  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 extend a mathematical model of the pituitary-thyroid feedback loop such that
the intake of methimazole, a common antithyroid agent, can be considered. Based
on this extension, 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, (ii) patients are
additionally affected by high intrathyroidal iodide concentrations and take the
medication orally and, (iii) patients suffering from a life-threatening
thyrotoxicosis, in which the medication is usually given intravenously. Our
results suggest that determining the medication dosages by means of an MPC
scheme is a promising alternative to the currently applied trial-and-error
approach.
