Topological analysis of brain dynamics in autism based on graph and persistent homology.

Autism spectrum disorder (ASD) is a heterogeneous disorder with a rapidly growing prevalence. In recent years, the dynamic functional connectivity (DFC) technique has been used to reveal the transient connectivity behavior of ASDs' brains by clustering connectivity matrices in different states. However, the states of DFC have not been yet studied from a topological point of view. In this paper, this study was performed using global metrics of the graph and persistent homology (PH) and resting-state functional magnetic resonance imaging (fMRI) data. The PH has been recently developed in topological data analysis and deals with persistent structures of data. The structural connectivity (SC) and static FC (SFC) were also studied to know which one of the SC, SFC, and DFC could provide more discriminative topological features when comparing ASDs with typical controls (TCs). Significant discriminative features were only found in states of DFC. Moreover, the best classification performance was offered by persistent homology-based metrics and in two out of four states. In these two states, some networks of ASDs compared to TCs were more segregated and isolated (showing the disruption of network integration in ASDs). The results of this study demonstrated that topological analysis of DFC states could offer discriminative features which were not discriminative in SFC and SC. Also, PH metrics can provide a promising perspective for studying ASD and finding candidate biomarkers.