Adjoint method for a tumor growth PDE-constrained optimization problem

Abstract

In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumor growth model. The model for the tumor 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 of a coupled system of partial differential equations whose spatial domain is the tumor, 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 <em>in vitro</em> 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.