Filtered correlation and allowed frequency spectra in dynamic functional connectivity

Background: Dynamic functional connectivity enables us to study brain connectivity occurring at different frequencies. Techniques like sliding window correlation allow for the estimation of time varying connectivity and its frequency spectrum content. Since correlation is equal to the cosine of the phase (cos θ) between activation amplitudes of two brain regions, we assume that phase is the relevant functional connectivity feature and leave out any contamination from activation amplitudes. New method: First, this work studies the conditions by which time varying correlation can be separated from nuisance activation amplitudes that are not phase related. Second, we propose the filtered sliding window correlation to perform time varying estimation of cosine-phase (cos θ (t)) and nuisance filtering in one single step. Results: Mathematical models predict the correlation frequencies that should be filtered out to avoid overlap with the activation amplitude spectra. Filtered sliding window correlation excluded nuisance frequencies with an accurate estimation of time varying correlation. Real data outcomes empirically suggest that fMRI frequencies of interest extend up to 0.05 Hz. Comparison with existing methods: Compared with sliding window methods, the filtered sliding window correlation achieves better estimation for frequencies of interest. Conclusions: The filtered sliding window correlation approach allows controlling for nuisance frequencies unrelated to time varying phase estimation.