A semi-mechanistic mathematical framework for simulating multi-hormone dynamics in reproductive endocrinology.

Background: The dynamic interplay of ovarian hormones is central to reproductive physiology, yet the complexity of their cyclic variations poses challenges for analysis, simulation, and teaching. This study presents a framework for generating physiologically constrained, multi-hormone synthetic time series that capture intra- and inter-individual variability across phenotypes. Methods: We developed a semi-mechanistic mathematical framework to generate synthetic multi-hormone profiles (estradiol, FSH, LH, AMH, testosterone, GnRH) using parametric equations embedding known physiological feedbacks (e.g., estradiol-LH delay, estradiol suppression of FSH). Stochastic components were calibrated to reported physiological ranges. Eumenorrheic and PCOS-like phenotypes were defined through parameter adjustments. Data were analysed using Principal Component Analysis (PCA) for phenotype separation, and evaluated in a supervised setting using logistic regression with stratified train/test splitting, reporting accuracy, sensitivity, specificity, and ROC AUC. Results: Eumenorrheic profiles displayed classical mid-cycle estradiol and LH peaks, biphasic FSH, and stable AMH and testosterone levels. In contrast, PCOS profiles showed elevated LH and testosterone, high AMH, blunted estradiol, and dysregulated GnRH pulsatility. PCA revealed clear separation between phenotypes (PC1 +PC2 = 82 % variance), and k-means clustering (k = 2) accurately grouped individuals without label information. PCA showed clear separation between phenotypes, consistent with known endocrine patterns. Logistic regression achieved 100 % accuracy, sensitivity, and specificity, with an AUC of 1.00, confirming robust, phenotype-discriminative features in the synthetic dataset. Conclusion: This simulation framework reproduces physiologically accurate hormone dynamics and discriminates ovulatory from anovulatory cycles, offering applications in AI training, phenotype discovery, and medical education.