Regularized positive-definite fourth order tensor field estimation from DW-MRI.
Regularized positive-definite fourth order tensor field estimation from DW-MRI.
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DOI：
10.1016/j.neuroimage.2008.10.056
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发表时间：
2009-03
期刊：
影响因子：
5.7
通讯作者：
Vemuri BC
中科院分区：
文献类型：
--
作者：
Barmpoutis A;Hwang MS;Howland D;Forder JR;Vemuri BC
在扩散加权磁共振图像（DW-MRI）处理中，通常使用二阶张量来近似DW-MRI数据的每个晶格点处的扩散率函数。从这个张量近似，可以计算有用的标量（例如，各向异性，平均扩散率），其已在临床上用于监测脑病，硬化，缺血和其他脑部疾病。现在众所周知，这种二阶张量近似无法捕获复杂的局部组织结构，例如交叉纤维，因此，从这些张量导出的标量在这些位置处非常不准确。在本文中，我们采用四阶对称正定（SPD）张量近似表示的扩散函数，并提出了一种新的技术来估计这些张量的DW-MRI数据保证SPD属性。在文献中已经报道了关于扩散率函数的高阶张量近似的几篇文章，但它们都不能保证估计的正性，这是一个基本的约束，因为扩散率的负值是没有意义的。在本文中，我们表示的四阶张量作为三元四次，然后应用希尔伯特定理的三元四次沿着岩泽参数化，以保证从DW-MRI数据的SPD四阶张量近似。该模型的性能被描绘在合成数据以及从一组切除的控制和受伤的大鼠脊髓的真实的DW-MRI上，显示出对标量的准确估计，例如广义各向异性和迹线以及纤维取向。
In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing, a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. From this tensor approximation, one can compute useful scalar quantities (e.g. anisotropy, mean diffusivity) which have been clinically used for monitoring encephalopathy, sclerosis, ischemia and other brain disorders. It is now well known that this 2nd-order tensor approximation fails to capture complex local tissue structures, e.g. crossing fibers, and as a result, the scalar quantities derived from these tensors are grossly inaccurate at such locations. In this paper we employ a 4th order symmetric positive-definite (SPD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the SPD property. Several articles have been reported in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positivity of the estimates, which is a fundamental constraint since negative values of the diffusivity are not meaningful. In this paper we represent the 4th-order tensors as ternary quartics and then apply Hilbert’s theorem on ternary quartics along with the Iwasawa parametrization to guarantee an SPD 4th-order tensor approximation from the DW-MRI data. The performance of this model is depicted on synthetic data as well as real DW-MRIs from a set of excised control and injured rat spinal cords, showing accurate estimation of scalar quantities such as generalized anisotropy and trace as well as fiber orientations.
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DOI：
10.1006/jmrb.1994.1037
发表时间：
1994-03-01
期刊：
JOURNAL OF MAGNETIC RESONANCE SERIES B
影响因子：
--
作者：
BASSER, PJ;MATTIELLO, J;LEBIHAN, D
通讯作者：
LEBIHAN, D
影响因子：
4.4
作者：
Basser, Peter J.;Pajevic, Sinisa
通讯作者：
Pajevic, Sinisa
DOI：
10.1016/j.jmr.2011.09.022
发表时间：
1996-06-01
期刊：
JOURNAL OF MAGNETIC RESONANCE SERIES B
影响因子：
--
作者：
Basser, PJ;Pierpaoli, C
通讯作者：
Pierpaoli, C
影响因子：
5.7
作者：
Ozarslan, Evren;Shepherd, Timothy M.;Mareci, Thomas H.
通讯作者：
Mareci, Thomas H.
影响因子：
5.7
作者：
Jian, Bing;Vemuri, Baba C.;Mareci, Thomas H.
通讯作者：
Mareci, Thomas H.