基于神经网络拟合的腹部化学交换饱和转移成像

磁共振成像（Magnetic Resonance Imaging，MRI）化学交换饱和转移（Chemical Exchange Saturation Transfer，CEST）技术在临床诊断中展现了巨大的潜力，但在腹部成像中受到主磁场偏移量大的挑战，而且利用传统的非对称性分析法得到的酰胺质子转移（Amide Proton Transfer，APT）成像对比度受到核奥氏增强（Nuclear Overhauser Enhancement，NOE）效应的干扰.本文提出了一种基于神经网络拟合的CEST后处理方法，对每个像素采集得到的Z谱特征进行识别，不需要额外序列扫描即可得到背景参考Z谱与主磁场偏移量，用以校正和获得理想的Z谱，并进一步分离得到源自APT效应与NOE效应的信号.鸡蛋清和健康志愿者腹部成像结果显示，本文提出的基于神经网络的CEST后处理方法效果较好.     

Generalized equation for describing the magnetization in spoiled gradient-echo imaging

The purpose of this study was to demonstrate a generalized equation for describing the magnetization in spoiled gradient-echo (SPGR) imaging in which the in-pulse relaxation and magnetization transfer (MT) effects are taken into account. First, the time-dependent Bloch equations for the two-pool exchange model with MT effect were reduced to an inhomogeneous linear differential equation, and then a simple equation was derived to solve it using a matrix operation. Second, the equations describing the magnetization before and after the radiofrequency (RF) pulse were derived based on the above solution for the RF-pulse excitation and evolution phases. Finally, a generalized equation describing the steady-state magnetization was derived. The validity of this equation was investigated by comparing with the transverse magnetization obtained by the regular Ernst equation and analytical solution in which the in-pulse transverse relaxation is considered. When the same assumption was made in our method, there were good agreements between them, indicating the validity of our method. The in-pulse transverse and longitudinal relaxations decreased the transverse magnetization compared to the case in which these effects were neglected, whereas MT increased it. In conclusion, we derived a generalized equation for describing the magnetization in SPGR imaging. This equation will provide a suitable basis for understanding the signal intensity in SPGR imaging and/or T₁ measurement using an SPGR sequence in cases in which the effect of in-pulse relaxation and/or MT cannot be neglected.     

1.5 T磁共振化学交换饱和转移成像的影响因素分析

本文探讨1.5 T磁共振化学交换饱和转移（Chemical Exchange Saturation Transfer,CEST）成像的影响因素.通过试管模型和临床病例,采用GE Signa HDe 1.5 T磁共振成像（Magnetic Resonance Imaging,MRI）扫描仪分别进行不同矩阵、激励次数、翻转角、磁化传递翻转角的CEST成像对比分析,以及不同激励次数、磁化传递翻转角的Z谱分析,并从成像组织、成像设备、成像技术等方面对原始图信号、酰胺质子转移（Amide Proton Transfer,APT）信号及Z谱进行分析研究.实验结果表明1.5 T MRI扫描仪的CEST图像信噪比相对较低,且磁场稳定性及均匀度影响了CEST成像的效果.在其他参数不变的情况下,降低采集矩阵和增加激励次数与翻转角可以增加原始图像信噪比.磁化传递翻转角为105°时,CEST成像效果最好.激励次数为2、磁化传递翻转角为105°时,所得数据符合组织Z谱情况.模型Z谱在磁化传递频率为-294~-194 Hz范围可显示30%谷氨酸（Glu）、碘剂（I₃₂₀）、纯水（H₂O）、肌酸（Cr）的信号差异,与H₂O差异最大处在-244~-214 Hz.原始图像信号30% I₃₂₀明显高于Glu、H₂O、Cr,Cr略低于Glu,APT图Cr略低于Glu.25例脑肿瘤的APT图呈高信号、12例脑梗塞的APT图呈低信号,CEST原始图像均可区分病变区域.有12例因采集时间、患者配合情况、环境及室温等影响导致CEST成像的失败.由此得出1.5 T场强下,CEST技术受到成像组织、设备、技术等因素的影响,需要进行多方面优化.在保证磁场稳定性及均匀度的情况下,优化参数的CEST成像和Z谱成像可以区分代谢物及其浓度.     

基于CEST机制的pH成像方法、原理和应用

化学交换饱和转移（Chemical Exchange Saturation Transfer,CEST）技术作为一种新型的磁共振成像（Magnetic Resonance Imaging,MRI）技术.它的原理为溶质池中被激发饱和的质子与游离水中未被饱和的质子间的化学交换,能够引起水质子磁共振信号的下降,从而获得组织内生物分子的相关信息.由于质子间的交换速率k_ex与组织微环境的pH值之间存在直接联系,因而可以通过溶质质子的CEST信号对活体组织进行pH成像.目前用于pH成像的溶质分子既包括内源性游离的蛋白质、多肽分子,还包括一系列的外源性小分子和金属螯合物.通过不同类型的比率法、内源性胺和酰胺浓度-独立检测（Amine and Amide Concentration-independent Detection,AACID）等成像方法,能够获得肾脏、中风脑组织以及肿瘤组织的pH图谱.本文详细总结了2000年以来利用CEST技术进行pH成像方面的研究进展,包括对比剂、成像方法和相关应用,展望了活体组织pH成像的发展趋势和应用前景.     

Chemical exchange saturation transfer MRI using intermolecular double-quantum coherences with multiple refocusing pulses

Chemical exchange saturation transfer (CEST) provides a new type of image contrast in MRI. Due to the intrinsically low CEST effect, new and improved experimental techniques are required to achieve reliable and quantitative CEST images. In the present work, we proposed a novel and more sensitive CEST acquisition approach, based on the intermolecular double-quantum coherence with a module of multiple refocusing pulses (iDQC-MRP). Experiments were performed on creatine and egg white phantoms using a Varian 7 T animal MRI scanner. The iDQC-MRP CEST technique showed a substantial enhancement in CEST and nuclear Overhauser enhancement (NOE) signal intensities, compared to the standard single-quantum coherence approach. In addition, the iDQC-MRP approach increased the signal-to-noise ratio of acquired saturation images, compared to the conventional iDQC approach. The new iDQC-MRP CEST sequence provides a promising way for exploiting in vivo CEST and NOE imaging applications.     

Simultaneous determination of labile proton concentration and exchange rate utilizing optimal RF power: Radio frequency power (RFP) dependence of chemical exchange saturation transfer (CEST) MRI

Chemical exchange saturation transfer (CEST) MRI is increasingly used to probe mobile proteins and microenvironment properties, and shows great promise for tumor and stroke diagnosis. However, CEST MRI contrast mechanism is complex, depending not only on the CEST agent concentration, exchange and relaxation properties, but also varying with experimental conditions such as magnetic field strength and RF power. Hence, it remains somewhat difficult to quantify apparent CEST MRI contrast for properties such as pH, temperature and protein content. In particular, CEST MRI is susceptible to RF spillover effects in that RF irradiation may directly saturate the bulk water MR signal, leading to an optimal RF power at which the CEST contrast is maximal. Whereas RF spillover is generally considered an adverse effect, it is noted here that the optimal RF power strongly varies with exchange rate, although with negligible dependence on labile proton concentration. An empirical solution suggested that optimal RF power may serve as a sensitive parameter for simultaneously determining the labile proton content and exchange rate, hence, allowing improved characterization of the CEST system. The empirical solution was confirmed by numerical simulation, and experimental validation is needed to further evaluate the proposed technique.     

Numerical method for hydrodynamic modulation equations describing Bloch oscillations in semiconductor superlattices

We present a finite difference method to solve a new type of nonlocal hydrodynamic equations that arise in the theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices. The hydrodynamic equations describe the evolution of the electron density, electric field and the complex amplitude of the Bloch oscillations for the electron current density and the mean energy density. These equations contain averages over the Bloch phase which are integrals of the unknown electric field and are derived by singular perturbation methods. Among the solutions of the hydrodynamic equations, at a 70 K lattice temperature, there are spatially inhomogeneous Bloch oscillations coexisting with moving electric field domains and Gunn-type oscillations of the current. At higher temperature (300 K) only Bloch oscillations remain. These novel solutions are found for restitution coefficients in a narrow interval below their critical values and disappear for larger values. We use an efficient numerical method based on an implicit second-order finite difference scheme for both the electric field equation (of drift-diffusion type) and the parabolic equation for the complex amplitude. Double integrals appearing in the nonlocal hydrodynamic equations are calculated by means of expansions in modified Bessel functions. We use numerical simulations to ascertain the convergence of the method. If the complex amplitude equation is solved using a first order scheme for restitution coefficients near their critical values, a spurious convection arises that annihilates the complex amplitude in the part of the superlattice that is closer to the cathode. This numerical artifact disappears if the space step is appropriately reduced or we use the second-order numerical scheme.     

Analysis of a time fractional wave-like equation with the homotopy analysis method

The time fractional wave-like differential equation with a variable coefficient is studied analytically. By using a simple transformation, the governing equation is reduced to two fractional ordinary differential equations. Then the homotopy analysis method is employed to derive the solutions of these equations. The accurate series solutions are obtained. Especially, when ?f=?g=−1, these solutions are exactly the same as those results given by the Adomian decomposition method. The present work shows the validity and great potential of the homotopy analysis method for solving nonlinear fractional differential equations. The basic idea described in this Letter is expected to be further employed to solve other similar nonlinear problems in fractional calculus.     

Time-dependent radiative transfer with automatic flux limiting

We discuss a simple method for solving the time-dependent transfer problem. This scheme is automatically flux-limited and affords physical insight into how flux limitation occurs. We then develop a second-order, time-dependent radiation energy equation that is similar in form to the diffusion limit radiation energy equation. This time-dependent energy equation approaches physically reasonable equations in optically thick and thin regions. Computational aspects of solving this energy equation are discussed.     

Experimental characterization of intermolecular multiple-quantum coherence pumping efficiency in solution NMR

The behavior of intermolecular multiple-quantum coherences in a variety of simple liquids with different chemical and magnetic properties is investigated experimentally and modeled by numerical simulations based on modified Bloch equations. The effects of spin concentration, temperature, intramolecular conformational flexibility, chemical exchange, and spin-spin coupling on the formation of high-order coherences are examined. It is shown that any process that makes the Larmor frequency time-dependent may interfere with the formation of these coherences. Good agreement is achieved between experiments and simulation, using independently known values of the magnetization density, the rate constants for translational diffusion, spin-spin and spin-lattice relaxation, and radiation damping.     

求sine-Gordon 型方程孤波解的一种统一方法

借助于一个辅助常微分方程的解，提出了一种求sine-Gordon 型方程孤波解的统一方法，并用该法简洁地求得了三个著名的sine-Gordon 型方程，即单sine-Gordon 方程、双sine-Gordon 方程和mKdV-sine-Gordon方程的精确孤波解。     

A new class of contrast agents for MRI based on proton chemical exchange dependent saturation transfer (CEST)

It has been previously shown that intrinsic metabolites can be imaged based on their water proton exchange rates using saturation transfer techniques. The goal of this study was to identify an appropriate chemical exchange site that could be developed for use as an exogenous chemical exchange dependent saturation transfer (CEST) contrast agent under physiological conditions. These agents would function by reducing the water proton signal through a chemical exchange site on the agent via saturation transfer. The ideal chemical exchange site would have a large chemical shift from water. This permits a high exchange rate without approaching the fast exchange limit at physiological pH (6.5-7.6) and temperature (37 degrees C), as well as minimizing problems associated with magnetic field susceptibility. Numerous candidate chemicals (amino acids, sugars, nucleotides, heterocyclic ring chemicals) were evaluated in this preliminary study. Of these, barbituric acid and 5, 6-dihydrouracil were more fully characterized with regard to pH, temperature, and concentration CEST effects. The best chemical exchange site found was the 5.33-ppm indole ring -NH site of 5-hydroxytryptophan. These data demonstrate that a CEST-based exogenous contrast agent for MRI is feasible.     

Measurement of APT using a combined CERT-AREX approach with varying duty cycles

The goal is to develop an imaging method where contrast reflects amide-water magnetization exchange, with minimal signal contributions from other sources. Conventional chemical exchange saturation transfer (CEST) imaging of amides (often called amide proton transfer, or APT, and quantified by the metric MTR_asym) is confounded by several factors unrelated to amides, such as aliphatic protons, water relaxation, and macromolecular magnetization transfer. In this work, we examined the effects of combining our previous chemical exchange rotation (CERT) approach with the non-linear AREX method while using different duty cycles (DC) for the label and reference scans. The dependencies of this approach, named AREX_double,vdc, on tissue parameters, including T₁, T₂, semi-solid component concentration (f_m), relayed nuclear Overhauser enhancement (rNOE), and nearby amines, were studied through numerical simulations and control sample experiments at 9.4 T and 1 μT irradiation. Simulations and experiments show that AREX_double,vdc is sensitive to amide-water exchange effects, but is relatively insensitive to T₁, T₂, f_m, nearby amine, and distant aliphatic protons, while the conventional metric MTR_asym, as well as several other APT imaging methods, are significantly affected by at least some of these confounding factors.     

Application of Improved (G'/G)–Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations

In this work, the improved (G'/G)-expansion method is proposed for constructing more general exact solutions of nonlinear evolution equation with the aid of symbolic computation. In order to illustrate the validity of the method we choose the RLW equation and SRLW equation. As a result, many new and more general exact solutions have been obtained for the equations. We will compare our solutions with those gained by the other authors.     

Analytic solutions of the optical Bloch equations

We present analytic solutions of optical Bloch equations. We found that the solutions exhibit two different types of the behavior: one is oscillatory, and the other is a simple decay. The boundary dividing the two different types of solutions is exactly calculated in a two-dimensional space of the laser detuning and Rabi frequency. We also obtained simple analytic solutions for special conditions.     

Analytical solutions of the simplified spherical harmonics equations

We derived analytical solutions of the simplified spherical harmonics equations, an approximation of the radiative transfer equation, for infinitely extended scattering media. The derived equations are simple (sum of exponential functions) and quickly evaluated. We compared the solutions with Monte Carlo simulations in the steady-state and time domains and found much better agreement compared to solutions of the diffusion equation, especially for large absorption coefficients, short time values, and small distances from the source.     

Self-induced transparency of very short optical pulses

Solutions to a first order wave equation, appropriate to ultrashort optical pulse theory and to the optical undamped Bloch equations are presented. Detuning is shown to play essential role in the physical interpretation of these solutions. Related cases have been discussed by Courtens and by Lee. It is noted that the rotating wave approximation introduces strong restrictions on the range of validity of possible solutions. Pulses with Lorentzian shapes, while implied by the equations, appear to be without physical significance.     

New Doubly Periodic Solutions of Nonlinear Evolution Equations via Weierstrass Elliptic Function Expansion Algorithm

A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the correspondingsystem of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2 1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.     

Application of Computer Algebra in Solving Chaffee--Infante Equation

In this paper, a series of two line-soliton solutions and double periodic solutions of Chaffee-Infante equation have been obtained by using a new transformation. Unlike the existing methods which are used to find multiple soliton solutions of nonlinear partial differential equations, this approach is constructive and pure algebraic. The results found here are tested on computer and therefore their validity is ensured.     

7 T 下脂肪对基于 NOE 的磁共振对比成像的影响

核 Overhauser 增强(NOE)效应在高场下的化学交换饱和转移中会造成 Z 谱高场位置的负背景信号,有望成为一种新的磁共振成像(MRI)对比机制．然而,研究指出, NOE信号的发生区域与主要的脂肪信号的频率位置有重叠,因此 MRI 中观察到的 NOE 信号有可能混合了脂肪信号．该文通过鸡蛋的模型实验,初步分析了脂肪含量较高的组织内脂肪信号对 NOE 效应的影响,并通过健康大鼠鼠脑及颅内肿瘤大鼠鼠脑实验,分析了脂肪对脑部 NOE 对比成像及基于 NOE 对比成像的疾病诊断的影响．结果表明,脂肪含量较高的组织内脂肪信号会引起伪 NOE 效应,并影响 NOE对比图像的准确性．