@misc{RoeblitzStoetzelDeuflhardetal., author = {R{\"o}blitz, Susanna and St{\"o}tzel, Claudia and Deuflhard, Peter and Jones, Hannah M. and Azulay, David-Olivier and van der Graaf, Piet and Martin, Steven}, title = {A mathematical model of the human menstrual cycle for the administration of GnRH analogues}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12732}, number = {11-16}, abstract = {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.}, language = {en} } @misc{BoerStoetzelRoeblitzetal., author = {Boer, H. Marike T. and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Deuflhard, Peter and Veerkamp, Roel F. and Woelders, Henri}, title = {A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11682}, number = {10-06}, abstract = {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.}, language = {en} }