Sensitivity Analysis in Mathematical Models of the Hypothalamus-Pituitary-Thyroid Axis

Abstract

Mathematical models are promising and important for advancing the current medical practice in the field of endocrinology. To assess the reliability of the range of mathematical models describing the hypothalamuspituitary- thyroid axis and to establish their applicability in clinical decision support, we conducted a local and global sensitivity analysis of the model. Thyroid regulation in euthyroid and diseased individuals may be quantified and dynamic behavior predicted through mathematical models, thereby revolutionizing the current clinical practice. We investigated the influence of model parameters of a selected mathematical model utilizing ordinary differential equations describing the HPT-axis. Motivated by a graphical depiction of the varying influence of the model parameters, feasible methods such as a local sensitivity analysis are conducted. Furthermore, to account for the influence of parameters on the output variance of the considered model, the theory of Sobol’ indices is utilized. Although the system of differential equations describing the hormone concentrations of thyroid-simulating hormones and unbound Thyroxine has similar equation structures, the results of the sensitivity analyses varied according to the equation.