Distortions in EEG interregional phase synchrony by spherical spline interpolation: causes and remedies

Measures of the coherence of electroencephalography (EEG) time-series recorded at spatially distant points on the scalp are often used by researchers to characterize the dynamic interactions of brain regions. In dense-array EEG recordings, one or more electrode signals often contain prominent artifact necessitating replacement of the recorded data with an estimated signal using interpolation from data in valid recordings from the surrounding electrodes. Typically the signal estimation is carried out using spherical spline interpolation (SSI; Perrin et al., 1989); however, it is shown that this can introduce an erroneous increase in coherence between signals because the estimated signal is derived from elements in common recordings from other electrode sites. Although SSI performance depends on three SSI parameters, including interpolation order m , the Legendre polynomial order n , and regularization parameter λ , clear guidelines on how to optimally choose parameters have yet to be established for ensuring the temporal features of interpolated signals are accurate. Using a cross validation approach we compared interpolated and original signals in 64 and 128 channel resting EEG data systematically examining the effect of data interpolation across various sets of SSI parameters, frequency bands, and locations of interpolated electrodes and electrode pairs on a standard measure of phase coherence (phase locking value: PLV). We found substantial PLV inflation with SSI, which was greater in 128 channel than in 64 channel EEG data and greater for neighboring electrodes than distant electrodes. Furthermore, the amount of PLV distortions varied across the locations of interpolated signals. Performance of SSI was highly dependent on the three SSI parameters, and the effect of each parameter was dependent on the levels of other parameters. Although SSI parameters commonly recommended in the literature led to notable and concerning PLV inflation, application of SSI with alternative and optimal parameter values led to accurate and nearly distortion-free phase coherence values (i.e., PLV) from estimated signals.