Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization.
Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization.
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DOI：
10.1016/j.neuroimage.2015.07.039
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发表时间：
2015-11-01
期刊：
影响因子：
5.7
通讯作者：
Snyder AZ
中科院分区：
文献类型：
--
作者：
Brier MR;Mitra A;McCarthy JE;Ances BM;Snyder AZ
功能连接指的是大脑区域之间共享的信号，通常在无任务状态下进行评估。通常使用皮尔逊相关性来量化信号对之间的功能连通性。然而，静息状态fMRI是一个呈现复杂协方差结构的多变量过程。部分协方差估计两个大脑区域之间共享的唯一方差，不包括任何广泛共享的方差，因此适用于多变量fMRI数据集的分析。然而，部分协方差的计算需要对协方差矩阵求逆，而在大多数功能连通性研究中，由于秩亏，协方差矩阵是不可逆的。在这里，我们应用Ledoit-Wolf收缩(L2正则化)来求逆高维粗体协方差矩阵。我们研究了基于部分协方差的功能连接的网络组织和脑状态依赖。虽然RSN通常是根据共享方差来定义的，但令人惊讶的是，移除广泛共享的方差改进了弹簧嵌入图形模型中RSN的分离。这一结果表明，配对唯一共享方差在RSN协方差组织中发挥着迄今未被认识到的作用。此外，将偏相关应用于睁眼和闭眼状态下获得的fMRI数据，揭示了丘脑和视觉皮质之间独特的共同差异的焦点变化。这一结果表明，静息状态BOLD时间序列的偏相关除了反映结构连通性外，还反映了功能过程。
Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a complicated covariance structure. Partial covariance assesses the unique variance shared between two brain regions excluding any widely shared variance, hence is appropriate for the analysis of multivariate fMRI datasets. However, calculation of partial covariance requires inversion of the covariance matrix, which, in most functional connectivity studies, is not invertible owing to rank deficiency. Here we apply Ledoit-Wolf shrinkage (L2 regularization) to invert the high dimensional BOLD covariance matrix. We investigate the network organization and brain-state dependence of partial covariance-based functional connectivity. Although RSNs are conventionally defined in terms of shared variance, removal of widely shared variance, surprisingly, improved the separation of RSNs in a spring embedded graphical model. This result suggests that pair-wise unique shared variance plays a heretofore unrecognized role in RSN covariance organization. In addition, application of partial correlation to fMRI data acquired in the eyes open vs. eyes closed states revealed focal changes in uniquely shared variance between the thalamus and visual cortices. This result suggests that partial correlation of resting state BOLD time series reflect functional processes in addition to structural connectivity.