Skip to main content
SpringerLink
Log in

Analysis of Travelling Waves Associated with the Modelling of Aerosolised Skin Grafts

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

A previous model developed by the authors investigates the growth patterns of keratinocyte cell colonies after they have been applied to a burn site using a spray technique. In this paper, we investigate a simplified one-dimensional version of the model. This model yields travelling wave solutions and we analyse the behaviour of the travelling waves. Approximations for the rate of healing and maximum values for both the active healing and the healed cell densities are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barrandon, Y., 1993. The epidermal stem cell: An overview. Semin. Dev. Biol. 4(4), 209–215.

    Article  Google Scholar 

  • Chalumeau, M., Saulnier, J.-P., Ainaud, P., Lebever, H., Stephanazzi, J., Lecoadou, A., Carsin, H., 1999. Initial general management and surgery of six extensively burned children treated with cultured epidermal autografts. J. Pediatr. Surg. 34(4), 602–605.

    Article  Google Scholar 

  • DeLuca, M., Albanese, E., Bondanza, S., Megna, M., Ugozzoli, L., Molina, F., Cancedda, R., Santi, P.L., Bormioli, M., Stella, M., 1989. Multicentre experience in the treatment of burns with autologous and allogenic cultured epithelium, fresh or preserved in a frozen state. Burns 15(5), 303–309.

    Article  Google Scholar 

  • Fraulin, F.O.G., Bahoric, A., Harrop, A.R., Hiruki, T., Clarke, H.M., 1998. Autotransplantation of epithelial cells in the pig via an aerosol vehicle. J. Burn Care Rehabil. 19, 337–345.

    Article  Google Scholar 

  • Gaffney, E.A., Maini, P.K., Sherratt, J.A., Tuft, S., 1999. The mathematical modelling of cell kinetics in corneal epithelial wound healing. J. Theor. Biol. 197, 15–40.

    Article  Google Scholar 

  • Gallico, G.G., O’Connor, N.E., Compton, C.C., Kehinde, O., Green, H., 1984. Permanent coverage of large burn wounds with autologous cultured human epithelium. N. Engl. J. Med. 311, 448.

    Article  Google Scholar 

  • Green, H., 1991, Cultured cells for the treatment of disease. Sci. Am. 265(5), 96–102.

    Article  Google Scholar 

  • Green, H., Kehinde, O., Thomas, J., 1979. Growth of cultured human epidermal cells into multiple epithelia suitable for grafting. Proc. Natl. Acad. Sci. USA 76(11), 5665–5668.

    Article  Google Scholar 

  • Harris, P.A., Leigh, I.M., Navsaria, H.A., 1998. Pre-confluent keratinocyte grafting: The future for cultured skin replacements? Burns 24, 591–593.

    Article  Google Scholar 

  • Maini, P.K., McElwain, D.L.S., Leavesley, D.I., 2004. Travelling waves in a wound healing assay. Appl. Math. Lett. 17(5), 575–580.

    Article  MATH  MathSciNet  Google Scholar 

  • Murray, J.D., 2002. Mathematical Biology I: An Introduction, vol. 1, 3rd edition. Springer-Verlag, New York.

    Google Scholar 

  • O’Connor, N.E., Mulliken, J.B., Banks-Schlegel, S., Kehinde, O., Green, H., 1981. Grafting of burns with cultured epithelium prepared from autologous epidermal cells. Lancet 1–75.

  • Pettet, G.J., Byrne, H.M., McElwain, D.L.S., Norbury, J., 1996a. A model of wound healing angiogenesis in soft-tissue. Math. Biosci. 136, 35–64.

    Article  MATH  Google Scholar 

  • Pettet, G.J., Chaplain, M.A., McElwain, D.L.S., Byrne, H.M., 1996b. On the role of angiogenesis in wound healing. Proc. R. Soc. Lond. B 263, 1487–1493.

    Article  Google Scholar 

  • Sherratt, J.A., 2000. Wavefront propagation in a competition equation with a new motility term modelling contact inhibition between cell populations. Proc. R. Soc. Lond. A 456, 2365–2386.

    Article  MATH  MathSciNet  Google Scholar 

  • Denman, P.K., McElwain, D.L.S., Harkin, D.G., Upton, Z., 2006. Mathematical modelling of aerosolised skin grafts incorporating keratinocyte clonal subtypes. Bulletin of Mathematical Biology, in press.

  • Williamson, J.S., Snelling, C.F.T., Clugston, P., Macdonald, I.B., Germann, E., 1995. Cultured epithelial autograft: Five years of clinical experience with twenty-eight patients. J. Trauma Inj. Infect. Crit. Care 39(2), 309–319.

    Article  Google Scholar 

  • Wood, F., 2003. Clinical potential of autologous epithelial suspension. Wounds 15(1), 16–22.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Queensland University of Technology, G.P.O. Box 2434, Brisbane, 4001, Australia

    Paula K. Denman & D. L. Sean McElwain

  2. The Mathematical Institute, Oxford University, 24-29 St. Giles, Oxford, OX1 3LB, UK

    John Norbury

Authors
  1. Paula K. Denman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. L. Sean McElwain
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. John Norbury
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paula K. Denman.

Additional information

PACS 92B05

Rights and permissions

Reprints and permissions

About this article

Cite this article

Denman, P.K., McElwain, D.L.S. & Norbury, J. Analysis of Travelling Waves Associated with the Modelling of Aerosolised Skin Grafts. Bull. Math. Biol. 69, 495–523 (2007). https://doi.org/10.1007/s11538-006-9138-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-006-9138-0

Keywords

Search

Navigation