## Numerical and Discrete Modeling of Reproductive Endocrinological Networks

- This thesis deals with the mathematical modeling of endocrinological networks that are underlying the female hormone cycle. These networks consist of a variety of biological mechanisms in different parts of the organism. Their interaction leads to periodic changes of various substances that are necessary for reproduction. In every cycle, hormones are secreted from the hypothalamic-pituitary-gonadal axis into the bloodstream, where they distribute and influence several functions in the body. Their most important task in reproduction is to regulate processes in the ovaries, where follicles and corpus luteum develop. These produce steroids that are released into the blood and from therein regulate the processes in the hypothalamic-pituitary-gonadal axis. The hormonal cycle is thus a result of a large feedback loop, whose self-regulation is a complex interplay of multiple components. For the modeling of these processes, a high abstraction level is required, which can be realized by various modeling approaches. In this work, some of these approaches are implemented. The first step in all approaches is the representation of the most important mechanisms in a flowchart. In the next step, this can be implemented as a system of ordinary differential equations using Hill functions, as a piecewise defined affine differential equation model, or directly as a purely regulatory model. Using this approach, a differential equation model for the hormonal cycle of cows is developed. This is compared with a more advanced model of the menstrual cycle in humans. Both models are validated by comparing simulations with measured values, and by studying external influences such as drug administration. For the example of the bovine estrous cycle, continuous analysis methods are used to investigate stability, follicular wave patterns, and robustness with respect to parameter perturbations. Furthermore, the model is substantially reduced while preserving the main simulation results. To take a look at alternative modeling approaches, corresponding discrete models are derived, exemplified for the bovine model. For a piecewise affine version of the model, parameter constraints for the continuous model are calculated. Stability is analyzed globally for a purely discrete model. In addition, core discrete models are derived, which retain the dynamic properties of the original model.

Author: | Claudia Stötzel |
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Document Type: | Doctoral Thesis |

Fulltext Url: | http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000097416 |

Granting Institution: | Freie Universität Berlin |

Advisor: | Peter Deuflhard |

Date of final exam: | 2014/07/03 |

Year of first publication: | 2014 |