The analysis of the resting-state functional connectome commonly relies on graph representations. However, the graph-based approach is restricted to pair-wise interactions, not suitable to capture high-order interactions, i.e., more than two regions. This work investigates the existence of cycles of synchronization emerging at the individual level in the resting-state fMRI dynamic. These cycles or loops correspond to more than three regions interacting in pairs surrounding a closed space in the resting dynamic. We devised a strategy for characterizing these loops on the fMRI resting-state using persistent homology, a data analysis strategy based on topology aimed to characterize high-order connectivity features robustly. This approach describe the loops exhibited at the individual level on a population of 198 healthy controls. Results suggest that these synchronization cycles emerge robustly across different connectivity scales. In addition, these high-order features seem to be supported by a particular anatomical substrate. These topological loops constitute evidence of resting-state high order arrangements of interaction hidden on classical pair-wise models. These cycles may have implications for the synchronization mechanisms commonly described in the resting state.

Functional connectivity describes relationships between brain regions that are based on graph representations. Graph-based approaches are limited to pairwise interactions, which are not suitable for describing higher-order interactions and meaningful topological structures such as loops and voids. This work uses Persistent Homology (PH) to investigate the existence of synchronization loops arising at the individual level in resting-state fMRI. These loops correspond to more than three regions interacting in pairs surrounding a closed space. Our results indicate that these loops emerge across different scales of connectivity that appear to be supported by a particular anatomical substrate; moreover, they provide a kind of evidence for higher-order arrangements of interactions that seem to have implications for the described synchronization mechanisms in the resting-state.

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Handling Editor: Olaf Sporns

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