The avascular tumour growth in the presence of inhomogeneous physical parameters imposed from a finite spherical nutritive environment
type: Item
instance of: scholarly article
title: The avascular tumour growth in the presence of inhomogeneous physical parameters imposed from a finite spherical nutritive environment
zbMATH Open document ID: 1402.92245
DOI: 10.1155/2012/175434
author: Foteini Kariotou
author: Panayiotis Vafeas
published in: International Journal of Differential Equations
publication date: 2013-06-10T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 92C37
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 6172112
zbMATH Keywords: avascular tumour growth
zbMATH Keywords: finite spherical nutritive environment
Wikidata QID: Q58702752
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/175434
OpenAlex ID: W2064606823
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description: scientific article; zbMATH DE number 6172112