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International Journal of Differential Equations
Volume 2012, Article ID 175434, 25 pages
Research Article

The Avascular Tumour Growth in the Presence of Inhomogeneous Physical Parameters Imposed from a Finite Spherical Nutritive Environment

1School of Science and Technology, Hellenic Open University, 262 22 Patras, Greece
2Department of Engineering Sciences, University of Patras, 265 04 Patras, Greece

Received 20 April 2012; Accepted 22 July 2012

Academic Editor: Shaher Momani

Copyright © 2012 Foteini Kariotou and Panayiotis Vafeas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A well-known mathematical model of radially symmetric tumour growth is revisited in the present work. Under this aim, a cancerous spherical mass lying in a finite concentric nutritive surrounding is considered. The host spherical shell provides the tumor with vital nutrients, receives the debris of the necrotic cancer cells, and also transmits to the tumour the pressure imposed on its exterior boundary. We focus on studying the type of inhomogeneity that the nutrient supply and the pressure field imposed on the host exterior boundary, can exhibit in order for the spherical structure to be supported. It turns out that, if the imposed fields depart from being homogeneous, only a special type of interrelated inhomogeneity between nutrient and pressure can secure the spherical growth. The work includes an analytic derivation of the related boundary value problems based on physical conservation laws and their analytical treatment. Implementations in cases of special physical interest are examined, and also existing homogeneous results from the literature are fully recovered.