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. Author Summary 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 ultraslow brain wave in the resting state and (b) the detection of directed activity between brain regions that fluctuate in the presence of tasks and stimuli, without relying on frequency domain or correlation-based analysis—a novel contribution to existing literature.

Author Summary Age-related declines in cognition are associated with widespread structural and functional brain changes as well as changes in the elasticity of cerebral arteries. In this study, using an exploratory hierarchical model as a guide, and novel measures of cerebral arterial elasticity (pulse-DOT—the arterial pulse based on diffuse optical tomography), we show, for the first time, that cerebral arterial stiffness is strongly correlated with measures of functional brain network segregation, even after partialing out the effects of age. These findings suggest that preventing cerebral arterial stiffening could induce a neurophysiological cascade beneficial for preserving cognition in aging. Abstract Age-related declines in cognition are associated with widespread structural and functional brain changes, including changes in resting-state functional connectivity and gray and white matter status. Recently we have shown that the elasticity of cerebral arteries also explains some of the variance in cognitive and brain health in aging. Here, we investigated how network segregation, cerebral arterial elasticity (measured with pulse-DOT—the arterial pulse based on diffuse optical tomography) and gray and white matter status jointly account for age-related differences in cognitive performance. We hypothesized that at least some of the variance in brain and cognitive aging is linked to reduced cerebrovascular elasticity, leading to increased cortical atrophy and white matter abnormalities, which, in turn, are linked to reduced network segregation and decreases in cognitive performance. Pairwise comparisons between these variables are consistent with an exploratory hierarchical model linking them, especially when focusing on association network segregation (compared with segregation in sensorimotor networks). These findings suggest that preventing or slowing age-related changes in one or more of these factors may induce a neurophysiological cascade beneficial for preserving cognition in aging.