A mathematical model of tissue replacement during epidermal wound healing

Abstract A mathematical model, which describes the control of the development and growth of a healing unit, is presented. The replacement of epidermal injured tissue, which is controlled by a negative feedback mechanism, is modeled in one-dimensional geometry. The model is based on diffusion equations that relate the production of macrophage-derived growth factors (MDGFs) to oxygen availability, the capillary density growth to MDGF production and concentration, and the oxygen concentration to the growth of capillary density. The results of the model suggest that the normal healing of a circular epidermal wound depends on the oxygen supply, and in order for successful healing to take place, the oxygen concentration within the wound space must be at low levels.

[1]  J. Bereiter-Hahn.  Epidermal Cell Migration and Wound Repair , 1986 .

[2]  Jonathan A. Sherratt,et al.  Models of epidermal wound healing , 1990, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[3]  J A Sherratt,et al.  Mathematical modeling of corneal epithelial wound healing. , 1994, Mathematical biosciences.

[4]  T. K. Hunt,et al.  Regulation of wound-healing angiogenesis-effect of oxygen gradients and inspired oxygen concentration. , 1981, Surgery.

[5]  F. Arnold,et al.  Angiogenesis in wound healing. , 1991, Pharmacology & therapeutics.

[6]  A. E. Savakis,et al.  Models of shrinking clusters with applications to epidermal wound healing , 1997 .

[7]  J. Davidson,et al.  Anipulation of the Wound‐Healing Process with Basic Fibroblast Growth Factor a , 1991 .

[8]  I. K. Cohen,et al.  Wound Healing: Biochemical & Clinical Aspects , 1992 .

[9]  J A Sherratt,et al.  A mechanochemical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile. , 1995, Journal of theoretical biology.

[10]  G. Schultz,et al.  Growth factors and wound healing: Part II. Role in normal and chronic wound healing. , 1993, American journal of surgery.

[11]  M A Rupnick,et al.  Chemotaxis of human microvessel endothelial cells in response to acidic fibroblast growth factor. , 1990, Laboratory investigation; a journal of technical methods and pathology.

[12]  E. H. Mercer.  The cancer cell. , 1962, British medical bulletin.

[13]  G. Odland,et al.  HUMAN WOUND REPAIR , 1968, The Journal of cell biology.

[14]  J. Bereiter-Hahn,et al.  Biology of the Integument , 1984, Springer Berlin Heidelberg.