Biomechanical problems that involve multiple scales and interfaces occur in many different areas. One example is the mathematical modelling of tumour growth. Sharp interphase models of prevascular in vivo tumour growth are based on coupled systems. These consist of a reaction-diffusion equation describing the evolution of the nutrient concentration (mostly oxygen or glucose) and an elliptic equation for the internal pressure. Surface tension counteracts the internal pressure and leads to a boundary condition, coupling the pressure to the mean curvature of the tumour surface. The motion of the boundary of the tumour is governed by the Stefan condition. Besides the coupling of the nutrient concentration and the pressure on the moving interface, there is another coupling in the bulk by the so-called proliferation rate of the model.
A second research field is related to bone mechanics. It is well known that bone tissue is stimulated mechanically for growth and repair, e.g. fracture healing. In a first-order approach this can be modelled within purely macroscopic phenomenological models, where the growth equations are derived within a thermodynamically consistent constitutive framework.
Projects with internal funding:
Projects with external funding/topics for Ph.D. theses:
- In vivo tumour growth models.
- Bio-active contact between implant and bone and effects of bio-coating on implants.
- Cell-surface interaction under environmental conditions.
- Individual therapies on fracture healing.
- Mechanically induced nutrient maintenance of joint cartilage.