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This work deals with the reduction of a previously developed ODE model for the bovine estrous cycle. After applying a method for exploring the parameter space by Apri et al. (2012), we perform structure-based reduction steps and several system specific adaptations. Overall, the original model consisting of 15 ODEs and 60 parameters is reduced to a model of 10 odes and 38 parameters. The reduced model qualitatively reproduces the state trajectories of the original model.
In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.
Exploration of different wave patterns in a model of the bovine estrous cycle by Fourier analysis
(2016)
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.
To counteract the antagonistic relationship between milk yield and fertility in dairy cow, a
deeper understanding of the underlying biological mechanisms is required. For this purpose,
we study physiological networks related to reproduction and metabolism in dairy cows. We
interactively develop dynamic, mechanistic models by fitting the models to experimental data
and mechanistic knowledge. We have already developed models for potassium balance and
hormonal regulation of fertility in the dairy cow, which will briefly be reviewed here. The main
focus of this article is a glucose-insulin model currently developed by us. This model links the
bovine hormonal cycle and the potassium balance to glucose and thus to energy metabolism.
The models can be applied in scientific research, education, experimental planning, drug
development and production on farms.