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通过方向加权和正则化实现扩散峰度张量的高级拟合。

Advanced fit of the diffusion kurtosis tensor by directional weighting and regularization.

机构信息

Department of Medical Physics in Radiology, German Cancer Research Center, DKFZ, Heidelberg, Germany.

出版信息

Magn Reson Med. 2012 May;67(5):1401-11. doi: 10.1002/mrm.23133. Epub 2011 Aug 16.

Abstract

The diffusional kurtosis is an indicator for diffusion restrictions in biological tissue. It is observed experimentally that the kurtosis is largest for directions perpendicular to the fiber direction in white matter. The directional dependence of the kurtosis can be described by the diffusion kurtosis tensor. Since the intention of diffusion kurtosis imaging is to detect diffusion restrictions, the fit of the kurtosis tensor should be dominated by directions perpendicular to the fibers. In this work, it is shown that the basic approach, which is solving the occurring linear system by a pseudoinverse matrix, may completely fail in this regard if the diffusion is highly anisotropic. This problem is solved by adapting the weights of the fit--and thus emphasizing directions of restricted water motion--using a direct fit of the kurtosis tensor to the measured kurtosis values. Moreover, due to its large number of degrees of freedom, the kurtosis tensor can assume complicated shapes resulting in a fit which is sensitive to noise. This article demonstrates that the quality of the kurtosis tensor calculation can be further improved if the fit is regularized by suppressing too large and too small kurtosis tensor values and thus restricting the possible tensor shapes.

摘要

扩散峰度是用于描述生物组织中扩散受限的指标。实验观察到,在各向同性组织中,白质纤维垂直方向的各向异性峰度最大。扩散峰度的各向异性可以用扩散峰度张量来描述。由于扩散峰度成像的目的是检测扩散受限,因此拟合峰度张量应该主要由与纤维垂直的方向主导。在这项工作中,我们表明,如果扩散非常各向异性,那么通过伪逆矩阵求解线性系统的基本方法在这方面可能完全失败。通过直接拟合测量得到的峰度值到拟合峰度张量,可以解决这个问题,从而强调受限水分子运动的方向。此外,由于其自由度数量较多,峰度张量可能会呈现复杂的形状,从而导致对噪声敏感的拟合。本文表明,如果通过抑制过大和过小的峰度张量值并限制可能的张量形状来正则化拟合,可以进一步提高峰度张量计算的质量。

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