Mathematical modelling of hydrocortisone replacement therapy

Evans, Rosemary (2025). Mathematical modelling of hydrocortisone replacement therapy. University of Birmingham. Ph.D.

Preview

Evans2025PhD.pdf
Text - Accepted Version
Available under License All rights reserved.
Download (18MB) | Preview

Abstract

Cortisol is a stress hormone produced by the adrenal glands and is responsible for multiple processes in the body, including regulating blood pressure and sugar and managing the sleep/wake cycle. Adrenal insufficiency is a condition characterised by inadequate production of cortisol resulting in symptoms such as fatigue, weakness, and weight loss.

Hormone replacement therapy attempts to artificially regulate cortisol for patients with adrenal insufficiency, however this treatment is rarely personalised to an individual. In this thesis we develop mathematical models to predict hormone dynamics after the delivery of hydrocortisone (the term for cortisol delivered as a medication). We apply these models to assess differences in cortisol response after two commonly used delivery methods, namely a continuous intravenous infusion regime (CIV), and regular intravenous bolus injections (BIV). We fit these models to published experimental data from an in-patient study.

Driven by the desire to study the most parsimonious model that contains the dominant processes affecting blood cortisol levels, the models consider the substantial role of binding protein in changing cortisol dynamics, as well as its effects on excretion. For simplicity, other metabolic processes and distribution across physiological compartments (such as organs or tissues) are neglected. The resulting models comprise five free parameters common to both delivery modes. Additionally, by exploiting the disparity of time scales in the system we obtain asymptotically reduced models of each delivery mode, involving just four free parameters.

One critically important (but often neglected) aspect of models of this type is the desire to recover unique parameter values upon fitting to experimental data. We assess both the structural and practical identifiability of the derived models, highlighting those parameters which can be reliably inferred and those which cannot. We find that the models are practically identifiable for all model parameters except the binding and unbinding rates. This limitation is mitigated by the relative lack of sensitivity of cortisol dynamics to the precise value of these rates; instead it is the ratio of binding versus unbinding that governs dynamics. In all cases (except in the addition of significant noise) this ratio is shown to be practically recoverable. We further consider the question of whether low time-resolution measurements of combined concentrations of free and bound circulating cortisol enable model parameters to be uniquely estimated and/or inferred.

Finally, the models are fitted using both frequentist and Bayesian approaches, the latter having the added benefit of providing estimates regarding the uncertainty in the parameters which affect the dynamics. Parameter estimates from fitting the BIV model alone, and both BIV and CIV models simultaneously show good agreement, but differ from fitting only the CIV model. These differences highlight the advantage of integrating data from multiple modes of delivery to extract the dominant mechanisms of cortisol response thereby offering the potential to tailor treatments specific to an individual patient.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):