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The Effect of Bacteria on Epidermal WoundHealing

Published online by Cambridge University Press:  28 April 2010

E. Agyingi ,
S. Maggelakis  and
D. Ross
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Abstract

Epidermal wound healing is a complex process that repairs injured tissue. The complexityof this process increases when bacteria are present in a wound; the bacteria interactiondetermines whether infection sets in. Because of underlying physiological problemsinfected wounds do not follow the normal healing pattern. In this paper we present amathematical model of the healing of both infected and uninfected wounds. At the core ofour model is an account of the initiation of angiogenesis by macrophage-derived growthfactors. We express the model as a system of reaction-diffusion equations, and we presentresults of computations for a version of the model with one spatial dimension.

Keywords

wound healingangiogenesisgrowth factorsbacteria infection
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 3: Mathematical modeling in the medical sciences , 2010 , pp. 28 - 39
Copyright
© EDP Sciences, 2010

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References

Arnold, F. West, D. C.. Angiogenesis in wound healing. Pharmac. Ther. 52 (1992), 407-422.CrossRefGoogle ScholarPubMed
Bowler, P.G.. The 105 bacterial growth guideline: reassessing its clinical relevance in wound healing. Ostomy/Wound Manage 49 (2003),44-53. Google Scholar
W.S. Bullough. Cell Replacement after Tissue Damage in C. Illingworth (Ed.), Wound Healing, Churchill, London 1966.
Cai, A.Q., Landman, K.A., Hughes, B.D.. Multi-scale modeling of a wound-healing cell migration assay. J. Theoret. Biol. 245 (2007) no. 3, 576–594. CrossRefGoogle ScholarPubMed
R.A.F. Clark. Overview and general considerations of wound repair. In: The Molecular and Cellular Biology of Wound Repair (R. A. F. Clark and P. M. Hendson, eds) 3-34, Plenum, New York 1988.
Clark, R.A.F. Wound repair. Curr. Opin. Cell Biol. 1 (1989), 1000-1008.CrossRefGoogle ScholarPubMed
Clark, R.A.F. Growth factors and wound repair. J. Cell. Biochem. 46 (1991), 1-2.CrossRefGoogle ScholarPubMed
Clark, R.A.F. Regulation of fibroplasia in cutaneous wound repair. Am. J. Med. Sci. 306 (1993), 42-48.CrossRefGoogle ScholarPubMed
Edwards, R., Harding, K.G.. Bacteria and wound healing. Current Opinion in Infectious Diseases: 17(2004), no. 2, 91-96. CrossRefGoogle ScholarPubMed
Enoch, S. Harding, K.. Wound bed preparation: the science behind the removal of barriers to healing. Wounds 15 (2003), 213-229.Google Scholar
Gaffney, E.A., Pugh, K., Maini, P.K., Arnold, F.. Investigating a simple model of cutaneous wound healing angiogenesis. J. Math. Biol. 45 (2002), no. 4, 337-374. CrossRefGoogle ScholarPubMed
Hilhorst, D., King, J.R., Röger, M.. Travelling-wave analysis of a model describing tissue degradation by bacteria. European J. Appl. Math. 18 (2007), no. 5, 583-605. CrossRefGoogle Scholar
Hilhorst, D., King, J.R., Röger, M.. Mathematical analysis of a model describing the invasion of bacteria in burn wounds. Nonlinear Anal. 66 (2007), no. 5, 1118-1140. CrossRefGoogle Scholar
King, J.R., Kooerber, A.J.. Modeling host tissue degradation by extracelluar bacterial pathogens. Mathematical Medicine and Biology 20(2003), 227-260. CrossRefGoogle Scholar
Koerber, A.J., Kingand, J.R., Williams, P.. Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: “quorum”sensing by a single bacterium. J. Math. Biol. 50 (2005), no. 4, 440-488. CrossRefGoogle Scholar
Koerber, A.J., King, J.R., Ward, J.P., Williams, P., Croft, J.M., Sockett, R.E.. A mathematical model of partial-thickness burn-wound infection by Pseudomonas aeruginosa: quorum sensing and the build-up to invasion. Bulletin of mathematical biology. 64 (2002), no. 2:239-59. CrossRefGoogle ScholarPubMed
S.A. Maggelakis, A.E. Savakis. Modeling techniques in epidermal wound healing. Computational methods in biophysics, biomaterials, biotechnology and medical systems: algorithm development, mathematical analysis, and diagnostics, 2 (2003), 91-118, Kluwer Acad. Publ., Boston, MA.
Maggelakis, S.A. A mathematical model of tissue replacement during epidermal wound healing. Applied Mathematical modelling 27 (2003), 189-196.CrossRefGoogle Scholar
Maggelakis, S.A. Modeling the role of angiogenesis in epidermal wound healing. Discrete and Continuous Dynmical Systems Series B 4 (2004), 267-273.CrossRefGoogle Scholar
McDougall, S., Dallon, J., Sherratt, J., Maini, P.. Fibroblast migration and collagen deposition during dermal wound healing: mathematical modelling and clinical implications. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 364 (2006), no. 1843, 1385-1405. CrossRefGoogle ScholarPubMed
Odland, G. Ross, R.. Human wound repair: I. Epidermal regeneration. J. Cell Biol. 39 (1968), 135-151.CrossRefGoogle ScholarPubMed
Pettet, G.J., Byrne, H.M., McElwain, D. L., Norbury, J.. A model of wound-healing angiogenesis in soft tissue. Mathematical biosciences. 136 (1996), no. 1, 35-63. CrossRefGoogle Scholar
Pettet, G.J., Chaplain, A.J., McElwain, D.L.S. Byrne, H.M.. On the role of angiogenesis in wound healing. Proc. R. Soc. Lond. B 263 (1996), 1487-1493.CrossRefGoogle ScholarPubMed
Polverini, P.J., Cotran, P.S., Gimbrone, M.A. Unanue, E.R.. Activated macrophages induce vascular proliferation. Nature. 269 (1977), 804-806.CrossRefGoogle ScholarPubMed
Robson, M.C., Stenberg, B.D. Heggers, J.P.. Wound healing alterations caused by infections. Clin. Plast. Surg. 17 (1990), 485-492.Google Scholar
R. Rudolph, J. Vande Berg, H.P. Egrlich. Wound contraction and scar contracture. In: Wound Healing: Biochemical and Clinical Aspects (I. K. Cohen, R. F. Diegelmann and W. J. Lindblad. eds) Saunders, Philadelphia (1992), 96-114.
Sherratt, J.A. Murray, J.D.. Models of epidermal wound healing. Proc. R. Soc. Lond. B 241 (1990), 29-36.CrossRefGoogle ScholarPubMed
Sherratt, J.A. Murray, J.D.. Mathematical analysis of a basic model of epidermal wound healing. J. Math Biol. 29 (1991), 389-404.CrossRefGoogle ScholarPubMed
Tindall, M.J., Porter, S.L., Maini, P.K., Gaglia, G., Armitage, J.P.. Overview of mathematical approaches used to model bacterial chemotaxis. I. The single cell. Bull. Math. Biol. 70 (2008), no. 6, 1525-1569. CrossRefGoogle ScholarPubMed
Tindall, M.J., Maini, P.K., Porter, S.L., Armitage, J.P.. Overview of mathematical approaches used to model bacterial chemotaxis. II. Bacterial populations. Bull. Math. Biol. 70 (2008), no. 6, 1570–1607. CrossRefGoogle ScholarPubMed
Waugh, H.V., Sherratt, J.A.. Macrophage dynamics in diabetic wound healing. Bull. Math. Biol. 68 (2006) no. 1, 197–207. CrossRefGoogle Scholar