Speakers
Description
Endocrine regulatory systems play a pivotal role in preserving physiological homeostasis through intricate hormonal feedback mechanisms. Mathematical models formulated as systems of ordinary differential equations (ODEs) provide a quantitative framework for investigating the dynamics of such regulatory processes.
In this study, we examine established ODE models describing endocrine feedback systems. These models encompass those of the hypothalamic–pituitary–thyroid\cite{pandi} and hypothalamic–pituitary–ovarian\cite{gra} axes. In order to characterize the local stability properties of these models, a numerical analysis of the eigenvalues\cite{hai} of the Jacobian matrices is performed, with the matrices evaluated at physiologically relevant equilibrium states. The resulting eigenvalue spectra offer insight into the stability of equilibrium states, the associated relaxation dynamics, and the presence of stiffness in the governing equations. Furthermore, systematic exploration of parameter variations is undertaken to investigate the influence of physiological changes on the stability structure of the models and the potential induction of qualitative transitions in system behavior, such as shifts from stable regulation to oscillatory dynamics.
The analysis contributes to a more profound quantitative understanding of endocrine regulatory mechanisms and may support future efforts to connect mathematical models with clinical observations of endocrine dysfunction.
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},
file = {:C\:/Users/Clara Horvath/Nextcloud/mse-blmm/Projekte/Thyroid Modelling/Quellen/+A patient-specific model of the negative-feedback control of thehypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's)thyroiditis.pdf:PDF},
}
@Article{gra,
author = {Erica J. Graham and Noémie Elhadad and David Albers},
journal = {Mathematical Biosciences},
title = {Reduced model for female endocrine dynamics: Validation and functional variations},
year = {2023},
issn = {0025-5564},
pages = {108979},
volume = {358},
comment = {Model, ODE},
file = {:Reduced model for female endocrine dynamics.pdf:PDF},
keywords = {Ovulation, Endocrinology, Polycystic ovary syndrome},
priority = {prio1},
}
@book{hai,
series = {Springer series in computational mathematics},
publisher = {Springer},
title = {Solving ordinary differential equations},
language = {eng},
address = {Berlin [u.a.]},
author = {Hairer, Ernst and Nørsett, Syvert P and Wanner, Gerhard},
keywords = {Gewöhnliche Differentialgleichung ; Numerisches Verfahren},
}
