Linked Life Data

9080687

Source:http://linkedlifedata.com/resource/pubmed/id/9080687

Statements in which the resource exists as a subject.
PredicateObject
rdf:type
lifeskim:mentions
pubmed:issue
1
pubmed:dateCreated
1997-4-25
pubmed:abstractText
A system of nonlinear partial differential equations is proposed as a model for the growth of an avascular-tumour spheroid. The model assumes a continuum of cells in two states, living or dead, and, depending on the concentration of a generic nutrient, the live cells may reproduce (expanding the tumour) or die (causing contraction). These volume changes resulting from cell birth and death generate a velocity field within the spheroid. Numerical solutions of the model reveal that after a period of time the variables settle to a constant profile propagating at a fixed speed. The travelling-wave limit is formulated and analytical solutions are found for a particular case. Numerical results for more general parameters compare well with these analytical solutions. Asymptotic techniques are applied to the physically relevant case of a small death rate, revealing two phases of growth retardation from the initial exponential growth, the first of which is due to nutrient-diffusion limitations and the second to contraction during necrosis. In this limit, maximal and "linear' phase growth speeds can be evaluated in terms of the model parameters.
pubmed:language
eng
pubmed:journal
pubmed:citationSubset
IM
pubmed:status
MEDLINE
pubmed:month
Mar
pubmed:issn
0265-0746
pubmed:author
pubmed:issnType
Print
pubmed:volume
14
pubmed:owner
NLM
pubmed:authorsComplete
Y
pubmed:pagination
39-69
pubmed:dateRevised
2006-11-15
pubmed:meshHeading
pubmed:year
1997
pubmed:articleTitle
Mathematical modelling of avascular-tumour growth.
pubmed:affiliation
Department of Theoretical Mechanics, University of Nottingham, UK.
pubmed:publicationType
Journal Article, Review, Research Support, Non-U.S. Gov't