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In this Master Thesis, the modelling process and the required biological background to adequately
describe the hormonal dynamics of the human menstrual cycle are presented. The aim
of this Master thesis project is to establish a mathematical routine that enables prediction of
potentially fertile time windows.
A system of four parameter dependent ordinary differential equations coupled with two algebraic
equations is built, accounting for the main kinetic drivers of the human menstrual cycle { basal
body temperature, estradiol, progesterone, luteinizing and follicle stimulating hormone.
The key parameters are identifed using a nonlinear least squares approach to match the model to
individual data. Aiming to solve the optimality problem arising, the Newton and Gauss-Newton
method are examined and their local convergence theory is outlined. By the nature of the application,
a globalised Gauss-Newton method seems more convenient. An adaptive trust region
approach to determine the step lengths is chosen, which together with an linearly-implicit Euler
extrapolation for the given differential algebraic equation system makes parameter estimation
possible.
The simulation results are discussed particularly in view of limitations and problems arising
through the modelling approach.