Mathematical modelling of tumour angiogenesis

Mathematical models prove valuable tools to study the proof-of-concept and underlying mechanisms of a tumour progression. They enable us to explore possible radio-, chemo- and various therapy combinations that until now have been only a promising hypothesis because of huge costs of their clinical studies. Here we present a family of mathematical models of tumour angiogenesis, which were successfully compared to biological data. In addition, after modifications they can describe the effect of anti-angiogenic treatment for various vessels targeting agents, as well as the impact of cytotoxic agents on proliferating cancer cells. We present two ways in which the anti-angiogenic treatment cam be incorporated into the model. One describes the agents directly targeting tumour vessels, whereas the second focuses on agents interfering with angiogenic signalling. We illustrate differences between those two approaches by presenting fitting results to biological data.