The Development of a Spatial Pattern in a Model for Cancer Growth

Solid tumour growth is a very complicated phenomenon which presents the mathematical modeller with a correspondingly complex set of problems to solve. Deciding which simplifying assumptions to make is a non-trivial task. Experimentally it is possible to grow small avascular nodules (multicell spheroids) whose growth kinetics approximate in vivo tumours such as carcinoma. These spherical colonies of cells receive nutrients and dispose of waste products via diffusion processes alone and as such reach a diffusion-limited steady state size a few millimetres in diameter. As the tumour grows and increases in size, cells towards the centre of the tumour are starved of vital nutrients and die. A central necrotic core is thus formed which is surrounded by a thin outer layer of live, proliferating cells.