A fine-grained understanding of dynamics in cortical networks is crucial to unpacking brain function. Resting-state functional magnetic resonance imaging (fMRI) gives rise to time series recordings of the activity of different brain regions, which are aperiodic and lack a base frequency. Cyclicity Analysis, a novel technique robust under time-reparametrizations, is effective in recovering the temporal ordering of such time series, collectively considered components of a multi-dimensional trajectory.Here, we extend this analytical method for characterizing the dynamic interaction between distant brain regions and apply it to data from the Human Connectome Project. Our analysis detected cortical traveling waves of activity propagating along a spatial axis resembling cortical hierarchical organization with consistent lead-lag relationships between specific brain regions in resting state scans.In fMRI scans involving tasks, we observed short bursts of task-modulated strong temporal ordering that dominate overall lead-lag relationships between pairs of regions in the brain which align temporally with stimuli from the tasks. Our results suggest a possible role played by waves of excitation sweeping through brain regions that underlie emergent cognitive functions.

While brain network studies initially used correlated signals from brain regions to infer their network structure, recent efforts have focused on the dynamic aspects of such networks. This study extends the Cyclicity Analysis (CA) method - a technique developed for aperiodic time series analysis - to the Human Connectome Project. Notably, CA makes no assumptions about the statistics of the data and works despite possibly nonlinear changes to the timeline of the observations. Using CA, we provide evidence for (a) the propagation of an ultra-slow brain wave in the resting state and (b) the detection of directed activity between brain regions that fluctuate in the presence of tasks & stimuli, without relying on frequency domain or correlation-based analysis - a novel contribution to existing literature.

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Handling Editor: Randy McIntosh

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