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

Handle URI:
http://hdl.handle.net/10754/600199
Title:
Wound healing angiogenesis: The clinical implications of a simple mathematical model
Authors:
Flegg, Jennifer A.; Byrne, Helen M.; Flegg, Mark B.; Sean McElwain, D.L.
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. © 2012 Elsevier Ltd.
Citation:
Flegg JA, Byrne HM, Flegg MB, Sean McElwain DL (2012) Wound healing angiogenesis: The clinical implications of a simple mathematical model. Journal of Theoretical Biology 300: 309–316. Available: http://dx.doi.org/10.1016/j.jtbi.2012.01.043.
Publisher:
Elsevier BV
Journal:
Journal of Theoretical Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
May-2012
DOI:
10.1016/j.jtbi.2012.01.043
PubMed ID:
22326476
Type:
Article
ISSN:
0022-5193
Sponsors:
This work was supported by the award of a doctoral scholarship to J.A.F. from the Institute of Health and Biomedical Innovation at Queensland University of Technology and was funded by Australian Research Council's Discovery Projects funding scheme (Project no. DP0878011). This research was carried out while H.M.B. was visiting Queensland University of Technology, funded by the Institute of Health and Biomedical Innovation and the Discipline of Mathematical Sciences. Computational resources and services used in this work were provided by the HPC and Research Support Unit, QUT. This publication was based on work supported in part by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorFlegg, Jennifer A.en
dc.contributor.authorByrne, Helen M.en
dc.contributor.authorFlegg, Mark B.en
dc.contributor.authorSean McElwain, D.L.en
dc.date.accessioned2016-02-28T06:45:03Zen
dc.date.available2016-02-28T06:45:03Zen
dc.date.issued2012-05en
dc.identifier.citationFlegg JA, Byrne HM, Flegg MB, Sean McElwain DL (2012) Wound healing angiogenesis: The clinical implications of a simple mathematical model. Journal of Theoretical Biology 300: 309–316. Available: http://dx.doi.org/10.1016/j.jtbi.2012.01.043.en
dc.identifier.issn0022-5193en
dc.identifier.pmid22326476en
dc.identifier.doi10.1016/j.jtbi.2012.01.043en
dc.identifier.urihttp://hdl.handle.net/10754/600199en
dc.description.abstractNonhealing 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. © 2012 Elsevier Ltd.en
dc.description.sponsorshipThis work was supported by the award of a doctoral scholarship to J.A.F. from the Institute of Health and Biomedical Innovation at Queensland University of Technology and was funded by Australian Research Council's Discovery Projects funding scheme (Project no. DP0878011). This research was carried out while H.M.B. was visiting Queensland University of Technology, funded by the Institute of Health and Biomedical Innovation and the Discipline of Mathematical Sciences. Computational resources and services used in this work were provided by the HPC and Research Support Unit, QUT. This publication was based on work supported in part by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherElsevier BVen
dc.subjectAsymptotic analysisen
dc.subjectChronic wounden
dc.subjectHyperbaric oxygen therapyen
dc.subjectNumerical solutionen
dc.titleWound healing angiogenesis: The clinical implications of a simple mathematical modelen
dc.typeArticleen
dc.identifier.journalJournal of Theoretical Biologyen
dc.contributor.institutionQueensland University of Technology QUT, Brisbane, Australiaen
dc.contributor.institutionUniversity of Nottingham, Nottingham, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en

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