@misc{StoetzelPloentzkeRoeblitz, author = {St{\"o}tzel, Claudia and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Advances in modelling of the bovine estrous cycle: Administration of PGF2alpha}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12740}, number = {11-17}, abstract = {Our model of the bovine estrous cycle is a set of ordinary differential equations which generates hormone profiles of successive estrous cycles with several follicular waves per cycle. It describes the growth and decay of the follicles and the corpus luteum, as well as the change of the key substances over time. In this work we describe recent improvements of this model, including the introduction of new components, and elimination of time delays. We validate our model by showing that the simulations agree with observations from synchronization studies and with measured progesterone data after a single dose administration of synthetic prostaglandin F2alpha.}, language = {en} } @misc{PloentzkeBergOlanyetal., author = {Pl{\"o}ntzke, Julia and Berg, Mascha and Olany, Amiya and Leonhard-Marek, Sabine and M{\"u}ller, Kerstin-Elisabeth and R{\"o}blitz, Susanna}, title = {Modeling potassium balance in dairy cows}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17749}, abstract = {Potassium is fundamental for cell functioning including signal transduction, acid-base- and water-metabolism. Since diet of dairy cows is generally rich in potassium, hypokalemia was not in the focus of research for long time. Furthermore, hypokalemia was not frequently diagnosed because blood potassium content is difficult to measure. In recent years, measurement methods have been improved. Nowadays hypokalemia is increasingly diagnosed in cows with disorders such as abomasal displacement, ketosis or down cow syndrome, calling for intensified research on this topic. In this report we describe the development of a basic mechanistic, dynamic model of potassium balance based on ordinary differential and algebraic equations. Parameter values are obtained from data of a clinical trial in which potassium balance and the influence of therapeutic intervention in glucose and electrolyte metabolism on potassium balance in non-lactating dairy cows were studied. The model is formulated at a high abstraction level and includes information and hypotheses from literature. This work represents a first step towards the understanding and design of effective prophylactic feed additives and treatment strategies.}, language = {en} } @article{StoetzelPloentzkeHeuwieseretal.2012, author = {St{\"o}tzel, Claudia and Pl{\"o}ntzke, Julia and Heuwieser, Wolfgang and R{\"o}blitz, Susanna}, title = {Advances in modelling of the bovine estrous cycle: Synchronization with PGF2alpha}, series = {Theriogenology}, volume = {78}, journal = {Theriogenology}, doi = {10.1016/j.theriogenology.2012.04.017}, pages = {1415 -- 1428}, year = {2012}, language = {en} } @article{StoetzelEhrigBoeretal., author = {St{\"o}tzel, Claudia and Ehrig, Rainald and Boer, H. Marike T. and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Exploration of different wave patterns in a model of the bovine estrous cycle by Fourier analysis}, series = {BIOMAT - Proceedings of the 14th International Symposium on Mathematical and Computational Biology, Bedlewo, Poland}, journal = {BIOMAT - Proceedings of the 14th International Symposium on Mathematical and Computational Biology, Bedlewo, Poland}, abstract = {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.}, language = {en} } @article{BergPloentzkeLeonhardMareketal., author = {Berg, Mascha and Pl{\"o}ntzke, Julia and Leonhard-Marek, Sabine and M{\"u}ller, Kerstin-Elisabeth and R{\"o}blitz, Susanna}, title = {A dynamic model to simulate potassium balance in dairy cows}, series = {Journal of Dairy Science}, volume = {100}, journal = {Journal of Dairy Science}, number = {12}, doi = {10.3168/jds.2016-12443}, pages = {9799 -- 9814}, abstract = {High-performing dairy cows require a particular composition of nutritional ingredients, adapted to their individual requirements and depending on their production status. The optimal dimensioning of minerals in the diet, one being potassium, is indispensable for the prevention of imbalances. Potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, and it is closely related to glucose and electrolyte metabolism. In this paper, we present a dynamical model for potassium balance in lactating and nonlactating dairy cows based on ordinary differential equations. Parameter values were obtained from clinical trial data and from the literature. To verify the consistency of the model, we present simulation outcomes for 3 different scenarios: potassium balance in (1) nonlactating cows with varying feed intake, (2) nonlactating cows with varying potassium fraction in the diet, and (3) lactating cows with varying milk production levels. The results give insights into the short- and long-term potassium metabolism, providing an important step toward the understanding of the potassium network, the design of prophylactic feed additives, and possible treatment strategies.}, language = {en} } @inproceedings{SchaeferPloentzkeRoeblitz, author = {Sch{\"a}fer, Stefan and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Mathematical Modelling of Follicular Maturation in Cows and Women}, series = {49. Jahrestagung der Physiologie und Pathologie der Fortpflanzung und gleichzeitig 41. Veterin{\"a}r-Humanmedizinische Gemeinschaftstagung 2016, Leipzig.}, booktitle = {49. Jahrestagung der Physiologie und Pathologie der Fortpflanzung und gleichzeitig 41. Veterin{\"a}r-Humanmedizinische Gemeinschaftstagung 2016, Leipzig.}, language = {en} } @inproceedings{LangePloentzkeSchaeferetal., author = {Lange, Alexander and Pl{\"o}ntzke, Julia and Sch{\"a}fer, Stefan and R{\"o}blitz, Susanna}, title = {Follicular maturation in cows: mathematical models and data}, series = {10. European Conference on Mathematical and Theoretical Biology}, booktitle = {10. European Conference on Mathematical and Theoretical Biology}, language = {en} } @misc{OmariPloentzkeBergetal., author = {Omari, Mohamed and Pl{\"o}ntzke, Julia and Berg, Mascha and R{\"o}blitz, Susanna}, title = {Modelling of glucose-insulin metabolism and its effect on the estrous cycle in bovine}, series = {Annual Meeting of the Population Approach Group in Europe}, journal = {Annual Meeting of the Population Approach Group in Europe}, language = {en} } @misc{LangeSchwiegerPloentzkeetal., author = {Lange, Alexander and Schwieger, Robert and Pl{\"o}ntzke, Julia and Sch{\"a}fer, Stefan and R{\"o}blitz, Susanna}, title = {Follicular competition: the selection of dominant follicles as a synergistic effect}, issn = {1438-0064}, doi = {https://doi.org/10.1007/s00285-018-1284-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63863}, abstract = {The estrous cycle of mono-ovulatory species such as cows or humans, is known to show two or more waves of follicular growth and decline between two successive ovulations. Within each wave, there is one dominant follicle escorted by subordinate follicles of varying number. Under the surge of the luteinizing hormone a growing dominant follicle ovulates. Rarely the number of ovulating follicles exceeds one. In the biological literature, the change of hormonal concentrations and individually varying numbers of follicular receptors are made responsible for the selection of exactly one dominant follicle, yet a clear cause has not been identified. In this paper, we suggest a synergistic explanation based on competition, formulated by a parsimoniously defined system of ordinary differential equations (ODEs) that quantifies the time evolution of multiple follicles and their competitive interaction during one wave. Not discriminating between follicles, growth and decline are given by fixed rates. Competition is introduced via a growth-suppressing term, equally supported by all follicles. We prove that the number of dominant follicles is determined exclusively by the ratio of follicular growth and competition. This number turns out to be independent of the number of subordinate follicles. The asymptotic behavior of the corresponding dynamical system is investigated rigorously, where we demonstrate that the omega-limit set only contains fixed points. When also including follicular decline, our ODEs perfectly resemble ultrasound data of bovine follicles. Implications for the involved but not explicitly modeled hormones are discussed.}, language = {en} } @misc{StoetzelEhrigBoeretal., author = {St{\"o}tzel, Claudia and Ehrig, Rainald and Boer, H. Marike T. and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Exploration of different wave patterns in a model of the bovine estrous cycle by Fourier analysis}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57039}, abstract = {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.}, language = {en} }