Mathematical modeling of the interaction between endocrine systems and EEG signals.

Introduction: The intricate interplay between endocrine systems and EEG signals is pivotal for understanding and managing physiological and neurological health. Traditional mathematical models often fail to capture the nonlinear dynamics, feedback mechanisms, and cross-system interactions inherent in these processes, limiting their applicability in clinical and research settings. Methods: This study proposes a novel framework for modeling and analyzing the interaction between endocrine regulatory systems and EEG signals, leveraging advanced methodologies such as the Hormone Interaction Dynamics Network (HIDN) and the Adaptive Hormonal Regulation Strategy (AHRS). HIDN integrates graph-based neural architectures with recurrent dynamics to encapsulate the spatialtemporal interdependencies among endocrine glands, hormones, and EEG signal fluctuations. AHRS complements this by dynamically optimizing therapeutic interventions using real-time feedback and patient-specific parameters, ensuring adaptability to individual variability and external perturbations. Results: The proposed model excels in scalability, precision, and robustness, addressing challenges like sparse clinical data, temporal resolution, and multi-hormonal regulation. Experimental validation demonstrates its efficacy in predicting hormone dynamics, EEG signal patterns, and therapeutic outcomes under varying conditions. Discussion: This interdisciplinary approach bridges the gap between computational modeling and practical healthcare applications, advancing our understanding of endocrine-neurological interactions.