A mathematical model of the HPA axis demonstrates bifurcations under varying stress and systemic conditions

Abstract

In this study, we develop a mathematical model of the hypothalamic pituitary adrenal (HPA) axis and systematically investigate the model complexity required to reproduce observed hormone dynamics. The model is fitted to ACTH and cortisol measurements from five healthy volunteers reported in the literature. We show that simultaneous reproduction of both hormone profiles requires a delay differential equation model with at least five state variables among the model architectures considered. Following fitting the volunteer data, we investigate the response of the model to sustained stress using bifurcation analysis. The coupled system exhibits bifurcations over a range of stress intensities. This analysis reveals bifurcations whose critical stress thresholds depend strongly on the modulatory state of the system. These results provide a mathematical framework for investigating transitions between physiological and dysregulated HPA axis dynamics, which may be related to states of health and disease.