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.

Chronic tinnitus is a common and sometimes debilitating condition that lacks scientific consensus on physiological models of how the condition arises as well as any known cure. In this study, we applied a novel cyclicity analysis, which studies patterns of leader-follower relationships between two signals, to resting-state functional magnetic resonance imaging (rs-fMRI) data of brain regions acquired from subjects with and without tinnitus. Using the output from the cyclicity analysis, we were able to differentiate between these two groups with 58–67% accuracy by using a partial least squares discriminant analysis. Stability testing yielded a 70% classification accuracy for identifying individual subjects’ data across sessions 1 week apart. Additional analysis revealed that the pairs of brain regions that contributed most to the dissociation between tinnitus and controls were those connected to the amygdala. In the controls, there were consistent temporal patterns across frontal, parietal, and limbic regions and amygdalar activity, whereas in tinnitus subjects, this pattern was much more variable. Our findings demonstrate a proof-of-principle for the use of cyclicity analysis of rs-fMRI data to better understand functional brain connectivity and to use it as a tool for the differentiation of patients and controls who may differ on specific traits. Author Summary Chronic tinnitus is a common, yet poorly understood, condition without a known cure. Understanding differences in the functioning of brains of tinnitus patients and controls may lead to better knowledge regarding the physiology of the condition and to subsequent treatments. There are many ways to characterize relationships between neural activity in different parts of the brain. Here, we apply a novel method, called cyclicity analysis, to functional MRI data obtained from tinnitus patients and controls over a period of wakeful rest. Cyclicity analysis lends itself to interpretation as analysis of temporal orderings between elements of time-series data; it is distinct from methods like periodicity analysis or time correlation analysis in that its theoretical underpinnings are invariant to changes in time scales of the generative process. In this proof-of-concept study, we use the feature generated from the cyclicity analysis of the fMRI data to investigate group level differences between tinnitus patients and controls. Our findings indicate that temporal ordering of regional brain activation is much more consistent in the control population than in tinnitus population. We also apply methods of classification from machine learning to differentiate between the two populations with moderate amount of success.