  In this paper we present a method for estimating unknown parameters that
appear on an avascular, spheric tumour growth model. The model for the tumour
is based on nutrient driven growth of a continuum of live cells, whose birth
and death generate volume changes described by a velocity field.
  The model consists on a coupled system of partial differential equations
whose spatial domain is the tumour, that changes in size over time. Thus, the
situation can be formulated as a free boundary problem.
  After solving the forward problem properly, we use the model for the
estimation of parameters by fitting the numerical solution with real data,
obtained via in vitro experiments and medical imaging. We define an appropriate
functional to compare both the real data and the numerical solution. We use the
adjoint method for the minimization of this functional, getting a better
performance than the obtained with the pattern search method.
