M 1011

Tissue modelling is important for the simulation of organ development, tumor growth, cancer metastasis and skin evolution that follows deep tissue injury. Since dermal tissues contain, next to solid collagen, non-connected cells that contain liquid, interconnected small blood vessels, these tissues exhibit porous, viscous and elastic features. For this reason, we treat skin as a visco-poroelastic medium. Furthermore, in some of our projects, we are interested in the evolution of skin after a serious injury. The damage is repaired by the regeneration of provisionary collagen that has a microstructure that is different from the microstructure of undamaged tissue. This introduces permanent strains and deformations locally in and near the scar environment. We model this by introducing morphoelasticity to the viscous-poroelastic description of the tissue. The talk will display some of the stability and monotonicity results that numerical schemes can suffer from. Furthermore, if time permits, we will consider an immersed interface method for the simulation of boundary forces that are exerted by cells and tumors that are pressing against their immediate environment.

Prof. Fred Vermolen

Uni Hasselt