Mathematical Modeling of Free Thyroxine Concentrations During Methimazole Treatment for Graves’ Disease: Development and Validation of a Computer-Aided Thyroid Treatment Method

Verena Theiler-Schwetz, Thomas Benninger, Christian Trummer, Stefan Pilz*, Markus Reichhartinger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Background: Methimazole (MMI) is the first-line treatment for patients with Graves’ disease (GD). While there are empirical recommendations for initial MMI doses, there is no clear guidance for subsequent MMI dose titrations. We aimed to (a) develop a mathematical model capturing the dynamics of free thyroxine (FT4) during MMI treatment (b), validate this model by use of numerical simulation in comparison with real-life patient data (c), develop the software application Digital Thyroid (DigiThy) serving either as a practice tool for treating virtual patients or as a decision support system with dosing recommendations for MMI, and (d) validate this software framework by comparing the efficacy of its MMI dosing recommendations with that from clinical endocrinologists.
Methods: Based on concepts of automatic control and by use of optimization techniques, we developed two first order ordinary differential equations for modeling FT4 dynamics during MMI treatment. Clinical data from patients with GD derived from the outpatient clinic of Endocrinology at the Medical University of Graz, Austria, were used to develop and validate this model. It was subsequently used to create the web-based software application DigiThy as a simulation environment for treating virtual patients and an autonomous computer-aided thyroid treatment (CATT) method providing MMI dosing recommendations.
Results: Based on MMI doses, concentrations of FT4, thyroid-stimulating hormone (TSH), and TSH-receptor antibodies (TRAb), a mathematical model with 8 patient-specific constants was developed. Predicted FT4 concentrations were not significantly different compared to the available consecutively measured FT4 concentrations in 9 patients with GD (52 data pairs, p=0.607). Treatment success of MMI dosing recommendations in 41 virtually generated patients defined by achieved target FT4 concentrations preferably with low required MMI doses was similar between CATT and usual care. Statistically, CATT was significantly superior (p<0.001).
Conclusions: Our mathematical model produced valid FT4 predictions during MMI treatment in GD and provided the basis for the DigiThy application already serving as a training tool for treating virtual patients. Clinical trial data are required to evaluate whether DigiThy can be approved as a decision support system with automatically generated MMI dosing recommendations.
Original languageEnglish
Article number841888
Number of pages13
JournalFrontiers in Endocrinology
Publication statusPublished - 31 May 2022


  • biomedical modeling
  • computer-aided treatment
  • Graves’ disease
  • hyperthyroidism
  • mathematical thyroid model

ASJC Scopus subject areas

  • Endocrinology, Diabetes and Metabolism

Fields of Expertise

  • Human- & Biotechnology


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