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Mathematical Model of Hyperbaric Oxygen Therapy Applied to Chronic Diabetic Wounds

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Abstract

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.

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Abbreviations

HBOT:

hyperbaric oxygen therapy

ECM:

extracellular matrix

EC:

endothelial cells

PDGF:

platelet derived growth factor

VEGF:

vascular endothelial growth factor

atm:

atmospheres

MMPs:

matrix metalloproteinases

PDEs:

partial differential equations

References

  • Abidia, A., Laden, G., Kuhan, G., Johnson, B.F., Wilkinson, A.R., Renwick, P.M., Masson, E.A., McCollum, P.T., 2003. The role of hyperbaric oxygen therapy in ischaemic diabetic lower extremity ulcers: a double-blind randomised-controlled trial. Eur. J. Vasc. Endovasc. Surg. 25, 513–518.

    Article  Google Scholar 

  • Acker, T., Beck, H., Plate, K.H., 2001. Cell type specific expression of vascular endothelial growth factor and angiopoietin-1 and -2 suggests an important role of astrocytes in cerebellar vascularization. Mech. Dev. 108(1–2), 45–57.

    Article  Google Scholar 

  • Adams, R.H., Alitalo, K., 2007. Molecular regulation of angiogenesis and lymphangiogenesis. Nature Rev. Mol. Cell Biol. 8, 464–478.

    Article  Google Scholar 

  • Agren, M.S., Eaglstein, W.H., Ferguson, M.W.J., Harding, K.G., Moore, K., Saarialho-Kere, U.K., Schultz, G.S., 2000. Causes and effects of the chronic inflammation in venous leg ulcers. Acta Derm. Venereol. Suppl. 210, 3–17.

    Google Scholar 

  • Al-Waili, N.S., Butler, G.J., 2006. Effects of hyperbaric oxygen on inflammatory response to wound and trauma: possible mechanism of action. Sci. World 6, 425–441.

    Google Scholar 

  • Alessio, M., Gruarin, P., Castagnoli, C., Trombotto, C., Stella, M., 1998. Primary ex vivo culture of keratinocytes isolated from hypertrophic scars as a means of biochemical characterization of CD36. Int. J. Clin. Lab. Res. 28(1), 47–54.

    Article  Google Scholar 

  • Allen, D.B., Maguire, J.J., Mahdavian, M., Wicke, C., Marcocci, L., Scheuenstuhl, H., Chang, M., Le, A.X., Hopf, H.W., Hunt, T.K., 1997. Wound hypoxia and acidosis limit neutrophil bacterial killing mechanisms. Arch. Surg. 132(9), 991–996.

    Google Scholar 

  • Anonymous, 1999. American diabetes association: consensus development conference on diabetic foot wound care. Diabetes Care 22, 1354–1360.

    Article  Google Scholar 

  • Babul, S., Rhodes, E.C., 2000. The role of hyperbaric oxygen therapy in sports medicine. Sports Med. 30(6), 395–403.

    Article  Google Scholar 

  • Balding, D., McElwain, D.L.S., 1985. A mathematical model of tumour-induced capillary growth. J. Theor. Biol. 114(1), 53–73.

    Article  Google Scholar 

  • Bauer, S.M., Bauer, R.J., Liu, Z.J., Chen, H., Goldstein, L., Velazquez, O.C., 2005a. Vascular endothelial growth factor-C promotes vasculogenesis, angiogenesis, and collagen constriction in three-dimensional collagen gels. J. Vasc. Surg. 41(4), 699–707.

    Article  Google Scholar 

  • Bauer, S.M., Bauer, R.J., Velazquez, O.C., 2005b. Angiogenesis, vasculogenesis, and induction of healing in chronic wounds. Vasc. Endovasc. Surg. 39(4), 293–306.

    Article  Google Scholar 

  • Boykin, J.V., Baylis, C., 2007. Hyperbaric oxygen therapy mediates increased nitric oxide production associated with wound healing: a preliminary study. Adv. Skin Wound Care 20(7), 382–389.

    Article  Google Scholar 

  • Byrne, H.M., Chaplain, M.A.J., 1996. Explicit solutions of a simplified model of capillary sprout growth during tumour angiogenesis. Appl. Math. Lett. 9(1), 69–74.

    Article  MATH  MathSciNet  Google Scholar 

  • Byrne, H.M., Chaplain, M.A.J., Evans, D.L., Hopkinson, I., 2000. Mathematical modelling of angiogenesis in wound healing: comparison of theory and experiment. J. Theor. Med. 2, 175–197.

    MATH  Google Scholar 

  • Carmeliet, P., 2004. Manipulating angiogenesis in medicine. J. Int. Med. 255, 538–561.

    Article  Google Scholar 

  • Chang, N., Goodson, W.H., Gottrup, F., Hunt, T.K., 1983. Direct measurement of wound and tissue oxygen tension in postoperative patients. Ann. Surg. 197(4), 470–478.

    Article  Google Scholar 

  • Chaplain, M.A.J., Orme, M.E., 1998. Mathematical Modeling of Tumor-Induced Angiogenesis, Birkhauser, Bosu. Chapter 3.4, pp. 205–240.

    Google Scholar 

  • Chen, C., Schultz, G.S., Bloch, M., Edwards, P.D., Tebes, S., Mast, B.A., 1999. Molecular and mechanistic validation of delayed healing rat wounds as a model for human chronic wounds. Wound Repair Regen. 7(6), 486–494.

    Article  Google Scholar 

  • Chen, S., Yu, C., Cheng, Y., Yu, S., Lo, H., 2007. Effects of hyperbaric oxygen therapy on circulatory interleukin-8, nitric oxide, and insulin-like growth factors in patients with type 2 diabetes mellitus. Clin. Biochem. 40, 30–36.

    Article  Google Scholar 

  • Chen, W.Y.J., Rogers, A.A., 2007. Recent insights into the causes of chronic leg ulceration in venous diseases and implications on other types of chronic wounds. Wound Repair Regen. 15(4), 434–449.

    Article  Google Scholar 

  • Cianci, P., 2004. Advances in the treatment of the diabetic foot: is there a role for adjunctive hyperbaric oxygen. Wound Repair Regen. 12(1), 2–10.

    Article  Google Scholar 

  • Clark, R.A.F., 1996. In: The Molecular and Cellular Biology of Wound Repair, Wound Repair Overview and Considerations, pp. 3–35. Plenum, New York. Chapter 1.

    Google Scholar 

  • Clark, R.A.F., Ghosh, K., Tonnesen, M.G., 2007. Tissue engineering for cutaneous wounds. J. Investig. Dermatol. 127, 1018–1029.

    Article  Google Scholar 

  • Cliff, W.J., 1963. Observations on healing tissue: a combined light and electron microscopic investigation. Philos. Trans. R. Soc. Lond. Ser. B, Biol. Sci. 246(733), 305–325.

    Article  Google Scholar 

  • Cook, J., 1995. Mathematical models for dermal wound healing: wound contraction and scar formation. PhD thesis, University of Washington.

  • David, L.A., Sandor, G.K.B., Evans, A.W., Brown, D.H., 2001. Hyperbaric oxygen therapy and mandibular osteoradionecrosis: a retrospective study and analysis of treatment outcomes. J. Can. Dent. Assoc. 67, 384.

    Google Scholar 

  • Dewhirst, M.W., 1994. Determination of local oxygen consumption rates in tumors. Cancer Res. 54(13), 3333–3336.

    Google Scholar 

  • Diegelmann, R.F., Evans, M.C., 2004. Wound healing: an overview of acute, fibrotic and delayed healing. Frontiers Biosci. 9, 283–289.

    Article  Google Scholar 

  • Dimitrijevich, S.D., Paranjape, S., Wilson, J.R., Gracy, R.W., Mills, J.G., 1999. Effect of hyperbaric oxygen on human skin cells in culture and in human dermal and skin equivalents. Wound Repair Regen. 7(1), 53–64.

    Article  Google Scholar 

  • Dor, Y., Djonov, V., Keshet, E., 2003. Making vascular networks in the adult: branching morphogenesis without a roadmap. Trends Cell Biol. 13(3), 131–136.

    Article  Google Scholar 

  • Edelstein, L., 1982. The propagation of fungal colonies: a model for tissue growth. J. Theor. Biol. 98, 671–701.

    Article  MathSciNet  Google Scholar 

  • Edelstein, L., Segel, L.A., 1983. Growth and metabolism in mycelial fungi. J. Theor. Biol. 104(22), 187–210.

    Article  Google Scholar 

  • Edelstein, L., Hadar, Y., Chet, I., Henis, Y., Segel, L.A., 1983. A model for fungal colony growth applied to sclerotium reolfsii. J. Gen. Microbiol. 129, 1873–1881.

    Google Scholar 

  • Eginton, M.T., Brown, K.R., Seabrook, G.R., Towne, J.B., Cambria, R.A., 2003. A prospective randomized evaluation of negative-pressure wound dressings for diabetic foot wounds. J. Ann. Vasc. Surg. 17(6), 645–649.

    Article  Google Scholar 

  • Enoch, S., Price, P., 2004. Cellular, molecular and biochemical differences in the pathophysiology of healing between acute wounds, chronic wounds and wounds in the aged. World Wide Wounds. Available from http://www.worldwidewounds.com//2004/august/Enoch/Pathophysiology-Of-Healing.html.

  • Faglia, E., Favales, F., Aldeghi, A., Calia, P., Quarantiello, A., Oriani, G., Michael, M., Campagnoli, P., Morabito, A., 1996. Adjunctive systemic hyperbaric oxygen therapy in treatment of severe prevalently ischemic diabetic foot ulcers. Diabetes Care 19(12), 1338–1343.

    Article  Google Scholar 

  • Fife, C.E., Buyukcakir, C., Otto, G.H., Sheffield, P.J., Warriner, R.A., Love, T.L., Mader, J., 2002. The predictive value of transcutaneous oxygen tension measurement in diabetic lower extremity ulcers treated with hyperbaric oxygen therapy: a retrospective analysis of 1144 patients. Wound Repair Regen. 10(4), 198–207.

    Article  Google Scholar 

  • Flegg, J.A., McElwain, D.L.S., Byrne, H.M., Turner, I.W., 2009. A three species model to simulate application of hyperbaric oxygen therapy to chronic wounds. PLoS Comput. Biol. 5(7), e1000451.

    Article  MathSciNet  Google Scholar 

  • Fries, R.B., Wallace, W.A., Roy, S., Kuppusamy, P., Bergdall, V., Gordillo, G.M., Melvin, W.S., Sen, C.K., 2005. Dermal excisional wound healing in pigs following treatment with topically applied pure oxygen. Mutat. Res.-Fundam. Mol. Mech. Mutagenes. 579(1–2), 172–181.

    Article  Google Scholar 

  • Gaffney, E.A., Pugh, K., Maini, P.K., Arnold, F., 2002. Investigating a simple model of cutaneous wound healing angiogenesis. J. Math. Biol. 45(4), 337–374.

    Article  MATH  MathSciNet  Google Scholar 

  • Gajendrareddy, P.K., Sen, C.K., Horan, M.P., Marucha, P.T., 2005. Hyperbaric oxygen therapy ameliorates stress-impaired dermal wound healing. Brain Behav. Immun. 19(3), 217–222.

    Article  Google Scholar 

  • Gallagher, K.A., Goldstein, L.J., Thom, S.R., Velazquez, O.C., 2006. Hyperbaric oxygen and bone marrow-derived endothelial progenitor cells in diabetic wound healing. Vascular 14(6), 328–37.

    Article  Google Scholar 

  • Gill, A.L., Bell, C.N.A., 2004. Hyperbaric oxygen: its uses, mechanisms of action and outcomes. Q. J. Med. 97, 385–395.

    Google Scholar 

  • Gordillo, G.M., Sen, C.K., 2003. Revisiting the essential role of oxygen in wound healing. Am. J. Surg. 186, 259–263.

    Article  Google Scholar 

  • Gordillo, G.M., Roy, S., Khanna, S., Schlanger, R., Khanderlwal, S., Phillips, G., Sen, C., 2008. Topical oxygen therapy induces vascular endothelial growth factor expression and improves closure of clinically presented chronic wounds. Clin. Exp. Pharmacol. Physiol. 35, 957–964.

    Article  Google Scholar 

  • Gottrup, F., 2004. Oxygen in wound healing and infection. World J. Surg. 28(3), 312–315.

    Article  Google Scholar 

  • Grey, J.E., Harding, K.G. (Eds.), 2006. ABC of Wound Healing. Blackwell, Oxford.

    Google Scholar 

  • Hammarlund, C., Sundberg, T., 1994. Hyperbaric oxygen reduced size of chronic leg ulcers: a randomised double-blind study. Plast. Reconstr. Surg. 93(4), 829–834.

    Article  Google Scholar 

  • Harmey, J.H., Dimitriadis, E., Kay, E., Redmond, H.P., Bouchier-Hayes, D., 1998. Regulation of macrophage production of vascular endothelial growth factor (VEGF) by hypoxia and transforming growth factor β−1. Ann. Surg. Oncol. 5(3), 271–278.

    Article  Google Scholar 

  • Hehenberger, K., Brismar, K., Lind, F., Kratz, G., 1997. Dose-dependent hyperbaric oxygen stimulation of human fibroblast proliferation. Wound Repair Regen. 5(2), 147–150.

    Article  Google Scholar 

  • Hollander, D.A., Hakimi, M.Y., Hartmann, A., Wilhelm, K., Windolf, J., 2000. The influence of hyperbaric oxygenation (HBO) on proliferation and differentiation of human keratinocyte cultures in vitro. Cell Tissue Bank. 1, 261–269.

    Article  Google Scholar 

  • Hopf, H.W., Gibson, J.J., Angeles, A.P., Constant, J.S., Feng, J.J., Rollins, M.D., Hussain, M.Z., Hunt, T.K., 2005. Hyperoxia and angiogenesis. Wound Repair Regen. 13(6), 558–564.

    Article  Google Scholar 

  • Hopf, H.W., Ueno, C., Aslam, R., Burnand, K., Fife, C., Grant, L., Holloway, A., Iafrati, M.D., Mani, R., Misare, B., Rosen, N., Shapshak, D., Slade, J.B., West, J., Barbul, A., 2006. Guidelines for the treatment of arterial insufficiency ulcers. Wound Repair Regen. 14(6), 693–710.

    Article  Google Scholar 

  • Hunt, T.K., Zederfeldt, B., Goldstick, T.K., 1969. Oxygen and healing. Am. J. Surg. 118(4), 521–525.

    Article  Google Scholar 

  • Hunt, T.K., Twomey, P., Zederfeldt, B., Dunphy, J.E., 1967. Respiratory gas tensions and pH in healing wounds. Am. J. Surg. 114(2), 302–7.

    Article  Google Scholar 

  • Ichioka, S., Ando, T., Shibata, M., Sekiya, N., Nakatsuka, T., 2008. Oxygen consumption of keloids and hypertrophic scars. Ann. Plast. Surg. 60(2), 194.

    Article  Google Scholar 

  • James, P.B., Scott, B., Allen, M.W., 1993. Hyperbaric oxygen therapy in sports injuries. Physiotherapy 79(8), 571–572.

    Article  Google Scholar 

  • Keller, E.F., Segel, L.A., 1971. Traveling bands of chemotactic bacteria: a theoretical analysis. J. Theor. Biol. 30, 235–248.

    Article  Google Scholar 

  • Kessler, L., Bilbault, P., Ortega, F., Grasso, C., Passemard, R., Stephan, D., Pinget, M., Schneider, F., 2003. Hyperbaric oxygenation accelerates the healing rate of nonischemic chronic diabetic foot ulcers. Diabetes Care 26(8), 2378–2382.

    Article  Google Scholar 

  • Knighton, D.R., Silver, I.A., Hunt, T.K., 1981. Regulation of wound-healing angiogenesis—effect of oxygen gradients and inspired oxygen concentration. Surgery 90, 262–270.

    Google Scholar 

  • Leach, R.M., Rees, P.J., Wilmshurst, P., 1998. ABC of oxygen: hyperbaric oxygen therapy. Br. Med. J. 317, 1140–1143.

    Google Scholar 

  • Lerman, O.Z., Galiano, R.D., Armour, M., Levine, J.P., Gurtner, G.C., 2003. Cellular dysfunction in the diabetic fibroblast. Am. J. Pathol. 162(1), 303–312.

    Google Scholar 

  • Levine, H.A., Sleeman, B.D., Nilsen-Hamilton, M., 2000. A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis. Math. Biosci. 168(1), 77–115.

    Article  MATH  MathSciNet  Google Scholar 

  • Levine, H.A., Pamuk, S., Sleeman, B.D., Nilsen-Hamilton, M., 2001. Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma. Bull. Math. Biol. 63(5), 801–863.

    Article  Google Scholar 

  • Levine, H.A., Pamuk, S., Sleeman, B.D., Nilsen-Hamilton, M., 2002. Mathematical modelling of tumour angiogenesis and the action of angiostatin as a protease inhibitor. J. Theor. Med. 4(2), 133–145.

    Article  MATH  Google Scholar 

  • Lin, H., Chi, S., Perng, W., Wu, C., Lin, Z., Huang, K., 2008. Hyperbaric oxygen attenuates cell growth in skin fibroblasts cultured in a high-glucose medium. Wound Repair Regen. 16(4), 513–519.

    Article  Google Scholar 

  • Mace, K.A., Yu, D.H., Paydar, K.Z., Boudreau, N., Young, D.M., 2007. Sustained expression of Hif-1alpha in the diabetic environment promotes angiogenesis and cutaneous wound repair. Wound Repair Regen. 15(5), 636–645.

    Article  Google Scholar 

  • Mathieu, D., 2002. Hyperbaric Surgery, Hyperbaric Oxygen Therapy in the Management of Non-healing Wounds, pp. 317–339. Best Publishing Company. Chapter 12.

  • Moore, K., Ruge, F., Harding, K.G., 1997. T lymphocytes and the lack of activated macrophages in wound margin biopsies from chronic leg ulcers. Br. J. Dermatol. 137, 188–194.

    Article  Google Scholar 

  • Murray, J.D., Oster, G.F., Harris, A.K., 1983. A mechanical model for mesenchymal morphogenesis. J. Math. Biol. 17(1), 125–129.

    Article  MATH  Google Scholar 

  • Murray, J.D., Maini, P.K., Tranquillo, R.T., 1988. Mechanochemical models for generating biological pattern and form in development. Phys. Rep. 171(2), 59–84.

    Article  MathSciNet  Google Scholar 

  • Niklas, A., Brock, D., Schober, R., Schulz, D., Schneider, A., 2004. Continuous measurements of cerebral tissue oxygen pressure during hyperbaric oxygenation–HBO effects on brain edema and necrosis after severe brain trauma in rabbits. J. Neurol. Sci. 219(1–2), 77–82.

    Article  Google Scholar 

  • Oberringer, M., Meins, C., Bubel, M., Pohlemann, T., 2007. A new in vitro wound model based on the co-culture of human dermal microvascular endothelial cells and human dermal fibroblasts. Biol. Cell. 99(4), 197–207.

    Article  Google Scholar 

  • Olaso, E., Labrador, J.P., Wang, L.H., Ikeda, K., Eng, F.J., Klein, R., Lovett, D.H., Lin, H.C., Friedman, S.L., 2002. Discoidin domain receptor 2 regulates fibroblast proliferation and migration through the extracellular matrix in association with transcriptional activation of matrix metalloproteinase-2. J. Biol. Chem. 277(5), 3606–3613.

    Article  Google Scholar 

  • Olsen, L., Sherratt, J.A., Maini, P.K., 1995. A mechanochemical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile. J. Theor. Biol. 177, 113–128.

    Article  Google Scholar 

  • Olsen, L., Sherratt, J.A., Maini, P.K., Arnold, F., 1997. A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis. Math. Med. Biol. 14(4), 261–281.

    Article  MATH  Google Scholar 

  • Olsen, L., Maini, P.K., Sherratt, J.A., 1998. Spatially varying equilibria of mechanical models: application to dermal wound contraction. Math. Biosci. 147(1), 113–129.

    Article  MATH  MathSciNet  Google Scholar 

  • Oyibo, S.O., Jude, E.B., Tarawneh, I., Nguyem, H.C., Armstrong, D.G., Harkless, L.B., Boulton, A.J.M., 2001. The effects of ulcer size and site, patient’s age, sex and type and duration of diabetes on the outcome of diabetic foot ulcers. Diabetic Med. 18(2), 133–138.

    Article  Google Scholar 

  • Panovska, J., Byrne, H.M., Maini, P.K., 2008. A theoretical study of the response of vascular tumours to different types of chemotherapy. Math. Comput. Model. 47, 560–579.

    Article  MATH  MathSciNet  Google Scholar 

  • Pettet, G.J., Byrne, H.M., McElwain, D.L.S., Norbury, J., 1996a. A model of wound-healing angiogenesis in soft tissue. Math. Biosci. 136(1), 35–63.

    Article  MATH  Google Scholar 

  • Pettet, G.J., Chaplain, M.A.J., McElwain, D.L.S., Byrne, H.M., 1996b. On the role of angiogenesis in wound healing. Proc. R. Soc. Lond. B 263(1376), 1487–1493.

    Article  Google Scholar 

  • Piantadosi, C.A., 1999. Physiology of hyperbaric hyperoxia. Respir. Care Clin. North Am. 5(1), 7–19.

    Google Scholar 

  • Polverini, P.J., 1995. The pathophysiology of angiogenesis. Critical Rev. Oral Biol. Med. 6(3), 230–247.

    Article  Google Scholar 

  • Polverini, P.J., 2002. Angiogenesis in health and disease: insights into basic mechanisms and therapeutic opportunities. J. Dent. Educ. 66(8), 962–975.

    Google Scholar 

  • Raa, A., Stansberg, C., Steen, V.M., Bjerkvig, R., Reed, R.K., Stuhr, L.E.B., 2007. Hyperoxia retards growth and induces apoptosis and loss of glands and blood vessels in DMBA-induced rat mammary tumors. BMC Cancer 7, 23.

    Article  Google Scholar 

  • Said, H.K., Hijjawi, J., Roy, N., Mogford, J., Mustoe, T., 2005. Transdermal sustained-delivery oxygen improves epithelial healing in a rabbit ear wound model. Arch. Surg. 140, 998–1004.

    Article  Google Scholar 

  • Schugart, R.C., Friedman, A., Zhao, R., Sen, C.K., 2008. Wound angiogenesis as a function of tissue oxygen tension: a mathematical model. Proc. Natl. Acad. Sci. 105(7), 2628.

    Article  Google Scholar 

  • Sen, C.K., Khanna, S., Gordillo, G., Bagchi, D., Bagchi, M., Roy, S., 2002. Oxygen, oxidants, and antioxidants in wound healing. Ann. N.Y. Acad. Sci. 957, 239–249.

    Article  Google Scholar 

  • Sen, C.K., Gordillo, G.M., Roy, S., Kirsner, R., Lambert, L., Hunt, T.K., Gottrup, F., Gurtner, G.C., Longaker, M.T., 2009. Human skin wounds: a major and snowballing threat to public health and the economy. Wound Repair Regen. 17(6), 763–771.

    Article  Google Scholar 

  • Serini, G., Ambrosi, D., Giraudo, E., Gamba, A., Preziosi, L., Bussolino, F., 2003. Modeling the early stages of vascular network assembly. EMBO J. 22, 1771–1779.

    Article  Google Scholar 

  • Sheffield, P.J., 1985. Tissue oxygen measurements with respect to soft tissue wound healing with normobaric and hyperbaric oxygen. HBO Rev. 6(1), 18–46.

    Google Scholar 

  • Silverman, W.A., 2004. A cautionary tale about supplemental oxygen: the albatross of neonatal medicine. Pediatrics 113(2), 394–396.

    Article  Google Scholar 

  • Simons, M., 2005. Angiogenesis, arteriogenesis, and diabetes paradigm reassessed? J. Am. College Cardiol. 46(5), 835–837.

    Article  MathSciNet  Google Scholar 

  • Singer, A.J., Clark, R.A.F., 1999. Cutaneous Wound Healing. New Engl. J. Med. 341(10), 738–746.

    Article  Google Scholar 

  • Slovis, N., 2006. Veterinary hyperbaric medicine society: review of hyperbaric medicine. On line.

  • Sola, A., Saldeño, Y.P., Favareto, V., 2008. Clinical practices in neonatal oxygenation: where have we failed? What can we do? J. Perinatol. 28(1), S28–34.

    Article  Google Scholar 

  • Sun, S., Wheeler, M.F., Obeyesekere, M., Patrick, C., 2005. Nonlinear behaviors of capillary formation in a deterministic angiogenesis model. Nonlinear Anal. 63, 2273–2246.

    Article  Google Scholar 

  • Tandara, A.A., Mustoe, T.A., 2004. Oxygen in wound healing—more than a nutrient. World J. Surg. 28, 294–300.

    Article  Google Scholar 

  • Thackham, J.A., McElwain, D.L.S., Long, B., 2008. The use of hyperbaric oxygen therapy to treat chronic wounds: a review. Wound Repair Regen. 16(3), 321–330.

    Article  Google Scholar 

  • Thackham, J.A., McElwain, D.L.S., Turner, I.W., 2009. Computational approaches to solving equations arising from wound healing. Bull. Math. Biol. 71, 211–246.

    Article  MATH  MathSciNet  Google Scholar 

  • Thom, S.R., 2009. Oxidative stress is fundamental to hyperbaric oxygen therapy. J. Appl. Phys. 106, 988–995.

    Article  Google Scholar 

  • Tompach, P.C., Lew, D., Stoll, J.L., 1997. Cell response to hyperbaric oxygen treatment. Int. J. Oral. Maxillofac. Surg. 26(2), 82–86.

    Article  Google Scholar 

  • Trabold, O., Wagner, S., Wicke, H., Scheuenstuhl, C., Hussain, M.Z., Rosen, N., Seremetiev, A., Becker, H.D., Hunt, T.K., 2003. Lactate and oxygen constitute a fundamental regulatory mechanism in wound healing. Wound Repair Regen. 11(6), 504–509.

    Article  Google Scholar 

  • Tranquillo, R.T., Murray, J.D., 1992. Continuum model of fibroblast-driven wound contraction: inflammation-mediation. J. Theor. Biol. 158, 135–172.

    Article  Google Scholar 

  • Williams, R.L., 1997. Hyperbaric oxygen therapy and the diabetic foot. J. Am. Podiatr. Med. Assoc. 87(6), 279–292.

    Google Scholar 

  • Woo, T.C., Joseph, D., Oxer, H., 1997. Hyperbaric oxygen treatment for radiation proctitis. Int. J. Radiat. Oncol. Biol. Phys. 38(3), 619–22.

    Google Scholar 

  • Xue, C., Friedman, A., Sen, C.K., 2009. A mathematical model of ischemic cutaneous wounds. Proc. Nat. Acad. Sci. 106(39), 16782.

    Article  Google Scholar 

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Flegg, J.A., Byrne, H.M. & McElwain, D.L.S. Mathematical Model of Hyperbaric Oxygen Therapy Applied to Chronic Diabetic Wounds. Bull. Math. Biol. 72, 1867–1891 (2010). https://doi.org/10.1007/s11538-010-9514-7

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