Quantitative Biomedicine

Applications

This research topic focusses on modeling complex material systems with different phases including multiphase and interfacial flows, damage and fatigue modeling, topology optimization and complex materials. Physical phenomena modelled involve fluid flow, diffuse transport and (visco)elastic deformation in the context of phase separation and phase transitions. Applications range from biology to physics and engineering. [>> more]

Mathematical models and computational techniques are nowadays utilized in medical sciences for noninvasive diagnostic, diseases characterization, therapy planning, and treatment monitoring. The research at WIAS focuses on efficient and robust models for biological tissues and fluids, on the usage of advanced mathematical models in data assimilation and medical imaging applications, as well as on techniques in optimization, machine learning, and optimal control for decision support in biomedicine. [>> more]

Image processing tools based on mathematical algorithms from statistics or variational methods enable a bulk of applications in the medical sciences. They range from image enhancement to automatic image analysis. In many cases, a significant improvement in the results results of image analysis can be achieved by integrating the physics of the imaging process. Applications of these methods range from tomography images to various modalities of magnetic resonance imaging. [>> more]

Archive

Further application topics where the institute has expertise in:

Research in this field focuses on mathematical aspects of biological evolution through stochastic modelling. The main areas are the effects of complex fitness landscapes on molecular evolution, the study of sexual selection by stochastic modelling of mating preferences and emerging mating patterns, genealogies of the mathematical seed-bank model and mathematical modelling of controlled evolution under experimental conditions. [>> more]