Modeling and Predictive Control for the Treatment of Hyperthyroidism

TL;DR

This work addresses the challenge of dosing antithyroid therapy for hyperthyroidism by replacing trial-and-error with a model-based approach. It extends the pituitary-thyroid feedback model to include intrathyroidal methimazole dynamics via a Bateman concentration model $MMI_{Pl}(t)$ and a Michaelis-Menten link to intrathyroidal $MMI_{th}(t)$ that modulates TPO activity $TPO_a(t)$, yielding thyroid production $G_T(t)=G_{T,nom}\,G_{T,co}\,TPO_a(t)$. An MPC scheme is developed to compute optimal dosages, with horizon $T$, sampling time $ obreakspace\\delta$, discrete dosing, and CasADi implementation, aiming to tracking healthy setpoints while smoothing dosage changes. In simulations for Graves' disease and thyrotoxicosis, MPC stabilizes hormone levels under disturbances and across administration routes, outperforming guideline-based dosing in reaching setpoints, while highlighting practical challenges such as state estimation and patient-specific parameter fitting for clinical translation.

Abstract

In this work, we propose an approach to determine the dosages of antithyroid agents to treat hyperthyroid patients. Instead of relying on a trial-and-error approach as it is commonly done in clinical practice, we suggest to determine the dosages by means of a model predictive control (MPC) scheme. To this end, we first extend a mathematical model of the pituitary-thyroid feedback loop such that the intake of methimazole, a common antithyroid agent, can be considered. Second, based on the extended model, we develop an MPC scheme to determine suitable dosages. In numerical simulations, we consider scenarios in which (i) patients are affected by Graves' disease and take the medication orally and (ii) patients suffering from a life-threatening thyrotoxicosis, in which the medication is usually given intravenously. Our conceptual study suggests that determining the medication dosages by means of an MPC scheme could be a promising alternative to the currently applied trial-and-error approach.

Figures (4)

• Figure 2: Illustration of the guidelines given by the American Thyroid association (ATA) Ross2016. The treating physician may encounter many difficulties to select one precise dosage using these (rather vague) recommendations.
• Figure 3: Simulation results of an exemplary treatment based on the guidelines introduced in Ross2016. We apply the mean medication dosage for each interval, e.g., if the concentration of $FT_4$ (which is proportional to $T_4$) is within $27 - 42 \: pmol/L$, we apply $7.5 \: m g$. As disturbances, we consider forgotten dosages and measurement noise as explained in Section \ref{['sec:simulations']}.
• Figure 4: Course of the hormone concentrations and the corresponding MMI dosages that are taken orally once per day. The dosages are determined by the MPC scheme introduced in Subsection \ref{['subsec:MPC']}. As explained in Section \ref{['sec:simulations']}, we consider forgotten dosages, a model-plant mismatch, and some measurement noise as disturbances.
• Figure 5: Course of the hormone concentrations and the corresponding MMI dosages that are injected intravenously twice a day. The dosages are determined by the MPC scheme introduced in Subsection \ref{['subsec:MPC']}. As explained in Section \ref{['sec:simulations']}, we consider a model-plant mismatch and some measurement noise as disturbances.