A novel tensor distribution model for the diffusion-weighted MR signal
A novel tensor distribution model for the diffusion-weighted MR signal
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DOI：
10.1016/j.neuroimage.2007.03.074
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发表时间：
2007-08-01
期刊：
影响因子：
5.7
通讯作者：
Mareci, Thomas H.
中科院分区：
文献类型：
--
作者：
Jian, Bing;Vemuri, Baba C.;Mareci, Thomas H.
扩散MRI是一种非侵入性成像技术，可以测量水分子通过体内组织的扩散。水扩散的方向特征允许人们推断组织中普遍存在的连接模式，并且可能跟踪这种连接随时间的变化以用于各种临床应用。在本文中，我们提出了一种新的扩散加权MR信号衰减的统计模型，假设水分子扩散可以由扩散张量的连续混合物来表征。一个有趣的观察是，这种连续混合和MR信号衰减通过对称正定矩阵上的概率分布的拉普拉斯变换而相关。然后，我们表明，当混合分布是一个Wishart分布，所得到的封闭形式的拉普拉斯变换导致Rigaut-type渐近分形表达式，这已在过去被用于解释的MR信号衰减现象，但从来没有一个严格的数学理由，直到现在。我们的模型不仅包括传统的扩散张量模型作为一个特殊的情况下的限制，但也可以进行调整，以描述复杂的组织结构，涉及多个纤维种群。使用这种新的模型结合球面反卷积方法，我们提出了一个有效的方案，用于估计水分子位移概率函数的体素的基础上。仿真和真实的数据的实验结果表明，所提出的算法的鲁棒性和准确性。(c)2007爱思唯尔公司All rights reserved.
Diffusion MRI is a non-invasive imaging technique that allows the measurement of water molecule diffusion through tissue in vivo. The directional features of water diffusion allow one to infer the connectivity patterns prevalent in tissue and possibly track changes in this connectivity over time for various clinical applications. In this paper, we present a novel statistical model for diffusion-weighted MR signal attenuation which postulates that the water molecule diffusion can be characterized by a continuous mixture of diffusion tensors. An interesting observation is that this continuous mixture and the MR signal attenuation are related through the Laplace transform of a probability distribution over symmetric positive definite matrices. We then show that when the mixing distribution is a Wishart distribution, the resulting closed form of the Laplace transform leads to a Rigaut-type asymptotic fractal expression, which has been phenomenologically used in the past to explain the MR signal decay but never with a rigorous mathematical justification until now. Our model not only includes the traditional diffusion tensor model as a special instance in the limiting case, but also can be adjusted to describe complex tissue structure involving multiple fiber populations. Using this new model in conjunction with a spherical deconvolution approach, we present an efficient scheme for estimating the water molecule displacement probability functions on a voxel-by-voxel basis. Experimental results on both simulations and real data are presented to demonstrate the robustness and accuracy of the proposed algorithms. (c) 2007 Elsevier Inc. All rights reserved.