TY - GEN A1 - Weiser, Martin A1 - Erdmann, Bodo A1 - Deuflhard, Peter T1 - On Efficiency and Accuracy in Cardioelectric Simulation N2 - Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy. T3 - ZIB-Report - 08-41 KW - elektrische Herzanregung KW - Diskretisierungsfehler KW - splitting KW - mass lumping KW - cardioelectric excitation KW - discretization error KW - splitting KW - mass lumping Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10934 SN - 1438-0064 ER - TY - GEN A1 - Reinecke, Isabel A1 - Deuflhard, Peter T1 - A Complex Mathematical Model of the Human Menstrual Cycle N2 - This paper aims at presenting the complex coupled network of the human menstrual cycle to the interested community. Beyond the presently popular smaller models, where important network components arise only as extremely simplified source terms, we add: the GnRH pulse generator in the hypothalamus, receptor binding, and the biosynthesis in the ovaries. Simulation and parameter identification are left to a forthcoming paper. T3 - ZIB-Report - 06-18 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9112 ER - TY - GEN A1 - Boer, H. Marike T. A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Deuflhard, Peter A1 - Veerkamp, Roel F. A1 - Woelders, Henri T1 - A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions N2 - 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. T3 - ZIB-Report - 10-06 KW - cow KW - reproduction KW - hormone patterns KW - ordinary differential equations KW - systems biology Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11682 SN - 1438-0064 ER - TY - GEN A1 - Röblitz, Susanna A1 - Stötzel, Claudia A1 - Deuflhard, Peter A1 - Jones, Hannah M. A1 - Azulay, David-Olivier A1 - van der Graaf, Piet A1 - Martin, Steven T1 - A mathematical model of the human menstrual cycle for the administration of GnRH analogues N2 - 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. T3 - ZIB-Report - 11-16 KW - human menstrual cycle KW - systems biology KW - mathematical modelling KW - GnRH analogues KW - differential equations Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12732 ER - TY - GEN A1 - Stötzel, Claudia A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - Advances in modelling of the bovine estrous cycle: Administration of PGF2alpha N2 - 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. T3 - ZIB-Report - 11-17 KW - cow KW - reproduction KW - hormone patterns KW - differential equations KW - systems biology Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12740 ER - TY - GEN A1 - Berg, Mascha A1 - Ritter, Julia A1 - Röblitz, Susanna T1 - A mathematical model for the Zinc response of young pigs N2 - In a number of studies the feeding of pharmacological levels of Zinc to weanling pigs was examined. The publications agree in the fact that the achieved performance increase of the pigs depends on the amount of Zinc as well as on the type of mineral complex used as feed additive. The results are based on measurements of the animals' body weight and the Zinc concentration in the blood within the first two weeks of the experiments. From the measurement values, conclusions are drawn about adequate Zinc doses, but a deeper understanding of the physiological processes that influence the Zinc distribution in the organism is still missing. In this report, we want to close this gap by using a systems biology approach. We present a small mathematical model that describes the organic feedback mechanisms with the help of differential equations. The simulation results not only match with measurement values, but also give insight into non-measurable processes, which will hopefully contribute to animal experiments being organized in a more selective and reduced way. T3 - ZIB-Report - 11-05 KW - systems biology KW - ordinary differential equations KW - feeding study KW - weanling pigs Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12191 ER - TY - GEN A1 - Plöntzke, Julia A1 - Berg, Mascha A1 - Olany, Amiya A1 - Leonhard-Marek, Sabine A1 - Müller, Kerstin-Elisabeth A1 - Röblitz, Susanna T1 - Modeling potassium balance in dairy cows N2 - 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. T3 - ZIB-Report - 13-09 KW - systems biology KW - differential equations KW - metabolism Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17749 SN - 1438-0064 ER - TY - GEN A1 - Bondouy, Manon A1 - Röblitz, Susanna T1 - Mathematical modeling of follicular development in bovine estrous cycles N2 - Normal follicular growth is a prerequisite for successful fertilization of dairy cows. However, submission rates have been decreasing during the last decades because animals are not ovulating at the planned time of mating or insemination. In this study we use a mathematical model to investigate mechanisms that lead to anestrus. This model is derived by coupling two previously published models: a small model for the development of multiple follicles (Smith et al., 2004), and a large estrous cycle model (St\"otzel et al., 2012). We first investigate the influence of synchronization protocols on the time-shift of ovulation. In a second scenario we simulate an extended period of anestrus as it typically occurs after calving. T3 - ZIB-Report - 12-26 KW - ordinary differential equations KW - systems biology KW - reproduction KW - dairy cows Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15585 SN - 1438-0064 ER -