Adjoint method for a tumour growth PDE-constrained optimization problem

DAMIÁN A. KNOPOFF; DAMIÁN FERNÁNDEZ; GERMÁN ARIEL TORRES; CRISTINA TURNER

COMPUTERS & MATHEMATICS WITH APPLICATIONS (1987)

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2013 vol. 66 p. 1104 - 1119

0898-1221

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 direct problem properly, we use the model for the estimation of parameters by fitting the numerical solution with real data, obtained via extit{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.