Mijangos Martin, Pacheco Lucero, Bravetti Alessandro, González-García Nadia, Padilla Pablo, Velasco-Segura Roberto
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico City, Mexico.
Facultad de Medicina, Universidad Nacional Autónoma de México, Mexico City, Mexico.
PLoS One. 2024 Sep 16;19(9):e0310165. doi: 10.1371/journal.pone.0310165. eCollection 2024.
Analyzing functional brain activity through functional magnetic resonance imaging (fMRI) is commonly done using tools from graph theory for the analysis of the correlation matrices. A drawback of these methods is that the networks must be restricted to values of the weights of the edges within certain thresholds and there is no consensus about the best choice of such thresholds. Topological data analysis (TDA) is a recently-developed tool in algebraic topology which allows us to analyze networks through combinatorial spaces obtained from them, with the advantage that all the possible thresholds can be considered at once. In this paper we applied TDA, in particular persistent homology, to study correlation matrices from rs-fMRI, and through statistical analysis, we detected significant differences between the topological structures of adolescents with inhaled substance abuse disorder (ISAD) and healthy controls. We interpreted the topological differences as indicative of a loss of robustness in the functional brain networks of the ISAD population.
通过功能磁共振成像（fMRI）分析大脑功能活动通常使用图论工具来分析相关矩阵。这些方法的一个缺点是网络必须限制在边权重值的特定阈值范围内，并且对于此类阈值的最佳选择尚无共识。拓扑数据分析（TDA）是代数拓扑中最近开发的一种工具，它使我们能够通过从网络获得的组合空间来分析网络，其优点是可以一次性考虑所有可能的阈值。在本文中，我们应用TDA，特别是持久同调，来研究静息态功能磁共振成像（rs-fMRI）的相关矩阵，并通过统计分析，检测出患有吸入性物质滥用障碍（ISAD）的青少年与健康对照组在拓扑结构上的显著差异。我们将拓扑差异解释为ISAD人群功能性脑网络稳健性丧失的指标。
