Multiscale Detrended Cross-Correlation Coefficient: Estimating Coupling in Nonstationary 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. Pearsons 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. Author SummaryThe brain consists of a vastly interconnected network of regions. To estimate the connection strength of such networks the coupling between different brain regions should be calculated. This can be achieved by using a series of statistical methods that capture the connection strength between signals originating across the brain, one of them being Pearsons correlation (rP). Despite its benefits, rP is not suitable for realistic estimation of brain network architecture. In this study, we introduced a novel estimator called multiscale detrended cross-correlation coefficient (MDC3). Firstly, we showed that MDC3 was more accurate than rP using simulated signals with known connection strength, as well as simulated brain activity emerging from realistic brain simulations. Next, we constructed brain networks based on real-life brain activity, recorded using two different methodologies. 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 studies of brain networks.