Linear and Nonlinear Oscillatory Functional Brain Networks in Euthymic Bipolar Disorder Classification

Functional brain network (FBN) dysconnectivity has been repeatedly reported in bipolar disorder (BD). However, it remains unclear how this dysconnectivity manifests from the perspective of oscillatory FBNs, that is, which network measures and frequency bands most reliably capture this alteration. Moreover, it is unknown whether this dysconnection is predominantly expressed through linear or nonlinear interactions. Here, we investigated properties of oscillatory FBNs in individuals with euthymic BD. Networks were constructed using linear and nonlinear connectivity measures applied to source-localized resting-state electroencephalography (EEG) current density signals. We then quantified whole-FBN and nodal features using conventional and spectral graph theory methods to characterize disorder-related network mechanisms and evaluate their potential as biomarkers. Significant group differences between BD and control groups were observed in the theta and alpha1 bands. Dynamical whole-FBN alterations were detected primarily in linear oscillatory FBNs, with reduced Shannon entropy and energy in the BD group. These effects were replicated using machine learning, achieving 85% classification accuracy with entropy and energy as the most informative features. In contrast, nodal-level differences emerged mainly in nonlinear FBNs, revealing increased centrality in frontal, and decreased centrality across temporal, and limbic regions. These findings emphasize distinct, frequency-specific roles of linear and nonlinear oscillatory FBNs in BD, with global dysconnectivity reflected in linear FBNs and local alterations captured by nonlinear connectivity. Moreover, network measures related to synchronization stability and complexity more effectively capture BD-related dysconnectivity, suggesting that dynamic features of oscillatory FBNs may serve as potential biomarkers for BD.