Multiscale Detrended Cross-Correlation Coefficient: Estimating Coupling in Nonstationary Neurophysiological Signals

Abstract

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 (rP) is a common metric of coupling in FC studies. Yet rP 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 rP 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 rP networks. Based on our results, we believe that MDC3 is a valid alternative to rP that should be incorporated in future FC studies.