Multiscale detrended cross-correlation coefficient: estimating coupling in non-stationary neurophysiological signals

The brain consists of a vastly interconnected network of regions, the connectome. By estimating the statistical interdependence of neurophysiological time series, we can measure the functional connectivity (FC) of this connectome. Pearson's correlation (<i>r</i> _P) is a common metric of coupling in FC studies. Yet <i>r</i> _P does not account properly for the non-stationarity of the signals recorded in neuroimaging. In this study, we introduced a novel estimator of coupled dynamics termed multiscale detrended cross-correlation coefficient (MDC₃). Firstly, we showed that MDC₃ had higher accuracy compared to <i>r</i> _P and lagged covariance using simulated time series with known coupling, as well as simulated functional magnetic resonance imaging (fMRI) signals with known underlying structural connectivity. Next, we computed functional brain networks based on empirical magnetoencephalography (MEG) and fMRI. We found that by using MDC₃ we could construct networks of healthy populations with significantly different properties compared to <i>r</i> _P networks. Based on our results, we believe that MDC₃ is a valid alternative to <i>r</i> _P that should be incorporated in future FC studies.