A mathematical model of the human menstrual cycle for the administration of GnRH analogues

J Theor Biol. 2013 Mar 21:321:8-27. doi: 10.1016/j.jtbi.2012.11.020. Epub 2012 Dec 1.


The paper presents a differential equation model for the feedback mechanisms between gonadotropin-releasing hormone (GnRH), follicle-stimulating hormone (FSH), luteinizing hormone (LH), development of follicles and corpus luteum, and the production of estradiol (E2), progesterone (P4), inhibin A (IhA), and inhibin B (IhB) during the female menstrual cycle. Compared to earlier human cycle models, there are three important differences: The model presented here (a) does not involve any delay equations, (b) is based on a deterministic modeling of the GnRH pulse pattern, and (c) contains less differential equations and less parameters. These differences allow for a faster simulation and parameter identification. The focus is on modeling GnRH-receptor binding, in particular, by inclusion of a pharmacokinetic/pharmacodynamic (PK/PD) model for a GnRH agonist, Nafarelin, and a GnRH antagonist, Cetrorelix, into the menstrual cycle model. The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle of 12 healthy women. It correctly predicts hormonal changes following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle.

MeSH terms

  • Biological Availability
  • Cell Membrane / metabolism
  • Computer Simulation
  • Corpus Luteum / metabolism
  • Female
  • Follicle Stimulating Hormone / blood
  • Gonadotropin-Releasing Hormone / administration & dosage
  • Gonadotropin-Releasing Hormone / analogs & derivatives*
  • Gonadotropin-Releasing Hormone / pharmacokinetics
  • Humans
  • Luteinizing Hormone / blood
  • Menstrual Cycle / physiology*
  • Models, Biological
  • Nafarelin / administration & dosage
  • Nafarelin / pharmacokinetics
  • Time Factors


  • Nafarelin
  • Gonadotropin-Releasing Hormone
  • Luteinizing Hormone
  • Follicle Stimulating Hormone
  • cetrorelix