Evaluating phase synchronization methods in fMRI: A comparison study and new approaches

Abstract

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 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 importance of band-pass filtering the data to obtain valid results. Further, we contrast this approach with the use of Empirical Mode Decomposition (EMD) to achieve similar goals. 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.

Keywords: Circular statistics; Functional connectivity; Instantaneous phase synchronization; Phase synchronization detection; Resting-state fMRI; Time-varying phase synchronization.

Fig. 1.

A schematic of the approach to calculate the instantaneous phase (IP) framework.

Fig. 2.

A single realization of Simulation 1. (a) A pair of signals x(t) and y(t) generated from an independent Gaussian process. (b) The difference in the estimated phase between the signals at each time point. (c) The circular distribution of the phase difference time course in a polar coordinate system. (d) Same results in histogram form.

Fig. 3.

Results of Simulation 1 without band-pass filtering. The bold line indicates the estimated value, while the shaded area represents the 95% confidence interval. Results are shown for: (a) PLV using a sliding window; (b) circular-circular correlation using a sliding window; (c) toroidal-circular correlation using a sliding window; (d) phase coherence; and (e) CRP. The sliding window techniques are evaluated at three different window lengths.

Fig. 4.

Results of Simulation 1 with band-pass filtering. The bold line indicates the estimated value, while the shaded area represents the 95% confidence interval. Results are shown for: (a) PLV using a sliding window; (b) circular-circular correlation using a sliding window; (c) toroidal-circular correlation using a sliding window; (d) phase coherence; and (e) CRP. The sliding window techniques are evaluated at three different window lengths.

Fig. 5.

Results of Simulation 2 without band-pass filtering. (a) The ground truth phase shift between the two signals as a function of time. Results are shown for: (b) PLV using a sliding window; (c) circular-circular correlation using a sliding window; (d) toroidal-circular correlation using a sliding window; (e) phase coherence; and (f) CRP. The sliding window techniques are evaluated at three different window lengths.

Fig. 6.

Results of Simulation 2 with band-pass filtering. (a) The ground truth phase shift between the two signals as a function of time. Results are shown for: (b) PLV using a sliding window; (c) circular-circular correlation using a sliding window; (d) toroidal-circular correlation using a sliding window; (e) phase coherence; and (f) CRP. The sliding window techniques are evaluated at three different window lengths.

Fig. 7.

Results of Simulation 3 without band-pass filtering. (a) The ground truth phase shift between the two signals as a function of time. Results are shown for: (b) PLV using a sliding window; (c) circular-circular correlation using a sliding window; (d) toroidal-circular correlation using a sliding window; (e) phase coherence; and (f) CRP. The sliding window techniques are evaluated at three different window lengths.

Fig. 8.

Results of Simulation 3 with band-pass filtering. (a) The ground truth phase shift between the two signals as a function of time. Results are shown for: (b) PLV using a sliding window; (c) circular-circular correlation bsing a sliding window; (d) toroidal-circular correlation using a sliding window; (e) phase coherence; and (f) CRP. The sliding window techniques are evaluated at three different window lengths.

Fig. 9.

Analysis of the Kirby21 Data. After applying each method the time-varying connectivity measures were clustered into 2 reoccurring brain states. Results are shown for both sessions (top to bottom) for: PLV using a sliding window; circular-circular correlation (CIRC) using a sliding window; toroidal-circular correlation (TORC) using a sliding window; phase coherence (PC); cosine of the relative phase (CRP); correlation-based sliding window (CSW); and prewhitened correlation-based sliding window (PW-CSW). The sliding window techniques are evaluated with window length 30 time points.