Institute of Imaging Science, Vanderbilt University, Nashville, Tennessee 37232, USA.
Med Phys. 2010 Aug;37(8):4274-87. doi: 10.1118/1.3456113.
The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework.
To estimate the true fiber direction (propagation vector), the a priori and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre-estimated variance, overcomes the effect of noise and PVA in this work.
The algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it for in vivo DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca's to SMA and Broca's to Wernicke's) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler's) approach [P. J. Basser et al., "In vivo fiber tractography using DT-MRI data," Magn. Reson. Med. 44(4), 625-632 (2000)], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu's method [Y. Lu et al., "Improved fiber tractography with Bayesian tensor regularization," Neuroimage 31(3), 1061-1074 (2006)] and Friman's stochastic approach [O. Friman et al., "A Bayesian approach for stochastic white matter tractography," IEEE Trans. Med. Imaging 25(8), 965-978 (2006)]. Overall performance of the approach is found to be superior to above two methods, particularly when the signal-to-noise ratio was low.
The authors observed that an adaptive sampling of the tensor element vectors, estimated as a function of the variance in a Bayesian framework, can effectively delineate neuronal fibers to analyze the structure-function relationship in human brain. The simulated and in vivo results are in good agreement with the theoretical aspects of the algorithm.
本研究旨在设计一种更适合于重建与人类大脑中功能重要区域相关纤维的神经元纤维追踪算法。大脑中的功能激活通常发生在灰质区域。因此，这些区域边界的纤维髓鞘较少，导致传统追踪方法在追踪它们之间的纤维连接时性能不佳。该区域较低的分数各向异性使得在存在噪声的情况下甚至更难以追踪纤维。在这项工作中，作者专注于基于贝叶斯正则化框架的重建这些纤维通路的随机方法。
为了估计真实的纤维方向（传播向量），提前计算先验和条件概率密度函数，并将其建模为多元正态分布。估计张量元素向量的方差与噪声和部分体积平均（PVA）引起的不确定性相关联。在这项工作中，通过对估计张量元素向量进行自适应和多次采样，克服了噪声和 PVA 的影响，该向量是预先估计方差的函数。
该算法已使用各种合成数据集进行了严格测试。对结果与标准算法的定量比较促使作者将其应用于体内 DTI 数据分析。该算法已被用于在 12 名健康受试者的两个主要语言通路（Broca 到 SMA 和 Broca 到 Wernicke 的）中描绘纤维。尽管均值的标准偏差略大于传统（欧拉）方法[P. J. Basser 等人，“使用 DT-MRI 数据进行体内纤维束追踪”，《磁共振医学》44（4），625-632（2000）]，但该方法提取的纤维数量明显更高。作者还将所提出的方法的性能与 Lu 的方法[Y. Lu 等人，“使用贝叶斯张量正则化改进纤维束追踪”，《神经影像学》31（3），1061-1074（2006）]和 Friman 的随机方法[O. Friman 等人，“基于贝叶斯的随机白质纤维束追踪方法”，《IEEE 医学成像汇刊》25（8），965-978（2006）]进行了比较。总体而言，该方法的性能优于上述两种方法，尤其是在信噪比较低时。
作者观察到，在贝叶斯框架中，作为方差函数估计的张量元素向量的自适应采样可以有效地描绘神经元纤维，以分析人类大脑的结构-功能关系。模拟和体内结果与算法的理论方面非常吻合。
