Das Anup, Sampson Aaron L, Lainscsek Claudia, Muller Lyle, Lin Wutu, Doyle John C, Cash Sydney S, Halgren Eric, Sejnowski Terrence J
Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA 92093, U.S.A., and Computational Neurobiology Laboratory, Salk Institute for Biological Studies, La Jolla, CA 92037, U.S.A.
Computational Neurobiology Laboratory, Salk Institute for Biological Studies, La Jolla, CA 92037, U.S.A.
Neural Comput. 2017 Mar;29(3):603-642. doi: 10.1162/NECO_a_00936. Epub 2017 Jan 17.
The correlation method from brain imaging has been used to estimate functional connectivity in the human brain. However, brain regions might show very high correlation even when the two regions are not directly connected due to the strong interaction of the two regions with common input from a third region. One previously proposed solution to this problem is to use a sparse regularized inverse covariance matrix or precision matrix (SRPM) assuming that the connectivity structure is sparse. This method yields partial correlations to measure strong direct interactions between pairs of regions while simultaneously removing the influence of the rest of the regions, thus identifying regions that are conditionally independent. To test our methods, we first demonstrated conditions under which the SRPM method could indeed find the true physical connection between a pair of nodes for a spring-mass example and an RC circuit example. The recovery of the connectivity structure using the SRPM method can be explained by energy models using the Boltzmann distribution. We then demonstrated the application of the SRPM method for estimating brain connectivity during stage 2 sleep spindles from human electrocorticography (ECoG) recordings using an [Formula: see text] electrode array. The ECoG recordings that we analyzed were from a 32-year-old male patient with long-standing pharmaco-resistant left temporal lobe complex partial epilepsy. Sleep spindles were automatically detected using delay differential analysis and then analyzed with SRPM and the Louvain method for community detection. We found spatially localized brain networks within and between neighboring cortical areas during spindles, in contrast to the case when sleep spindles were not present.
大脑成像的相关方法已被用于估计人类大脑中的功能连接性。然而，即使两个脑区没有直接连接，由于它们与来自第三个区域的共同输入存在强烈相互作用，这两个脑区可能仍会显示出非常高的相关性。针对这个问题，之前提出的一种解决方案是使用稀疏正则化逆协方差矩阵或精度矩阵（SRPM），假设连接结构是稀疏的。该方法产生偏相关性，以测量区域对之间的强直接相互作用，同时消除其他区域的影响，从而识别出条件独立的区域。为了测试我们的方法，我们首先展示了在哪些条件下，对于弹簧 - 质量示例和RC电路示例，SRPM方法确实能够找到一对节点之间的真实物理连接。使用SRPM方法恢复连接结构可以通过使用玻尔兹曼分布的能量模型来解释。然后，我们展示了SRPM方法在利用[公式：见正文]电极阵列从人类皮层脑电图（ECoG）记录中估计第二阶段睡眠纺锤波期间大脑连接性方面的应用。我们分析的ECoG记录来自一名32岁的男性患者，该患者患有长期药物抵抗性左颞叶复杂部分性癫痫。使用延迟差分分析自动检测睡眠纺锤波，然后用SRPM和用于社区检测的鲁汶方法进行分析。我们发现在纺锤波期间，相邻皮质区域内和之间存在空间定位的脑网络，这与不存在睡眠纺锤波的情况形成对比。
