out for four models, consisting of the head and the neck; the head, neck, and shoulders; the head, neck, and thorax; and the head tilted backwards, including the neck and the shoulders. Considerable magnetic field inhomogeneities were observed in the inferior frontal lobes and inferior temporal lobes, particularly near the sphenoid sinus and the temporal bones. Air/tissue interfaces at the shoulders were found to induce substantial magnetic field inhomogeneities in the occipital lobes and the cerebellum, whereas air/tissue interfaces in the lungs appeared to have less influence on the magnetic field in the brain. Tilting the head backwards could significantly reduce the field inhomogeneities superior to the planum sphenoidale as well as in the occipital lobes and the cerebellum.     

Kinetic theory of time correlation functions for a dense one-component plasma in a magnetic field

The time-dependent correlations of a one-component plasma in a uniform magnetic field are studied with the help of kinetic theory. The time correlation functions of the particle density, the momentum density, and the kinetic energy density are evaluated for large time intervals. In the collision-dominated regime the results agree with those found from linearized magnetohydrodynamics.     

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讨论了静态非均匀磁场中的磁场旋度对带电粒子引导中心漂移的影响。运用三维矢量分析的方法,将带电粒子垂直于磁场运动所引起的磁场漂移分为两项,分别由磁场的曲率和磁场的旋度决定。给出了螺旋状环形磁场中由磁场旋度引起的磁场漂移的近似表达式,讨论了该漂移成分对于该磁场中通行粒子轨道和捕获粒子轨道的可能影响。结果表明,带电粒子垂直于磁场运动所引起的磁场漂移主要由磁场的曲率决定,而磁场旋度对该漂移的影响比较微弱。     

磁场旋度对磁场漂移的影响

讨论了静态非均匀磁场中的磁场旋度对带电粒子引导中心漂移的影响。运用三维矢量分析的方法,将带电粒子垂直于磁场运动所引起的磁场漂移分为两项,分别由磁场的曲率和磁场的旋度决定。给出了螺旋状环形磁场中由磁场旋度引起的磁场漂移的近似表达式,讨论了该漂移成分对于该磁场中通行粒子轨道和捕获粒子轨道的可能影响。结果表明,带电粒子垂直于磁场运动所引起的磁场漂移主要由磁场的曲率决定,而磁场旋度对该漂移的影响比较微弱。     

Determination of the effective correlation time modulating 1H NMR relaxation processes of bound water in protein solutions

The relaxation in protein solutions has mainly been studied by nuclear magnetic relaxation dispersion (NMRD) techniques. NMRD data have mostly been analyzed in terms of fast chemical exchange of water between free water and water bound to proteins. Several approaches were used for the estimation of correlation time modulating the relaxation mechanism of bound water. On the other hand, in a nuclear magnetic resonance experiment, the relaxation rates of protein solutions (1/T1 and 1/T2) and also those of free water (1/T1f and 1/T2f) are measurable. However, the relaxation rates of bound water (1/T1b and 1/T2b) are not. Despite this, equating (1/T1-1/T1f)/2(1/T2-1/T2f) to (1/T1b)/2(1/T2b) leads to an expression involving only an effective tau that is related to the rotational correlation time (tau r) of proteins. Equating the ratios may therefore give a simple alternative method for the determination of tau r even if this method is limited to a single resonance frequency. In this work, a formula was derived for the solution of the effective tau. Then, the 1/T1 and 1/T2 in solutions of two globular proteins (lysozyme and albumin) and one nonglobular protein (gamma-globulin) were measured for different amounts of each protein. Next, the values of 1/T1 and 1/T2 were plotted vs. protein concentrations, and then the slopes of the fits were used in the derived equation for determining the effective tau values. Finally, the rotational correlation time tau r, calculated from tau, was used in the Stokes-Einstein relation to reproduce relevant radii. The effective tau values of lysozyme, albumin and gamma-globulin were found to be 5.89 ns, 7.03 ns and 8.8 ns, respectively. tau r values of albumin and lysozyme produce their Stokes radii. The present data suggest that use of the measurable ratio in the derived formula may give a simple way for the determination of the correlation times of lysozyme and albumin.     

Polarization and transmission of microwaves in the magnetic suspension in the applied magnetic field

The production method of magnetic suspension consisting of ferromagnetic particles dispersed in cedarwood oil is presented at the beginning of this article. Next, the set-up for microwaves generation using a klystron is described. The main part of this paper concerning microwave transmission and polarization during its passage in samples of the produced magnetic suspension placed in a magnetic field is based on the following parameters: induction of this field, filling factor of magnetic suspension by ferromagnetic particles, dimensions of particles, viscosity of liquid carrier, and ratio of the magnetic field changes. Conducted investigations show that microwaves are damped and polarized in these magnetic suspensions. Obtained results are discussed and observed effects are explained by ordering of ferromagnetic particles in magnetic suspension by applied magnetic field.     

The effect of an oblique magnetic field on the superparamagnetic relaxation time

The effect of a constant magnetic field, applied at an angle ψ to the easy axis of magnetization, on the Néel relaxation time τ of a single domain ferromagnetic particle with uniaxial anisotropy is investigated by calculating the smallest non-vanishing eigenvalue of the appropriate Fokker-Planck equation as a function of ψ. The curve of λ₁ versus ψ is symmetric about ψ = 90°. Thus the maximum decrease in τ occurs at ψ = 45° with maximum increase to a value exceeding that at ψ = 0, at ψ = 90°, the ψ = 0 value being again attained at ψ = 180°. The results are shown to be consistent with the behaviour predicted by the Kramers theory of the rate of escape of particles over potential barriers. This theory when applied to the potential barriers for the ψ = 90° orientation for rotation in space yields a simple approximate formula for the escape rate which is in reasonable agreement with the exact λ₁ calculated from the Fokker-Planck equation.     

Effect of low and zero magnetic field on the hyperpolarization lifetime in parahydrogenated perdeuterated molecules

Hyperpolarization can be kept for times longer than T₁ if it is maintained in a singlet state, from which transitions are not allowed. Another, more direct, way to slower the relaxation process consists in the use of perdeuterated molecules. Here both methods have been applied and the hyperpolarization (induced by para-H₂) decay rate has been measured at two different magnetic fields: earth field and zero field. While relaxation is very slow at earth field, it becomes faster at zero field: this rather unexpected finding has been explained on the basis of isotropic mixing between ¹H and ²H.     

Relaxation time for a charge carrier due to its scattering from other charge carriers in superlattices

A calculation of relaxation time for (i) electron–electron scattering in a modulation-doped superlattice of type-I and (ii) electron–electron, hole–hole and electron–hole scattering processes in a compositional superlattice of type-II has been performed, using Fermi's golden rule. As compared to a two-dimensional electron gas system, both intralayer and interlayer interactions, between charge carriers in a superlattice, contribute to relaxation time. It is found that scattering processes at all possible value of momentum transfer contribute to relaxation time, for a given value of temperature and carrier density. We further find interlayer interactions in a superlattice make a significant contribution to relaxation time. Relaxation time is found to decrease on increasing temperature, carrier density and single particle energy, in a superlattice. The computed relaxation time for an electron (hole) in a superlattice enhances on increasing the width of layer consisting of electrons (holes). The electron–hole (hole–electron) scattering process in a type-II superlattice yields maximum contribution to the relaxation time when a hole layer lies exactly in between two consecutive electron layers.     

厅堂混响时间的声场控制方法及实验研究

本文首先论述厅堂声场控制的各种方法，然后利用混响反馈法和卷积法分别进行了实验研究，其中着重对卷积法的实验系统进行阐述，指出卷积法具有混响时间调节方便、控制范围大等优点，混响时间可提高三倍以上．     

Modified 6-state and 8-state potts models in magnetic field

The exact solutions for the modified 6-state and 8-state Potts models in an external magnetic field are obtained within the framework of the Kramers-Wannier transfer matrix. The explicit analytical expressions for thermodynamic quantities such as magnetization, magnetic susceptibility and specific heat are derived and analyzed at length as functions of temperature and magnetic field.     

Carrier mobility and relaxation time in BiCuSeO

To obtain thermoelectric properties of materials, a constant relaxation time approximation is generally employed. By employing deformation potential theory, a derivation of relaxation time and carrier mobility of BiCuSeO system is proposed combining with density functional theory calculation. And the inter-valley scattering, acoustic phonon scattering and ionized impurity scattering were considered in the model. The calculated values of relaxation time and carrier mobility in BiCuSeO are in good agreement with the results of experiment. The results suggest that acoustic phonon scattering is in dominant and the constant relaxation time approximation is reasonable in lightly doped sample, and the ionized impurity scattering play a significant role in heavily doped system.     

Relaxation phenomena of polar non-polar liquid mixtures under low and high frequency electric field

Simultaneous calculation of the dipole moment μ_j and the relaxation time τ_j of a certain number of non-spherical rigid aliphatic polar liquid molecules (j) in non-polar solvents (i) under 9.8 GHz electric field is possible from real ε′_ij and imaginary ε″_ij parts of the complex relative permittivity ε*_ij. The low frequency and infinite frequency permittivities ε_0ij and ε_∞ij measured by Purohitet al [1,2] and Srivastava and Srivastava [3] at 25, 35 and 30°C respectively are used to obtain static μ_s. The ratio of the individual slopes of imaginary σ″_ij and real σ′_ij parts of high frequency (hf) complex conductivity σ*_ij with weight fractionsw _jatw _j → 0 and the slopes of σ″_ij— σ′_ij curves for differentw _js [4] are employed to obtain τ_js. The former method is better in comparison to the existing one as it eliminates polar-polar interaction. The hf μ_js in Coulomb metre (C m) when compared with static and reported μs indicate that μ_s s favour the monomer formations which combine to form dimers in the hf electric field. The comparison among μs shows that a part of the molecule is rotating under X-band electric field [5]. The theoretical μ_theos from available bond angles and bond moments of the substituent polar groups attached to the parent molecules differ from the measured μ_js and μs to establish the possible existence of mesomeric, inductive and electromeric effects in polar liquid molecules.     

One-dimensional 3-state and 4-state standard Potts models in magnetic field

The exact solutions for 3-state and 4-state standard Potts models in external magnetic field are obtained within the framework of the Kramers-Wannier transfer matrix. The explicit analytical expressions for thermodynamic quantities such as magnetization, magnetic susceptibility and specific heat are derived and analysed at length as functions of temperature and magnetic field.     

Effect of the correlation properties of one-and three-dimensional inhomogeneities on the high-frequency magnetic susceptibility of sinusoidal superlattices

The effect of one-(1D) and three-dimensional (3D) inhomogeneities on the high-frequency magnetic susceptibility at the boundary of the first Brillouin zone of a ferromagnetic superlattice is studied. The study is performed with an earlier developed method of random spatial modulation (RSM) of the superlattice period. In this method, structural inhomogeneities are described in terms of the random-phase model, in which the phase depends on three coordinates in the general case. The frequency spacing Δν_m between two peaks in the imaginary part of the averaged Green’s function, which characterizes the gap width in the frequency spectrum at the boundary of the Brillouin zone, is calculated as a function of both the root-mean-square fluctuations γ_i and the correlation wavenumbers η_i of phase inhomogeneities (i = 1 and 3 for 1D and 3D inhomogeneities, respectively). The function Δν_m(γ₁, η₁) for 1D inhomogeneities is shown to be symmetric with respect to interchanging the variables γ ₁ ² and η₁, whereas the function Δν_m(γ₃, η₃) for 3D inhomogeneities is strongly asymmetric with respect to interchanging γ ₂ ³ and η₃. This effect is associated with the difference in form between the correlation functions of 1D and 3D inhomogeneities and can be used to determine the dimensionality of inhomogeneities from the results of spectral studies of such superlattices.     

时域磁场积分方程时间步进算法稳定性研究

从时域磁场积分方程时间步进算法出发,结合范数概念,从理论上推导得到了感应电流稳定的充分条件. 满足该条件,可以保证任何形式的入射波入射时,计算结果都后时稳定. 同时通过推导得到了表征感应电流递推关系的因子,该因子的大小可以表征感应电流收敛性的相对好坏. 最后通过数值算例验证了感应电流稳定的充分条件, 以及利用本文推导的感应电流递推因子表征感应电流后时稳定性的准确性. 关键词： 时域磁场积分方程 时间步进算法 后时不稳定性     

Advantages of using multiple-echo image combination and asymmetric triangular phase masking in magnetic resonance venography at 3 T

The present work explores the possibility of localizing veins with magnetic resonance venography using susceptibility weighted imaging. It also seeks new approaches, directed by the spatial specificity of activated brain regions, that have sufficient precision for practical use in functional MRI studies. A 3D flow compensated multiple gradient echo sequence, featuring optimized T2* weighting within a reasonable time of acquisition (11 min) and a small voxel size (0.5x0.5x1 mm3), was used to acquire MR images at 3 T. Post-processing consisted of homodyne filtering, linear phase scaling and magnitude masking prior to minimum intensity projection (mIP). The multiple echo approach provided a satisfactory (48+/-7%) increase in signal-to-noise ratio with respect to conventional methods. Specific features of the blood oxygenation level-dependent phase effect were simulated and used for designing and exploring different phase masking methods in relation to vessel morphology and MRI voxel geometry. As with simulations, the best results were obtained with an asymmetric triangular phase masking, featuring an improved venographic contrast without any increase in the full-width at half-maximum. The multiple echo approach provided satisfactory vessel localization capacity by using asymmetric triangular phase masking and a 4-mm-thick mIP. The venographic contrast obtained enabled the detection of vessels with diameter down to approximately 500 microm, suggesting the applicability of the proposed method as an additional technique in fMRI studies.     

用于时延估计的一种相关峰内插算法

本文介绍一种基于余弦函数的相关峰内插算法，在时延估计系统中，为了减少运算量和增加观察时间，采用内插算法是必要的，因为在频率估算时应用了迭代算法，所以无论对于ｃｏｓｘ，ｓｉｘ／ｘ或实际的相关峰，都有相当高的内插精度。