@article{WeberFischerDamerauetal., author = {Weber, Marie-Christin and Fischer, Lisa and Damerau, Alexandra and Ponomarev, Igor and Pfeiffenberger, Moritz and Gaber, Timo and G{\"o}tschel, Sebastian and Lang, Jens and R{\"o}blitz, Susanna and Buttgereit, Frank and Ehrig, Rainald and Lang, Annemarie}, title = {Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation}, series = {Biofabrication}, volume = {12}, journal = {Biofabrication}, number = {4}, doi = {10.1088/1758-5090/aba08f}, abstract = {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.}, language = {en} } @article{PloentzkeBergEhrigetal., author = {Pl{\"o}ntzke, Julia and Berg, Mascha and Ehrig, Rainald and Leonhard-Marek, Sabine and M{\"u}ller, Kerstin-Elisabeth and R{\"o}blitz, Susanna}, title = {Model Based Exploration of Hypokalemia in Dairy Cows}, series = {Scientific Reports}, volume = {12, 19781}, journal = {Scientific Reports}, doi = {10.1038/s41598-022-22596-0}, abstract = {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.}, language = {en} } @article{OmariLangePloentzkeetal.2019, author = {Omari, Mohamed and Lange, Alexander and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Model-based exploration of the impact of glucose metabolism on the estrous cycle dynamics in dairy cows}, series = {Biology Direct}, volume = {15}, journal = {Biology Direct}, doi = {10.1186/s13062-019-0256-7}, year = {2019}, language = {en} } @article{KruegerLeenersTroncietal., author = {Kr{\"u}ger, Tillmann and Leeners, Brigitte and Tronci, Enrico and Mancini, Toni and Ille, Fabian and Egli, Marcel and Engler, Harald and R{\"o}blitz, Susanna and Frieling, Helge and Sinke, Christopher and Jahn, Kirsten}, title = {The androgen system across the menstrual cycle: Hormonal, (epi-)genetic and psychometric alterations}, series = {Physiology and Behavior}, journal = {Physiology and Behavior}, doi = {https://doi.org/10.1016/j.physbeh.2022.114034}, language = {en} } @article{KlebanovSikorskiSchuetteetal., author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Objective priors in the empirical Bayes framework}, series = {Scandinavian Journal of Statistics}, volume = {48}, journal = {Scandinavian Journal of Statistics}, number = {4}, publisher = {Wiley Online Library}, doi = {10.1111/sjos.12485}, pages = {1212 -- 1233}, abstract = {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.}, language = {en} } @article{FrankSikorskiRoeblitz, author = {Frank, Anna-Simone and Sikorski, Alexander and R{\"o}blitz, Susanna}, title = {Spectral clustering of Markov chain transition matrices with complex eigenvalues}, series = {Journal of Computational and Applied Mathematics}, volume = {444}, journal = {Journal of Computational and Applied Mathematics}, doi = {10.1016/j.cam.2024.115791}, pages = {115791}, abstract = {The Robust Perron Cluster Analysis (PCCA+) has become a popular spectral clustering algorithm for coarse-graining transition matrices of nearly decomposable Markov chains with transition states. Originally developed for reversible Markov chains, the algorithm only worked for transition matrices with real eigenvalues. In this paper, we therefore extend the theoretical framework of PCCA+ to Markov chains with a complex eigen-decomposition. We show that by replacing a complex conjugate pair of eigenvectors by their real and imaginary components, a real representation of the same subspace is obtained, which is suitable for the cluster analysis. We show that our approach leads to the same results as the generalized PCCA+ (GPCCA), which replaces the complex eigen-decomposition by a conceptually more difficult real Schur decomposition. We apply the method on non-reversible Markov chains, including circular chains, and demonstrate its efficiency compared to GPCCA. The experiments are performed in the Matlab programming language and codes are provided.}, language = {de} } @article{FischerHolzhausenRoeblitz, author = {Fischer-Holzhausen, Sophie and R{\"o}blitz, Susanna}, title = {Hormonal regulation of ovarian follicle growth in humans: Model-based exploration of cycle variability and parameter sensitivities}, series = {Journal of Theoretical Biology}, journal = {Journal of Theoretical Biology}, doi = {https://doi.org/10.1016/j.jtbi.2022.111150}, abstract = {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.}, language = {en} } @article{FischerHolzhausenRoeblitz, author = {Fischer-Holzhausen, Sophie and R{\"o}blitz, Susanna}, title = {Mathematical modelling of follicular growth and ovarian stimulation}, series = {Current Opinion in Endocrine and Metabolic Research}, journal = {Current Opinion in Endocrine and Metabolic Research}, doi = {https://doi.org/10.1016/j.coemr.2022.100385}, language = {en} } @article{FischerEhrigSchaeferetal., author = {Fischer, Sophie and Ehrig, Rainald and Sch{\"a}fer, Stefan and Tronci, Enrico and Mancini, Toni and Egli, Marcel and Ille, Fabian and Kr{\"u}ger, Tillmann H. C. and Leeners, Brigitte and R{\"o}blitz, Susanna}, title = {Mathematical Modelling and Simulation Provides Evidence for New Strategies of Ovarian Stimulation}, series = {Frontiers in Endocrinology}, volume = {12}, journal = {Frontiers in Endocrinology}, doi = {10.3389/fendo.2021.613048}, abstract = {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.}, language = {en} } @article{BergPloentzkeSiebertetal., author = {Berg, Mascha and Pl{\"o}ntzke, Julia and Siebert, Heike and R{\"o}blitz, Susanna}, title = {Modelling Oscillatory Patterns in the Bovine Estrous Cycle with Boolean Delay Equations}, series = {Bulletin of Mathematical Biology}, volume = {83}, journal = {Bulletin of Mathematical Biology}, number = {121}, doi = {10.1007/s11538-021-00942-z}, pages = {1 -- 25}, abstract = {Boolean delay equations (BDEs), with their relatively simple and intuitive mode of modelling, have been used in many research areas including, for example, climate dynamics and earthquake propagation. Their application to biological systems has been scarce and limited to the molecular level. Here, we derive and present two BDE models. One is directly derived from a previously published ordinary differential equation (ODE) model for the bovine estrous cycle, whereas the second model includes a modification of a particular biological mechanism. We not only compare the simulation results from the BDE models with the trajectories of the ODE model, but also validate the BDE models with two additional numerical experiments. One experiment induces a switch in the oscillatory pattern upon changes in the model parameters, and the other simulates the administration of a hormone that is known to shift the estrous cycle in time. The models presented here are the first BDE models for hormonal oscillators, and the first BDE models for drug administration. Even though automatic parameter estimation still remains challenging, our results support the role of BDEs as a framework for the systematic modelling of complex biological oscillators.}, language = {en} }