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Formulation and numerical simulations of a continuum model of avascular tumor growth.
MedLine Citation:
PMID:  21396381     Owner:  NLM     Status:  Publisher    
Abstract/OtherAbstract:
In this paper we present a continuum mathematical model for a multicellular spheroid that mimics the micro-environment within avascular tumor growth. The model consists of a coupled system of nonlinear convection-diffusion-reaction equations. This system is solved using a previously developed conservative Galerkin characteristics method. In the model considered, there are three cell types: the proliferative cells, the quiescent non-dividing cells which stay in the G(0) phase of the cell cycle and the necrotic cells. The model includes viable cell diffusion, diffusion of cellular material and the removal of necrotic cells. We assume that the nutrients diffuse passively and are consumed by the proliferative and quiescent tumor cells depending on the availability of resources (oxygen, glucose, etc.). The numerical simulations are performed using different sets of parameters, including biologically realistic ones, to explore the effects of each of these model parameters on reaching the steady state. The present results, taken together with those reported earlier, indicate that the removal of necrotic cells and the diffusion of cellular material have significant effects on the steady state, reflecting growth saturation, the number of viable cells, and the spheroid size.
Authors:
Mohammed Shuker Mahmood; Silvia Mahmood; Dušan Dobrota
Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2011-3-8
Journal Detail:
Title:  Mathematical biosciences     Volume:  -     ISSN:  1879-3134     ISO Abbreviation:  -     Publication Date:  2011 Mar 
Date Detail:
Created Date:  2011-3-14     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  0103146     Medline TA:  Math Biosci     Country:  -    
Other Details:
Languages:  ENG     Pagination:  -     Citation Subset:  -    
Copyright Information:
Copyright © 2011. Published by Elsevier Inc.
Affiliation:
Department of Applied Mathematics, Mechanical Engineering Faculty, University of Žilina, 010 26 Žilina, Slovakia.
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