Quantitative Biomedicine deals with the modeling, analysis, simulation, or optimization of complex systems in clinical and biological applications. These topics concern the understanding of cellular, biochemical, and biomolecular processes, as well as the solution of relevant problems in medical engineering. In this area, interdisciplinary contributions to the fields of medical imaging and clinical diagnostics are enormously important.
S. Katz, A. Caiazzo, B. Moreau, U. Wilbrandt, J. Brüning, L. Goubergrits, V. John, Impact of turbulence modeling on the simulation of blood flow in aortic coarctation, International Journal of Numerical Methods in Biomedical Engineering, 39 (2023), pp. e3695/1--e3695/36, DOI 10.1002/cnm.3695.
One major research topic at WIAS is the physics-based modeling of medical images. This includes the development of mathematical methods for classical tasks of image processing like registration, denoising, equalization, and segmentation, but also (low-rank - sparse) data decomposition and functional correlations, e.g., in neurological processes, as well as data assimilation problems for integrating available images into physical models. These processes typically lead to complex, nonlinear, or nonsmooth inverse problems where both analysis, optimization and statistics play a central part.
Further research concentrates on the development, the analysis, and the simulation of mathematical models for a better understanding of biological flows and biological tissues. Current topics include the modeling of blood flows in the cardiovascular system, the development of multiscale methods for the simulation of vascularized tissues and biomaterials.
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.
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.