Anisotropy Preserving DTI Processing

Statistical analysis of diffusion tensor imaging (DTI) data requires a computational framework that is both numerically tractable (to account for the high dimensional nature of the data) and geometric (to account for the nonlinear nature of diffusion tensors). Building upon earlier studies exploiting a Riemannian framework to address these challenges, the present paper proposes a novel metric and an accompanying computational framework for DTI data processing. The proposed approach grounds the signal processing operations in interpolating curves. Well-chosen interpolating curves are shown to provide a computational framework that is at the same time tractable and information relevant for DTI processing. In addition, and in contrast to earlier methods, it provides an interpolation method which preserves anisotropy, a central information carried by diffusion tensor data.     

A Riemannian Framework for Tensor Computing

Tensors are nowadays a common source of geometric information. In this paper, we propose to endow the tensor space with an affine-invariant Riemannian metric. We demonstrate that it leads to strong theoretical properties: the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries (null eigenvalues are at the infinity), the geodesic between two tensors and the mean of a set of tensors are uniquely defined, etc. We have previously shown that the Riemannian metric provides a powerful framework for generalizing statistics to manifolds. In this paper, we show that it is also possible to generalize to tensor fields many important geometric data processing algorithms such as interpolation, filtering, diffusion and restoration of missing data. For instance, most interpolation and Gaussian filtering schemes can be tackled efficiently through a weighted mean computation. Linear and anisotropic diffusion schemes can be adapted to our Riemannian framework, through partial differential evolution equations, provided that the metric of the tensor space is taken into account. For that purpose, we provide intrinsic numerical schemes to compute the gradient and Laplace-Beltrami operators. Finally, to enforce the fidelity to the data (either sparsely distributed tensors or complete tensors fields) we propose least-squares criteria based on our invariant Riemannian distance which are particularly simple and efficient to solve.     

3D space-varying coefficient models with application to diffusion tensor imaging

The present methodological development and the primary application field originate from diffusion tensor imaging (DTI), a powerful nuclear magnetic resonance technique which enables the quantification of microscopical tissue properties. The current analysis framework of separate voxelwise regressions is reformulated as a 3D space-varying coefficient model (SVCM) for the entire set of diffusion tensor images recorded on a 3D voxel grid. The SVCM unifies the three-step cascade of standard data processing (voxelwise regression, smoothing, interpolation) into one framework based on B-spline basis functions. Thereby strength is borrowed from spatially correlated voxels to gain a regularization effect right at the estimation stage. Two SVCM variants are conceptualized: a full tensor product approach and a sequential approximation, rendering the SVCM numerically and computationally feasible even for the huge dimension of the joint model in a realistic setup. A simulation study shows that both approaches outperform the standard method of voxelwise regression with subsequent regularization. Application of the fast sequential method to real DTI data demonstrates the inherent ability to increase the grid resolution by evaluating the incorporated basis functions at intermediate points. The resulting continuous regularized tensor field may serve as basis for multiple applications, yet, ameloriation of local adaptivity is desirable.     

3D space-varying coefficient models with application to diffusion tensor imaging

The present methodological development and the primary application field originate from diffusion tensor imaging (DTI), a powerful nuclear magnetic resonance technique which enables the quantification of microscopical tissue properties. The current analysis framework of separate voxelwise regressions is reformulated as a 3D space-varying coefficient model (SVCM) for the entire set of diffusion tensor images recorded on a 3D voxel grid. The SVCM unifies the three-step cascade of standard data processing (voxelwise regression, smoothing, interpolation) into one framework based on B-spline basis functions. Thereby strength is borrowed from spatially correlated voxels to gain a regularization effect right at the estimation stage. Two SVCM variants are conceptualized: a full tensor product approach and a sequential approximation, rendering the SVCM numerically and computationally feasible even for the huge dimension of the joint model in a realistic setup. A simulation study shows that both approaches outperform the standard method of voxelwise regression with subsequent regularization. Application of the fast sequential method to real DTI data demonstrates the inherent ability to increase the grid resolution by evaluating the incorporated basis functions at intermediate points. The resulting continuous regularized tensor field may serve as basis for multiple applications, yet, ameloriation of local adaptivity is desirable.     

A canonical form-based approach to affine registration of DTI

Due to the orientation feature of diffusion tensor images (DTI), tensors need to be reoriented during an affine registration. There exists two active reorientation schemes: finite strain (FS) and preserving principal direction (PPD). However, FS scheme limits its application on rigid deformation and PPD scheme suffers from computation load caused by the iteration. In order to overcome these shortcomings, we propose a canonical form-based affine registration of DTI, named as CFARD. We transform voxel sets into canonical forms where an affine registration is simplified as a rigid registration, while still preserves the effects of non-rigid components. This transforming thus extends the application of FS scheme to affine deformation. Furthermore, to reduce computation load, the quaternion technique is skillfully employed to seek a closed-form solution of the optimal rotation where no iteration is required. Extensive experiments are conducted on synthetic and real DTI data from the human brain. In contrast to four existing algorithms, the proposed CFARD improves the consistency between tensor orientation and the anatomical structures after deformation, and performs a better balance between accuracy and computational complexity.

     

基于黎曼度量的复杂参数曲面有限元网格生成方法

给出了三维空间的黎曼度量和曲面自身的黎曼度量相结合的三维复杂参数曲面自适应网格生成的改进波前推进算法.详细阐述了曲面参数域上任意一点的黎曼度量的计算和插值方法;采用可细化的栅格作为背景网格,在降低了程序实现的难度的同时提高了网格生成的速度;提出按层推进和按最短边推进相结合的方法,在保证边界网格质量的同时,提高曲面内部网格的质量.三维自适应黎曼度量的引入,提高了算法剖分复杂曲面的自适应性.算例表明,该算法对复杂曲面能够生成高质量的网格,而且整个算法具有很好的时间特性和可靠性.     

A Riemannian scalar measure for diffusion tensor images

We study a well-known scalar quantity in Riemannian geometry, the Ricci scalar, in the context of diffusion tensor imaging (DTI), which is an emerging non-invasive medical imaging modality. We derive a physical interpretation for the Ricci scalar and explore experimentally its significance in DTI. We also extend the definition of the Ricci scalar to the case of high angular resolution diffusion imaging (HARDI) using Finsler geometry. We mention that the Ricci scalar is not only suitable for tensor valued image analysis, but it can be computed for any mapping .     

Analysis of sub-anatomic diffusion tensor imaging indices in white matter regions of Alzheimer with MMSE score

In this study, an attempt has been made to find the correlation between diffusion tensor imaging (DTI) indices of white matter (WM) regions and mini mental state examination (MMSE) score of Alzheimer patients. Diffusion weighted images are obtained from the ADNI database. These are preprocessed for eddy current correction and removal of non-brain tissue. Fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD) and axial diffusivity (DA) indices are computed over significant regions (Fornix left, Splenium of corpus callosum left, Splenium of corpus callosum right, bilateral genu of the corpus callosum) affected by Alzheimer disease (AD) pathology. The correlation is computed between diffusion indices of the significant regions and MMSE score using linear fit technique so as to find the relation between clinical parameters and the image features. Binary classification has been employed using support vector machine, decision stumps and simple logistic classifiers on the extracted DTI indices along with MMSE score to classify Alzheimer patients from healthy controls. It is observed that distinct values of DTI indices exist for the range of MMSE score. However, there is no strong correlation (Pearson's correlation coefficient ‘r’ varies from 0.0383 to −0.1924) between the MMSE score and the diffusion indices over the significant regions. Further, the performance evaluation of classifiers shows 94% accuracy using SVM in differentiating AD and control. In isolation clinical and image features can be used for prescreening and diagnosis of AD but no sub anatomic region correlation exist between these features set. The discussion on the correlation of diffusion indices of WM with MMSE score is presented in this study.     

High Angular Resolution Diffusion MRI Segmentation Using Region-Based Statistical Surface Evolution

In this article we develop a new method to segment high angular resolution diffusion imaging (HARDI) data. We first estimate the orientation distribution function (ODF) using a fast and robust spherical harmonic (SH) method. Then, we use a region-based statistical surface evolution on this image of ODFs to efficiently find coherent white matter fiber bundles. We show that our method is appropriate to propagate through regions of fiber crossings and we show that our results outperform state-of-the-art diffusion tensor (DT) imaging segmentation methods, inherently limited by the DT model. Results obtained on synthetic data, on a biological phantom, on real datasets and on all 13 subjects of a public NMR database show that our method is reproducible, automatic and brings a strong added value to diffusion MRI segmentation.

Fused DTI/HARDI visualization

High-angular resolution diffusion imaging (HARDI) is a diffusion weighted MRI technique that overcomes some of the decisive limitations of its predecessor, diffusion tensor imaging (DTI), in the areas of composite nerve fiber structure. Despite its advantages, HARDI raises several issues: complex modeling of the data, nonintuitive and computationally demanding visualization, inability to interactively explore and transform the data, etc. To overcome these drawbacks, we present a novel, multifield visualization framework that adopts the benefits of both DTI and HARDI. By applying a classification scheme based on HARDI anisotropy measures, the most suitable model per imaging voxel is automatically chosen. This classification allows simplification of the data in areas with single fiber bundle coherence. To accomplish fast and interactive visualization for both HARDI and DTI modalities, we exploit the capabilities of modern GPUs for glyph rendering and adopt DTI fiber tracking in suitable regions. The resulting framework, allows user-friendly data exploration of fused HARDI and DTI data. Many incorporated features such as sharpening, normalization, maxima enhancement and different types of color coding of the HARDI glyphs, simplify the data and enhance its features. We provide a qualitative user evaluation that shows the potentials of our visualization tools in several HARDI applications.     

变参数active demons算法下的多通道弥散张量图像配准

目的 弥散张量图像（DTI）配准不仅要保证配准前后图像解剖结构的一致性，还要保持张量方向的一致性。demons算法下的多通道DTI配准方法可充分利用张量的信息，改善配准质量，但大形变区域配准效果不理想，收敛速度慢。active demons算法能够加快收敛速度，但图像的拓扑结构容易改变。由此提出一种变参数active demons算法下的多通道DTI配准方法。方法 综合active demons算法中平衡系数能加快收敛速度、均化系数能提高DTI配准精度的优点，手动选择一个均化系数，并在算法收敛过程中随着高斯核的减小动态调整平衡系数。在配准开始时采用较小的平衡系数获得较快的收敛速度，随着收敛的加深逐渐增大平衡系数获得较小的配准误差。结果 active demons方法能改善DTI大形变区域的配准问题，但均化系数太小会改变图像拓扑结构。固定均化系数，引入单一的平衡系数能加快收敛速度，但会导致拓扑结构改变。变参数active demons方法有效提高了配准的收敛速度，明显改善大形变区域的配准效果，同时能保持图像拓扑结构不变。变参数active demons配准后的10组数据均获得最小均方差（MSE）和最大特征值特征向量对重叠率（OVL），配准精度最高。在0.05的配对样本t检验水平下，变参数active demons和active demons方法配准后的MSE、OVL的差异均有统计学意义；变参数active demons和demons方法配准后的MSE、OVL的差异均有统计学意义（p<0.05）。结论 变参数active demons算法下的多通道DTI配准方法明显提高了配准精度和速度，改善了demons方法不能有效配准大形变区域的问题，同时能够保持配准前后图像的拓扑结构，尤其适合个体间形变较大的DTI配准。     

Vertex-centroid finite volume scheme on tetrahedral grids for conservation laws

Vertex-centroid schemes are cell-centered finite volume schemes for conservation laws which make use of both centroid and vertex values to construct high-resolution schemes. The vertex values must be obtained through a consistent averaging (interpolation) procedure while the centroid values are updated by the finite volume scheme. A modified interpolation scheme is proposed which is better than existing schemes in giving positive weights in the interpolation formula. A simplified reconstruction scheme is also proposed which is also more efficient and leads to more robust schemes for discontinuous problems. For scalar conservation laws, we develop limited versions of the schemes which are stable in maximum norm by constructing suitable limiters. The schemes are applied to compressible flows governed by the Euler equations of inviscid gas dynamics.     

DTI扩散张量的一种稳健估计方法

为了获得更精确的DTI扩散张量场,提出了一种基于约束M估计子的稳健估计方法,首先对扩散加权图像序列进行双树复数小波降噪预处理,以减少热噪声影响,然后通过试探法找到一个合适的回归起始点,并通过Cholesky分解对扩散张量进行正定约束,最后寻找局部最小获得DTI扩散张量的约束M估计,并在模拟二阶张量场和真实DTI数据集上进行了实验.与最小二乘法和M估计子回归模型相比,该方法可以更有效地排除热噪声和生理性离群点影响,对DTI扩散张量估计很有价值.     

张量值图像插值方法综述

在图像处理和计算机视觉的许多任务中,经常需要对图像进行插值从而得到像素点之间的信息。标量值图像的插值方法已经得到充分的发展,但张量值图像的插值方法还没有深刻的发展和认识。通过对比较零散的张量值图像插值方法的研究现状进行了系统综述,从数学理论框架的角度出发,将现有的张量值图像插值方法进行全面分析和分类,指出欧氏理论框架计算张量会带来的问题,梳理从欧氏框架到黎曼度量框架的研究脉络,并比较了张量值图像插值方法的评价指标。最后,给出了张量值图像插值方法未来研究方向的建议。     

Revisit and compare Ma equivalence and Zhang equivalence of minimum velocity norm (MVN) type

In this paper, by revisiting Ma et al.’s inspiring work (specifically, Ma equivalence, ME) and Zhang et al.’s inspiring work (specifically, Zhang equivalence, ZE), which both investigate the equivalence relationships of redundancy-resolution schemes at two different levels, but with different formulations, the general scheme formulations and equivalence analyses of ME and ZE are presented. Besides, being a case study, the ME and ZE of minimum velocity norm (MVN) type are investigated for the inverse-kinematics (IK) problem solving. Moreover, the link and difference between the MVN-type ME and ZE are analyzed, summarized and presented methodologically, systematically, and computationally in this paper. In order to numerically compare the ME and ZE of MVN type, a Rhodonea-path tracking task based on PUMA560 robot manipulator is tested and fulfilled by employing the original velocity-level MVN schemes and its equivalent acceleration-level MVN schemes of ME and ZE. The simulative and numerical results not only verify the effectiveness of the velocity-level and acceleration-level schemes of MVN-type ME and ZE, but also validate the reasonableness of such two proved equivalence relationships. More importantly, these results show quantitatively and comparatively the respective advantages and future applications of MVN-type ME and ZE for the IK problem solving.     

Overview + Detail Visualization for Ensembles of Diffusion Tensors

A Diffusion Tensor Imaging (DTI) group study consists of a collection of volumetric diffusion tensor datasets (i.e., an ensemble) acquired from a group of subjects. The multivariate nature of the diffusion tensor imposes challenges on the analysis and the visualization. These challenges are commonly tackled by reducing the diffusion tensors to scalar‐valued quantities that can be analyzed with common statistical tools. However, reducing tensors to scalars poses the risk of losing intrinsic information about the tensor. Visualization of tensor ensemble data without loss of information is still a largely unsolved problem. In this work, we propose an overview + detail visualization to facilitate the tensor ensemble exploration. We define an ensemble representative tensor and variations in terms of the three intrinsic tensor properties (i.e., scale, shape, and orientation) separately. The ensemble summary information is visually encoded into the newly designed aggregate tensor glyph which, in a spatial layout, functions as the overview. The aggregate tensor glyph guides the analyst to interesting areas that would need further detailed inspection. The detail views reveal the original information that is lost during aggregation. It helps the analyst to further understand the sources of variation and formulate hypotheses. To illustrate the applicability of our prototype, we compare with most relevant previous work through a user study and we present a case study on the analysis of a brain diffusion tensor dataset ensemble from healthy volunteers.     

Examination of characteristics method with cubic interpolation for advection–diffusion equation

In this study, the use of the characteristics method integrated with the Hermite cubic interpolation or the cubic-spline interpolation on the space line or the time line, i.e., the HCSL scheme, the CSSL scheme, the HCTL scheme, and the CSTL scheme, respectively, for solving the advection–diffusion equation is examined. The advection and diffusion of a Gaussian concentration distribution in a uniform flow with constant diffusion coefficient is used to conduct this investigation. The effects of parameters, such as Peclet number, Courant number, and the reachback number, on these four schemes used herein for solving the advection–diffusion equation are investigated. The simulated results show that the CSSL scheme is comparable to the HCSL scheme, and the two schemes seem insensitive to Courant number as compared with the HCTL scheme and the CSTL scheme. With large Peclet number, for small Courant number the HCTL scheme is more accurate than the HCSL scheme and the CSSL scheme. However, for large Courant number the HCTL scheme has worse computed results in comparison with the HCSL scheme and the CSSL scheme. With small Peclet number, the HCTL scheme, the HCSL scheme, and the CSSL scheme have close simulated results. Despite Peclet number, for small Courant number the CSTL scheme is comparable to the HCTL scheme, but for large Courant number the former scheme provides unacceptable simulated results in which very large numerical diffusion is induced due to the effect of the natural endpoint constraint. For large Peclet number the HCSL scheme and the CSSL scheme integrated with the reachback technique can improve simulated results, but for small Peclet number the HCSL scheme and the CSSL scheme seem not to be influenced by increasing the reachback number.     

GraceDTI:一个扩散张量成像数据处理与可视化系统

随着高场磁共振的发展和应用,扩散张量磁共振成像(DTI)已经逐步成为一种重要的临床磁共振检查模式。研究了DTI数据的处理和可视化问题,介绍开发的用于DTI图像数据处理和可视化的软件——GraceDTI系统。该系统提供了从扩散张量图像的估计重建、各种导出参数图像的生成、张量场可视化和纤维跟踪与可视化在内的完整的DTI处理与分析功能。该系统可用于临床DTI的辅助诊断,还可作为DTI图像处理的研究平台。     

Predicting the Results of RNA Molecular Specific Hybridization Using Machine Learning

Ribonucleic acid (RNA) hybridization is widely used in popular RNA simulation software in bioinformatics. However, limited by the exponential computational complexity of combinatorial problems, it is challenging to decide, within an acceptable time, whether a specific RNA hybridization is effective. We hereby introduce a machine learning based technique to address this problem. Sample machine learning (ML) models tested in the training phase include algorithms based on the boosted tree (BT), random forest (RF), decision tree (DT) and logistic regression (LR), and the corresponding models are obtained. Given the RNA molecular coding training and testing sets, the trained machine learning models are applied to predict the classification of RNA hybridization results. The experiment results show that the optimal predictive accuracies are 96.2%, 96.6%, 96.0% and 69.8% for the RF, BT, DT and LR-based approaches, respectively, under the strong constraint condition, compared with traditional representative methods. Furthermore, the average computation efficiency of the RF, BT, DT and LR-based approaches are 208 679, 269 756, 184 333 and 187 458 times higher than that of existing approach, respectively. Given an RNA design, the BT-based approach demonstrates high computational efficiency and better predictive accuracy in determining the biological effectiveness of molecular hybridization.      

A New Tensorial Framework for Single-Shell High Angular Resolution Diffusion Imaging

Single-shell high angular resolution diffusion imaging data (HARDI) may be decomposed into a sum of eigenpolynomials of the Laplace-Beltrami operator on the unit sphere. The resulting representation combines the strengths hitherto offered by higher order tensor decomposition in a tensorial framework and spherical harmonic expansion in an analytical framework, but removes some of the conceptual weaknesses of either. In particular it admits analytically closed form expressions for Tikhonov regularization schemes and estimation of an orientation distribution function via the Funk-Radon Transform in tensorial form, which previously required recourse to spherical harmonic decomposition. As such it provides a natural point of departure for a Riemann-Finsler extension of the geometric approach towards tractography and connectivity analysis as has been stipulated in the context of diffusion tensor imaging (DTI), while at the same time retaining the natural coarse-to-fine hierarchy intrinsic to spherical harmonic decomposition.