Endocrine Abstracts

Current cortisol dosing regimes for patients with adrenal insufficiency are unable to accurately replicate the physiological profile of healthy patients. This work is part of an interdisciplinary study with the aim of using mathematical approaches to understand the treatment strategies for patients with adrenal insufficiency. We also aim to then tailor treatments specific to an individual or situation. We present a simplified model of hydrocortisone delivery via intravenous bolus (IV) and continuous intravenous infusion (CIV). The model is formulated in terms of linear kinetics and considers the dynamics of glucocorticoid-protein binding. We utilise the disparity of system rates to simplify our model. In the case of IV dosing, we can divide the model into 2 regions which includes finding a balance equation to describe behaviour for all time after the dose has been delivered. We aim to fit this simplified model to patient response data to estimate model parameters. This should allow us to optimise and personalise treatment strategies to work out what works best for specific patients. When a high dose of hydrocortisone is delivered, we find a famous mathematical quantity, The Golden Ratio, appears in the level of binding protein. The objective of this analysis is to fit our model parameters to recently published data on 50mg dosing every 6 h (or a 200mg continuous infusion) using Bayesian inference with the software Stan.