Multi-gradient pulse investigations of fluid transport in porous media.

NMR pulsed field gradient (PFG) experiments employing the application of n gradient pulses k(1) ellipsis k(n) are discussed in a general way as an n-fold encoding of position at successive times. The experiments are then represented by a sampling of n-dimensional k-space, K(n). Various parameters of motion can be derived from the evolution of correlations within the n-dimensional position (r-)space, R(n), which is the Fourier conjugate space to K(n). A wide class of NMR experiments may be described by this formalism, where the dimension of the experiment is often reduced by imposing conditions to the free variables. This is demonstrated for the case of displacement measurements where the condition summation operatork(i) = 0 is met. The two simplest pulse sequences which allow one to correlate displacements at two different times with each other are presented. While the three-pulse version of SERPENT encodes displacements in two interleaved time intervals Delta(1) and Delta(2), the four-pulse VEXSY experiment includes a mixing time tau(m) in between both encoding intervals Delta. The behaviour of fluid transport subject to external pressure through a model porous system is demonstrated by means of numerical simulations of SERPENT and VEXSY experiments for water flowing through a packed bed of monosized spherical particles. Displacements parallel (Z) and perpendicular (X) to the main flow direction are determined and the 2-D joint probability densities and the conditional probabilities are discussed along with the correlation coefficients related to the displacements at different encoding times. It is shown that all possible correlations between Z and X(2) in VEXSY decay with time constants comparable to the average time needed for a fluid molecule to cover one bead diameter, while a negative correlation is observed between transverse (X) displacements which is explained by molecules flowing along streamlines which follow the circumference of the spherical particles. Correlations for displacements during the different times in SERPENT generally decay much slower and provide complementary information about the evolution of displacements with time.     

Spectrally resolved velocity exchange spectroscopy of two-phase flow

The Velocity EXchange SpectroscopY (VEXSY) technique, which provides a means to correlate macroscopic molecular displacements measured during two intervals separated by a variable mixing period, has been applied for the first time to a system of two-phase flow. The chemical shift difference between water and methyl protons has been exploited to simultaneously determine the probability of displacements, or propagator, of both components in a water/silicone oil mixture flowing through a glass bead pack. The joint two-time probability densities as well as the conditional probabilities of velocities show a clearly distinct dispersion behaviour of both fluids which is a consequence of the different wetting properties of the fluids with respect to the glass surface of the bead pack.     

Double PGSE NMR with Stimulated Echoes: Phase Cycles for the Selection of Desired Encoding

When two pairs of position-encoding pulses are used in a pulsed gradient spin echo (PGSE) NMR experiment, it is possible to examine velocity fluctuations. The one-dimensional version of double PGSE NMR uses identical pulse pairs whose amplitudes are stepped simultaneously. In the two-dimensional version (VEXSY) the pulse pairs are stepped independently, resulting in a velocity exchange spectrum. A key limitation in such experiments is transverse relaxation, so that stimulated echoes are often used as the method of choice. It is shown here that the use of stimulated echoes results in a superposition of signals arising from different magnetization pathways such that the spin phases may reflect both the sum and difference of displacements over the pulse pair encoding times, as well as the displacement over the exchange time between the pulse pairs. A phase cycle scheme that selects desired encodings as required is demonstrated.     

Time-dependent velocities in porous media dispersive flow.

Pulsed Gradient Spin Echo (PGSE) NMR methods may be used to measure the asymptotic dispersion coefficient as well as the velocity autocorrelation function (VACF) in porous media flow. The VACF can be measured in the frequency domain using repetitive gradient pulse trains, and in the time domain using double PGSE encoding. The one dimensional double PGSE method, and the two dimensional velocity exchange experiment (VEXSY) are briefly outlined and their application to flow in monodisperse 0.5 mm diameter beads packs described, both axial and transverse VACFs being examined. The measured correlation times are shown to agree well with calculated values. The asymptotic dispersion coefficients agree with literature values in the case of transverse flow while in axial flow it is shown that asymptotic conditions are not achieved, even for observation times longer than the correlation time for flow around a bead.     

NMR imaging of thermal convection patterns

Two special magnetic resonance imaging techniques were applied to the Rayleigh/Bénard problem of thermal convection for the first time. The methods were tested using a water cell with horizontal bottom and top covers kept at different temperatures with a downward gradient. Using Fourier encoding velocity imaging (FEVI) a five-dimensional image data set was recorded referring to two space dimensions of slice-selective images and all three components of the local velocity vector. On this basis, the fields of the velocity components or of the velocity magnitude were evaluated quantitatively and rendered as gray shade images. Furthermore the convection rolls were visualized with the aid of two- or three-dimensional multistripe/multiplane tagging imaging pulse sequences based on two or three DANTE combs for the space directions to be probed. Movies illustrating the fluid motions by convection in all three space dimensions were produced. It is demonstrated that the full spatial information of the convection rolls is accessible with microscopic resolution of typically 100 × 100 × 100 μm³. This resolution is effectively limited by flow displacements in the echo time, which should be well within the voxel dimension. The main perspective of this work is that the combined application of FEVI and multistripe/multiplane tagging imaging permits quantitative examinations of thermal convection for arbitrary boundary conditions and with imposed through-flow apart from the direct visualization of convective flow in the form of movies.     

Background gradient suppression in pulsed gradient stimulated echo measurements

Pulsed gradient spin echo (PGSE) experiments can be used to measure the probability distribution of molecular displacements. In homogeneous samples this reports on the molecular diffusion coefficient, and in heterogeneous samples, such as porous media and biological tissue, such measurements provide information about the sample's morphology. In heterogeneous samples however background gradients are also present and prevent an accurate measurement of molecular displacements. The interference of time independent background gradients with the applied magnetic field gradients can be removed through the use of bipolar gradient pulses. However, when the background gradients are spatially non-uniform molecular diffusion introduces a temporal modulation of the background gradients. This defeats simple bipolar gradient suppression of background gradients in diffusion related measurements. Here we introduce a new method that requires the background gradients to be constant over coding intervals only. Since the coding intervals are typically at least an order of magnitude shorter than the storage time, this new method succeeds in suppressing cross-terms for a much wider range of heterogeneous samples.     

Motion analysis of light-powered autonomous silver chloride nanomotors

Powered by UV light, nano/micrometer-sized silver chloride particles exhibit autonomous movement and form "schools" in aqueous solution, i.e. regions in which the number density of particles is significantly higher than the global average. In this paper, the silver chloride particles in such a system are classified by their proximity to other AgCl particles -be they isolated, coupled or schooled- and their motion paths are tracked and analyzed. By plotting time-averaged mean squared displacements of each particle over various time intervals from 0.1s to 15.0s, we discover different diffusive behaviors for the three classes of silver chloride particles.     

Computer simulation of the spin-echo spatial distribution in the case of restricted self-diffusion

This article concerns the question of a proper stochastic treatment of the spin-echo self-diffusion attenuation of confined particles that arises when short gradient pulse approximation fails. Diffusion is numerically simulated as a succession of random steps when motion is restricted between two perfectly reflecting parallel planes. With the magnetic field gradient perpendicular to the plane boundaries, the spatial distribution of the spin-echo signal is calculated from the simulated trajectories. The diffusion propagator approach (Callaghan, "Principles of Nuclear Magnetic Resonance Microscopy," Oxford Univ. Press, Oxford, 1991), which is just the same as the evaluation of the spin-echo attenuation by the method of cumulant expansion in the Gaussian approximation, with Einstein's approximation of the velocity correlation function (VCF) (delta function), agrees with the results of simulation only for the particle displacements that are much smaller than the size of the confinement. A strong deviation from the results of the simulation appears when the bouncing rate from the boundaries increases at intermediate and long gradient sequences. A better fit, at least for intermediate particle displacements, was obtained by replacing the VCF with the Oppenheim--Mazur solution of the Langevin equation (Oppenheim and Mazur, Physica 30, 1833--1845, 1964), which is modified in a way to allow for spatial dependence of particle displacements. Clearly, interplay of the correlation dynamics and the boundary conditions is taking place for large diffusion displacements. However, the deviation at long times demonstrates a deficiency of the Gaussian approximation for the spin echo of diffusion inside entirely closed pores. Here, the cumulants higher than the second one might not be negligible. The results are compared with the experiments on the edge enhancement by magnetic resonance imaging of a pore.     

Nonlinear amplitude approximation for bilinear systems

An efficient method to predict vibration amplitudes at the resonant frequencies of dynamical systems with piecewise-linear nonlinearity is developed. This technique is referred to as bilinear amplitude approximation (BAA). BAA constructs a single vibration cycle at each resonant frequency to approximate the periodic steady-state response of the system. It is postulated that the steady-state response is piece-wise linear and can be approximated by analyzing the response over two time intervals during which the system behaves linearly. Overall the dynamics is nonlinear, but the system is in a distinct linear state during each of the two time intervals. Thus, the approximated vibration cycle is constructed using linear analyses. The equation of motion for analyzing the vibration of each state is projected along the overlapping space spanned by the linear mode shapes active in each of the states. This overlapping space is where the vibratory energy is transferred from one state to the other when the system switches from one state to the other. The overlapping space can be obtained using singular value decomposition. The space where the energy is transferred is used together with transition conditions of displacement and velocity compatibility to construct a single vibration cycle and to compute the amplitude of the dynamics. Since the BAA method does not require numerical integration of nonlinear models, computational costs are very low. In this paper, the BAA method is first applied to a single-degree-of-freedom system. Then, a three-degree-of-freedom system is introduced to demonstrate a more general application of BAA. Finally, the BAA method is applied to a full bladed disk with a crack. Results comparing numerical solutions from full-order nonlinear analysis and results obtained using BAA are presented for all systems.     

基于Pareto优化理论的多目标超椭梯度线圈设计

磁共振系统梯度线圈设计是一个多目标优化问题,在设计时需要综合考虑能耗、磁场能、线性度等设计要求.这些设计要求通常难以同时获得极小解,因此在设计梯度线圈时需要权衡线圈的各方面的设计需求.本文基于柱面可展性和流函数设计方法,结合Pareto优化方法实现了在超椭圆柱设计表面上梯度线圈的多目标设计.分别分析了磁场能、能耗目标对梯度线圈线性度、线圈构型的影响;并在Pareto解空间中分析各目标的相互变化关系,通过数值算例验证了该方法在超椭梯度线圈设计时的有效性与灵活性.优化结果显示,在满足线性度误差小于5%,能耗与磁场能分别小于用户设定值的设计约束下,梯度线圈的多目标设计存在多个局部优化解.该方法可以直观地比较相同目标函数值的情况下各单目标的具体表现,有利于实现不同的设计要求下梯度线圈的最终定型设计.     

基于预滤波迭代梯度法的运动估计

提出一种对小平移和大平移图像序列进行运动估计的新算法 预滤波迭代梯度法,预滤波迭代梯度法就是先对图像进行低通滤波,然后用迭代梯度法进行运动估计。结果表明,该方法比梯度法、预滤波梯度法和迭代梯度法具有更高的估计精度,而且可以很好地抑制噪声的影响。     

Transient displacement induced in shear wave elastography: comparison between analytical results and ultrasound measurements

It is now accepted that an effective way to investigate the elastic properties of soft tissues is to generate a localized transient acoustic radiation force and to follow the associated displacements in the time/space domain. Shear waves induced by this stress field are particularly interesting in this kind of medium because they are governed by the shear elastic modulus mu, which is directly linked to the Young modulus, and spatial distribution and temporal evolution of the transient motion induced must therefore be obtained in detail. We report here a model based on the elastodynamic Green's function formalism to describe these displacements. 3D simulation of radiation force in homogenous elastic media was performed and the displacement curves computed at different radial distances for different temporal force profiles. Amplitude and duration of displacement were found to be reliable parameters to characterize the elastic properties of the medium. Experimental measurements were performed in a homogeneous agar-gelatin tissue-mimicking phantom, and two transducers were used to generate the radiation force and follow the induced displacements. Displacements obtained from different lateral locations around the applied force axis were then used to reconstruct the shear-wave propagation in a scan plane as a function of time. The experimental displacements/curves agreed with the theoretical profiles obtained by the elastodynamic Green's function formalism.     

T₂ distribution mapping profiles with phase-encode MRI

Two 1-D phase-encode sequences for T? mapping, namely CPMG-prepared SPRITE and spin-echo SPI, are presented and compared in terms of image quality, accuracy of T? measurements and the measurement time. The sequences implement two different approaches to acquiring T?-weighted images: in the CPMG-prepared SPRITE, the T?-weighting of magnetization precedes the spatial encoding, while in the spin-echo SPI, the T?-weighting follows the spatial encoding. The sequences are intended primarily for T? mapping of fluids in porous solids, where using frequency encode techniques may be problematic either due to local gradient distortions or too short T?. Their possible applications include monitoring fluid-flow processes in rocks, cement paste hydration, curing of rubber, filtering paramagnetic impurities and other processes accomplished by changing site-specific T?.     

Gradient induced artifacts in simultaneous EEG-fMRI: Effect of synchronization on spiral and EPI k-space trajectories

The nature of the gradient induced electroencephalography (EEG) artifact is analyzed and compared for two functional magnetic resonance imaging (fMRI) pulse sequences with different k-space trajectories: echo planar imaging (EPI) and spiral. Furthermore, the performance of the average artifact subtraction algorithm (AAS) to remove the gradient artifact for both sequences is evaluated. The results show that the EEG gradient artifact for spiral sequences is one order of magnitude higher than for EPI sequences due to the chirping spectrum of the spiral sequence and the dB/dt of its crusher gradients. However, in the presence of accurate synchronization, the use of AAS yields the same artifact suppression efficiency for both pulse sequences below 80 Hz. The quality of EEG signal after AAS is demonstrated for phantom and human data. EEG spectrogram and visual evoked potential (VEP) are compared outside the scanner and use both EPI and spiral pulse sequences. MR related artifact residues affect the spectra over 40 Hz (less than 0.2 μV up to 120 Hz) and modify the amplitude of P1, N2 and P300 in the VEP. These modifications in the EEG signal have to be taken into account when interpreting EEG data acquired in simultaneous EEG-fMRI experiments.     

Density-Matrix Calculations of the 1.5 T Citrate Signal Acquired with Volume-Localized STEAM Sequences

Citrate detection and quantitation with proton spectroscopic methods are of current interest as potential tools in the diagnosis and staging of prostate cancer. Thestimulatedechoacquisitionmode (STEAM) sequence is a commonly used volume-localization method for detecting citrate signal. Since the¹H citrate resonance at clinically available field strengths arises from a strongly coupled two-spin system, the 90° RF pulses and localizing gradients used in STEAM sequences result in a complicated dependence of signal intensity on timing intervals and gradient amplitudes. The density-matrix formalism has been applied to arrive at a general solution to this problem. Citrate-signal properties at 1.5 T for different gradient localization schemes are examined with the solution. Optimal interpulse delays, deleterious gradient balances, zero-quantum oscillations with mixing time, and a low-frequency, large-amplitude oscillation with echo time are identified for signals acquired with the standard disposition of gradients in STEAM. The generality of the solution also allows for an examination of nonstandard gradient disposition schemes for enhancing citrate signal and for quantifying the sensitivity of such approaches to both field inhomogeneities and off-resonance effects.     

A novel sensitivity-based method for damage detection of structures under unknown periodic excitations

This paper presents a technique for damage detection in structures under unknown periodic excitations using the transient displacement response. The method is capable of identifying the damage parameters without finding the input excitations. We first define the concept of displacement space as a linear space in which each point represents displacements of structure under an excitation and initial condition. Roughly speaking, the method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering this novel geometrical viewpoint, an equation called kernel parallelization equation (KPE) is derived for damage detection under unknown periodic excitations and a sensitivity-based algorithm for solving KPE is proposed accordingly. The method is evaluated via three case studies under periodic excitations, which confirm the efficiency of the proposed method.     

Comparative analysis of Reaction-Diffusion Manifold based reduced models for Head-On- and Side-Wall-Quenching flames

In this study, multi-dimensional molecular transport phenomena during Flame-Wall-Interactions (FWI) and their effects on model reduction strategies are investigated. In order to access the problem, the standard configurations of a two-dimensional Side-Wall Quenching (SWQ) flame and a one-dimensional Head-On Quenching (HOQ) flame are used and compared. In the case of the SWQ configuration it is shown that the gradients of the species scatter significantly both in the physical space and in the state space. Moreover, the gradient vector of the specific enthalpy describing energy losses towards the wall is not aligned with the gradient vectors of the species, which can be considered as a typical case while a flame in application might approach to the wall at any arbitrary transversal direction. This observation motivates to take the gradients’ scattering and multi-dimensional transport phenomena into account during model reduction to describe reliably the quenching process.The Reaction-Diffusion Manifold (REDIM) method is applied in this work. The method allows to take into account multi-dimensional transport in a very generic way. In order to generate the REDIM, gradient estimates are approximated by using a Singular-Value Decomposition (SVD) of SWQ detailed gradients fields. Two-dimensional REDIMs for both cases are constructed and compared to each other. Different transport (diffusion) models are implemented to compare quantitatively the manifolds with HOQ and SOQ gradients estimates. The comparison shows that the differences between reduced models with varying transport models is significantly larger than the differences for varying configurations (multidimensional gradient estimates). This justifies the use of a relatively simple REDIM for more complicated geometries and configurations. This simplifies the treatment and model reduction procedure significantly for such complicated transient phenomena.     

Value of RARE-MRI sequences in the diagnosis of lymphangiomatosis in children

Three patients suffering from extensive cavernous lymphangiomatosis are presented here. They were examined by MRI using RARE-MR hydrography (rapid acquisition with relaxation enhancement) as well as conventional spin-echo sequences. RARE sequences, which depict each fluid-filled lymphatic space, can be used for screening. RARE-sequences help to shorten investigation time, particularly in cases involving the skeleton. The imaging strategy can be changed according to the results of this sequence. It may be performed prior to spin-echo sequences and facilitates follow-up investigations. RARE sequences distinguish between lymphangiomatosis and hemangiomatosis, or a combination of the two.     

Nodal and modal strategies for longitudinal thermal diffusivity profile estimation: Application to the non destructive evaluation of SiC/SiC composites under uniaxial tensile tests

In this paper, infrared image sequences of a SiC/SiC composite excited with a non uniform heat pulse (also known as Flash) are processed using two different strategies. In a first approach, a modal strategy based on the decomposition of infrared sequences in an orthogonal basis is applied. A discrete version of the heat equation is solved in the transformed space using only a very limited number of modes for which the sensitivity to diffusivity is optimal. In a second time, a nodal approach that consists in solving locally a finite difference scheme is performed at each pixel. A new sensitivity analysis based on a local correlation study of the partial derivatives of the experimental data (transformed or not) allows validating the relevance of each approach, and determining the optimal space where to perform estimations. As a result, effective local longitudinal diffusivity profiles of a SiC/SiC composite under mechanical testing are provided and analyzed to detect the presence of microcracks.     

基于动态时间弯曲的X射线变电流投影融合方法

针对变电流投影融合中的阈值选择问题,提出了一种基于动态时间弯曲的变电流投影融合方法.该方法首先计算不同电流下投影的灰度值-有效边缘梯度序列,然后利用动态时间弯曲距离对预处理后的序列进行相似匹配,自动判断最佳融合阈值,最后根据阈值确定不同电流投影的子区域并对其进行融合,实现了探测器动态范围的扩展.本文方法计算的各角度下融合阈值的平均误差仅为2.26%,能够避免人工选择融合阈值的主观性,基于融合后重建图像的信噪比与几何尺寸测量准确度均优于固定融合阈值的方法.