  In the present work we consider the mathematical model that describes brain
tumour growth (glioblastomas) under medical treatment. Based on the medical
study presented by R. Stupp et al. (New Engl Journal of Med 352: 987-996, 2005)
which evidence that, combined therapies such as, radiotherapy and chemotherapy,
produces negative tumour-growth, and using the mathematical model of P. K.
Burgess et al. (J Neuropath and Exp Neur 56: 704-713, 1997) as an starting
point, we present a model for tumour growth under medical treatment represented
by a non-linear partial differential equation that is solved using the Adomian
Decomposition Method (ADM). It is also shown that the non-linear term
efficiently models the effects of the combined therapies. By means of a proper
use of parameters, this model could be used for calculating doses in
radiotherapy and chemotherapy.
