Multiscale Detrended Cross-Correlation Coefficient: Estimating Coupling in Nonstationary Neurophysiological Signals
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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 ( r P ) is a common metric of coupling in FC studies. Yet r 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 (MDC 3 ). Firstly, we showed that MDC 3 had higher accuracy compared to r P 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 MDC 3 we could construct networks of healthy populations with significantly different properties compared to r P networks. Based on our results, we believe that MDC 3 is a valid alternative to r P that should be incorporated in future FC studies.
Author Summary
The 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 Pearson’s correlation ( r P ). Despite its benefits, r P is not suitable for realistic estimation of brain network architecture. In this study, we introduced a novel estimator called multiscale detrended cross-correlation coefficient (MDC 3 ). Firstly, we showed that MDC 3 was more accurate than r P 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 MDC 3 we could construct networks of healthy populations with significantly different properties compared to r P networks. Based on our results, we believe that MDC 3 is a valid alternative to r P that should be incorporated in future studies of brain networks.
