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Mathematical Modelling of Aerosolised Skin Grafts Incorporating Keratinocyte Clonal Subtypes

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Abstract

Severe burns can be very traumatic for the patient, and while burns caused by industrial or domestic accidents are common, there are also increasing numbers of burns associated with terrorism. A novel technique to assist in the healing process is to spray skin cells, keratinocytes, that are cultured from the patient’s own tissue, directly onto the burn site. This process involves taking some undamaged skin from the patient, allowing the skin cells to proliferate rapidly in the laboratory over a period of 5–10 days, harvesting and separating the cells and then spraying them onto the burn. This paper deals with keratinocytes that have been cultured in vitro for a short period of time (early passage cultured cells). The spraying process has yet to be optimised with respect to the seeding density required for fastest re-epithelisation and thus there is a need for this process to be modelled. In this paper, we review some of the skin biology and develop a mathematical model of the growth patterns of cell colonies after they have been applied using a aerosolised technique. The model allows us to predict coverage over time and can be used as a decision support tool for clinicians.

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References

  • Bahoric, A., Harrop, A.R., Clarke, H.M., Zuker, R.M., 1997. Aerosol vehicle for delivery of epidermal cells — An in vitro study. Can. J. Plast. Surg. 5(3), 153–156.

    Google Scholar 

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

    Article  Google Scholar 

  • Barrandon, Y., Green, H., 1985. Cell size as a determinant of the clone-forming ability of human keratinocytes. Proc. Natl. Acad. Sci. U.S.A. 82, 5390–5394.

    Article  Google Scholar 

  • Barrandon, Y., Green, H., 1987. Three clonal types of keratinocyte with different capacities for multiplication. Proc. Natl. Acad. Sci. U.S.A. 84, 2302–2306.

    Article  Google Scholar 

  • Blanpain, C., Lowry, W.E., Geoghegan, A., Polak, L., Fuchs, E., 2004. Self-renewal, multipotency, and the existence of two cell populations within an epithelial stem cell niche. Cell 118, 635–648.

    Article  Google Scholar 

  • Boyce, S.T., Warden, G.D., 2002. Principles and practices for treatment of cutaneous wounds with cultured skin substitutes. Am. J. Surg. 183, 445–456.

    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 

  • Chester, D.L., Balderson, D.S., Papini, R.P.G., 2004. A review of keratinocyte delivery to the wound bed. J. Burn Care Rehabil. 25, 266–275.

    Article  Google Scholar 

  • Clark, R.A.F., 1991. Cutaneous wound repair. In: Goldsmith, L.A. (Ed.), Physiology, Biochemistry, and Molecular Biology of the Skin, vol. 1, 2nd edition. Oxford University Press, Oxford, pp. 576–601, chapter 20.

    Google Scholar 

  • Cohen, K., 1997. An overview of wound healing biology. In: Ziegler, T.R., Pierce, G.F., Herndon, D.N. (Eds.), Growth Factors and Wound Healing: Basic Science and Potential Clinical Applications. Springer-Verlag, Berlin, pp. 3–7, chapter 1.

    Google Scholar 

  • Cohen, M., Bahoric, A., Clarke, H.M., 2001. Aerosolization of epidermal cells with fibrin glue for the epithelialization of porcine wounds with unfavorable topography. Plastic Reconstruc. Surg. 107, 1208–1215.

    Article  Google Scholar 

  • Coulomb, B., Dubertret, L., 2002. Skin cell culture and wound healing. Wound Repair Regen. 10(2), 109–112.

    Article  Google Scholar 

  • Dale, P.D., Maini, P.K., Sherratt, J.A., 1994. Mathematical modelling of corneal epithelial wound healing. Math. Biosci. 124, 127–147.

    Article  MATH  Google Scholar 

  • Davidson, J.M., 1998. Animal models for wound repair. Arch. Dermatol. Res. 290(0), S1–S11.

    Article  Google Scholar 

  • Dellambra, E., Vailly, J., Pellegrini, G., Bondanza, S., Golisano, O., Macchia, C., Zambruno, G., Meneguzzi, G., DeLuca, M., 1998. Corrective transduction of human epidermal stem cells in laminin-5-dependent junctional epidermolysis bullosa. Human Gene Ther. 9, 1359–1370.

    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 

  • Denman, P.K., McElwain, D.L.S., Norbury, J., 2006. Analysis of travelling waves associated with the modelling of aerosolised skin grafts. Bulletin of Mathematical Biology, in press.

  • Dennis, C., 2005. Hard graft. Nature 436, 166–167.

    Article  Google Scholar 

  • Dunn, J.M., 1987. Local wound care in the diabetic. Clin. Podiatric Med. Surg. 4(2), 413–418.

    Google Scholar 

  • Edmondson, S.R., Thumiger, S.P., Werther, G.A., Wraight, C.J., 2003. Epidermal homeostasis: The role of the growth hormone and insulin-like growth factor systems. Endocrine Rev. 24(6), 737–764.

    Article  Google Scholar 

  • Ellsbury, D.L., George, C.S., 2004, September. Dehydration. eMedicine.

  • Fisher, R.A., 1937. The wave of advance of advantageous genes. Ann. Eugenics 7, 353–369.

    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 Rehab. 19, 337–345.

    Article  Google Scholar 

  • Freedberg, I.M., Tomic-Canic, M., Komine, M., Blumenberg, M., 2001. Keratins and the keratinocyte activation cycle. J. Invest. Dermatol. 116(5), 633–640.

    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. New Engl. J. Med. 311, 448.

    Google Scholar 

  • Grazul-Bilska, A.T., Johnson, M.L., Bilski, J.J., Redmer, D.A., Reynolds, L.P., Abdullah, A., Abdullah, K.M., 2003. Wound healing: The role of growth factors. Drugs Today 39(10), 787–800.

    Article  Google Scholar 

  • Green, H., 1980. The keratinocyte as differentiated cell type. Harvey Lect. 74, 101–139.

    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. U.S.A. 76(11), 5665–5668.

    Article  Google Scholar 

  • Hansbrough, J.F., Rennekampff, H.O., 1997. Cultured skin cells for wound closure and for promoting wound healing. In: Ziegler, T.R., Pierce, G.F., Herndon, D.N. (Eds.), Growth Factors and Wound Healing: Basic Science and Potential Clinical Applications. Springer-Verlag, Berlin, pp. 37–55, chapter 4.

    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 

  • Heideman, M., Bengtsson, A., 1992. The immunologic response to thermal injury. World J. Surg. 16, 53–56.

    Article  Google Scholar 

  • Heng, B.C., Cao, T., Liu, H., Phan, T.T., 2005. Directing stem cells into the keratinocyte lineage in vitro. Exp. Dermatol. 14, 1–16.

    Article  Google Scholar 

  • Jones, I., Currie, L., Martin, R., 2002. A guide to biological skin substitutes. Br. J. Plastic Surg. 55, 185–193.

    Article  Google Scholar 

  • Jones, P.H., Watt, F.M., 1993. Separation of human epidermal stem cells from transit amplifying cells on the basis of differences in integrin function and expression. Cell 73, 713–724.

    Article  Google Scholar 

  • MacLellan, D.G., 2004. Wound management in Australia: Progress and promise. Wounds 16(5), 183–188.

    Google Scholar 

  • Maini, P.K., McElwain, D.L.S., Leavesley, D.I., 2004a. Traveling wave model to interpret a wound-healing cell migration assay for human peritoneal mesothelial cells. Tissue Eng. 10(3/4), 475–482.

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Martin, P., 1997. Wound healing — Aiming for perfect skin regeneration. Science 276(5309), 75.

    Article  Google Scholar 

  • Mathor, M.B., Ferrari, G., Dellambra, E., Cilli, M., Mavilio, F., Cancedda, R., De Luca, M., 1996. Clonal analysis of stably transduced human epidermal stem cells in culture. Proc. Natl. Acad. Sci. U.S.A. 93, 10371–10376.

    Article  Google Scholar 

  • Moore, K., 2001. The scientific basis of wound healing. Adv. Tissue Bank. 5, 379–397.

    Google Scholar 

  • Morrison, S.J., Shah, N.M., Anderson, D.J., 1997. Regulatory mechanisms in stem cell biology. Cell 88, 287–298.

    Article  Google Scholar 

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

    Google Scholar 

  • Murray, J.D., 2003. Mathematical Biology. vol. II: Spatial Models and Biomedical Applications, 3rd edition. Springer-Verlag, Berlin.

    Google Scholar 

  • Navarro, F.A., Stoner, M.L., Park, C.S., Huertas, J.C., Lee, H.B., Wood, F.M., Orgill, D.P., 2000. Sprayed keratinocytes suspensions accelerate epidermal coverage in a porcine microwound model. J. Burn Care Rehab. 21, 513–518.

    Article  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, pp. 1–75.

  • Odland, G.F., 1991. Structure of the skin. In: Goldsmith, L.A. (Ed.), Physiology, Biochemistry, and Molecular Biology of the Skin, vol. 1, 2nd edition. Oxford University Press, Oxford, pp. 3–62, chapter 1.

    Google Scholar 

  • Papini, S., Cecchetti, D., Campani, D., Fitzgerald, W., Grivel, J.C., Chen, S., Margolis, L., Revoltella, R.P., 2003. Isolation and clonal analysis of human epidermal keratinocyte stem cells in long-term culture. Stem Cells 21, 481–494.

    Article  Google Scholar 

  • Pellegrini, G., Golisano, O., Paterna, P., Lambiase, A., Bonini, S., Rama, P., De Luca, M., 1999. Location and clonal analysis of stem cells and their differentiated progeny in the human ocular surface. J. Cell Biol. 145(4), 769–782.

    Article  Google Scholar 

  • Potten, C.S., 2002. Keratinocyte stem cells: A commentary. J. Invest. Dermatol. 119(4), 888–899.

    Article  Google Scholar 

  • Pruitt, B.A., 1992. Progress in burn care — Introduction. World J. Surg. 16, 1.

    Google Scholar 

  • Rochat, A., Kobayashi, K., Barrandon, Y., 1994. Location of stem cells of human hair follicles by clonal analysis. Cell 76, 1063–1073.

    Article  Google Scholar 

  • Ronfard, V., Rives, J., Neveux, Y., Carsin, J., Barrandon, Y., 2000. Long-term regeneration of human epidermis on third degree burns transplanted with autologous cultured epithelium grown on a fibrin matrix. Transplantation 70(11), 1588–1598.

    Article  Google Scholar 

  • Rosenberg, L., 2003. Wound healing, growth factors. eMedicine.

  • Sheardown, H., Cheng, Y.L., 1996. Mechanisms of corneal epithelial wound healing. Chem. Eng. Sci. 51(19), 4517–4529.

    Article  Google Scholar 

  • Sheridan, R., 2001. Clinical use of cultured keratinocytes. In: Cultured Human Keratinocytes and Tissue Engineered Skin Substitutes. Stuttgar, Thieme, pp. 268–274.

  • Sherratt, J.A., Dallon, J.C., 2002. Theoretical models on wound healing: Past successes and future challenges. C. R. Biol. 325, 557–564.

    Article  Google Scholar 

  • Sherratt, J.A., Murray, J.D., 1990. Models of epidermal wound healing. Proc. R. Soc. Lond., Ser. B 241, 29–36.

    Article  Google Scholar 

  • Sherratt, J.A., Murray, J.D., 1991. Mathematical analysis of a basic model for epidermal wound healing. J. Math. Biol. 29, 389–404.

    Article  MATH  Google Scholar 

  • Sherratt, J.A., Murray, J.D., 1992a. Epidermal wound healing: A theoretical approach. Comment. Theor. Biol. 2(5), 315–333.

    Google Scholar 

  • Sherratt, J.A., Murray, J.D., 1992b. Epidermal wound healing: The clinical implications of a simple mathematical model. Cell Transplant. 1, 365–371.

    Google Scholar 

  • Stenn, K.S., Malhotra, R., 1992. Wound Healing: Biochemical and Clinical Aspects. WB Saunders, Philadelphia, pp. 115–127, chapter 7.

  • Taylor, G., Lehrer, M.S., Jensen, P.J., Sun, T., Lavker, R.M., 2000. Involvement of follicular stem cells in forming not only the follicle but also the epidermis. Cell 102, 451–461.

    Article  Google Scholar 

  • Tortora, G.J., Grabowski, S.R., 2000. Principles of Anatomy and Physiology, 9th edition. Wiley, New York.

    Google Scholar 

  • Watt, F.M., 1998. Epidermal stem cells: Markers, patterning and the control of cell fate. Philos. Trans. R. Soc. Lond., Ser. B 353, 831–837.

    Article  Google Scholar 

  • Wearing, H.J., Sherratt, J.A., 2000. Keratinocyte growth factor signalling: A mathematical model of dermal—epidermal interactions in epidermal wound healing. Math. Biosci. 165, 41–62.

    Article  Google Scholar 

  • 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 Injury 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 

  • Yamaguchi, Y., Yoshikawa, K., 2001. Cutaneous wound healing: An update. J. Dermatol. 28, 521–534.

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, 4001, Australia

    Paula K. Denman & D. L. Sean McElwain

  2. School of Life Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, 4001, Australia

    Damien G. Harkin & Zee Upton

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  1. Paula K. Denman
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  2. D. L. Sean McElwain
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  3. Damien G. Harkin
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  4. Zee Upton
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Correspondence to Paula K. Denman.

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PACS: 92B05

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Denman, P.K., McElwain, D.L.S., Harkin, D.G. et al. Mathematical Modelling of Aerosolised Skin Grafts Incorporating Keratinocyte Clonal Subtypes. Bull. Math. Biol. 69, 157–179 (2007). https://doi.org/10.1007/s11538-006-9082-z

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