Comparison of mathematical tumor growth models

Tumor cells need a set of functional capabilities for development and growth. One of these capabilities is angiogenesis; tumor cells have to become able to force new vessel formation to ensure oxygen and nutrient supply. In the literature, there are several different growth models which aim to describe the growth characteristics. The model creation is a trade-off problem. On the one hand, the model has to be sufficiently complex to describe all the important processes which take part in the system; however, on the other hand, the model has to be sufficiently simple and manageable for real-life usability and - taking into account the applicability of biomedical control theory - for controller design. We discuss some relevant tumor growth models used in the literature showing their complexity and their modeling power.