Frequency-resolved dynamic functional connectivity and scale-invariant connectivity-state behavior

Investigating temporal variability of functional connectivity is an emerging field in connectomics. Entering dynamic functional connectivity by applying sliding window techniques on resting-state fMRI (rs-fMRI) time courses emerged from this topic. We introduce frequency-resolved dynamic functional connectivity (frdFC) by means of multivariate empirical mode decomposition (MEMD) followed up by filter-bank investigations. We develop our method on the most canonical form by applying a sliding window approach to the intrinsic mode functions (IMFs) resulting from MEMD. We explore two modifications: uniform-amplitude frequency scales by normalizing the IMFs by their instantaneous amplitude and cumulative scales. By exploiting the well established concept of scale-invariance in resting-state parameters, we compare our frdFC approaches. In general, we find that MEMD is capable of generating time courses to perform frdFC and we discover that the structure of connectivity-states is robust over frequency scales and even becomes more evident with decreasing frequency. This scale-stability varies with the number of extracted clusters when applying k-means. We find a scale-stability drop-off from k = 4 to k = 5 extracted connectivity-states, which is corroborated by null-models, simulations, theoretical considerations, filter-banks, and scale-adjusted windows. Our filter-bank studies show that filter design is more delicate in the rs-fMRI than in the simulated case. Besides offering a baseline for further frdFC research, we suggest and demonstrate the use of scale-stability as a quality criterion for connectivity-state and model selection. We present first evidence showing that scale-invariance plays an important role in connectivity-state considerations. A data repository of our frequency-resolved time-series is provided.