Multi-Scale Modeling and Simulation of Transport Processes in an Elastically Deformable Perforated Medium.

In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement.

Modeling of the early stage of atherosclerosis with emphasis on the regulation of the endothelial permeability.

In this paper, we develop a mathematical model for the early stage of atherosclerosis, as a chronic inflammatory disease. It includes also processes that are relevant for the "thickening" of the vessel walls, and prepares a more complete model including also the later stages of atherosclerosis. The model consists of partial differential equations: Navier-Stokes equations modeling blood flow, Biot equations modeling the fluid flow inside the poroelastic vessel wall, and convection/chemotaxis-reaction-diffusion equations modeling transport, signaling and interaction processes initiating inflammation and atherosclerosis.

ROS and pentose phosphate pathway: mathematical modelling of the metabolic regulation in response to xenobiotic-induced oxidative stress and the proposed Impact of the gluconate shunt.

Elevated intracellular levels of reactive oxygen species (ROS), e.g. resulting from exposure to xenobiotics, can cause severe damages.

Model-Based Design of Biochemical Microreactors.

Mathematical modeling of biochemical pathways is an important resource in Synthetic Biology, as the predictive power of simulating synthetic pathways represents an important step in the design of synthetic metabolons. In this paper, we are concerned with the mathematical modeling, simulation, and optimization of metabolic processes in biochemical microreactors able to carry out enzymatic reactions and to exchange metabolites with their surrounding medium. The results of the reported modeling approach are incorporated in the design of the first microreactor prototypes that are under construction.

Mathematical modeling and simulation of the evolution of plaques in blood vessels.

In this paper, a model is developed for the evolution of plaques in arteries, which is one of the main causes for the blockage of blood flow. Plaque rupture and spread of torn-off material may cause closures in the down-stream vessel system and lead to ischemic brain or myocardial infarctions. The model covers the flow of blood and its interaction with the vessel wall.

Derivation and analysis of a system modeling the chemotactic movement of hematopoietic stem cells.

It has been shown that hematopoietic stem cells migrate in vitro and in vivo following the gradient of a chemotactic factor produced by stroma cells. In this paper, a quantitative model for this process is presented. The model consists of chemotaxis equations coupled with an ordinary differential equation on the boundary of the domain and subjected to nonlinear boundary conditions.