磁共振扩散张量成像中扩散敏感梯度磁场方向分布方案的研究进展

磁共振扩散张量成像可以定量无创研究人体内水分子在三维空间中的各向异性扩散规律,进而获取重要的病理及生理信息.为了得到水分子各向异性扩散信息,需要按照一定的方案依次施加不同方向的扩散敏感梯度磁场,测量水分子在这些方向上的扩散系数用以估算扩散张量.扩散张量成像测量结果的准确程度受梯度磁场方向分布方案的影响,本文对扩散敏感梯度磁场方向分布方案进行综述,包括完全随机方案、启发式方案、规则多面体式方案和数值优化方案等,分析这些方案的优势与局限性,并提出需进一步研究的问题.     

描述人体内水分子扩散各向异性特征的新方法

通过核磁共振扩散张量成像(DTI)得到的特定值域的扩散各向异性指数(DAI) 可用于揭示水分子扩散椭球的形态学特征, 定量反映被成像物体内部水分子扩散的优势方向和强度, 间接得到被成像物体内部的组织结构信息. DAI的可靠性直接影响对DTI数据的分析和理解. 本文基于扩散张量椭球的几何学信息, 提出利用扩散椭球几何比(EGR)定量描述水分子扩散的各向异性程度. 通过蒙特卡罗模拟实验和对人脑DTI数据进行分析, 并与当前广泛应用的水分子扩散各向异性分数(FA)和近期文献提出的扩散椭球面积比(EAR)进行对比. 实验发现EGR在不同级别噪声影响下的对比度效果和抗噪性都优于FA及EAR. 而且EGR 加入了体积修正, 增强了盘形扩散张量情况下的敏感性, 能够更好地鉴别神经纤维束交叉情况, 对于各向异性扩散程度较高的白质深层和相对均质的表层都有较好的量化区分结果. 关键词： 扩散系数 各向异性扩散 扩散张量成像 扩散椭球几何比     

数据采集方案对神经扩散模型影响的评估

基于单次数据采集的多种扩散模型联合应用已逐渐成为临床研究的热点,本研究比较了三种采集方案对于神经扩散模型定量计算的影响,包括Q空间笛卡尔网格（QGrid）、多壳层异向（Free）和多壳层同向（MDDW）采集方案,涉及的扩散模型包含扩散张量成像（DTI）;扩散峰度成像（DKI）;神经突方向分散度和密度成像（NODDI）;平均表观传播（MAP）模型.结果表明DTI和DKI模型对采集方案相对不敏感,而NODDI和MAP对采集方案和最大b值的设置相对较敏感,并且QGrid和Free方案一致性较高,因此在大样本和多中心研究中需要考虑采集方案的选择.此外,考虑到QGrid和Free方案分别在结合更多扩散模型和神经纤维束成像应用上更具优势,因此推荐使用.     

多维梯度折射率介质内辐射传递的扩散近似

推导多维梯度折射率介质内稳态辐射传递的扩散近似方程.使用有限元法对扩散近似进行离散和求解,利用两个二维半透明介质的稳态辐射传递问题验证该扩散近似的精度及适用性.算例考虑介质为均匀折射率及梯度折射率两种情况.利用扩散近似分别求解辐射平衡时的边界热流、介质内温度场分布,并与辐射传递方程的求解结果进行对比分析.结果表明:介质折射率变化、散射特性、光学厚度及散射反照率均直接影响扩散近似的精度;在光学厚及强散射条件下,该扩散近似可以作为一种快速算法应用于梯度折射率介质稳态辐射传递的求解.     

氧气在梯度磁场中流动及扩散行为研究

氧气是顺磁性气体，氮气是抗磁性气体，其在梯度磁场中具有不同的磁特性。氮气与氧气在受到梯度磁场影响时，其流动及扩散情况会呈现不同的行为特性。本文建立多通道层叠磁体阵列结构试验系统，并根据高纯氮气在多通道层叠磁体阵列结构气流通道中流动时气体中氧含量的变化，进行空气中氧气以及高纯氮气在具有梯度磁场作用时的流动及扩散情况的研究...     

基于自适应扩散模型的单帧红外条纹非均匀性校正算法

针对红外焦平面成像系统存在列向条纹非均匀性的现象,采用了一种基于自适应PM扩散模型的非均匀校正新算法。首先,综合利用图像梯度信息和局部灰度统计信息,自适应计算PM模型的扩散阈值;然后将每列像素的PM模型估计值作为该列像素的期望值;最后采用最陡下降法迭代计算得到每列像元的校正参数,并对结果进行循环校正以提高校正效果。实验结果表明:该算法可以保护图像边缘信息,与同类算法相比,能够更有效地抑制条纹非均匀性,并且能够防止图像产生鬼影。     

静电场中水分子的扩散与液固相变

扩散与相变是本科阶段基础物理教学的重要内容.本文以体相水分子系统为例,基于分子动力学模拟,研究静电场环境下水分子的扩散和相变.在较小电场强度情况下,水分子表现出显著的大角度跳跃转动,且转动频次随电场呈先增加后减小的非单调行为.这种大角度跳跃转动的反常电场依赖性与水分子扩散系数随电场强度变化的非单调性存在较强相关性.在电场强度较大时,水分子系统发生液固相变,即电致结冰,并观察到了两种冰相沿电场方向的层状混合堆叠结构.该分子动力学模拟有助于学生从微观层次理解分子扩散与相变等物理现象的分子机制,可作为教学实例培养本科生的科研实践能力.     

多孔介质体元内随机运动的核磁共振成像研究

多孔介质体元内随机运动的核磁共振成像是一种透视流体微观无规则运动的方法.在多孔介质中,存在两种无规则运动.一种是分于扩散.它是由于分子的布朗运动引起的;另一种是弥散,它是由多孔介质中毛管网络的复杂结构造成的.多孔介质中的液体弥散和分子扩散会在成像体无内产生相位分散.这种相位分散致使回波信号发生衰减.采用适当的梯度脉冲.可以从这种信号衰减中获得视扩散系数(ADC)的分布图像.本文作者在4.7T高场超导核磁共振成像系统上.采用特制的高梯度线圈获得了扩散和机扩散系数分布的图像.在水和丙酮模型中获得了扩散系教图像,其扩散系数值与标准值相符.在人体肾结石中获得了扩散系数分布图像,在不同流速下,获得了多孔介质中的视扩散系数分布图像.并分析了视扩散系数与速度的关系.在多孔介质中定量确定扩散系数和机扩散系数及其空间分布将会极大地提高核磁共振成像技术在渗流力学研究中的应用能力.     

短脉冲激光与介质相互作用的扩散模型

推导了扩散近似方程,通过半无限大均匀介质计算,用扩散理论分析解验证了数值方法的有效性.模拟了光在非均匀介质内的传输过程,给出了介质内光通量随时间变化的空间分布.结果表明,该基于扩散模型的数值方法能够模拟短脉冲光在强散射介质中的传播过程以及漫散射光的时间变化特性,并且借助于光通量空间分布能够准确模拟非均匀介质内内含物的位置.     

载流子扩散对CCD调制传递函数的影响

由于电荷耦合器件(CCD)具有许多优于其他成像器件的特点,因此其应用领域已被不断地扩展,调制传递函数(MTF)可作为客观评价其成像质量的有效方法。从载流子扩散对其传递函数影响出发,分析其数学模型, 并利用该模型进一步探讨光谱不均匀性,不同扩散长度及初始耗尽宽度对MTF的影响,最后给出了仿真试验结果。     

Mapping eddy current induced fields for the correction of diffusion-weighted echo planar images

Diffusion-weighted echo-planar magnetic resonance imaging is potentially of great importance as a diagnostic imaging tool; however, the technique currently suffers a number of limitations, including the image distortion caused by the eddy current induced fields when the diffusion-weighting magnetic field gradient pulses are applied. The distortions cause mis-registration between images with different diffusion-weighting, that then results in artifacts in quantitative diffusion images. A method is presented to measure the magnetic fields generated from the eddy currents for each of three orthogonal gradient pulse vectors, and then to use these to ascertain the image distortion that occurs in subsequent diffusion-weighted images with arbitrary gradient pulse vector amplitude and direction, and image plane orientation. The image distortion can then be reversed. Both temporal and spatial dependence of the residual eddy current induced fields are included in the analysis. Image distortion was substantially reduced by the correction scheme, for arbitrary slice position and angulation. This method of correction is unaffected by the changes in image contrast that occur due to diffusion weighting, and does not need any additional scanning time during the patient scan. It is particularly suitable for use with single-shot echo planar imaging.     

Condition number as a measure of noise performance of diffusion tensor data acquisition schemes with MRI

Diffusion tensor mapping with MRI can noninvasively track neural connectivity and has great potential for neural scientific research and clinical applications. For each diffusion tensor imaging (DTI) data acquisition scheme, the diffusion tensor is related to the measured apparent diffusion coefficients (ADC) by a transformation matrix. With theoretical analysis we demonstrate that the noise performance of a DTI scheme is dependent on the condition number of the transformation matrix. To test the theoretical framework, we compared the noise performances of different DTI schemes using Monte-Carlo computer simulations and experimental DTI measurements. Both the simulation and the experimental results confirmed that the noise performances of different DTI schemes are significantly correlated with the condition number of the associated transformation matrices. We therefore applied numerical algorithms to optimize a DTI scheme by minimizing the condition number, hence improving the robustness to experimental noise. In the determination of anisotropic diffusion tensors with different orientations, MRI data acquisitions using a single optimum b value based on the mean diffusivity can produce ADC maps with regional differences in noise level. This will give rise to rotational variances of eigenvalues and anisotropy when diffusion tensor mapping is performed using a DTI scheme with a limited number of diffusion-weighting gradient directions. To reduce this type of artifact, a DTI scheme with not only a small condition number but also a large number of evenly distributed diffusion-weighting gradients in 3D is preferable.     

A diffusion gradient optimization framework for spinal cord diffusion tensor imaging

The uncertainty in the estimation of diffusion model parameters in diffusion tensor imaging (DTI) can be reduced by optimally selecting the diffusion gradient directions utilizing some prior structural information. This is beneficial for spinal cord DTI, where the magnetic resonance images have low signal-to-noise ratio and thus high uncertainty in diffusion model parameter estimation. Presented is a gradient optimization scheme based on D-optimality, which reduces the overall estimation uncertainty by minimizing the Rician Cramer-Rao lower bound of the variance of the model parameter estimates. The tensor-based diffusion model for DTI is simplified to a four-parameter axisymmetric DTI model where diffusion transverse to the principal eigenvector of the tensor is assumed isotropic. Through simulations and experimental validation, we demonstrate that an optimized gradient scheme based on D-optimality is able to reduce the overall uncertainty in the estimation of diffusion model parameters for the cervical spinal cord and brain stem white matter tracts.     

On the down-sampling of diffusion MRI data along the angular dimension

BackgroundIt has been established that the diffusion gradient directions in diffusion MRI should be uniformly distributed in 3D spherical space, so that orientation-dependent diffusion properties (e.g., fractional anisotropy or FA) can be properly quantified. Sometimes the acquired data need to be down-sampled along the angular dimension before computing diffusion properties (e.g., to exclude data points corrupted by motion artifact; to harmonize data obtained with different protocols). It is important to quantitatively assess the impact of data down-sampling on measurement of diffusion properties.Materials and methodsHere we report 1) a numerical procedure for down-sampling diffusion MRI (e.g., for data harmonization), and 2) a spatial uniformity index of diffusion directions, aiming to predict the quality of the chosen down-sampling schemes (e.g., from data harmonization; or rejection of motion corrupted data points). We quantitatively evaluated human diffusion MRI data, which were down-sampled from 64 or 60 diffusion gradient directions to 30 directions, in terms of their 1) FA value accuracy (using fully-sampled data as the ground truth), 2) FA fitting residuals, and 3) spatial uniformity indices.ResultsOur experimental data show that the proposed spatial uniformity index is correlated with errors in FA obtained from down-sampled diffusion MRI data. The FA fitting residuals that are typically used to assess diffusion MRI quality are not correlated with either FA errors or spatial uniformity index.ConclusionsThese results suggest that the spatial uniformity index could be more valuable in assessing quality of down-sampled diffusion MRI data, as compared with FA fitting residual measures. We expect that our implemented software procedure should prove valuable for 1) guiding data harmonization for multi-site diffusion MRI studies, and 2) assessing the impact of rejecting motion corrupted data points on the accuracy of diffusion measures.     

Anisotropic water diffusion in macroscopically oriented lipid bilayers studied by pulsed magnetic field gradient NMR

The anisotropy, D(parallel)/D( perpendicular ), of water diffusion in fully hydrated bilayers of dimyristoylphosphatidylcholine at 29 degrees C has been measured by pulsed magnetic field gradient (pfg) NMR. By using NMR imaging hardware to produce magnetic field gradients in an arbitrary direction with respect to a stack of macroscopically aligned lipid bilayers, translational diffusion of water was measured as a function of the angle between the direction of the magnetic field gradient and the normal of the lipid membrane. The observed diffusion coefficient is found to depend strongly on this angle. The anisotropy cannot be accurately determined due to the very small value of D( perpendicular ), but a lower limit of about 70 can be estimated from the observed diffusion coefficients. The results are discussed in terms of the relatively low permeability of water across the lipid bilayer, instrumental limitations, and/or possible defects in the lamellae.     

Diffusion tensor encoding schemes optimized for white matter fibers with selected orientations

A method to produce gradient encoding schemes that minimize the noise of diffusion tensor imaging (DTI) indices for selected fiber orientations has been developed. The accuracy of DTI measurements depends on the gradient encoding scheme used. Most current acquisition schemes contain diffusion directions uniformly distributed in 3D space in order to provide equal noise levels for fibers in any orientation. However, when considering specific fiber bundles such as the corticospinal tract (CST) or parts of fiber bundles, the range of fiber orientations of interest may be limited. We hypothesized that, when studying fiber tracts with a limited range of orientations, measuring diffusion in directions that are uniformly distributed in 3D space may be suboptimal for the noise levels of various DTI indices. Therefore, we first used simulations to determine six diffusion directions that minimize the noise of DTI measurements for selected fiber orientations. The resulting optimized set of directions was then tested on the right CST of a healthy human subject, and its performance was compared with that of conventional acquisition strategies. Both the simulations and the experiments on the human subject demonstrated that the new scheme significantly reduced the standard deviation of DTI indices for tensors with primary eigenvectors within a selected range of orientations.     

Double-spin-echo diffusion weighting with a modified eddy current adjustment

Magnetic field inhomogeneities like eddy current-related gradient fields cause geometric distortions in echo-planar imaging (EPI). This in particular affects diffusion-weighted imaging where these distortions vary with the direction of the diffusion weighting and hamper the accurate determination of diffusion parameters. The double-spin-echo preparation often used aims to reduce the cumulative eddy current effect by adjusting the diffusion-weighting gradient pulse durations to the time constant of the dominant eddy current contribution. However, eddy currents with a variety of time constants may be present and cause residual distortions. Here, a modification is proposed where the two bipolar gradient pairs of the preparation are adjusted independently to different time constants. At the expense of a slightly prolonged echo time, residual geometric distortions and correspondingly increased values of the diffusion anisotropy can be reduced as is demonstrated in phantoms and the human brain. Thus, it may help to improve the reliability of diffusion-weighted EPI.     

Measurement of diffusion in the presence of shear flow

We demonstrate here a method whereby molecular diffusion coefficients may be measured in the presence of the deformational flow field of a rheo-NMR cell. The method, which uses a repetitive CPMG train of rf pulses interspersed with magnetic field gradient pulses, allows the anisotropic diffusion spectrum to be directly probed. We focus on the cylindrical Couette cell, for which the radial, tangential, and axial directions correspond to the hydrodynamic velocity gradient, velocity, and vorticity directions. While ideal Couette flow does not perturb the vorticity direction, it does perturb diffusion measurements for the velocity gradient direction, and to a lesser extent, the velocity direction. We show that with closely spaced gradient pulses operating in a flow-compensating mode, there exists a diffusion limit below which one cannot measure, that scales as T(2)gamma(4), where gamma is the shear rate and T the gradient pulse repetition period. For a typical rheo-NMR cell, and for the more challenging velocity gradient direction, diffusion rates above 10(-12) m(2) s(-1) can be accurately measured (to 1% error) at shear rates up to 3s(-1). We demonstrate the use of the method in measuring the diffusion spectrum of a lyotropic lamellar phase under shear.     

Velocity imaging by ex situ NMR

A pulsed field gradient stimulated spin-echo NMR sequence is combined with imaging methods to spatially resolve velocity distributions and to measure 2D velocity maps ex situ. The implementation of these techniques in open sensors provides a powerful non-invasive tool to measure molecular displacement in a large number of applications inaccessible to conventional closed magnets. The method is implemented on an open tomograph that provides 3D spatial localization by combining slice selection in the presence of a uniform static magnetic field gradient along the depth direction with pulsed field gradients along the two lateral directions. Different pipe geometries are used to demonstrate that the sequence performs well even in the extremely inhomogeneous B0 and B1 fields of these sensors.