核磁共振实验的计算机辅助教学

基于核磁共振的经典理论——Bloch方程,运用Matlab程序对核磁共振实验的各个环节(观察核磁共振信号、自由衰减信号、自旋回波信号等)进行了可视化模拟,帮助学生认识和理解核磁共振,辅助实验教学.     

基于Bloch方程的核磁共振数值求解

核磁共振已成为分子科学、材料科学和生命科学等领域研究物质结构、动态过程及物理特性最有效的工具之一.本文将基于Bloch方程研究核磁共振现象及相关实验参数如共振频率和弛豫时间,同时对实验中常用的脉冲序列如Single Pulse,Inversion Recovery,Spin Echo,CPMG等进行系统模拟,揭示出不同脉冲序列的物理意义.     

优化重聚脉冲提高梯度场核磁共振信号强度

缩短射频脉冲宽度, 有助于解决脉冲电力消耗大、样品吸收率高、信噪比低等极端条件核磁共振探测的关键问题. 本文首先分析射频脉冲角度对核磁共振自旋回波信号强度的影响机理, 基于Bloch方程推导了回波信号幅度与扳转角、重聚角的关系. 在特制核磁共振分析仪上采用变脉冲角度技术, 分别在均匀磁场和梯度磁场条件下实现对扳转角和重聚角与回波信号强度关系的数值模拟和实验测量. 结果表明, 梯度场中, 扳转角为90°、重聚角为140°的射频脉冲组合获得最大首波信号强度, 比180°脉冲对应的回波幅值提高13%, 能耗降低至78%. 选用该重聚角(140°) 优化设计饱和恢复脉冲序列探测流体的纵向弛豫时间T₁特性, 准确获得 T₁分布.该结果对于低电力供应、且对信噪比有较高要求的核磁共振测量, 如随钻核磁共振测井和在线核磁共振快速检测等, 具有重要意义. 关键词： 核磁共振 信号强度 重聚脉冲角度 Bloch方程     

油水饱和球管孔隙模型弛豫的理论计算与计算机模拟

根据Brownstein-Tarr理论,采用特征函数展开法,通过求解基于扩散效应的Bloch控制方程,给出了油水饱和球管孔隙模型弛豫的理论计算公式.理论计算结果表明,在水润湿条件下,油的弛豫过程只与含油饱和度有关,而与岩石的孔隙结构无关.根据理论计算结果对球管模型中水的弛豫进行了数值模拟,模拟结果显示,球和管的主弛豫过程是一个单指数函数,其余部分与之相比可以忽略,即球管模型中水的弛豫可近似为一个双指数衰减过程. 关键词： 核磁共振 弛豫 球管孔隙模型 Bloch控制方程     

Bloch方程的精细时程积分及其在射频脉冲设计中的应用

射频脉冲的频率选择性直接影响磁共振成像的质量，而射频脉冲的优化设计又归结为对Bloch方程的求解.尽管在某些情况下Bloch方程存在解析解，但由于其缺乏通用性而且形式上过于复杂而难于得到实用.本文提出一种Bloch方程的精细时程积分算法，并结合全局优化算法给出一个完整的射频脉冲设计方案.精细积分算法具有高效、高精度的特点，对于射频脉冲的设计很有裨益.数值算例表明，设计所得的射频脉冲具有较好的频率选择性. 关键词： 磁共振成像 射频脉冲 Bloch方程 精细时程积分     

特形脉冲的设计与计算机模拟

根据LiouvillevonNeumann方程从理论上对特形脉冲做了全面的描述,提出了一种具体的调幅特形脉冲设计方案:首先将待设计的脉冲展成一个有限Fourier级数,然后根据Bloch方程的解析解准确计算出各阶正弦、余弦波的频谱,再将这些频谱组合后与该脉冲的理想频谱进行比较构成误差函数,最后运用鲍威尔-模拟退火组合优化算法计算出全局最优Fourier系数,即可得到所需脉冲的表达式.应用此设计方案,得到了体系处于热平衡态时的特形激励脉冲和反转脉冲的具体表达式.计算机模拟表明,所得脉冲的频谱具有较好的选择性 关键词： 核磁共振 特形脉冲 Bloch方程 鲍威尔模拟退火组合优化算法     

NMR的化学位移和自旋耦合分裂发现40周年

1946年E、M、Purcell[1]在Harvard和F、Bloch[2]在Stanford几乎同时用不同方法独立发现了核磁共振(Nuclear Magnetic Resonance,即NMR)现象。最初,NMR方法主要用于测量原子核的磁矩,并可提高测量精度。虞福春和W.G.Proctor曾进行了大量的原子核磁矩测量[3,4,5,6,7,8]。五十多年来,NMP波谱学取得了举世瞩目的进展。1952年Purcell和Bloch因发现核磁共振而共同荣获诺贝尔物理学奖金。 我国著名物理学家虞福春教授首先发现了化学位移并首先发现了自旋耦合分裂,为核磁共振的发展作了具有重要里程碑的奠基贡献。虞福春到斯坦福大学任F.Bloch教授     

飞秒相干光场激发固体样品的线性与上转换荧光光谱研究

用可变延时的双光束激光激发固态样品,同时测量样品的线性荧光和上转换荧光强度.理论上用Bloch方程描述了激发态吸收上转换过程,通过数量方法解Bloch方程,得到了与激发态吸收过程相关的各能级粒子数布居随时间的变化关系,计算出荧光强度,得到有一定延时的两束光的相干光谱,相干光谱的计算结果和实验结果一致。     

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.     

啁啾超短激光脉冲对二能级体系特性的调控

研究了啁啾超短激光脉冲与二能级体系近共振作用下的特性.采用光与物质相互作用的半经典理论,建立了含啁啾相位项的修正光学Bloch方程,并用高准确度、快速和可靠的四阶龙格-库塔法数值求解了该方程.通过数值计算,得到啁啾符号和啁啾量与Bloch矢量的关系,以及共振失谐量符号和啁啾符号对Bloch矢量性质影响的规律.结果表明,啁啾的符号和大小对Bloch矢量的瞬态相干过程和稳态特性都会产生明显的调制作用,由此可以通过调节激光脉冲的啁啾特性来实现对二能级体系性质的调控.     

A solution to Bloch NMR flow equations for the analysis of hemodynamic functions of blood flow system using m-Boubaker polynomials

This paper proposes a solution to Bloch NMR flow equations in biomedical fluid dynamics using a new set of real polynomials. In fact, the authors conjugated their efforts in order to take benefit from similarities between independent Bloch NMR flow equations yielded by a recent study and the newly proposed characteristic differential equation of the m-Boubaker polynomials. The main goal of this study is to establish a methodology of using mathematical techniques so that the accurate measurement of blood flow in human physiological and pathological conditions can be carried out non-invasively and becomes simple to implement in medical clinics. Specifically, the polynomial solutions of the derived Bloch NMR equation are obtained for use in biomedical fluid dynamics. The polynomials represent the T₂-weighted NMR transverse magnetization and signals obtained in terms of Boubaker polynomials, which can be an attractive mathematical tool for simple and accurate analysis of hemodynamic functions of blood flow system. The solutions provide an analytic way to interpret observables made when the rF magnetic fields are designed based on the Chebichev polynomials. The representative function of each component is plotted to describe the complete evolution of the NMR transverse magnetization component for medical and biomedical applications. This mathematical technique may allow us to manipulate microscopic blood (cells) at nano-scale. We may be able to theoretically simulate nano-devices that may travel through tiny capillaries and deliver oxygen to anemic tissues, remove obstructions from blood vessels and plaque from brain cells, and even hunt down and destroy viruses, bacteria, and other infectious agents.     

Mathematical model of the Bloch NMR flow equations for the analysis of fluid flow in restricted geometries using the Boubaker polynomials expansion scheme

In this study, the Bloch NMR flow equations are modelled into diffusion equation with constant transport coefficient in terms of the NMR transverse magnetization. Mathematical conditions are established for the diffusion coefficients to be constant or spatially varied with direction. When these conditions are met, the diffusion coefficients can then be easily evaluated in terms of Boubaker polynomials for the study of flow in restricted geometries.     

Geometric Phase and Sidebands

Geometric phase of mixed state is expanded for a two-level atom interacting with a quantized field mode, where master equation is a modified Bloch equation with constant terms that are used to explain emergence of sidebands in the spectrum of the fluorescent light. The results show that geometric phase transition is observed for medium initial angle when the Rabi frequency associated with the driving field becomes comparable to the spectral width of the atom. We find that the geometric phase transition depends on population inversion and Bloch radius, which is helpful to understand mechanism of sideband.     

光谱烧孔中孔的宽度和深度与烧孔光持续时间的关系

本文由光学Bloch方程出发,讨论了二能级系统光谱烧孔中孔宽和孔深与烧孔激光脉冲持续时间的关系.在强场下短脉冲烧孔中,用π脉冲可以得到足够深且宽度小于稳态值的孔.弱场下,孔深与烧孔时间成指数关系.Bloch方程的修正对上述两种条件下烧孔行为的描述无明显影响.以二能级系统光谱烧孔为基础,讨论了永久性光谱烧孔和光子选通光谱烧孔中孔的行为.     

Formulation of Zeeman modulation as a signal filter

The Bloch equation containing a Zeeman modulation field is solved analytically by treating the Zeeman modulation frequency as a perturbation. The absorption and dispersion signals at both 0 degrees and 90 degrees modulation phase are obtained. The solutions are valid to first order in the modulation frequency, but are otherwise valid for any value of modulation amplitude or microwave amplitude. A first order treatment of modulation frequency is shown to be a valid approximation over a wide range of typical experimental EPR conditions. The solutions derived from the Bloch equation suggest that the effect of over-modulation on first and second harmonic EPR spectra can be formulated as a mathematical filter that smoothes and broadens the under-modulated signal. The only adjustable filter parameter is a width that is equivalent to the applied peak-to-peak modulation amplitude. The true spin-spin and spin-lattice relaxation rates are completely determined from the under-modulated spectrum. The filters derived from the analytic solutions of the Bloch equation in the linear limit of modulation frequency are tested against numerical solutions of the Bloch equation that are valid for any modulation frequency to show their applicability. The filters are further tested using experimental EPR spectra. Experimental under-modulated spectra are mathematically filtered and compared with the experimental over-modulated spectra. The application of modulation filters to STEPR spectra is explored and limitations are discussed.     

Nonlinear identification of NMR spin systems by adaptive filtering

In this paper, we present two new methods for identifying NMR spin systems. These methods are based on nonlinear adaptive filtering. The spin system is assumed to be time-invariant with memory. The first method uses a truncated discrete Volterra series to describe the nonlinear relationship between excitation (input) and system response (output). First-, second-, and third-order kernels of this series are estimated employing the least mean square (LMS) algorithm. Three parallel filters can then model the NMR spin system so that its output is no more than simple sum of three convolution products between combinations of the input signal and filters coefficients. It is also shown that the contribution of the Volterra second-order term to the total system response is neglected compared with the contributions of the first- and the third-order terms. In the second identification method, the output signal is related to the input signal through a recursive nonlinear difference equation with constant coefficients. The LMS algorithm is used again to estimate the equation coefficients. The two methods are validated with a simulated NMR system model based on Bloch equations. The results and the performances of these methods are analyzed and compared. It is shown that our methods permit a simple identification of NMR spin systems. The field of applications of this study is promising in the optimization of NMR signal detection, especially in the cases of low signal-to-noise ratios where optimum signal filtering and analysis must be performed.     

Dilation of a non-quasifree dissipative evolution

A semigroup evolution for the 1/2-spin which admits a conservative dilation is known to be governed by a Bloch equation in a standard form. Here we construct a conservative dilation directly from the Bloch equation, thus yielding an example of a dilation scheme for an evolution which is not quasifree. Moreover, we show that this conservative evolution is never ergodic in the non-quasifree case.     

密度矩阵理论在动态NMR中的应用

在交换影响可观测得到的温度范围内作定态全线型拟合是确定速率常数和活化参数的最佳方法。对弱偶合交换体系,理论线型可用改型的Bloch方程计算,但强偶合体系就需作全密度矩阵处理。本文的目的是说明如何用密度矩阵方法计算线型。内容包括密度矩阵的基本理论,以及密度矩阵理论在分子内和分子间交换体系的NMR线型计算中的应用。