TY - GEN A1 - Dierkes, Thomas A1 - Wade, Moritz A1 - Nowak, Ulrich A1 - Röblitz, Susanna T1 - BioPARKIN - Biology-related Parameter Identification in Large Kinetic Networks N2 - Modelling, parameter identification, and simulation play an important rôle in Systems Biology. In recent years, various software packages have been established for scientific use in both licencing types, open source as well as commercial. Many of these codes are based on inefficient and mathematically outdated algorithms. By introducing the package BioPARKIN recently developed at ZIB, we want to improve this situation significantly. The development of the software BioPARKIN involves long standing mathematical ideas that, however, have not yet entered the field of Systems Biology, as well as new ideas and tools that are particularly important for the analysis of the dynamics of biological networks. BioPARKIN originates from the package PARKIN, written by P.Deuflhard and U.Nowak, that has been applied successfully for parameter identification in physical chemistry for many years. T3 - ZIB-Report - 11-15 KW - systems biology KW - ordinary differential equations KW - sensitivity analysis KW - parameter identification KW - affine invariant Gauss-Newton algorithm KW - numerical library KW - graphical user interface Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12706 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 - JOUR A1 - Dierkes, Thomas A1 - Röblitz, Susanna A1 - Wade, Moritz A1 - Deuflhard, Peter T1 - Parameter identification in large kinetic networks with BioPARKIN JF - CoRR - Computing Research Repository - arXiv.org Y1 - 2013 UR - arxiv.org/abs/1303.4928v2 VL - abs/1303.4928 ER - TY - JOUR 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 JF - Journal of Theoretical Biology Y1 - 2013 U6 - https://doi.org/10.1016/j.jtbi.2012.11.020 VL - 321 SP - 8 EP - 27 ER - TY - THES A1 - Brüggemann, Jo Andrea T1 - Numerical Modelling of the human menstrual cycle applied to ovulation prediction N2 - In this Master Thesis, the modelling process and the required biological background to adequately describe the hormonal dynamics of the human menstrual cycle are presented. The aim of this Master thesis project is to establish a mathematical routine that enables prediction of potentially fertile time windows. A system of four parameter dependent ordinary differential equations coupled with two algebraic equations is built, accounting for the main kinetic drivers of the human menstrual cycle { basal body temperature, estradiol, progesterone, luteinizing and follicle stimulating hormone. The key parameters are identifed using a nonlinear least squares approach to match the model to individual data. Aiming to solve the optimality problem arising, the Newton and Gauss-Newton method are examined and their local convergence theory is outlined. By the nature of the application, a globalised Gauss-Newton method seems more convenient. An adaptive trust region approach to determine the step lengths is chosen, which together with an linearly-implicit Euler extrapolation for the given differential algebraic equation system makes parameter estimation possible. The simulation results are discussed particularly in view of limitations and problems arising through the modelling approach. Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-46168 ER - TY - THES A1 - Stötzel, Claudia T1 - Numerical and Discrete Modeling of Reproductive Endocrinological Networks N2 - This thesis deals with the mathematical modeling of endocrinological networks that are underlying the female hormone cycle. These networks consist of a variety of biological mechanisms in different parts of the organism. Their interaction leads to periodic changes of various substances that are necessary for reproduction. In every cycle, hormones are secreted from the hypothalamic-pituitary-gonadal axis into the bloodstream, where they distribute and influence several functions in the body. Their most important task in reproduction is to regulate processes in the ovaries, where follicles and corpus luteum develop. These produce steroids that are released into the blood and from therein regulate the processes in the hypothalamic-pituitary-gonadal axis. The hormonal cycle is thus a result of a large feedback loop, whose self-regulation is a complex interplay of multiple components. For the modeling of these processes, a high abstraction level is required, which can be realized by various modeling approaches. In this work, some of these approaches are implemented. The first step in all approaches is the representation of the most important mechanisms in a flowchart. In the next step, this can be implemented as a system of ordinary differential equations using Hill functions, as a piecewise defined affine differential equation model, or directly as a purely regulatory model. Using this approach, a differential equation model for the hormonal cycle of cows is developed. This is compared with a more advanced model of the menstrual cycle in humans. Both models are validated by comparing simulations with measured values, and by studying external influences such as drug administration. For the example of the bovine estrous cycle, continuous analysis methods are used to investigate stability, follicular wave patterns, and robustness with respect to parameter perturbations. Furthermore, the model is substantially reduced while preserving the main simulation results. To take a look at alternative modeling approaches, corresponding discrete models are derived, exemplified for the bovine model. For a piecewise affine version of the model, parameter constraints for the continuous model are calculated. Stability is analyzed globally for a purely discrete model. In addition, core discrete models are derived, which retain the dynamic properties of the original model. Y1 - 2014 ER - TY - GEN A1 - Dierkes, Thomas T1 - Construction of ODE systems from time series data by a highly flexible modelling approach N2 - In this paper, a down-to-earth approach to purely data-based modelling of unknown dynamical systems is presented. Starting from a classical, explicit ODE formulation y=f(t,y) of a dynamical system, a method determining the unknown right-hand side f(t,y) from some trajectory data y_k(t_j), possibly very sparse, is given. As illustrative examples, a semi-standard predator-prey model is reconstructed from a data set describing the population numbers of hares and lynxes over a period of twenty years [1], and a simple damped pendulum system with a highly non-linear right-hand side is recovered from some artificial but very sparse data [2]. T3 - ZIB-Report - 15-59 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56768 SN - 1438-0064 ER - TY - JOUR A1 - Dierkes, Thomas T1 - Construction of ODE systems from time series data by a highly flexible modelling approach JF - ArXiv e-prints N2 - In this paper, a down-to-earth approach to purely data-based modelling of unknown dynamical systems is presented. Starting from a classical, explicit ODE formulation y=f(t,y) of a dynamical system, a method determining the unknown right-hand side f(t,y) from some trajectory data y_k(t_j), possibly very sparse, is given. As illustrative examples, a semi-standard predator-prey model is reconstructed from a data set describing the population numbers of hares and lynxes over a period of twenty years, and a simple damped pendulum system with a highly non-linear right-hand side is recovered from some artificial but very sparse data. Y1 - 2015 VL - math.NA 1512.03357 ER - TY - JOUR A1 - Fischer-Holzhausen, Sophie A1 - Röblitz, Susanna T1 - Hormonal regulation of ovarian follicle growth in humans: Model-based exploration of cycle variability and parameter sensitivities JF - Journal of Theoretical Biology N2 - We present a modelling and simulation framework for the dynamics of ovarian follicles and key hormones along the hypothalamic-pituitary-gonadal axis throughout consecutive human menstrual cycles. All simulation results (hormone concentrations and ovarian follicle sizes) are in biological units and can easily be compared to clinical data. The model takes into account variability in follicles' response to stimulating hormones, which introduces variability between cycles. The growth of ovarian follicles in waves is an emergent property in our model simulations and further supports the hypothesis that follicular waves are also present in humans. We use Approximate Bayesian Computation and cluster analysis to construct a population of virtual subjects and to study parameter distributions and sensitivities. The model can be used to compare and optimize treatment protocols for ovarian hyperstimulation, thus potentially forming the integral part of a clinical decision support system in reproductive endocrinology. Y1 - 2022 U6 - https://doi.org/https://doi.org/10.1016/j.jtbi.2022.111150 ER - TY - JOUR A1 - Fischer-Holzhausen, Sophie A1 - Röblitz, Susanna T1 - Mathematical modelling of follicular growth and ovarian stimulation JF - Current Opinion in Endocrine and Metabolic Research Y1 - 2022 U6 - https://doi.org/https://doi.org/10.1016/j.coemr.2022.100385 ER - TY - JOUR A1 - Krüger, Tillmann A1 - Leeners, Brigitte A1 - Tronci, Enrico A1 - Mancini, Toni A1 - Ille, Fabian A1 - Egli, Marcel A1 - Engler, Harald A1 - Röblitz, Susanna A1 - Frieling, Helge A1 - Sinke, Christopher A1 - Jahn, Kirsten T1 - The androgen system across the menstrual cycle: Hormonal, (epi-)genetic and psychometric alterations JF - Physiology and Behavior Y1 - 2022 U6 - https://doi.org/https://doi.org/10.1016/j.physbeh.2022.114034 ER -