Bulletin of Mathematical Biology

, Volume 59, Issue 6, pp 1077–1100 | Cite as

Role of fibroblast migration in collagen fiber formation during fetal and adult dermal wound healing

  • Paul D. Dale
  • Jonathan A. Sherratt
  • Philip K. Maini


Adult dermal wounds, in contrast to fetal wounds, heal with the formation of scar tissue. A crucial factor in determining the degree of scarring is the ratio of types I and III collagen, which regulates the diameter of the combined fibers. We developed a reaction-diffusion model which focuses on the control of collagen synthesis by different isoforms of the polypeptide transforming growth factor-β (TGFβ). We used the model to investigate the current controversy as to whether the fibroblasts migrate into the wound from the surrounding unwounded dermis or from the underlying subcutaneous tissue. Numerical simulations of a spatially independent, temporal model led to a value of the collagen ratio consistent with that of healthy tissue for the fetus, but corresponding to scarring in the adult. We investigated the effect of topical application of TGFβ and show that addition of isoform 3 reduces scar tissue formation, in agreement with the experiment. However, numerical solutions of the reaction-diffusion system do not exhibit this sensitivity to growth factor application. Mathematically, this corresponds to the observation that behind healing wavefront solutions, a particular healed state is always selected independent of transients, even though there is a continuum of possible positive steady states. We explain this phenomenon using a caricature system of equations, which reflects the key qualitative features of the full model but has a much simpler mathematical form. Biologically, our results suggest that the migration into a wound of fibroblasts and TGFβ from the surrounding dermis alone cannot account for the essential features of the healing process, and that fibroblasts entering from the underlying subcutaneous tissue are crucial to the healing process.


Wound Healing Wave Speed Travel Wave Solution Collagen Level Fetal Skin 
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Copyright information

© Society for Mathematical Biology 1997

Authors and Affiliations

  • Paul D. Dale
    • 1
  • Jonathan A. Sherratt
    • 2
  • Philip K. Maini
    • 1
  1. 1.Centre for Mathematical BiologyMathematical InstituteOxfordU.K.
  2. 2.Nonlinear Systems Laboratory, Mathematics InstituteUniversity of WarwickCoventryU.K.

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