  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.
