Model Predictive Controller to Regulate Cortisol Levels in Individuals With Adrenal Insufficiency

Renuka Joshi, Nayana Saha, Vittal Srinivasan, Stanislaw H. Zak, Cary N. Mariash

A model predictive controller (MPC) is used to construct a virtual assistant to aid a physician in prescribing cortisol replacement therapy for patients with adrenal insufficiency (AI). AI, also known as hypocortisolism, is a condition that occurs due to a low concentration of cortisol. This hormonal imbalance significantly impacts the individual's ability to regulate stress, metabolism, and immune responses. Thus, it is essential to maintain cortisol levels within a healthy range. The production of cortisol is governed by the hypothalamus-pituitary-adrenal (HPA) axis, a part of the endocrine system. In this paper, a novel mathematical model of the HPA axis is proposed that incorporates the endogenous circadian rhythm. This model simulates two conditions of hypocortisolism: primary and secondary AI. Adrenal insufficiency cannot be cured, but it can be treated with cortisol replacement therapy. The standard practice is to prescribe a therapeutic dose of hydrocortisone (HC). To evaluate the accuracy of the proposed HPA axis model, an open-loop cortisol replacement strategy with a fixed dosage is used to simulate both primary and secondary AI. The simulation results show that, analytically, it is possible to arrive at a fixed working cortisol replacement strategy. However, this strategy, though effective, is not optimal. To obtain optimal cortisol replacement strategies, an MPC is proposed. An important feature of MPC is that constraints on allowable cortisol replacement dosages can be rigorously addressed. This controller can serve as a virtual assistant to physicians in prescribing daily cortisol replacement therapy.