TY - THES A1 - Stötzel, Claudia T1 - Numerical and Discrete Modeling of Reproductive Endocrinological Networks N2 - 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. Y1 - 2014 ER - TY - JOUR A1 - Boer, H. Marike T. A1 - Röblitz, Susanna A1 - Stötzel, Claudia A1 - Veerkamp, Roel F. A1 - Kemp, Bas A1 - Woelders, Henri T1 - Mechanisms regulating follicle wave patterns in the bovine estrous cycle investigated with a mathematical model JF - Journal of Dairy Science Y1 - 2011 U6 - https://doi.org/10.3168/jds.2011-4400 VL - 94 IS - 12 SP - 5987 EP - 6000 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Röblitz, Susanna A1 - Stötzel, Claudia T1 - Mathematical Systems Biology at Zuse Institute Berlin (ZIB) JF - BioTOPics - Journal of Biotechnology in Berlin-Brandenburg Y1 - 2010 VL - 39 ER - TY - JOUR A1 - Stötzel, Claudia A1 - Ehrig, Rainald A1 - Boer, H. Marike T. A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - Exploration of different wave patterns in a model of the bovine estrous cycle by Fourier analysis JF - BIOMAT - Proceedings of the 14th International Symposium on Mathematical and Computational Biology, Bedlewo, Poland N2 - Cows typically have different numbers of follicular waves during their hormonal cycle. Understanding the underlying regulations leads to insights into the reasons for declined fertility, a phenomenon that has been observed during the last decades. We present a systematic approach based on Fourier analysis to examine how parameter changes in a model of the bovine estrous cycle lead to different wave patterns. Even without any biological considerations, this allows to detect the responsible model parameters that control the type of periodicity of the solution, thus supporting experimental planning of animal scientists. Y1 - 2014 ER - TY - JOUR A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Siebert, Heike T1 - Complementing ODE-based System Analysis Using Boolean Networks Derived from an Euler-like Transformation JF - PLOS ONE Y1 - 2015 U6 - https://doi.org/10.1371/journal.pone.0140954 ER - TY - JOUR A1 - Boer, H. Marike T. A1 - Apri, Mochamad A1 - Molenaar, Jaap A1 - Stötzel, Claudia A1 - Veerkamp, Roel F. A1 - Woelders, Henri T1 - Candidate mechanisms underlying atypical progesterone profiles as deduced from parameter perturbations in a mathematical model of the bovine estrous cycle JF - Journal of Dairy Science Y1 - 2012 UR - http://www.sciencedirect.com/science/article/pii/S0022030212003621 U6 - https://doi.org/10.3168/jds.2011-5241 VL - 95 IS - 7 SP - 3837 EP - 3851 ER - TY - JOUR A1 - Stötzel, Claudia A1 - Plöntzke, Julia A1 - Heuwieser, Wolfgang A1 - Röblitz, Susanna T1 - Advances in modelling of the bovine estrous cycle: Synchronization with PGF2alpha JF - Theriogenology Y1 - 2012 U6 - https://doi.org/10.1016/j.theriogenology.2012.04.017 VL - 78 SP - 1415 EP - 1428 ER - TY - CHAP A1 - Plöntzke, Julia A1 - Berg, Mascha A1 - Stötzel, Claudia A1 - Röblitz, Susanna T1 - A systems biology approach to bovine fertility and metabolism: Introduction of a glucose insulin model T2 - 15th International Symposium on Mathematical and Computational Biology, Rorkee, India Y1 - 2015 ER - TY - JOUR A1 - Boer, H. Marike T. A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Deuflhard, Peter A1 - Veerkamp, Roel F. A1 - Woelders, Henri T1 - A simple mathematical model of the bovine estrous cycle JF - Journal of Theoretical Biology Y1 - 2011 U6 - https://doi.org/10.1016/j.jtbi.2011.02.021 VL - 278 IS - 1 SP - 20 EP - 31 ER - TY - JOUR A1 - Röblitz, Susanna A1 - Stötzel, Claudia A1 - Deuflhard, Peter A1 - Jones, Hannah M. A1 - Azulay, David-Olivier A1 - van der Graaf, Piet A1 - Martin, Steven T1 - A mathematical model of the human menstrual cycle for the administration of GnRH analogues JF - Journal of Theoretical Biology Y1 - 2013 U6 - https://doi.org/10.1016/j.jtbi.2012.11.020 VL - 321 SP - 8 EP - 27 ER -