A Hormonal Assistant with a Flair for Math express
Inside each of us, invisible clocks are ticking. They control the release of cortisol — the hormone that helps us wake up in the morning, cope with anxiety, and keep our immune system on its toes. In adrenal insufficiency, these clocks break down: the body can't produce the right amount of cortisol on its own. Without treatment, a person feels constant fatigue, and even a common cold can become dangerous.
The authors built a mathematical model of the hypothalamic-pituitary-adrenal axis — the very system that triggers cortisol production. The model incorporates the circadian rhythm, so it mimics the natural rises and falls of the hormone throughout the day. They tested the standard treatment approach on this model: the patient receives a fixed dose of hydrocortisone at specific times. The calculations showed that this method works but is far from ideal — cortisol levels either plummet or spike.
Then came the model predictive controller — an algorithm that calculates the future. It's like an experienced navigator: it knows the map of the daily rhythm, remembers previous doses, and can foresee the consequences of each decision. The main advantage of such an assistant is that it strictly adheres to constraints and will never suggest a dose above the safe threshold. The doctor remains the captain but gets a precise calculation instead of relying on intuition.
Original abstract
as written by the authors arXiv:2607.08902
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.
Cortisol follows a strict daily schedule: its level peaks around 8 a.m. and bottoms out around midnight. That's why hydrocortisone tablets are usually taken two to three times a day to mimic the natural rhythm.