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Mathematical models of cell colonization of uniformly growing domains

Landman, Kerry A. , Pettet, Graeme J., & Newgreen, D.F. (2003) Mathematical models of cell colonization of uniformly growing domains. Bulletin of Mathematical Biology, 65(2), pp. 235-262.

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Abstract

During the development of vertebrate embryos, cell migrations occur on an underlying tissue domain in response to some factor, such as nutrient. Over the time scale of days in which this cell migration occurs, the underlying tissue is itself growing. Consequently cell migration and colonization is strongly affected by the tissue domain growth. Numerical solutions for a mathematical model of chemotactic migration with no domain growth can lead to travelling waves of cells with constant velocity; the addition of domain growth can lead to travelling waves with nonconstant velocity. These observations suggest a mathematical approximation to the full system equations, allowing the method of characteristics to be applied to a simplified chemotactic migration model. The evolution of the leading front of the migrating cell wave is analysed. Linear, exponential and logistic uniform domain growths are considered. Successful colonization of a growing domain depends on the competition between cell migration velocity and the velocity and form of the domain growth, as well as the initial penetration distance of the cells. In some instances the cells will never successfully colonize the growing domain. These models provide an insight into cell migration during embryonic growth, and its dependence upon the form and timing of the domain growth.

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26 citations in Scopus
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25 citations in Web of Science®

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ID Code: 8727
Item Type: Journal Article
Additional Information: For more information, please refer to the journal’s website (see hypertext link) or contact the author. Author contact details: g.pettet@qut.edu.au
DOI: 10.1016/S0092-8240(02)00098-8
ISSN: 0092-8240
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2003 Springer
Copyright Statement: The original publication is available at SpringerLink http://www.springerlink.com
Deposited On: 23 Jul 2007
Last Modified: 29 Feb 2012 23:01

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