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Licensed Unlicensed Requires Authentication Published by De Gruyter December 13, 2013

An inverse problem for the recovery of the vascularization of a tumor

  • Thierry Colin EMAIL logo , Angelo Iollo , Jean-Baptiste Lagaert and Olivier Saut

Abstract

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.

Received: 2013-1-15
Published Online: 2013-12-13
Published in Print: 2014-12-1

© 2014 by De Gruyter

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