Bulletin of Mathematical Biology

, Volume 58, Issue 4, pp 787–808 | Cite as

A mathematical model for fibro-proliferative wound healing disorders

  • Luke Olsen
  • Jonathan A. Sherratt
  • Philip K. Maini


The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable.

In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsenet al., J. theor. Biol. 177, 113–128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay.

Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states—a central property of the model, which is evident from stability and bifurcation analyses.

The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders.


Travel Wave Solution Hypertrophic Scar Normal Healing Wound Contraction Dermal Wound Healing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Asmussen, P. D. and B. Söllner. 1993.Wound Care. Principles of Wound Healing. Hamburg: Beiersdorf Medical Bibliothek.Google Scholar
  2. Bell, E., B. Ivarsson and C. Merrill. 1979. Production of a tissue-like structure by contraction of collagen lattices by human fibroblasts of different proliferative potentialin vitro.Proc. Natl. Acad. Sci. USA 76, 1274–1278.CrossRefGoogle Scholar
  3. Bowen-Pope, D. F., T. W. Malpass, D. M. Foster and R. Ross. 1984. Platelet-derived growth factorin vivo: levels, activity and rate of clearance.Blood 64, 458–469.Google Scholar
  4. Boykin, J. V. and J. A. Molnar. 1992. Burn scar and skin equivalents. InWound Healing: Biochemical and Clinical Aspects. I. K. Cohen, R. F. Diegelmann and W. J. Lindblad (Eds), pp. 523–540. Philadelphia: Saunders.Google Scholar
  5. Clark, R. A. F. 1988. Overview and general considerations of wound repair. InThe Molecular and Cellular Biology of Wound Repair. R. A. F. Clark and P. M. Henson (Eds), pp. 3–34. New York: Plenum.Google Scholar
  6. Clark, R. A. F. 1991. Growth factors and wound repair.J. Cell. Biochem. 46, 1–2.CrossRefGoogle Scholar
  7. Clark, R. A. F. 1993. Regulation of fibroplasia in cutaneous wound repair.Am. J. Med. Sci. 306, 42–48.Google Scholar
  8. Dale, P. D., P. K. Maini and J. A. Sherratt. 1994. Mathematical modelling of corneal epithelial wound healing.Math. Biosci. 124, 127–147.zbMATHCrossRefGoogle Scholar
  9. Ehrlich, H. P., A. Desmoulière, R. F. Diegelmann, I. K. Cohen, C. C. Compton, W. L. Garner, Y. Kapanci and G. Gabbiani. 1994. Morphological and immunochemical differences between keloid and hypertrophic scar.Am. J. Pathol. 145, 105–113.Google Scholar
  10. Flint, M. H. 1990. Connective tissue biology. InDupuytren's Disease: Biology and Treatment. R. M. McFarlane, D. A. McGrouther and M. H. Flint (Eds), p. 13–24. Edinburgh: Churchill Livingstone.Google Scholar
  11. Gabbiani, G. 1992. The biology of the myofibroblast.Kidney Int. 41, 530–532.Google Scholar
  12. Jennings, R. W. and T. K. Hunt. 1992. Overview of postnatal wound healing. InFetal Wound Healing, N. S. Adzick and M. T. Longaker (Eds), pp. 25–52. New York: Elsevier.Google Scholar
  13. Kirsner, R. S. and W. H. Eaglstein. 1993. The wound healing process.Dermatol. Clin. 11, 629–640.Google Scholar
  14. Martin, P., J. Hopkinson-Woolley and J. McCluskey. 1992. Growth factors and cutaneous wound repair.Prog. Growth Fact. Res. 4, 24–44.zbMATHGoogle Scholar
  15. Mast, B. A. 1992. The skin. InWound Healing: Biochemical and Clinical Aspects. I. K. Cohen, R. F. Diegelmann and W. J. Lindblad (Eds), pp. 344–355. Philadelphia: Saunders.Google Scholar
  16. McCann, B. G., A. Logan, H. Belcher, A. Warn and R. M. Warn. 1993. The presence of myofibroblasts in patients with Dupuytren's Contracture. A possible source for recurrence.J. Hand Surg. Br. 18, 656–661.CrossRefGoogle Scholar
  17. Murray, J. C. 1993. Scars and keloids.Dermatol. Clin. 11, 697–708.Google Scholar
  18. Murray, J. C. and S. R. Pinnell. 1992. Keloids and excessive dermal scarring. InWound Healing: Biochemical and Clinical Aspects. I. K. Cohen, R. F. Diegelmann and W. J. Lindblad (Eds), pp. 500–509, Philadelphia: Saunders.Google Scholar
  19. Murray, J. D. 1989.Mathematical Biology. New York: Springer-Verlag.Google Scholar
  20. Murray, J. D., P. K. Maini and R. T. Tranquillo. 1988. Mechanochemical models for generating biological pattern and form in development.Phys. Rep.,171, 59–84.MathSciNetCrossRefGoogle Scholar
  21. Olsen, L., J. A. Sherratt and P. K. Maini. 1995. A mechanochemical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile.J. theor. Biol. 177, 113–128.CrossRefGoogle Scholar
  22. Raines, E. W., D. F. Bowen-Pope and R. Ross. 1990. Platelet-derived growth factor. InHandbook of Experimental Pharmacology. M. B. Sporn and A. B. Roberts (Eds), Vol. 95, Part I, pp. 173–262. Heidelberg: Springer-Verlag.Google Scholar
  23. Rudolph, R., J. Vande Berg and H. P. Ehrlich. 1992. Wound contraction and scar contracture. InWound Healing: Biochemical and Clinical Aspects. I. K. Cohen, R. F. Diegelmann and W. J. Lindblad (Eds), pp. 96–114. Philadelphia: Saunders.Google Scholar
  24. Rudolph, R. and J. Vande Berg. 1991. The myofibroblast in Dupuytren's contracture.Hand Clin. 7, 683–692.Google Scholar
  25. Schürch, W., O. Skalli and G. Gabbiani. 1990. Cellular biology. InDupuytren's Disease: Biology and Treatment. R. M. McFarlane, D. A. McGrouther and M. H. Flint (Eds), pp. 31–47. Edinburgh: Churchill Livingstone.Google Scholar
  26. Sherratt, J. A., E. H. Sage and J. D. Murray. 1993. Chemical control of eukaryotic cell movement: a new model.J. theor. Biol. 162, 23–40.CrossRefGoogle Scholar
  27. Skalli, O. and G. Gabbiani. 1988. The biology of the myofibroblast. Relationship to wound contraction and fibrocontractive diseases. InThe Molecular and Cellular Biology of Wound Repair. R. A. F. Clark and P. M. Henson (Eds), pp. 373–402. New York: Plenum.Google Scholar
  28. Skalli, O., W. Schürch, T. Seemayer, R. Lagacé, D. Montandon, B. Pittet and G. Gabbiani. 1989. Myofibroblasts from diverse pathologic settings are heterogeneous in their content of actin isoforms and intermediate filament proteins.Lab. Invest. 60, 275–285.Google Scholar
  29. Sprugel, K. H., J. M. McPherson, A. W. Clowes and R. Ross. 1987. Effects of growth factorsin vivo.Am. J. Pathol. 129, 601–613.Google Scholar
  30. Tranquillo, R. T. and J. D. Murray. 1992. Continuum model of fibroblast-driven wound contraction: inflammation-mediation.J. theor. Biol. 158, 135–172.CrossRefGoogle Scholar
  31. Traqui, P., D. E. Woodward, G. C. Cruywagen, J. Cook and J. D. Murray. 1996. A mechanical model for fibroblast-driven wound healing.J. Biol. Systems, in press.Google Scholar
  32. Vande Berg, J. S., R. Rudolph, W. L. Poolman and D. R. Disharoon. 1988. Comparative growth dynamics and actin concentration between cultured human myofibroblasts from granulating wounds and dermal fibroblasts from normal skin.Lab. Invest. 61, 532–538.Google Scholar

Copyright information

© Society for Mathematical Biology 1996

Authors and Affiliations

  • Luke Olsen
    • 1
  • Jonathan A. Sherratt
    • 2
  • Philip K. Maini
    • 1
  1. 1.Centre for Mathematical BiologyMathematical InstituteOxfordUK
  2. 2.Nonlinear Systems Laboratory, Mathematics InstituteUniversity of WarwickCoventryUK

Personalised recommendations