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Lactating dairy cows require a particular composition of nutritional ingredients depending on their production status.
The optimal supply of energy and minerals in diet, one of them potassium, is indispensable for the prevention of disbalances like hypokalemia or hypoglycaemia.
Potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, and closely interacts with glucose and electrolyte metabolism, in which postpartum veterinary treatments frequently intervene.
We present a mechanistic, dynamic model for potassium balance together with a glucose insulin model in non-lactating and lactating dairy cows based on ordinary differential equations.
Parameter values were obtained from data of a clinical trial as well as from literature. To verify the mechanistic functioning of the model, we validate the model by comparing simulation outcomes with clinical study findings. Furthermore we perform numerical experiments and compare them with expected behaviour according to mechanistic knowledge. The results give insight into the dynamic behaviour of the network and open the way for further open questions and hypothesis to be tested.
The reproductive 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 ω-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.