A differential equation model of collagen accumulation in a healing wound

Bull Math Biol. 2012 Sep;74(9):2165-82. doi: 10.1007/s11538-012-9751-z. Epub 2012 Jul 19.


Wound healing is a complex biological process which involves many cell types and biochemical signals and which progresses through multiple, overlapping phases. In this manuscript, we develop a model of collagen accumulation as a marker of wound healing. The mathematical model is a system of ordinary differential equations which tracks fibroblasts, collagen, inflammation and pathogens. The model was validated by comparison to the normal time course of wound healing where appropriate activity for the inflammatory, proliferative and remodeling phases was recorded. Further validation was made by comparison to collagen accumulation experiments by Madden and Peacock (Ann. Surg. 174(3):511-520, 1971). The model was then used to investigate the impact of local oxygen levels on wound healing. Finally, we present a comparison of two wound healing therapies, antibiotics and increased fibroblast proliferation. This model is a step in developing a comprehensive model of wound healing which can be used to develop and test new therapeutic treatments.

Publication types

  • Comparative Study

MeSH terms

  • Collagen / metabolism*
  • Fibroblasts / metabolism
  • Humans
  • Inflammation / metabolism*
  • Inflammation / pathology
  • Models, Biological*
  • Oxygen / metabolism
  • Wound Healing / physiology*


  • Collagen
  • Oxygen