Modelling aspects of vascular cancer development

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 also affects processes occurring on the molecular level. Molecular and intra-cellular events in turn affect the vascular network and therefore the nutrient dynamics. Our approach is to model, using partial differential equations, processes on the tissue level, and couple these to the intra-cellular events (modelled by ordinary differential equations) via cells modelled as automaton units. Thus far, within this framework, we have investigated the effects on tumour cell dynamics of structural adaptation at the vessel level, have explored certain drug protocol treatments, and have modelled the cell cycle in order to account for the possible effects of p27 in hypoxia-induced quiescence in cancer cells. We briefly review these findings here