Estimation of functional connectivity from electromagnetic signals and the amount of empirical data required

Abstract

An increasing number of neuroimaging studies are concerned with the identification of interactions or statistical dependencies between brain areas. Dependencies between the activities of different brain regions can be quantified with functional connectivity measures such as the cross-correlation coefficient. An important factor limiting the accuracy of such measures is the amount of empirical data available. For event-related protocols, the amount of data also affects the temporal resolution of the analysis. We use analytical expressions to calculate the amount of empirical data needed to establish whether a certain level of dependency is significant when the time series are autocorrelated, as is the case for biological signals. These analytical results are then contrasted with estimates from simulations based on real data recorded with magnetoencephalography during a resting-state paradigm and during the presentation of visual stimuli. Results indicate that, for broadband signals, 50-100 s of data is required to detect a true underlying cross-correlations coefficient of 0.05. This corresponds to a resolution of a few hundred milliseconds for typical event-related recordings. The required time window increases for narrow band signals as frequency decreases. For instance, approximately 3 times as much data is necessary for signals in the alpha band. Important implications can be derived for the design and interpretation of experiments to characterize weak interactions, which are potentially important for brain processing.