Speaker
Description
The hypothalamic-pituitary-thyroid (HPT) axis regulates endocrine feedback mechanisms essential for metabolic homeostasis. Mathematical models based on ordinary differential equations provide a framework for studying hormonal regulations. Nevertheless, the integration of physiological models with patient-specific clinical data continues to present significant challenges.
In this study, a dynamic model of the HPT axis\cite{pandi} for the simulation of hypothyroidism is calibrated using clinical hormone measurements and analyzed with respect to its intrinsic fast–slow structure\cite{Kuehn}. The estimation of model parameters is achieved through the utilization of multiple objective functions, whose outcomes are subsequently compared to align simulated hormone dynamics with clinical data from the General Hospital of Vienna.
The calibrated system is studied using methods from singular perturbation theory\cite{wechsel}. The separation of physiological time scales can be exploited through the implementation of a fast-slow decomposition, which results in a reduced model. We examine whether this reduced formulation preserves the essential regulatory dynamics consistent with the Tikhonov–Fenichel theory\cite{tik}.
The reduced model reveals the dynamical organization of endocrine feedback mechanisms and thereby facilitates the analysis of stability and long-term behavior. Future work includes bifurcation analysis within the parameter ranges obtained from the data-driven calibration.
Bibliography
@Article{pandi,
author = {Balamurugan Pandiyan and Stephen J. Merrill and Salvatore Benvenga},
journal = {Mathematical medicine and biology: a journal of the IMA},
title = {A patient-specific model of the negative-feedback control of the hypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis.},
year = {2014},
pages = {226-58},
volume = {31 3},
}
@misc{wechsel,
title={Coordinate-independent model reductions of chemical reaction networks based on geometric singular perturbation theory},
author={Timothy Earl Figueroa Lapuz and Martin Wechselberger},
year={2026},
eprint={2508.03304},
archivePrefix={arXiv},
primaryClass={math.DS},
url={https://arxiv.org/abs/2508.03304},
}
@article{tik,
author = {Tikhonov, A. N.},
title = {Systems of Differential Equations Containing a Small Parameter Multiplying the Derivative},
journal = {Matematicheskii Sbornik},
year = {1952},
volume = {31},
pages = {575--586}
}
@book{Kuehn,
series = {Applied mathematical sciences},
publisher = {Springer},
isbn = {3319123157},
year = {2015},
title = {Multiple Time Scale Dynamics},
language = {eng},
address = {Cham [u.a.]},
author = {Kuehn, Christian},
keywords = {Mehrskalenmodell},
}
