Mathematical Model Analysis of the Hypothalamus-Pituitary-Thyroid Axis

Abstract

This paper presents an extensive local and global sensitivity analysis of a mathematical model describing the hypothalamus-pituitary-thyroid axis. The model is based on a system of differential equations describing the dynamic interactions between the key physiological variables: thyroid-stimulating hormone, free thyroxine, the functional size of the thyroid gland and anti-thyroid peroxidase antibodies. We employed the local sensitivity analysis to assess the response of the system to minor alternations in individual parameters, thereby providing insight into the immediate responsiveness of the hypothalamus-pituitary-thyroid axis. To extend the analysis, we also conducted a global sensitivity analysis using latin hypercube sampling combined with partial rank correlation coefficients. Latin hypercube sampling ensures efficient sampling, while partial rank correlation coefficients permit the examination of both linear and non-linear, but monotonic relationships between parameters and output. This dual approach provides a more comprehensive understanding of the impact of variations in key physiological factors on the system globally. Concluding, the findings of these sensitivity analyses have the potential to facilitate the development of patient-specific diagnostics, providing valuable insight into the individual variability in thyroid function.