A three dimensional model of wound healing: Analysis and computation

Avner Friedman, Bei Hu, Chuan Xue

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

This paper is concerned with a three-dimensional model of wound healing. The boundary of the wound is a free boundary, and the region surrounding it is viewed as a partially healed tissue, satisfying a viscoelastic constitutive law for the velocity v. In the partially healed region the densities of several types of cells and the concentrations of several chemical species satisfy a coupled system of parabolic equations, whereas the tissue density satisfies a hyperbolic equation. The parabolic equations include advection by the velocity v and chemotaxis/haptotaxis terms. We prove existence and uniqueness of a smooth solution of the free boundary problem, for some time interval 0 ≤ t ≤ T, T > 0. We also simulate the model equations to demonstrate the difference in the healing rate between normal wounds and chronic (or ischemic) wounds.

Original languageEnglish (US)
Pages (from-to)2691-2712
Number of pages22
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume17
Issue number8
DOIs
StatePublished - Nov 2012

Keywords

  • Existence and uniqueness of solutions
  • Free boundary problems
  • Ischemia
  • Viscoelasticity
  • Wound healing

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