Mathematical modelling of tumour growth and treatment.

We review some of the models that have been proposed to describe tumour growth and treatment. A first class is that of models which include the analysis of stresses. Here the question of blood vessel collapse in vascular tumours is treated briefly. Results on the existence of radially- and of non-radially-symmetric solutions are illustrated together with an investigation of their stability. Two sections are devoted to tumour cords (growing directly around a blood vessel), highlighting basic facts that are indeed important in the evolution of solid tumours in the presence of necrotic regions. Tumour cords are also taken as an example to deal with certain aspects of tumour treatment. The latter subject is too large to be treated exhaustively but a brief account of the mathematical modelling of hyperthermia is given.