Looking through the windows: a study about the dependency of phase-coupling estimates on the data length

Being able to characterize functional connectivity (FC) state dynamics in a real-time setting, such as in brain-computer interface, neurofeedback or closed-loop neurostimulation frameworks, requires the rapid detection of the statistical dependencies that quantify FC in short windows of data. The aim of this study is to characterize, through extensive realistic simulations, the reliability of FC estimation as a function of the data length. In particular, we focused on FC as measured by phase-coupling (PC) of neuronal oscillations, one of the most functionally relevant neural coupling modes.

We generated synthetic data corresponding to different scenarios by varying the data length, the signal-to-noise ratio, the phase difference value, the spectral analysis approach (Hilbert or Fourier) and the fractional bandwidth. We compared seven PC metrics, i.e. imaginary part of phase locking value (PLV), PLV of orthogonalized signals, phase lag index (PLI), debiased weighted PLI, imaginary part of coherency, coherence of orthogonalized signals and lagged coherence.

Our findings show that, for a signal-to-noise-ratio of at least 10 dB, a data window that contains 5 to 8 cycles of the oscillation of interest (e.g. a 500-800ms window at 10Hz) is generally required to achieve reliable PC estimates. In general, Hilbert-based approaches were associated with higher performance than Fourier-based approaches. Furthermore, the results suggest that, when the analysis is performed in a narrow frequency range, a larger window is required.

The achieved results pave the way to the introduction of best-practice guidelines to be followed when a real-time frequency-specific PC assessment is at target.