Modelling aspects of vascular cancer

The modelling of cancer provides an enormous mathematical challenge because of its inherent multi-scale nature. For example, in vascular tumours, nutrient is transported by the vascular system, which operates on a tissue level. However, it effects processes occuring on a molecular level. Molecular and intra-cellular events in turn effect the vascular network and therefore the nutrient dynamics. Our modelling approach is to model, using partial differential equations, processes on the tissue level and couple these to the intercellular events (modelled by ordinary differential equations) via cells modelled as automaton units. Thusfar, within this framework we have modelled structural adaptation at the vessel level and we have modelled the cell cycle in order to account for the effects of p27 during hypoxia. These preliminary results will be presented.