TY - GEN 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: follicle development and endocrine interactions N2 - Bovine fertility is the subject of extensive research in animal sciences, especially because fertility of dairy cows has declined during the last decades. The regulation of estrus is controlled by the complex interplay of various organs and hormones. Mathematical modeling of the bovine estrous cycle could help in understanding the dynamics of this complex biological system. In this paper we present a mathematical model of the bovine estrous cycle that includes the processes of follicle and corpus luteum development and the key hormones that interact to control these processes. Focus in this paper is on development of the model, but also some simulation results are presented, showing that a set of equations and parameters is obtained that describes the system consistent with empirical knowledge. Even though the majority of the mechanisms that are included are only known qualitatively as stimulatory or inhibitory effects, the model surprisingly well features quantitative observations made in reality. This model of the bovine estrous cycle could be used as a basis for more elaborate models with the ability to study effects of external manipulations and genetic differences. T3 - ZIB-Report - 10-06 KW - cow KW - reproduction KW - hormone patterns KW - ordinary differential equations KW - systems biology Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11682 SN - 1438-0064 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 - 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 - CHAP A1 - Boer, H. Marike T. A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Woelders, Henri T1 - A differential equation model to investigate the dynamics of the bovine estrous cycle T2 - Advances in Systems Biology Y1 - 2012 U6 - https://doi.org/10.1007/978-1-4419-7210-1_35 VL - 736 SP - 597 EP - 606 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 - GEN 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 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. T3 - ZIB-Report - 16-02 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57039 SN - 1438-0064 ER -