Sensitivity Analysis of a Mathematical Model Representing the Female Endocrine Cycle

Abstract

This paper presents an extensive global sensitivity analysis of a mathematical model describing the female endocrine cycle. The model, based on a system of differential equations, captures the dynamics of Luteinizing Hormone, Follicle-Stimulating Hormone, Estrogen, and Progesterone, along with their regulatory feedback mechanisms. We employed three complementary methods – Latin Hypercube Sampling, Partial Rank Correlation Coefficient, and extended Fourier Amplitude Sensitivity Test – to analyze both linear and non-linear parameter-output relationships. The extended Fourier Amplitude Sensitivity Test method, in particular, revealed non-monotonic and non-linear interactions between input and output, highlighting the complexity of the hypothalamus-pituitary-ovary axis. Our findings offer significant insights for future model refinement and pave mathematical ways towards better understanding of the female endocrine cycle and potential clinical applications, especially in the diagnosis and treatment of reproductive disorders.