Department of Computer Science, University of Illinois at Chicago, Chicago, 60607, USA.
Department of Physics, Pennsylvania State University, University Park, 16802, USA.
Sci Rep. 2021 Apr 14;11(1):8121. doi: 10.1038/s41598-021-87587-z.
We analyze networks of functional correlations between brain regions to identify changes in their structure caused by Attention Deficit Hyperactivity Disorder (ADHD). We express the task for finding changes as a network anomaly detection problem on temporal networks. We propose the use of a curvature measure based on the Forman-Ricci curvature, which expresses higher-order correlations among two connected nodes. Our theoretical result on comparing this Forman-Ricci curvature with another well-known notion of network curvature, namely the Ollivier-Ricci curvature, lends further justification to the assertions that these two notions of network curvatures are not well correlated and therefore one of these curvature measures cannot be used as an universal substitute for the other measure. Our experimental results indicate nine critical edges whose curvature differs dramatically in brains of ADHD patients compared to healthy brains. The importance of these edges is supported by existing neuroscience evidence. We demonstrate that comparative analysis of curvature identifies changes that more traditional approaches, for example analysis of edge weights, would not be able to identify.
我们分析大脑区域之间的功能相关网络，以识别注意力缺陷多动障碍（ADHD）引起的结构变化。我们将寻找变化的任务表示为关于时变网络的网络异常检测问题。我们提出使用基于 Forman-Ricci 曲率的曲率度量，该度量表达了两个连接节点之间的高阶相关性。我们关于比较这种 Forman-Ricci 曲率与另一个著名的网络曲率概念，即 Ollivier-Ricci 曲率的理论结果进一步证明了这两个网络曲率概念没有很好的相关性，因此这两种曲率度量中的一种不能用作另一种度量的通用替代品。我们的实验结果表明，与健康大脑相比，ADHD 患者大脑中的九条关键边缘的曲率差异很大。这些边缘的重要性得到了现有神经科学证据的支持。我们证明，曲率的比较分析可以识别出传统方法（例如边缘权重分析）无法识别的变化。
