Bulletin of Mathematical Biology

, Volume 72, Issue 7, pp 1867–1891

Mathematical Model of Hyperbaric Oxygen Therapy Applied to Chronic Diabetic Wounds

  • Jennifer A. Flegg
  • Helen M. Byrne
  • D. L. Sean McElwain
Original Article


The failure of certain wounds to heal (including diabetic foot ulcers) is a significant socioeconomic issue for countries worldwide. There is much debate about the best way to treat these wounds and one approach that is shrouded with controversy is hyperbaric oxygen therapy (HBOT), a technique that can reduce the risk of amputation in diabetic patients.

In this paper, we develop a six species mathematical model of wound healing angiogenesis and use it to investigate the effectiveness of HBOT, compare the response to different HBOT protocols and study the effect of HBOT on the healing of diabetic wounds that fail to heal for a variety of reasons. We vary the pressure level (1 atm–3 atm), percentage of oxygen inspired by the patient (21%–100%), session duration (0–180 minutes) and frequency (twice per day–once per week) and compare the simulated wound areas associated with different protocols after three weeks of treatment.

We consider a variety of etiologies of wound chronicity and show that HBOT is only effective in treating certain causes of chronic wounds. For a wound that fails to heal due to excessive, oxygen-consuming bacteria, we show that intermittent HBOT can accelerate the healing of a chronic wound but that sessions should be continued until complete healing is observed. Importantly, we also demonstrate that normobaric oxygen is not a replacement for HBOT and supernormal healing is not an expected outcome. Our simulations illustrate that HBOT has little benefit for treating normal wounds, and that exposing a patient to fewer, longer sessions of oxygen is not an appropriate treatment option.


Hyperbaric oxygen Optimal protocol Chronic wound Mathematical modelling Diabetes 



hyperbaric oxygen therapy


extracellular matrix


endothelial cells


platelet derived growth factor


vascular endothelial growth factor




matrix metalloproteinases


partial differential equations


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Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  • Jennifer A. Flegg
    • 1
  • Helen M. Byrne
    • 2
  • D. L. Sean McElwain
    • 1
  1. 1.Discipline of Mathematical Sciences and Institute of Health and Biomedical InnovationQueensland University of TechnologyBrisbaneAustralia
  2. 2.School of Mathematical SciencesUniversity of NottinghamNottinghamUK

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