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Wound healing angiogenesis : the clinical implications of a simple mathematical model

Flegg, Jennifer, Byrne, Helen, Flegg, Mark, & McElwain, D.L. Sean (2012) Wound healing angiogenesis : the clinical implications of a simple mathematical model. Journal of Theoretical Biology, 300, pp. 309-316.

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Abstract

Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds.

Impact and interest:

3 citations in Scopus
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3 citations in Web of Science®

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123 since deposited on 23 Feb 2012
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ID Code: 48798
Item Type: Journal Article
Keywords: chronic wound, hyperbaric oxygen therapy, numerical solution, asymptotic analysis
DOI: 10.1016/j.jtbi.2012.01.043
ISSN: 0022-5193
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Academic Press/Elsevier
Copyright Statement: This is the author’s version of a work that was accepted for publication in Journal of Theoretical Biology. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Theoretical Biology, [VOL 300, (2012)] DOI: 10.1016/j.jtbi.2012.01.043
Deposited On: 23 Feb 2012 11:39
Last Modified: 11 Sep 2013 15:00

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