A mathematical model of ischemic cutaneous wounds

Chuan Xue, Avner Friedman, Chandan K. Sen

Research output: Contribution to journalArticlepeer-review

99 Scopus citations


Chronic wounds represent a major public health problem affecting 6.5 million people in the United States. Ischemia, primarily caused by peripheral artery diseases, represents a major complicating factor in cutaneous wound healing. In this work, we sought to develop a mathematical model of ischemic dermal wounds. The model consists of a coupled system of partial differential equations in the partially healed region, with the wound boundary as a free boundary. The extracellular matrix (ECM) is assumed to be viscoelastic, and the free boundary moves with the velocity of the ECM at the boundary. The model equations involve the concentration of oxygen, PDGF and VEGF, the densities of macrophages, fibroblasts, capillary tips and sprouts, and the density and velocity of the ECM. Simulations of the model demonstrate how ischemic conditions may limit macrophage recruitment to the wound-site and impair wound closure. The results are in general agreement with experimental findings.

Original languageEnglish (US)
Pages (from-to)16782-16787
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number39
StatePublished - Sep 29 2009
Externally publishedYes


  • Free boundary
  • Ischemia
  • Viscoelasticity
  • Wound healing


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