Cordula Reisch

Verified @tu-bs.de

Institute for Partial Differential Equations
Technische Universität Braunschweig



           

https://researchid.co/cordulareisch

RESEARCH INTERESTS

Mathematical Modeling with ordinary and partial differential equations, qualitative behavior of solutions, spatial inhomogeneous reaction diffusion equations.
Applications in life sciences, engineering and environmental sciences.

14

Scopus Publications

Scopus Publications

  • Building up a model family for inflammations
    Cordula Reisch, Sandra Nickel, and Hans-Michael Tautenhahn
    Springer Science and Business Media LLC
    AbstractThe paper presents an approach for overcoming modeling problems of typical life science applications with partly unknown mechanisms and lacking quantitative data: A model family of reaction–diffusion equations is built up on a mesoscopic scale and uses classes of feasible functions for reaction and taxis terms. The classes are found by translating biological knowledge into mathematical conditions and the analysis of the models further constrains the classes. Numerical simulations allow comparing single models out of the model family with available qualitative information on the solutions from observations. The method provides insight into a hierarchical order of the mechanisms. The method is applied to the clinics for liver inflammation such as metabolic dysfunction-associated steatohepatitis or viral hepatitis where reasons for the chronification of disease are still unclear and time- and space-dependent data is unavailable.




  • Model certification problem for processes
    Dirk Langemann, Cordula Reisch, and Ulrich Römer
    Elsevier BV


  • Modelling health impacts of hepatitis–model selection and treatment plans
    Cordula Reisch
    Informa UK Limited
    ABSTRACT Hepatitis B and C are viruses causing liver infections and resulting in grave secondary diseases. While there are different treatments for chronic liver infections, the process of evolving chronic diseases is still not fully understood. This paper presents an economic-inspired model for the overall health of an infected organism. The health model is based on the results of a reaction diffusion model for describing the space-dependent dynamics of virus and T cells during a liver infection. The different treatments affect the parameters of the reaction diffusion model and influence therefore the well-being of the infected person during an infection. The health model is selected in a detailed process out of a class of possible models. The presented work provides a foundation for an optimal control problem for finding the best treatment strategy.

  • Entropy functionals for finding requirements in hierarchical reaction-diffusion models for inflammations
    Cordula Reisch and Dirk Langemann
    Wiley
    Based on an established model for liver infections, we open the discussion on the used reaction terms in the reaction‐diffusion system. The mechanisms behind the chronification of liver infections are widely unknown, therefore we discuss a variety of reaction functions. By using theorems about existence, uniqueness, and nonnegativity, we identify properties of reaction functions which are indispensable to modelling liver infections. We introduce an entropy functional for reaction‐diffusion models of this type, which allows predictions of the longtime behavior of the solutions. As a result, we find more conditions on the reaction functions to derive a model covering different inflammation courses. Finally, we discuss the models in the frame of a hierarchical model family.

  • Sensitivity Analysis for Vehicle Dynamics Models - An Approach to Model Quality Assessment for Automated Vehicles
    Marcus Nolte, Richard Schubert, Cordula Reisch, and Markus Maurer
    IEEE
    Model-based approaches have become increasingly popular in the domain of automated driving. This includes runtime algorithms, such as Model Predictive Control, as well as formal and simulative approaches for the verification of automated vehicle functions. With this trend, the quality of models becomes crucial for automated vehicle safety. Established tools from model theory which can be applied to assure model quality are uncertainty and sensitivity analysis [1]. In this paper, we conduct sensitivity analyses for a single and double track vehicle dynamics model to gain insights about the models' behavior under different operating conditions. We compare the models, point out the most important findings regarding the obtained parameters sensitivities, and provide examples of possible applications of the gained insights.

  • Modeling the Chronification Tendency of Liver Infections as Evolutionary Advantage
    Cordula Reisch and Dirk Langemann
    Springer Science and Business Media LLC

  • Chemotactic effects in reaction-diffusion equations for inflammation
    Cordula Reisch and Dirk Langemann
    Springer Science and Business Media LLC

  • Epistemology and mathematical modeling-formalizing the modeling process in natural sciences


  • A mathematical model of modelling – epistemology and natural sciences
    Dirk Langemann, Cordula Reisch, and Janina Dierkes
    Elsevier BV

  • LTP or LTD? Modeling the influence of stress on synaptic plasticity
    Achim Peters, Cordula Reisch, and Dirk Langemann
    Society for Neuroscience
    Abstract In cognitive memory, long-term potentiation (LTP) has been shown to occur when presynaptic and postsynaptic activities are highly correlated and glucocorticoid concentrations are in an optimal (i.e., low normal) range. In all other conditions, LTP is attenuated or even long-term depression (LTD) occurs. In this paper, we focus on NMDA receptor (NMDA-R)-dependent LTP and LTD, two processes involving various molecular mechanisms. To understand which of these mechanisms are indispensable for explaining the experimental evidence reported in the literature, we here propose a parsimonious model of NMDA-R-dependent synaptic plasticity. Central to this model are two processes. First, AMPA receptor-subunit trafficking; and second, glucocorticoid-dependent modifications of the brain-derived neurotrophic factor (BDNF)-receptor system. In 2008, we have published a core model, which contained the first process, while in the current paper we present an extended model, which also includes the second process. Using the extended model, we could show that stress attenuates LTP, while it enhances LTD. These simulation results are in agreement with experimental findings from other labs. In 2013, surprising experimental evidence showed that the GluA1 C-tail is unnecessary for LTP. When using our core model in its original form, our simulations already predicted that there would be no requirement for the GluA1 C-tail for LTP, allowing to eliminate a redundant mechanism from our model. In summary, we present a mathematical model that displays reduced complexity and is useful for explaining when and how LTP or LTD occurs at synapses during cognitive memory formation.