Philip Maini: Mathematical Modelling of Angiogenesis

Angiogenesis is the process by which the body generates new blood vessels. This occurs in the context of wound healing where, of course, it is beneficial to the body. However, it can also occur in cancer where it can enhance delivery of nutrients to the cancer and enable cancer cells to infiltrate the blood system and metastasize to vital organs, leading to the often fatal secondary tumours.
Understanding this process is a challenge for both experimentalists and theoreticians. I will review some recent work we have done on this problem which includes generating a new partial differential equation model for the so-called "snail-trail" movement of blood vessel cells to the tumour (Pillay et al, 2017), by developing a continuuum model of the process from a discrete description. I will then present a computational multiscale model for a key experimental assay that is used by experimentalists to measure the efficacy of anti-angiogenesis drugs and use it to make predictions (Grogan et al, 2018; 2017).