TY - THES A1 - Moualeu-Ngangue, Dany Pascal T1 - A Mathematical Tuberculosis Model in Cameroon N2 - This thesis firstly presents a nonlinear extended deterministic model for the transmission dynamics of tuberculosis, based on realistic assumptions and data collected from the WHO. This model enables a comprehensive qualitative analysis of various aspects in the outbreak and control of tuberculosis in Sub-Saharan Africa countries and successfully reproduces the epidemiology of tuberculosis in Cameroon for the past (from 1994-2010). Some particular properties of the model and its solution have been presented using the comparison theorem applied to the theory of differential equations. The existence and the stability of a disease free equilibrium has been discussed using the Perron-Frobenius theorem and Metzler stable matrices. Furthermore, we computed the basic reproduction number, i.e. the number of cases that one case generates on average over the course of its infectious period. Rigorous qualitative analysis of the model reveals that, in contrast to the model without reinfections, the full model with reinfection exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the basic reproduction ratio (R0), is less than unity. The global stability of the disease-free equilibrium has been discussed using the concepts of Lyapunov stability and bifurcation theory. With the help of a sensitivity analysis using data of Cameroon, we identified the relevant parameters which play a key role for the transmission and the control of the disease. This was possible applying sophisticated numerical methods (POEM) developed at ZIB. Using advanced approaches for optimal control considering the costs for chemoprophylaxis, treatment and educational campaigns should provide a framework for designing realistic cost effective strategies with different intervention methods. The forward-backward sweep method has been used to solve the numerical optimal control problem. The numerical result of the optimal control problem reveals that combined effort in education and chemoprophylaxis may lead to a reduction of 80\% in the number of infected people in 10 years. The mathematical and numerical approaches developed in this thesis could be similarly applied in many other Sub-Saharan countries where TB is a public health problem. Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:188-fudissthesis000000095327-7 UR - http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000095327 ER - TY - GEN A1 - Moualeu-Ngangue, Dany Pascal A1 - Röblitz, Susanna A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Parameter Identification for a Tuberculosis Model in Cameroon N2 - A deterministic model of tuberculosis in sub-Saharan Africa in general and Cameroon in particular including lack of access to the treatment and weak diagnose capacity is designed and analyzed with respect to its transmission dynamics. The model includes both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and most sensitive parameters of the model are identified using a state-of-the-art Gauss-Newton Method. In particular, parameters representing the proportion of individuals having access to medical facilities have a large impact on the dynamics of the disease. It has been shown that an increase of these parameter values over the time can significantly reduce the disease burden in the population within the next 15 years. T3 - ZIB-Report - 13-72 KW - Tuberculosis, parameter identification, sensitivity analysis, Gauss-Newton method, Nonlinear dynamical systems. Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43087 SN - 1438-0064 ER - TY - GEN A1 - Moualeu-Ngangue, Dany Pascal A1 - Weiser, Martin A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Optimal control for a tuberculosis model with undetected cases in Cameroon N2 - This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 % in 10 years T3 - ZIB-Report - 13-73 KW - Tuberculosis KW - Optimal control KW - Nonlinear dynamical systems Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43142 SN - 1438-0064 ER - TY - GEN A1 - Meisel, Kristin A1 - Röblitz, Susanna T1 - Mathematische Modellierung der Knochenremodellierung N2 - Knochenremodellierung beinhaltet den Auf- und Abbau der Knochenmasse durch die verschiedenen Knochenzellen und findet fast überall, auch am Skelett Erwachsener, statt. Für die Erneuerung der Knochensubstanz sind die Osteoblasten zuständig. Sie ersetzen exakt die Menge der Knochenmasse, welche zuvor durch Osteoklasten abgebaut wurde. Störungen dieses, durch viele Faktoren beeinflussten Prozesses führen zu pathologischen Veränderungen, beispielsweise zu Osteoporose oder Arthritis. Auf der Grundlage analysierter publizierter Modelle wurde ein Modell entwickelt, welches den Einfluss einiger dieser Faktoren realistisch abbildet. Auf diese Weise kann die Wirkung von basalem PTH, des RANKL-OPG-Systems ( RANKL: Receptor activator of nuclear factor kappa-B ligand, OPG: Osteoprotegerin) und des Estradiols auf den Knochenstoffwechsel am vorgestellten System untersucht werden. Außerdem wurde durch Estradiolmangel hervorgerufene Osteoporose und der kurative Effekt von synthetischen Medikamenten wie Estradiol oder intermittierend verabreichtem PTH modelliert. Mit der Parameterschätzung anhand des Gauß-Newton-Verfahrens wird des Weiteren eine Methode vorgestellt, die es ermöglicht, mathematische Modelle bestmöglich durch Variation der Parameterwerte an experimentelle Daten anzupassen. Das am Zuse-Institut Berlin entwickelte Softwarepaket POEM wendet diesen Algorithmus an und wird ebenfalls erläutert. T3 - ZIB-Report - 13-41 Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42010 SN - 1438-0064 ER - TY - JOUR A1 - Plöntzke, Julia A1 - Berg, Mascha A1 - Ehrig, Rainald A1 - Leonhard-Marek, Sabine A1 - Müller, Kerstin-Elisabeth A1 - Röblitz, Susanna T1 - Model Based Exploration of Hypokalemia in Dairy Cows JF - Scientific Reports N2 - Hypokalemia, characterized by too low serum potassium levels, is a severe mineral disorder which can be life threatening. It is increasingly diagnosed in veterinarian healthcare and a topic of ongoing research. In this paper, we explore the different originating conditions of hypokalemia: reduced potassium intake, increased excretion, acid-base disturbances, or increased insulin, by using a dynamic mathematical model for potassium balance in non-lactating and lactating cows. Simulations are compared with literature. The results give insights into the network dynamics and point to scenarios on which experimental effort should be focused. Application of mathematical models can assist in experimental planning as well as the reduction, refinement and replacement of animal experiments. Y1 - 2022 U6 - https://doi.org/10.1038/s41598-022-22596-0 VL - 12, 19781 ER - TY - JOUR A1 - Schwieger, Robert A1 - Siebert, Heike A1 - Röblitz, Susanna T1 - Correspondence of Trap Spaces in Different Models of Bioregulatory Networks JF - SIAM Journal on Applied Dynamical Systems N2 - Mathematical models for bioregulatory networks can be based on different formalisms, depending on the quality of available data and the research question to be answered. Discrete boolean models can be constructed based on qualitative data, which are frequently available. On the other hand, continuous models in terms of ordinary differential equations (ODEs) can incorporate time-series data and give more detailed insight into the dynamics of the underlying system. A few years ago, a method based on multivariate polynomial interpolation and Hill functions has been developed for an automatic conversion of boolean models to systems of ordinary differential equations. This method is frequently used by modellers in systems biology today, but there are only a few results available about the conservation of mathematical structures and properties across the formalisms. Here, we consider subsets of the phase space where some components stay fixed, called trap spaces, and demonstrate how boolean trap spaces can be linked to invariant sets in the continuous state space. This knowledge is of practical relevance since finding trap spaces in the boolean setting, which is relatively easy, allows for the construction of reduced ODE models. Y1 - 2018 U6 - https://doi.org/https://doi.org/10.1137/17M1155302 VL - 17 IS - 2 SP - 1742 EP - 1765 ER - TY - JOUR A1 - Lange, Alexander A1 - Schwieger, Robert A1 - Plöntzke, Julia A1 - Schäfer, Stefan A1 - Röblitz, Susanna T1 - Follicular competition in cows: the selection of dominant follicles as a synergistic effect JF - Journal of Mathematical Biology N2 - 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. Y1 - 2018 U6 - https://doi.org/https://doi.org/10.1007/s00285-018-1284-0 ER - TY - CHAP A1 - Mancini, Toni A1 - Mari, Federico A1 - Massini, Annalisa A1 - Melatti, Igor A1 - Salvo, Ivano A1 - Sinisi, Stefano A1 - Tronci, Enrico A1 - Ehrig, Rainald A1 - Röblitz, Susanna A1 - Leeners, Brigitte T1 - Computing Personalised Treatments through In Silico Clinical Trials. A Case Study on Downregulation in Assisted Reproduction T2 - Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion, Workshop of the Federated Logic Conference 2018 (FLoC 2018), Oxford N2 - In Silico Clinical Trials (ISCT), i.e., clinical experimental campaigns carried out by means of computer simulations, hold the promise to decrease time and cost for the safety and efficacy assessment of pharmacological treatments, reduce the need for animal and human testing, and enable precision medicine. In this paper we present a case study aiming at quantifying, by means of a multi-arm ISCT supervised by intelligent search, the potential impact of precision medicine approaches on a real pharmacological treatment, namely the downregulation phase of a complex clinical protocol for assisted reproduction. Y1 - 2018 U6 - https://doi.org/10.29007/g864 SP - 1 EP - 16 ER - TY - JOUR A1 - Moewis, Philippe A1 - Boeth, Heide A1 - Heller, Markus O. A1 - Yntema, Caroline A1 - Jung, Tobias A1 - Doyscher, Ralf A1 - Ehrig, Rainald A1 - Zhong, Yanlin A1 - Taylor, William R. T1 - Towards understanding knee joint laxity: Errors in non-invasive assessment of joint rotation can be corrected JF - Medical Engineering and Physics Y1 - 2014 U6 - https://doi.org/doi.org/10.1016/j.medengphy.2014.03.017 VL - 36 IS - 7 SP - 889 EP - 895 ER - TY - GEN A1 - Winkelmann, Stefanie T1 - Markov Control with Rare State Observation: Average Optimality N2 - This paper investigates the criterion of long-term average costs for a Markov decision process (MDP) which is not permanently observable. Each observation of the process produces a fixed amount of \textit{information costs} which enter the considered performance criterion and preclude from arbitrarily frequent state testing. Choosing the \textit{rare} observation times is part of the control procedure. In contrast to the theory of partially observable Markov decision processes, we consider an arbitrary continuous-time Markov process on a finite state space without further restrictions on the dynamics or the type of interaction. Based on the original Markov control theory, we redefine the control model and the average cost criterion for the setting of information costs. We analyze the constant of average costs for the case of ergodic dynamics and present an optimality equation which characterizes the optimal choice of control actions and observation times. For this purpose, we construct an equivalent freely observable MDP and translate the well-known results from the original theory to the new setting. T3 - ZIB-Report - 16-59 KW - Markov decision process KW - partial observability KW - average optimality KW - information costs Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60981 SN - 1438-0064 ER - TY - GEN A1 - Klebanov, Ilja A1 - Sikorski, Alexander A1 - Schütte, Christof A1 - Röblitz, Susanna T1 - Empirical Bayes Methods, Reference Priors, Cross Entropy and the EM Algorithm N2 - When estimating a probability density within the empirical Bayes framework, the non-parametric maximum likelihood estimate (NPMLE) usually tends to overfit the data. This issue is usually taken care of by regularization - a penalization term is subtracted from the marginal log-likelihood before the maximization step, so that the estimate favors smooth solutions, resulting in the so-called maximum penalized likelihood estimation (MPLE). The majority of penalizations currently in use are rather arbitrary brute-force solutions, which lack invariance under transformation of the parameters(reparametrization) and measurements. This contradicts the principle that, if the underlying model has several equivalent formulations, the methods of inductive inference should lead to consistent results. Motivated by this principle and using an information-theoretic point of view, we suggest an entropy-based penalization term that guarantees this kind of invariance. The resulting density estimate can be seen as a generalization of reference priors. Using the reference prior as a hyperprior, on the other hand, is argued to be a poor choice for regularization. We also present an insightful connection between the NPMLE, the cross entropy and the principle of minimum discrimination information suggesting another method of inference that contains the doubly-smoothed maximum likelihood estimation as a special case. T3 - ZIB-Report - 16-56 KW - parameter estimation KW - Bayesian inference KW - Bayesian hierarchical modeling KW - hyperparameter KW - hyperprior KW - EM algorithm KW - NPMLE KW - MPLE KW - DS-MLE KW - principle of maximum entropy KW - cross entropy KW - minimum discrimination information KW - reference prior KW - Jeffreys prior Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61230 SN - 1438-0064 ER - TY - GEN A1 - Klebanov, Ilja A1 - Sikorski, Alexander A1 - Schütte, Christof A1 - Röblitz, Susanna T1 - Empirical Bayes Methods for Prior Estimation in Systems Medicine N2 - One of the main goals of mathematical modelling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Therefore, before applying Bayes’ rule separately to the data of each patient (which is typically performed using a non-informative prior), it is meaningful to use empirical Bayes methods in order to construct an informative prior from all available data. We compare the performance of four priors - a non-informative prior and priors chosen by nonparametric maximum likelihood estimation (NPMLE), by maximum penalized lilelihood estimation (MPLE) and by doubly-smoothed maximum likelihood estimation (DS-MLE) - by applying them to a low-dimensional parameter estimation problem in a toy model as well as to a high-dimensional ODE model of the human menstrual cycle, which represents a typical example from systems biology modelling. T3 - ZIB-Report - 16-57 KW - Parameter estimation KW - Bayesian inference KW - Bayesian hierarchical modelling KW - NPMLE KW - MPLE KW - DS-MLE KW - EM algorithm KW - Jeffreys prior KW - reference prior KW - hyperparameter KW - hyperprior KW - principle of maximum entropy Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61307 SN - 1438-0064 ER - TY - CHAP A1 - Lange, Alexander A1 - Plöntzke, Julia A1 - Schäfer, Stefan A1 - Röblitz, Susanna T1 - Follicular maturation in cows: mathematical models and data T2 - 10. European Conference on Mathematical and Theoretical Biology Y1 - 2016 ER - TY - GEN A1 - Omari, Mohamed A1 - Plöntzke, Julia A1 - Berg, Mascha A1 - Röblitz, Susanna T1 - Modelling of glucose-insulin metabolism and its effect on the estrous cycle in bovine T2 - Annual Meeting of the Population Approach Group in Europe Y1 - 2016 ER - TY - JOUR A1 - Winkelmann, Stefanie T1 - Markov Control with Rare State Observation: Average Optimality JF - Markov Processes and Related Fields N2 - This paper investigates the criterion of long-term average costs for a Markov decision process (MDP) which is not permanently observable. Each observation of the process produces a fixed amount of information costs which enter the considered performance criterion and preclude from arbitrarily frequent state testing. Choosing the rare observation times is part of the control procedure. In contrast to the theory of partially observable Markov decision processes, we consider an arbitrary continuous-time Markov process on a finite state space without further restrictions on the dynamics or the type of interaction. Based on the original Markov control theory, we redefine the control model and the average cost criterion for the setting of information costs. We analyze the constant of average costs for the case of ergodic dynamics and present an optimality equation which characterizes the optimal choice of control actions and observation times. For this purpose, we construct an equivalent freely observable MDP and translate the well-known results from the original theory to the new setting. Y1 - 2017 VL - 23 SP - 1 EP - 34 ER - TY - JOUR A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - The Spatiotemporal Master Equation: Approximation of Reaction-Diffusion Dynamics via Markov State Modeling JF - Journal of Chemical Physics N2 - Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest.We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models (MSM) as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by Galerkin projection methods is presented. Y1 - 2016 U6 - https://doi.org/10.1063/1.4971163 VL - 145 IS - 21 ER - TY - JOUR A1 - Duwal, Sulav A1 - Winkelmann, Stefanie A1 - Schütte, Christof A1 - von Kleist, Max T1 - Optimal Treatment Strategies in the Context of 'Treatment for Prevention' against HIV/1 in Resource-Poor Settings JF - PloS Computational Biology N2 - An estimated 2.7 million new HIV-1 infections occurred in 2010. `Treatment-for-prevention’ may strongly prevent HIV-1 transmission. The basic idea is that immediate treatment initiation rapidly decreases virus burden, which reduces the number of transmittable viruses and thereby the probability of infection. However, HIV inevitably develops drug resistance, which leads to virus rebound and nullifies the effect of `treatment-for-prevention’ for the time it remains unrecognized. While timely conducted treatment changes may avert periods of viral rebound, necessary treatment options and diagnostics may be lacking in resource-constrained settings. Within this work, we provide a mathematical platform for comparing different treatment paradigms that can be applied to many medical phenomena. We use this platform to optimize two distinct approaches for the treatment of HIV-1: (i) a diagnostic-guided treatment strategy, based on infrequent and patient-specific diagnostic schedules and (ii) a pro-active strategy that allows treatment adaptation prior to diagnostic ascertainment. Both strategies are compared to current clinical protocols (standard of care and the HPTN052 protocol) in terms of patient health, economic means and reduction in HIV-1 onward transmission exemplarily for South Africa. All therapeutic strategies are assessed using a coarse-grained stochastic model of within-host HIV dynamics and pseudo-codes for solving the respective optimal control problems are provided. Our mathematical model suggests that both optimal strategies (i)-(ii) perform better than the current clinical protocols and no treatment in terms of economic means, life prolongation and reduction of HIV-transmission. The optimal diagnostic-guided strategy suggests rare diagnostics and performs similar to the optimal pro-active strategy. Our results suggest that ‘treatment-for-prevention’ may be further improved using either of the two analyzed treatment paradigms. Y1 - 2015 U6 - https://doi.org/10.1371/journal.pcbi.1004200 VL - 11 IS - 4 ER - TY - JOUR A1 - Haack, Fiete A1 - Röblitz, Susanna A1 - Scharkoi, Olga A1 - Schmidt, Burkhard A1 - Weber, Marcus T1 - Adaptive Spectral Clustering for Conformation Analysis JF - AIP Conference Proceedings Y1 - 2010 UR - http://link.aip.org/link/?APC/1281/1585/1 U6 - https://doi.org/10.1063/1.3498116 VL - 1281 IS - 1 SP - 1585 EP - 1588 PB - AIP ER - TY - JOUR A1 - Kube, Susanna A1 - Weber, Marcus T1 - A Coarse Graining Method for the Identification of Transition rates between Molecular Conformations JF - Journal of Chemical Physics Y1 - 2007 U6 - https://doi.org/10.1063/1.2404953 VL - 126 IS - 2 ER - TY - JOUR A1 - Lasser, Caroline A1 - Röblitz, Susanna T1 - Computing expectation values for molecular quantum dynamics JF - SIAM Journal on Scientific Computing Y1 - 2010 U6 - https://doi.org//10.1137/090770461 VL - 32 IS - 3 SP - 1465 EP - 1483 ER - TY - CHAP A1 - Weber, Marcus A1 - Kube, Susanna T1 - Robust Perron Cluster Analysis for Various Applications in Computational Life Science T2 - Computational Life Sciences Y1 - 2005 SP - 57 EP - 66 ER - TY - CHAP A1 - Kube, Susanna A1 - Weber, Marcus T1 - Computation of equilibrium densities in metastable dynamical systems by domain decomposition T2 - Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008 Y1 - 2008 VL - 1048 SP - 339 EP - 342 PB - AIP Conference Proceedings ER - TY - THES A1 - Reinecke, Isabel T1 - Mathematical modeling and simulation of the female menstrual cycle Y1 - 2009 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 - JOUR A1 - Stötzel, Claudia A1 - Plöntzke, Julia A1 - Heuwieser, Wolfgang A1 - Röblitz, Susanna T1 - Advances in modelling of the bovine estrous cycle: Synchronization with PGF2alpha JF - Theriogenology Y1 - 2012 U6 - https://doi.org/10.1016/j.theriogenology.2012.04.017 VL - 78 SP - 1415 EP - 1428 ER - TY - JOUR A1 - Boeth, Heide A1 - Duda, Georg A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Doyscher, Ralf A1 - Jung, Tobias A1 - Moewis, Philippe A1 - Scheffler, Sven A1 - Taylor, William R. T1 - Anterior cruciate ligament-deficient patients with passive knee joint laxity have a decreased range of anterior-posterior motion during active movements JF - The American Journal of Sports Medicine Y1 - 2013 U6 - https://doi.org/10.1177/0363546513480465 VL - 41 IS - 5 SP - 1051 EP - 7 ER - TY - CHAP A1 - Kube, Susanna A1 - Weber, Marcus T1 - Preserving the Markov Property of Reduced Reversible Markov Chains T2 - Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008 Y1 - 2008 VL - 1048 SP - 593 EP - 596 ER - TY - JOUR A1 - Weber, Marcus A1 - Kube, Susanna A1 - Walter, Lionel A1 - Deuflhard, Peter T1 - Stable Computation of Probability Densities of Metastable Dynamical Systems JF - SIAM J. Multiscale Model. Simul. Y1 - 2007 VL - 6 IS - 2 SP - 396 EP - 416 ER - TY - JOUR A1 - Kratzenstein, Stefan A1 - Kornaropoulos, Evgenios I. A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Pöpplau, Berry M. A1 - Taylor, William R. T1 - Effective marker placement for functional identification of the centre of rotation at the hip JF - Gait & Posture Y1 - 2012 U6 - https://doi.org/http://dx.doi.org/10.1016/j.gaitpost.2012.04.011 VL - 36 IS - 3 SP - 482 EP - 486 ER - TY - CHAP A1 - Taylor, William R. A1 - Fröhlich, Annika A1 - Buttgereit, Frank A1 - Ehrig, Rainald A1 - Witaschek, Tom A1 - Duda, Georg ED - Kersting, Uwe ED - Morlock, Michael ED - Jirova-Enzmann, Daniela ED - Dremstrup, Kim T1 - Metacarpophalangeal joint stiffness is reduced in patients affected by rheumatoid arthritis after glucocorticoid medication T2 - Proceedings of the ESM-2012, Aalborg Y1 - 2012 SP - 39 PB - Department of Health Science and Technology, Aalborg University ER - TY - JOUR A1 - Kube, Susanna A1 - Lasser, Caroline A1 - Weber, Marcus T1 - Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics JF - Journal of Computational Physics Y1 - 2008 U6 - https://doi.org/10.1016/j.jcp.2008.11.016 VL - 228 IS - 6 SP - 1947 EP - 1962 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Röblitz, Susanna A1 - Stötzel, Claudia T1 - Mathematical Systems Biology at Zuse Institute Berlin (ZIB) JF - BioTOPics - Journal of Biotechnology in Berlin-Brandenburg Y1 - 2010 VL - 39 ER - TY - JOUR A1 - Röblitz, Susanna A1 - Weber, Marcus T1 - Fuzzy Spectral Clustering by PCCA+ JF - Classification and Clustering: Models, Software and Applications Y1 - 2009 UR - http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Report&year=2009&number=26 IS - WIAS Report No. 26 SP - 73 EP - 79 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 - Knöchel, Jane T1 - Mathematische Modellierung metabolischer Einflussfaktoren auf den Milchkuhzyklus N2 - In den letzten Jahren ist die reproduktive Leistung von Milchkühen parallel zur steigenden Milchleistung drastisch gesunken. Um die zu Grunde liegenden biologischen Mechanismen besser zu verstehen, wurde in dieser Arbeit eine Modellerweiterung des vorhandenen Modells von Stötzel et al. (2011) um metabolische Einflussfaktoren angestrebt. Hierfür wurde zuerst aus veröffentlichten, experimentell gewonnen Erkenntnissen herausgearbeitet, wie die metabolischen Faktoren auf das periodische Zyklusverfahren der Milchkuh Einfluss nehmen. Daraus wurde ersichtlich, dass Glukose, Insulin und IGF-I die wichtigsten metabolischen Faktoren sind, aber lediglich IGF-I als dynamische Größe in das Modell eingeht. Zur Validierung des erweiterten Modells, wurden im Rahmen dieser Arbeit Szenarien aus der Literatur entwickelt, welche eine negative Energiebilanz oder den Effekt von Diätrestriktionen auf den Milchkuhzyklus simulieren sollten. Ferner wurden Messdaten für IGF, E2 und P4 von Kawashima et al. (2007) und Cerri et al. (2011) bereit gestellt. Das erweiterte Modell umfasst lediglich 8 Parameter mehr als das Ursprungsmodell, wobei gezeigt werden konnte, dass weder die Bedingung für die Lösbarkeit noch die Stabilität in den Anfangswerten eingebüßt wurde. Die Modellkurven konnten mittels des NLSCON erfolgreich an die bereitgestellten Messdaten für IGF, E2 und P4 angepasst werden. Anhand der Ergebnisse aus den Szenarien ließ sich zeigen, dass es teilweise gelingt über die metabolischen Einflussfaktoren eine negative Energiebilanz für unterernährte Kühe darzustellen. Die Rückführung in das periodische Zyklusverhalten verlief jedoch im Vergleich zu in vivo Beobachtungen zu schnell ab. Eine mögliche Erklärung hierfür ist ein zu geringer Einfluss von IGF-I auf das Modell. Darüber hinaus kam es trotz (stark) reduzierter LH-Konzentration zur Ovulation. Auf diesen Erkenntnissen aufbauend könnte in Zukunft die Follikelmodellierung modifiziert oder die Hillfunktion, die die Ovulation darstellt, überarbeitet werden. N2 - During the last few years there has been a drastic decline in the fertility of dairy cows. Therefore the goal of this work is to identify the underlying mechanisms for this problem by extending the model from Stötzel et al. (2011) to include the influence of metabolic factors. For this purpose the influence of the metabolic factors was determined based on published, experimentally obtained findings. The important metabolic factors were glucose, insulin and IGF-I, but only IGF-I was shown to be dynamic over the course of a cycle and therefore implemented into the model. To validate the chosen model extension we developed scenarios from the literature in order to simulate the impact of negative energy balance as well as the effect of diet restrictions on the bovine oestrous cycle. Furthermore we got measurement data from Kawashima et al. (2007) and Cerri et al. (2011) for IGF, E2 and P4. The new model has just 8 parameters more, while maintaining the same solvability and stability in the initial values. It was possible to fit the model with the use of NLSCON to the measurement data for IGF, E2 and P4. In addition the scenarios allowed us to show that the model is able to simulate a negative energy balance in parts. Merely the return into the cyclic behaviour was faster than observed in vivo. One possible explanation would be, that the influence of IGF-I on the model is not strong enough. The model showed a deficit while simulating the scenarios since a marked reduction of the LH concentration still led to ovulation. Thus future research could be done in this direction, where it would probably be necessary to modify the follicle function or the hill function responsible for ovulation. KW - Systembiologie Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-46170 N1 - Diplomarbeit ER - TY - THES A1 - Berg, Mascha T1 - Laufzeitoptimierung der Robusten Perron Cluster Analyse (PCCA+) Y1 - 2012 ER - TY - JOUR A1 - Röblitz, Susanna A1 - Weber, Marcus T1 - Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification JF - Advances in Data Analysis and Classification Y1 - 2013 U6 - https://doi.org/10.1007/s11634-013-0134-6 VL - 7 IS - 2 SP - 147 EP - 179 ER - TY - THES A1 - Meisel, Kristin T1 - Mathematische Modellierung der Knochenremodellierung Y1 - 2012 ER - TY - JOUR A1 - Haack, Fiete A1 - Fackeldey, Konstantin A1 - Röblitz, Susanna A1 - Scharkoi, Olga A1 - Weber, Marcus A1 - Schmidt, Burkhard T1 - Adaptive spectral clustering with application to tripeptide conformation analysis JF - The Journal of Chemical Physics Y1 - 2013 U6 - https://doi.org/10.1063/1.4830409 VL - 139 SP - 110 EP - 194 ER - TY - CHAP A1 - Schäfer, Stefan A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - Mathematical Modelling of Follicular Maturation in Cows and Women T2 - 49. Jahrestagung der Physiologie und Pathologie der Fortpflanzung und gleichzeitig 41. Veterinär-Humanmedizinische Gemeinschaftstagung 2016, Leipzig. Y1 - 2016 ER - TY - JOUR A1 - Klebanov, Ilja A1 - Sikorski, Alexander A1 - Schütte, Christof A1 - Röblitz, Susanna T1 - Objective priors in the empirical Bayes framework JF - Scandinavian Journal of Statistics N2 - When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the nonparametric case, the maximum likelihood estimate is known to overfit the data, an issue that is commonly tackled by regularization. However, the majority of regularizations are ad hoc choices which lack invariance under reparametrization of the model and result in inconsistent estimates for equivalent models. We introduce a nonparametric, transformation-invariant estimator for the prior distribution. Being defined in terms of the missing information similar to the reference prior, it can be seen as an extension of the latter to the data-driven setting. This implies a natural interpretation as a trade-off between choosing the least informative prior and incorporating the information provided by the data, a symbiosis between the objective and empirical Bayes methodologies. Y1 - 2021 U6 - https://doi.org/10.1111/sjos.12485 VL - 48 IS - 4 SP - 1212 EP - 1233 PB - Wiley Online Library ER - TY - GEN A1 - Omari, Mohamed A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - A pharmacokinetic-pharmacodynamic model for single dose administration of Dexamethasone in dairy cows N2 - We present a mechanistic pharmacokinetic-pharmacodynamic model to simulate the effect of dexamethasone on the glucose metabolism in dairy cows. The coupling of the pharmacokinetic model to the pharmacodynamic model is based on mechanisms underlying homeostasis regulation by dexamethasone. In particular, the coupling takes into account the predominant role of dexamethasone in stimulating glucagon secretion, glycogenolysis and lipolysis and in impairing the sensitivity of cells to insulin. Simulating the effect of a single dose of dexamethasone on the physiological behaviour of the system shows that the adopted mechanisms are able to induce a temporary hyperglycemia and hyperinsulinemia, which captures the observed data in non-lactating cows. In lactating cows, the model simulations show that a single dose of dexamethasone reduces the lipolytic effect, owing to the reduction of glucose uptake by the mammary gland. T3 - ZIB-Report - 19-53 KW - systems biology; modelling; differential equations; metabolism; nutrition; bovine; fertility; reproduction; hormones; follicles; Dexamethasone; PK-PD Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-75043 SN - 1438-0064 ER - TY - JOUR A1 - Omari, Mohamed A1 - Lange, Alexander A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - Model-based exploration of the impact of glucose metabolism on the estrous cycle dynamics in dairy cows JF - Biology Direct Y1 - 2019 U6 - https://doi.org/10.1186/s13062-019-0256-7 VL - 15 ER - TY - JOUR A1 - Weber, Marie-Christin A1 - Fischer, Lisa A1 - Damerau, Alexandra A1 - Ponomarev, Igor A1 - Pfeiffenberger, Moritz A1 - Gaber, Timo A1 - Götschel, Sebastian A1 - Lang, Jens A1 - Röblitz, Susanna A1 - Buttgereit, Frank A1 - Ehrig, Rainald A1 - Lang, Annemarie T1 - Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation JF - Biofabrication N2 - Understanding the pathophysiological processes of cartilage degradation requires adequate model systems to develop therapeutic strategies towards osteoarthritis (OA). Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific disease aspects. This study aimed to combine in vitro and in silico modeling based on a tissue-engineering approach using mesenchymal condensation to mimic cytokine-induced cellular and matrix-related changes during cartilage degradation. Thus, scaffold-free cartilage-like constructs (SFCCs) were produced based on self-organization of mesenchymal stromal cells (mesenchymal condensation) and i) characterized regarding their cellular and matrix composition or secondly ii) treated with interleukin-1β (IL-1β) and tumor necrosis factor α (TNFα) for 3 weeks to simulate OA-related matrix degradation. In addition, an existing mathematical model based on partial differential equations was optimized and transferred to the underlying settings to simulate distribution of IL-1β, type II collagen degradation and cell number reduction. By combining in vitro and in silico methods, we aim to develop a valid, efficient alternative approach to examine and predict disease progression and effects of new therapeutics. Y1 - 2020 U6 - https://doi.org/10.1088/1758-5090/aba08f VL - 12 IS - 4 ER - TY - JOUR A1 - Alves, Sónia A1 - Ehrig, Rainald A1 - Raffalt, Peter C. A1 - Bender, Alwina A1 - Duda, Georg A1 - Agres, Alison N. T1 - Quantifying Asymmetry in Gait: A Weighted Universal Symmetry Index to Evaluate 3D Ground Reaction Forces JF - Frontiers in Bioengineering and Biotechnology N2 - Though gait asymmetry is used as a metric of functional recovery in clinical rehabilitation, there is no consensus on an ideal method for its evaluation. Various methods have been proposed but are limited in scope, as they can often use only positive signals or discrete values extracted from time-scale data as input. By defining five symmetry axioms, a framework for benchmarking existing methods was established and a new method was described here for the first time: the weighted universal symmetry index (wUSI), which overcomes limitations of other methods. Both existing methods and the wUSI were mathematically compared to each other and in respect to their ability to fulfill the proposed symmetry axioms. Eligible methods that fulfilled these axioms were then applied using both discrete and continuous approaches to ground reaction force (GRF) data collected from healthy gait, both with and without artificially induced asymmetry using a single instrumented elbow crutch. The wUSI with a continuous approach was the only symmetry method capable of determining GRF asymmetries in different walking conditions in all three planes of motion. When used with a continuous approach, the wUSI method was able to detect asymmetries while avoiding artificial inflation, a common problem reported in other methods. In conclusion, the wUSI is proposed as a universal method to quantify three-dimensional GRF asymmetries, which may also be expanded to other biomechanical signals. Y1 - 2020 ER - TY - JOUR A1 - Fischer, Sophie A1 - Ehrig, Rainald A1 - Schäfer, Stefan A1 - Tronci, Enrico A1 - Mancini, Toni A1 - Egli, Marcel A1 - Ille, Fabian A1 - Krüger, Tillmann H. C. A1 - Leeners, Brigitte A1 - Röblitz, Susanna T1 - Mathematical Modelling and Simulation Provides Evidence for New Strategies of Ovarian Stimulation JF - Frontiers in Endocrinology N2 - New approaches to ovarian stimulation protocols, such as luteal start, random start or double stimulation, allow for flexibility in ovarian stimulation at different phases of the menstrual cycle which is especially useful when time for assisted reproductive technology is limited, e.g. for emergency fertility preservation in cancer patients. It has been proposed that the success of these methods is based on the continuous growth of multiple cohorts ("waves") of follicles throughout the menstrual cycle which leads to the availability of ovarian follicles for ovarian controlled stimulation at several time points. Though several preliminary studies have been published, their scientific evidence has not been considered as being strong enough to integrate these results into routine clinical practice. This work aims at adding further scientific evidence about the efficiency of variable-start protocols and underpinning the theory of follicular waves by using mathematical modelling and numerical simulations. For this purpose, we have modified and coupled two previously published models, one describing the time course of hormones and one describing competitive follicular growth in a normal menstrual cycle. The coupled model is used to test stimulation protocols in silico. Simulation results show the occurrence of follicles in a wave-like manner during a normal menstrual cycle and qualitatively predict the outcome of ovarian stimulation initiated at different time points of the menstrual cycle. Y1 - 2021 U6 - https://doi.org/10.3389/fendo.2021.613048 VL - 12 ER - TY - JOUR A1 - Lang, Annemarie A1 - Volkamer, Andrea A1 - Behm, Laura A1 - Röblitz, Susanna A1 - Ehrig, Rainald A1 - Schneider, Marlon A1 - Geris, Lisbet A1 - Wichard, Joerg A1 - Buttgereit, Frank T1 - In silico Methods - Computational Alternatives to Animal Testing JF - ALTEX N2 - A seminar and interactive workshop on “In silico Methods – Computational Alternatives to Animal Testing” was held in Berlin, Germany, organized by Annemarie Lang, Frank Butt- gereit and Andrea Volkamer at the Charité-Universitätsmedizin Berlin, on August 17-18, 2017. During the half-day seminar, the variety and applications of in silico methods as alternatives to animal testing were presented with room for scientific discus- sions with experts from academia, industry and the German fed- eral ministry (Fig. 1). Talks on computational systems biology were followed by detailed information on predictive toxicology in order to display the diversity of in silico methods and the potential to embrace them in current approaches (Hartung and Hoffmann, 2009; Luechtefeld and Hartung, 2017). The follow- ing interactive one-day Design Thinking Workshop was aimed at experts, interested researchers and PhD-students interested in the use of in silico as alternative methods to promote the 3Rs (Fig. 2). Forty participants took part in the seminar while the workshop was restricted to sixteen participants. Y1 - 2018 U6 - https://doi.org/10.14573/altex.1712031 VL - 35 IS - 1 SP - 126 EP - 128 ER - TY - GEN A1 - Helfmann, Luzie A1 - Djurdjevac Conrad, Natasa A1 - Djurdjevac, Ana A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - From interacting agents to density-based modeling with stochastic PDEs N2 - Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models. T3 - ZIB-Report - 19-21 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73456 SN - 1438-0064 ER - TY - GEN A1 - Omari, Mohamed A1 - Lange, Alexander A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - A Mathematical Model for the Influence of Glucose-Insulin Dynamics on the Estrous Cycle in Dairy Cows N2 - Nutrition plays a crucial role in regulating reproductive hormones and follicular development in cattle. This is visible particularly during the time of negative energy balance at the onset of milk production after calving. Here, elongated periods of anovulation have been observed, resulting from alterations in luteiniz- ing hormone concentrations, likely caused by lower glucose and insulin concen- trations in the blood. The mechanisms that result in a reduced fertility are not completely understood, although a close relationship to the glucose-insulin metabolism is widely supported. Following this idea, a mathematical model of the hormonal network combining reproductive hormones and hormones that are coupled to the glucose compartments within the body of the cow was developed. The model is built on ordinary differential equations and relies on previously introduced models on the bovine estrous cycle and the glucose-insulin dynam- ics. Necessary modifications and coupling mechanisms are thoroughly discussed. Depending on the composition and the amount of food, in particular the glu- cose content in the dry matter, the model quantifies reproductive hormones and follicular development over time. Simulation results for different nutritional regimes in lactating and non-lactating dairy cows are examined and compared with experimental studies. Regarding its applicability, this work is an early attempt towards developing in silico feeding strategies and may eventually help refining and reducing animal experiments. T3 - ZIB-Report - 19-22 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73475 SN - 1438-0064 ER -