Mathematische Modellierung der Hypothalamus-Hypophysen-Schilddrüsen Achse

The analysis of complex physiological processes represents a key challenge in modern medicine, particularly when multiple organs interact via non-linear feedback mechanisms. A prime example of this is the hypothalamic-pituitary-thyroid axis (HPT axis), whose dynamics are characterised by a finely tuned interplay of hormonal processes and feedback mechanisms. Individual clinical measurements often provide only momentary information on the state of the system and do not allow direct conclusions to be drawn about the underlying dynamic processes. Mathematical models offer the possibility of explicitly modelling these dynamics and analysing relationships between different influencing factors in a structured manner. In the context of modelling, biological processes are translated into formalised mathematical structures, typically in the form of ordinary differential equations. These describe the temporal development of hormone concentrations, considering production, degradation, transport and regulatory feedback. The compartment modelling approach enables a structured decomposition of the system into functional units, whilst non-linear modelling components such as Michaelis-Menten kinetics capture enzymatic processes realistically. The literature contains a wide variety of models with different degrees of detail and objectives, ranging from static relationships to high-dimensional dynamic systems. Among other things, these models allow analysis of stability, sensitivity of model parameters and long-term system behaviour, as well as the integration of clinical data for parameter determination. However, clear limitations are apparent at the same time. Many models capture only partial aspects of physiological reality, have been validated using insufficient datasets or exhibit simplified dynamic behaviour. Mathematical models nevertheless represent a promising tool for better understanding the complex endocrine system. However, comprehensive validation, further analytical characterisation and greater integration of clinical data are still required for future clinical application.