Mathematical modelling and numerical simulations of cancer growth and cancer induced angiogenesis.

Cancer growth is an interesting and complex biological process, a better understanding of which can help to develop new diagnosis, treatment and therapy strategies. Angiogenesis is one of the central hallmarks of cancer which supports cancer growth and spread. However, the angiogenesis can also be used for cancer diagnosis and for a target chemotherapy.
The talk will summarise few mathematical models for cancer growth and angiogenesis and discuss numerical simulations of the model equations. The mathematics models for cancer growth are based on the continuous description of biological processes using partial differential equations. For angiogenesis a hybrid approach combining continuous description for the dynamics of chemicals with discrete representation of blood vessels is used.