Mitochondrial dysfunction in EEG: high-beta specific metabolic/oxidative coupling with lactate in mania-predominant polarity

Psychiatric diseases are progressively recognized as disruptions in brain dynamics that can be measured using electrophysiological and metabolic indicators. Conventional EEG investigations utilizing power spectra or standard entropy metrics (sample entropy, multiscale entropy, permutation entropy) have shown diagnostic significance but are constrained in their ability to capture higher-order relationships. This work combines psychiatric ideas with sophisticated mathematical methods to discover new indicators of modified brain complexity. From an engineering standpoint, we provide entropy-doubling, an information-theoretic approach utilized for EEG signals for the first time. In contrast to conventional entropy measures, entropy-doubling assesses the evolution of informational complexity under distributional convolution, hence uncovering redundancy and structural scaling characteristics that are not discernible through existing metrics. We associate these metrics with biochemical markers, such as lactate, to investigate potential metabolic coupling of brain processes in bipolar disorder. It has the characteristics of a biphasic energy dysregulation. The aim of this study is to investigate the correlation between electrophysiological brain dynamics, as quantified by entropy doubling and Ruzsa distance measures derived from EEG signals, and lactate levels, in patients with bipolar disorder with mania-predominant polarity. According to our results, high-beta amplitude entropy provides the strongest and most consistent correlations with lactate. This combined framework of psychiatry and biomedical engineering provides a novel, interpretable pathway toward quantitative biomarkers in psychiatric research.