A three species model to simulate application of hyperbaric oxygen therapy to chronic wounds

Chronic wounds are a significant socioeconomic problem for governments worldwide. Approximately 15% of people who suffer from diabetes will experience a lower-limb ulcer at some stage of their lives, and 24% of these wounds will ultimately result in amputation of the lower limb. Hyperbaric Oxygen Therapy (HBOT) has been shown to aid the healing of chronic wounds; however, the causal reasons for the improved healing remain unclear and hence current HBOT protocols remain empirical. Here we develop a three-species mathematical model of wound healing that is used to simulate the application of hyperbaric oxygen therapy in the treatment of wounds. Based on our modelling, we predict that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds. Furthermore, treatment should continue until healing is complete, and HBOT will not stimulate healing under all circumstances, leading us to conclude that finding the right protocol for an individual patient is crucial if HBOT is to be effective. We provide constraints that depend on the model parameters for the range of HBOT protocols that will stimulate healing. More specifically, we predict that patients with a poor arterial supply of oxygen, high consumption of oxygen by the wound tissue, chronically hypoxic wounds, and/or a dysfunctional endothelial cell response to oxygen are at risk of nonresponsiveness to HBOT. The work of this paper can, in some way, highlight which patients are most likely to respond well to HBOT (for example, those with a good arterial supply), and thus has the potential to assist in improving both the success rate and hence the costeffectiveness of this therapy.

Mathematical modelling of chronic wound healing

Chronicwounds fail to proceed through an orderly process to produce anatomic and functional integrity and are a significant socioeconomic problem. There is much debate about the best way to treat these wounds. In this thesis we review earlier mathematical models of angiogenesis and wound healing. Many of these models assume a chemotactic response of endothelial cells, the primary cell type involved in angiogenesis. Modelling this chemotactic response leads to a system of advection-dominated partial differential equations and we review numerical methods to solve these equations and argue that the finite volume method with flux limiting is best-suited to these problems. One treatment of chronic wounds that is shrouded with controversy is hyperbaric oxygen therapy (HBOT). There is currently no conclusive data showing that HBOT can assist chronic wound healing, but there has been some clinical success. In this thesis we use several mathematical models of wound healing to investigate the use of hyperbaric oxygen therapy to assist the healing process - a novel threespecies model and a more complex six-species model. The second model accounts formore of the biological phenomena but does not lend itself tomathematical analysis. Bothmodels are then used tomake predictions about the efficacy of hyperbaric oxygen therapy and the optimal treatment protocol. Based on our modelling, we are able to make several predictions including that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds, treatment should continue until healing is complete and finding the right protocol for an individual patient is crucial if HBOT is to be effective. Analysis of the models allows us to derive constraints for the range of HBOT protocols that will stimulate healing, which enables us to predict which patients are more likely to have a positive response to HBOT and thus has the potential to assist in improving both the success rate and thus the cost-effectiveness of this therapy.

Application of hyperbaric oxygen in bone tissue engineering : effect of hyperbaric oxygen treatment on bone marrow stem cells

and non-union of bony fractures has been proposed since 1966, little has been known about the effect of HBOT on bone marrow stem cells (BMSC). The aim of this study is to investigate the effect of HBO treatment on osteogenetic differentiation of BMSC and potential application in bone tissue engineering. Adhesive stromal cells harvested from bone marrow were characterized by mesenchymal differentiation potential, cell surface markers and their proliferation capacity. Mesenchymal stem cells, which demonstrated osteogenic, chondrogenic and adipogenic differentiation potential and expressed positively for CD 29, CD 44, CD 73, CD 90, CD 105, CD 166 and negatively for CD34 and CD 45, were selected and treated in a laboratory-scale HBO chamber using different oxygen pressures and exposure times. No obvious effect of HBO treatment on BMSC proliferation was noticed. However, cytotoxic effects of HBO were considerably less pronounced when cells were cultured in medium supplemented with 10% FBS in comparison to medium supplemented with 2% FCS, as was evaluated by WST-1 assay. Under HBO treatment, bone nodules were formed in three days, which was clearly revealed by Von Kossa staining. In contrasts, without HBO treatment, bone nodules were not detected until 9-12 days using the same inducing culture media. Calcium deposition was also significantly increased after three days of HBO treatments compared to no HBO treatment. In addition it was also found that oxygen played a direct role in the enhancement of BMSC osteogenic differentiation, which was independent of the effect of air pressure.