Wound healing angiogenesis: The clinical implications of a simple mathematical model


Flegg, Jennifer A.
Byrne, Helen M.
Flegg, Mark B.
Sean McElwain, D.L.

KAUST Grant Number


Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds. © 2012 Elsevier Ltd.

Flegg JA, Byrne HM, Flegg MB, Sean McElwain DL (2012) Wound healing angiogenesis: The clinical implications of a simple mathematical model. Journal of Theoretical Biology 300: 309–316. Available: http://dx.doi.org/10.1016/j.jtbi.2012.01.043.

This work was supported by the award of a doctoral scholarship to J.A.F. from the Institute of Health and Biomedical Innovation at Queensland University of Technology and was funded by Australian Research Council's Discovery Projects funding scheme (Project no. DP0878011). This research was carried out while H.M.B. was visiting Queensland University of Technology, funded by the Institute of Health and Biomedical Innovation and the Discipline of Mathematical Sciences. Computational resources and services used in this work were provided by the HPC and Research Support Unit, QUT. This publication was based on work supported in part by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).

Elsevier BV

Journal of Theoretical Biology


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