  In recent years there has been growing interest in measuring time-varying
functional connectivity between different brain regions using resting-state
functional magnetic resonance imaging (rs-fMRI) data. One way to assess the
relationship between signals from different brain regions is to measure their
phase synchronization (PS) across time. There are several ways to perform such
analyses, and here we compare methods that utilize a PS metric together with a
sliding window, referred to here as windowed phase synchronization (WPS), with
those that directly measure the instantaneous phase synchronization (IPS). In
particular, IPS has recently gained popularity as it offers single time-point
resolution of time-resolved fMRI connectivity. In this paper, we discuss the
underlying assumptions required for performing PS analyses and emphasize the
necessity of band-pass filtering the data to obtain valid results. We review
various methods for evaluating PS and introduce a new approach within the IPS
framework denoted the cosine of the relative phase (CRP). We contrast methods
through a series of simulations and application to rs-fMRI data. Our results
indicate that CRP outperforms other tested methods and overcomes issues related
to undetected temporal transitions from positive to negative associations
common in IPS analysis. Further, in contrast to phase coherence, CRP unfolds
the distribution of PS measures, which benefits subsequent clustering of PS
matrices into recurring brain states.
