基于ADI-FDTD模拟的岩石核磁共振横向弛豫特征分析

将复杂的骨架-孔隙系统抽象成等效双孔介质,根据Bloch方程构建数学模型,用交替隐式时域有限差分(ADI-FDTD)和联合反演迭代法(SIRT)进行横向宏观磁化矢量的数值模拟与核磁共振T₂谱的反演,定量研究扩散系数、弛豫速率、孔隙组分比和孔隙宽度对核磁响应的影响.结果表明:横向宏观磁化矢量衰减速率与扩散系数和微孔隙分量成正比,与孔隙宽度成反比,与表面弛豫速率基本无关.当扩散系数较大、孔隙宽度较小时,核磁共振T₂谱难以直观反映孔隙组分及孔隙结构.应用核磁共振评价孔隙结构时需特别注意扩散系数和孔隙尺寸的影响.     

Weak-Diffusion Theory of NMR Signal in Magnetically Heterogeneous Media

A general theory is developed for the effect of molecular diffusion on the NMR signal obtained from magnetically heterogeneous media in the limit of weak diffusion. The theory is based on a rigorous expansion in the diffusion constantD, with the correction to first order inDbeing given explicitly for unrestricted, isotropic diffusion. The expansion allows for an arbitrary sequence of field gradients and 180° spin-flip pulses, making it applicable to a wide variety of NMR protocols. The theory may be useful for estimating the magnitude of diffusion effects and in determining some of a medium's microscopic magnetic properties.     

Surface-to-volume ratio with oscillating gradients

Restrictions to diffusion result in the dispersion of the bulk diffusion coefficient. We derive the exact universal high-frequency behavior of the diffusion coefficient in terms of the surface-to-volume ratio of the restrictions. This frequency dependence can be applied to quantify structure of complex samples with NMR using oscillating field gradients and static-gradient CPMG. We also demonstrate the inter-relations between different equivalent diffusion metrics, and describe how to calculate the effect of restrictions for arbitrary gradient waveforms.     

The effect of impermeable boundaries of arbitrary geometry on the apparent diffusion coefficient

The apparent diffusion coefficient (ADC) obtained from NMR measurements is modelled for diffusion in a compartment restricted by an impermeable boundary. For a given pulse sequence, the ADC can be determined from the connected velocity autocorrelation function (the second-order velocity cumulant), which we show can be expressed as a double surface integral over the boundary, involving the probability for molecules to diffuse from one boundary point to another. There is no restriction on the geometry of the boundary. This result allows a fast calculation of the ADC for an arbitrary time course of the diffusion-sensitizing gradient. Explicit examples are given for diffusion within three basic geometries for different pulse sequences. The ADCs measured with the Stejskal-Tanner pulse sequence and a more realistic pulse sequence with slice selection gradient and eddy current compensation are found to yield almost identical results. The application of the results are discussed in relation to determination of the microscopic structure of brain white matter.     

Evaluation of diffusional anisotropy and microscopic structure in skeletal muscles using magnetic resonance

The pulsed-gradient spin-echo (PGSE) nuclear magnetic resonance (NMR) method is used for detecting the diffusion of water molecules in biological tissues. Because tissues generally have diffusional anisotropy, their diffusion properties are denoted by a tensor. In this study, we evaluated the diffusional anisotropy and microscopic structure in atrophied skeletal muscles using the PGSE NMR method. The left sciatic nerve was severed in twelve 9-week-old rats. Neurotomy caused neurogenic muscular atrophy at the left gastrocnemius. At 2, 4 and 8 weeks after neurotomy, magnetic resonance signals were selectively acquired from a 2 x 2 x 2 mm(3) voxel, which was located on the left gastrocnemius. The diffusion tensor, the mean diffusivity (MD) and the fractional anisotropy (FA) were calculated from the signals. A theoretical model of the diffusion in muscles was derived from Tanner's equation. The muscle fiber diameter was estimated by fitting the model to the measured signals. The measurements were also performed for normal rats as controls. No significant difference was found in the MD and the estimated intracellular diffusion coefficient between the control group and the denervated group. The denervated group had significantly higher FA compared with the control group (P<.05). The estimated muscle fiber diameter of the denervated group was significantly smaller than the estimated value of the control group (P<.05). These differences were found at 8 weeks after neurotomy. The proposed method is effective for evaluating changes in the microscopic structure of skeletal muscles.     

Geometrical restrictions of water diffusion in aqueous protein systems. A study using NMR field-gradient techniques

Geometrical restrictions of water diffusion in different aqueous protein systems were studied using two versions of the NMR field gradient technique. The samples were aqueous systems of bovine serum albumin, gelatin and horse myoglobin at concentrations ranging from diluted solutions to almost dry powders being only partly hydrated. Hydrated protein aerogels were produced by the aid of a special preparation procedure and studied in addition. The experiments referred to the, temperature and concentration dependences of the water diffusion coefficient above and below the free-water freezing temperature. The diffusion coefficient within clusters of overlapping hydration shells is reduced by one order of magnitude compared with that of bulk water. Geometrical restrictions manifest themselves (a) by the obstruction effect observed at low protein concentrations, (b) by the topologically two-dimensional diffusion in the network of overlapping hydration shells, (c) by the percolation threshold appearing at about 15%_b.w. water and (d) by the anomalous diffusion behaviour concluded from the protein aerogel study.     

Modeling diffusion in white matter in the brain: a composite porous medium

We model diffusion in white matter fascicles as a problem of diffusion in an array of identical thick-walled cylindrical tubes immersed in an outer medium and arranged periodically in a regular lattice. The diffusing molecules have different diffusion coefficients and concentrations (or densities) within the tubes' inner core, membrane, myelin sheath, and within the outer medium. For an impermeable myelin sheath, diffusing molecules within the inner core are completely restricted, while molecules in the outer medium are hindered due to the tortuosity of the array of impenetrable tubes.     

Monte Carlo algorithm for drift and diffusion of ions in anisotropic,non-homogeneous media

A new Monte Carlo algorithm for ion transport in two-dimensional anisotropic media is reported. It is based on physical considerations of drift and diffusion in anisotropic media with or without an impermeable boundary. Inhomogeneities in the medium and electric field can be taken into account by averaging along the ion trajectory. The algorithm has been applied to the calculation of ion transport in liquid crystal displays and has been successfully compared with a finite difference program on a one-dimensional liquid crystal structure.     

Influence of anisotropy of the diffusion coefficient on the asymptotic behavior of a spatial atom distribution in structures with complex geometry

Obtained by the method of continual integration in the optimal trajectory approximation is the asymptotic behavior of the Green's function of the Fick equation with anisotropic diffusion coefficient in structures with complex geometry when the domain boundary is impermeable to the diffusing particles. Using the expression found for the Green's function, topological properties of the equal-concentration surfaces, particularly the topological singularities of a diffusion p-n-junction, are determined by means of the given initial distribution of the diffusing atoms.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 9–12, May, 1988.     

Macroscopic and Microscopic Fields in High-Resolution Liquid NMR

The microscopic magnetic-induction field “seen by each nucleus” in a material medium and which is generated by a rapidly time-dependent spin magnetization gives rise to surprising new features in high-resolution nuclear magnetic resonance experiments. The purpose of the present paper is to show how the relations between the macroscopic average fields, the magnetization, and the microscopic fields (which were studied and clarified long ago at thermal equilibrium) can be extended to the present NMR context in which the magnetization can become rapidly time dependent and unrelated to thermal equilibrium properties.     

An investigation of the salt dissociation effects on solid electrolyte interface (SEI) formation using linear carbonate-based electrolytes in lithium ion batteries

Lithium salts possess dissociating properties that are useful for passivation layer formation. In this study, these properties are investigated in the context of three kinds of linear carbonate electrolytes using several techniques, such as physical properties, AC impedance, electrochemical quartz crystal microbalance (EQCM), and nuclear magnetic resonance (NMR). The lithium salts are completely dissociated to the lithium ions by the unsymmetrical linear carbonate structure; therefore, the transference number and diffusion coefficient of the cations show that the lithium ions are important and dominate the ionic transfer and the passivation layer properties that are important and relate to battery performance. These data suggest that battery performance is influenced by ionic transfer properties, lithium salt and electrolyte structure.     

管内两层介质入口段扩散混合的耦合换热研究

对圆管内辐射物性不同的两层介质层流入口段,采用SIMPLEC算法与蒙特卡罗法数值模拟了二维稳态流动与扩散混合时的辐射-对流耦合换热。通过计算,分析了介质层几何参数、介质物性与流动参数对组份分布与耦合换热的影响。结果表明,介质组分的扩散混合对耦合换热存在明显的影响区域,且该影响区大于组分的扩散混合区;外层介质的吸收系数、入口截面的相对厚度对耦合换热的影响基本一致;质扩散系数对耦合换热的影响很小,入口雷诺数的增加会抑制质扩散。     

Pore-Size Distributions and Tortuosity in Heterogeneous Porous Media

The diffusion coefficient, measured at long observation times by pulsed-held-gradient NMR, can in principle be used to estimate the tortuosity of a porous medium. This method is useful for glass-sphere packs, but we find that it does not generally work for porous sedimentary rock. Natural sedimentary rocks are characterized by complex microgeometries and broad distributions of pore sizes, which cannot be adequately sampled by diffusing molecules in experimentally accessible observation times. The time-dependent diffusion coefficient D(t) can be distinctly irregular for rocks with very large pores. In heterogeneous porous media, determination of pore-size distribution by relaxation-time measurements and tortuosity by PFG diffusion measurements are mutually exclusive.     

Alternative Oblique-Incidence Reflectometry for Measuring Tissue Optical Properties

To deduce the optical properties, the absorption coefficient SmU_aand reduced scattering coefficient μ’_s, of turbid medium, Lin et al. (Appl. Opt. 34 (1995) 2362) proposed an oblique incidence reflectometry in which the diffusion approximation was assumed. In this paper we propose an alternative method which does not assume the diffusion approximation but uses a Monte Carlo light propagation model. Two features are extracted from the diffuse reflectance distribution detected on the medium surface, and optical properties are then estimated by looking up the predetermined table generated by Monte Carlo simulations. The validity of the proposed method has been confirmed by computer simulations.     

Simulation and experimental verification of the diffusion in an anisotropic fiber phantom

Diffusion weighted magnetic resonance imaging enables the visualization of fibrous tissues such as brain white matter. The validation of this non-invasive technique requires phantoms with a well-known structure and diffusion behavior. This paper presents anisotropic diffusion phantoms consisting of parallel fibers. The diffusion properties of the fiber phantoms are measured using diffusion weighted magnetic resonance imaging and bulk NMR measurements. To enable quantitative evaluation of the measurements, the diffusion in the interstitial space between fibers is modeled using Monte Carlo simulations of random walkers. The time-dependent apparent diffusion coefficient and kurtosis, quantifying the deviation from a Gaussian diffusion profile, are simulated in 3D geometries of parallel fibers with varying packing geometries and packing densities. The simulated diffusion coefficients are compared to the theory of diffusion in porous media, showing a good agreement. Based on the correspondence between simulations and experimental measurements, the fiber phantoms are shown to be useful for the quantitative validation of diffusion imaging on clinical MRI-scanners.     

A core-softened fluid model in disordered porous media. Grand canonical Monte Carlo simulation and integral equations

We have studied the microscopic structure and thermodynamic properties of a core-softened fluid model in disordered matrices of Lennard-Jones particles by using grand canonical Monte Carlo simulation. The dependence of density on the applied chemical potential (adsorption isotherms), pair distribution functions, as well as the heat capacity in different matrices are discussed. The microscopic structure of the model in matrices changes with density similar to the bulk model. Thus one should expect that the structural anomaly persists at least in dilute matrices. The region of densities for the heat capacity anomaly shrinks with increasing matrix density. This behavior is also observed for the diffusion coefficient on density from independent molecular dynamics simulation. Theoretical results for the model have been obtained by using replica Ornstein-Zernike integral equations with hypernetted chain closure. Predictions of the theory generally are in good agreement with simulation data, except for the heat capacity on fluid density. However, possible anomalies of thermodynamic properties for the model in disordered matrices are not captured adequately by the present theory. It seems necessary to develop and apply more elaborated, thermodynamically self-consistent closures to capture these features.     

颗粒介质中的粘滞系数

将颗粒介质看成是等效均匀介质, 其中的声衰减系数和声速等于该颗粒介质中的相应的量值(它们可由作者的理论给出), 等效静态密度可以用二元混合规则求得. 此外, 根据浓颗粒介质中相互作用的声传播理论, 当入射波为平面波时, 相互作用的次级波仍然是平面波. 在这样的情况下, 可以将三维非线性方程组简化为一维情况, 从而算得浓颗粒介质中的粘滞系数, 结果表明, 颗粒介质中的粘滞系数不仅依赖于颗粒的体积分数而且还与频率有关. 根据推导过程可知, 对比于爱因斯坦理论所能应用的限制, 本文的结果可以更广泛地应用于实际介质.     

在CP MAS NMR中测量质子自旋扩散速率的方法

自旋扩散在固体核磁共振的许多现象中都起着非常重要的作用。现有几种理论方案以估算扩散系数。然而在实践中这种估算既不实际也不可靠。本文提出了确定自旋扩散速率的新方案,它利用的是CP MAS NMR中的稀核退极化规律。带质子的稀核磁化矢量在退极化中表现出两个阶段,慢衰减的第二阶段是单一指数过程,它提供了自旋扩散速率的直接度量。自旋扩散实质上是极化转移的一种宏观表现形式,这种转移通过一系列成对自旋的flip-flop进行,可以用一维随机走步模型描述。从退磁过程半对数曲线的斜率可以求得平均flip-flop时间。自旋扩散系数可以由此估算。在一些典型的刚性有机固体和结晶高分子聚合物中,求得平均flip-flop的时间是700微秒左右。它比偶极相关时间大一个数量级。这意味着,自旋扩散时间常数与自旋—自旋弛豫时间常数是很不相同的,虽然这两个相应过程虽密切相关的。由质子线宽估计自旋扩散系数是不可靠的。