Clinical Research and Health Care

The health care system has experienced a proliferation of innovations aimed at enhancing life expectancy, quality of life, diagnostic and treatment options, as well as efficiency and cost effectiveness. The general trends into patient-specific treatment, optimal therapy planning, and molecular medicine require continuous innovations in our ability to understand bio-medical processes in detail. Predictive models for complex bio-medical processes and digital precision medicine more and more complement the traditional lab-based approaches to answer these needs.

Simultaneously, recent years have seen a revolution regarding experimental techniques in basic biomedical research. New techniques in microscopy, sequencing, and many other fields provide unprecedented resolution in observing cellular processes in vivo simultaneously on many temporal and spatial scales. The thus obtained data alone cannot uncover the hidden laws. But, in combination with new models and massive simulation, it promises deeper insights into the complex processes of life.

Mathematics is essential for more realistic modelling, simulation and visualization of life processes from the molecular up to the organ-level in combination with large-scale analysis of biomedical and medical imaging data. For example, there are many success stories regarding modelling, simulation and optimization based on partial differential equations in application to patient-specific surgery planning, joint movement, or in medical imaging. In addition, younger areas like stochastic optimal control of infection kinetics, metastability analysis of stochastic processes in application to molecular dynamics in drug design or particle-based reaction diffusion models for cellular processes have entered the focus of this application field.


  • reliable patient-specific joint simulations
  • PDE-constrained optimal control in biomechanics
  • seamless integration of molecular and cellular dynamics
  • stochastic optimal control of pharmacological interventions
  • data-driven multiscale modelling of cellular reaction networks
  • inverse problems in medical imaging
  • shape statistics and shape trajectories in anatomy reconstruction
  • multiscale modelling of ligand-target association in drug design