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

Please always quote using this URN: urn:nbn:de:0297-zib-12732
  • This study 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. In contrast to other models, this model does not involve delay differential equations and is based on deterministic modelling of the GnRH pulse pattern, which allows for faster simulation times and efficient parameter identification. These steps were essential to tackle the task of developing a mathematical model for the administration of GnRH analogues. The focus of this paper is on model development for GnRH receptor binding and the integration of a pharmacokinetic/pharmacodynamic model for the GnRH agonist Nafarelin and the GnRH antagonist Cetrorelix into the menstrual cycle model. The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle in 12 healthy women. Moreover, it correctly predicts the changes in the cycle following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle.

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Author:Susanna Röblitz, Claudia Stötzel, Peter Deuflhard, Hannah M. Jones, David-Olivier Azulay, Piet van der Graaf, Steven W. Martin
Document Type:ZIB-Report
Tag:GnRH analogues; differential equations; human menstrual cycle; mathematical modelling; systems biology
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L09 Inverse problems
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C31 Sensitivity, stability, parametric optimization
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C30 Physiology (general)
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C42 Systems biology, networks
Date of first Publication:2011/04/27
Series (Serial Number):ZIB-Report (11-16)
Published in:Appeared in: Journal of Theoretical Biology 321 (2013) pp. 8-27

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