Increasing Complexity of an Hypothalamus-Pituitary-Adrenal Axis Mathematical Model with Predictive Applications and Physiological Implications

Abstract

This study creates and analyzes a model of the Hypothalamus-Pituitary-Adrenal axis to better understand cortisol rhythmicity perpetuated by circadian inputs, system dynamics and feedback inherent within the system. Differential equations are created to model human physiology with cortisol and precursor hormone outputs fit to physiologic data. The model is created with an input of circadian cues from the hypothalamus which are designed to create a more realistic stimulation of the cortisol cascade over predecessors. The study also incorporates additional signaling pathways unique to this model. The project explores the properties of the model under mathematical analysis; then, the simulation of known medical pathologies is used to analyze the model's predictive ability. It is found that incorporating the additional signaling pathway of Arginine Vasopressin increases the model's predictive capability in certain pathological conditions over predecessor models. Additionally, the origination of ultradian rhythm is explored through simulation and two possible explanations are found. First, pulsatile release of Adrenocorticotropic Hormone combined with negative feedback into the system from glucocorticoid receptors elicits the observed ultradian oscillations in humans. Additionally, simulations of increased hypothalamic monitoring and control of cortisol concentrations create a natural oscillation within the desired period. Results from numerical perturbation simulations and dynamic sensitivity analysis are employed to offer justification for known pathological conditions developing from circadian dysregulation.