FÜR INFORMATIONSTECHNIK
BERLIN

# BovCycle

## Mathematical modeling of the bovine estrous cycle

 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 involved mechanisms improves insight in the underlying mechanisms, and could thereby help to find causes of declined fertility in dairy cows. We aim at finding parameterization for individual cows, studying genetic differences, and simulating external effects e.g. food, medication, behaviour.

To put the system of the bovine estrous cycle into a mathematical model, our approach is to first identify the most important components and mechanisms involved. On this basis, we then construct a mostly regulatory model, and translate it - often with the help of Hill functions - to a system of differential equations. It represents the dynamic changes of the components over time, and comprises all dynamic relations of the abstracted physiological system. Our current mathematical model includes the processes of follicle and corpus luteum development and the key hormones that interact to control these processes. It generates successive estrous cycles with two or three waves of follicle growth per cycle.

Flowchart of the mechanisms

The physiological compartments that are the most crucial for the regulation of the estrous cycle are the ovaries, the uterus, the hypothalamus and the anterior pituitary, connected by the blood stream (see Boer et al. A simple mathematical model for the bovine estrous cycle). Throughout a cycle, a cohort of follicles start to grow and produce estradiol (E2). In each follicular wave a dominant follicle emerges that in the first one or two instances does not ovulate, but undergoes regression under influence of progesterone (P4). The dominant follicle that develops in the last wave becomes the ovulatory follicle.

Some results of the simulations

The current model contains 15 differential equations and 60 parameters. Even though the majority of the mechanisms that are included in the model are based on relations that in literature have only been described qualitatively (i.e. stimulation and inhibition), the output of the model is surprisingly well in line with empirical data.