In this paper we present a simplified model of tumor growth and an associated inverse problem. Our model consists in describing the evolution of a population of cancer cells and the density of oxygen. The growth rate depends on the concentration of oxygen. The oxygen distribution is computed by means of a diffusion equation, the source term being localized on the blood vessels. We consider the inverse problem that consists in recovering the position of the blood vessels assuming the distribution of tumor cells. We use an adjoint method. Results relative to idealized clinical cases are discussed.
© 2014 by De Gruyter