Entropy of Chaotic Transitions of EEG Phase Growth in Bipolar Disorder With Lithium Carbonate

The application of chaos theory measures in the association of EEG signals which allows for differentiating pre and postmedicated epochs for bipolar patients. We propose a new approach on positive Schwarzian chaos necessary for a proof of EEG power spectrum of metastability. Shannon entropies of those concealed patterns of positive Schwarzian derivatives from canonical angle transformations of EEG phases from Hilbert transform are compared and found significantly statistical different between pre and post medication periods. Entropy change of chaotic transition measures were compared at first baseline and then at the end of first hour of 300 mg lithium carbonate intake for the same subject in depressive patients. With an application of Schwarzian derivative on the prediction of the von Bertalanffy’s models, integration and segregation of phase growth orbits of neural oscillations can be understood as an influence of chaos on mixing of frequencies. A first order curve-fitting function was performed to determine bifurcation parameter of von Bertalanffy’s model at each given overlapped EEG segment. Schwarzian derivative was positive near the origin which revealed robust chaos. We founded that treatment with Lithium carbonate significantly altered Schwarzian spectrum of chaotic structure and entropy change in Schwarzian amplitudes even though it was not observed in classical EEG power spectrum. Lithium carbonate reduced the strong chaos spectrum of EEG Schwarzian dynamics and removed sharp boundaries in bipolar spectrum.