Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 3, 2010
Mathematical modeling in the medical sciences
Page(s) 28 - 39
DOI https://doi.org/10.1051/mmnp/20105303
Published online 28 April 2010
  1. F. ArnoldD. C. West. Angiogenesis in wound healing. Pharmac. Ther. 52 (1992), 407-422.
  2. P.G. Bowler. The 105 bacterial growth guideline: reassessing its clinical relevance in wound healing. Ostomy/Wound Manage 49 (2003),44-53.
  3. W.S. Bullough. Cell Replacement after Tissue Damage in C. Illingworth (Ed.), Wound Healing, Churchill, London 1966.
  4. A.Q. Cai, K.A. Landman, B.D. Hughes. Multi-scale modeling of a wound-healing cell migration assay. J. Theoret. Biol. 245 (2007) no. 3, 576–594. [CrossRef] [MathSciNet] [PubMed]
  5. 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.
  6. R.A.F Clark. Wound repair. Curr. Opin. Cell Biol. 1 (1989), 1000-1008. [CrossRef] [PubMed]
  7. R.A.F Clark. Growth factors and wound repair. J. Cell. Biochem. 46 (1991), 1-2. [CrossRef]
  8. R.A.F Clark. Regulation of fibroplasia in cutaneous wound repair. Am. J. Med. Sci. 306 (1993), 42-48. [CrossRef] [PubMed]
  9. R. Edwards, K.G. Harding. Bacteria and wound healing. Current Opinion in Infectious Diseases: 17(2004), no. 2, 91-96. [CrossRef] [PubMed]
  10. S. EnochK. Harding. Wound bed preparation: the science behind the removal of barriers to healing. Wounds 15 (2003), 213-229.
  11. E.A. Gaffney, K. Pugh, P.K. Maini, F. Arnold. Investigating a simple model of cutaneous wound healing angiogenesis. J. Math. Biol. 45 (2002), no. 4, 337-374. [CrossRef] [MathSciNet] [PubMed]
  12. D. Hilhorst, J.R. King, M. Röger. Travelling-wave analysis of a model describing tissue degradation by bacteria. European J. Appl. Math. 18 (2007), no. 5, 583-605. [MathSciNet]
  13. D. Hilhorst, J.R. King, M. Röger. Mathematical analysis of a model describing the invasion of bacteria in burn wounds. Nonlinear Anal. 66 (2007), no. 5, 1118-1140. [CrossRef] [MathSciNet]
  14. J.R. King, A.J. Kooerber. Modeling host tissue degradation by extracelluar bacterial pathogens. Mathematical Medicine and Biology 20(2003), 227-260. [CrossRef]
  15. A.J. Koerber, J.R. Kingand, P. Williams. 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. [CrossRef] [MathSciNet] [PubMed]
  16. A.J. Koerber, J.R. King, J.P. Ward, P. Williams, J.M. Croft, R.E. Sockett. 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. [CrossRef] [PubMed]
  17. 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.
  18. S.A Maggelakis. A mathematical model of tissue replacement during epidermal wound healing. Applied Mathematical modelling 27 (2003), 189-196. [CrossRef]
  19. S.A Maggelakis. Modeling the role of angiogenesis in epidermal wound healing. Discrete and Continuous Dynmical Systems Series B 4 (2004), 267-273. [CrossRef]
  20. S. McDougall, J. Dallon, J. Sherratt, P. Maini. 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. [CrossRef] [MathSciNet]
  21. G. OdlandR. Ross. Human wound repair: I. Epidermal regeneration. J. Cell Biol. 39 (1968), 135-151. [CrossRef] [PubMed]
  22. G.J. Pettet, H.M. Byrne, D. L. McElwain, J. Norbury. A model of wound-healing angiogenesis in soft tissue. Mathematical biosciences. 136 (1996), no. 1, 35-63. [CrossRef] [PubMed]
  23. G.J. Pettet, A.J. Chaplain, D.L.S. McElwainH.M. Byrne. On the role of angiogenesis in wound healing. Proc. R. Soc. Lond. B 263 (1996), 1487-1493. [CrossRef]
  24. P.J. Polverini, P.S. Cotran, M.A. GimbroneE.R. Unanue. Activated macrophages induce vascular proliferation. Nature. 269 (1977), 804-806. [CrossRef] [PubMed]
  25. M.C. Robson, B.D. StenbergJ.P. Heggers. Wound healing alterations caused by infections. Clin. Plast. Surg. 17 (1990), 485-492. [PubMed]
  26. 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.
  27. J.A. SherrattJ.D. Murray. Models of epidermal wound healing. Proc. R. Soc. Lond. B 241 (1990), 29-36. [CrossRef]
  28. J.A. SherrattJ.D. Murray. Mathematical analysis of a basic model of epidermal wound healing. J. Math Biol. 29 (1991), 389-404. [CrossRef] [PubMed]
  29. M.J. Tindall, S.L. Porter, P.K. Maini, G. Gaglia, J.P. Armitage. Overview of mathematical approaches used to model bacterial chemotaxis. I. The single cell. Bull. Math. Biol. 70 (2008), no. 6, 1525-1569. [CrossRef] [MathSciNet] [PubMed]
  30. M.J. Tindall, P.K. Maini, S.L. Porter, J.P. Armitage. Overview of mathematical approaches used to model bacterial chemotaxis. II. Bacterial populations. Bull. Math. Biol. 70 (2008), no. 6, 1570–1607. [CrossRef] [MathSciNet] [PubMed]
  31. H.V. Waugh, J.A. Sherratt. Macrophage dynamics in diabetic wound healing. Bull. Math. Biol. 68 (2006) no. 1, 197–207. [CrossRef] [MathSciNet] [PubMed]

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