Hemodynamic cortical ripples through cyclicity analysis.

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 multidimensional trajectory. Here, we extend this analytical method for characterizing the dynamic interaction between distant brain regions and apply it to the 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 that 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.