The Relationship Between the Functional Integration and Topological Complexity of Human Electroencephalographic (EEG) Signals: Three Moderating Factors

Background and Objectives: A useful strategy to study the dynamic functioning of the human brain is to focus on the relationship between the brain’s functional integration and topological complexity. Theoretical analysis using information-theoretic metrics shows that the functional topological complexity of the brain has a curvilinear inverted-U relationship with its functional integration. This relationship is supported by simulation studies of the functional integration and topological complexity of cortical electroencephalographic (EEG) dipole sources. However, scalp-level EEG functional topological complexity follows an inverse relationship with functional integration. The present study investigated this discrepancy for the case of alpha-range (7–13 Hz) EEG signals predominant during wakeful resting brain states. Methods: Three different EEG source factors were explored that could affect the integration–complexity relationship for scalp-level EEG: volume conduction, regularity, and modularity. The EEG simulations parametrically manipulated the regularity and modularity of cortical EEG dipole source signals and their scalp-level projections to identify how EEG functional integration and topological complexity depended on these factors at the cortical and scalp levels before and after the spatial mixing effects of volume conduction. Simulation findings were compared with results obtained from empirically measured resting state EEG signals. Results: Simulated source-level EEG functional integration and topological complexity followed a curvilinear inverted-U relationship, whereas scalp-level functional topological complexity had an inverse relationship with functional integration, with this difference occurring for irregular (aperiodic) sources but not regular (periodic) sources. EEG source modularity was related to the functional integration–complexity relationship only for regular EEG signals. These findings were consistent with the results obtained from the empirical EEG signals. Conclusions: The discrepancy between source- and scalp-level EEG functional integration–complexity relationships primarily reflects the spatial mixing effects of volume conduction and its secondary effects on scalp EEG regularity.