title: A mathematical model for lymphangiogenesis in normal and diabetic wounds.
abstract: Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis) very few have been proposed for the regeneration of the lymphatic network. Moreover, lymphangiogenesis is markedly distinct from angiogenesis, occurring at different times and in a different manner. Here a model of five ordinary differential equations is presented to describe the formation of lymphatic capillaries following a skin wound. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from experimental and clinical data. The system is then solved numerically and the results are compared with the available biological literature. Finally, a parameter sensitivity analysis of the model is taken as a starting point for suggesting new therapeutic approaches targeting the enhancement of lymphangiogenesis in diabetic wounds. The work provides a deeper understanding of the phenomenon in question, clarifying the main factors involved. In particular, the balance between TGF-β and VEGF levels, rather than their absolute values, is identified as crucial to effective lymphangiogenesis. In addition, the results indicate lowering the macrophage-mediated activation of TGF-β and increasing the basal lymphatic endothelial cell growth rate, inter alia, as potential treatments. It is hoped the findings of this paper may be considered in the development of future experiments investigating novel lymphangiogenic therapies.
authors.affiliation: Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, Scotland, EH14 4AS, UK. Electronic address: ab584@hw.ac.uk.
authors.forename: Arianna
authors.initials: A
authors.lastname: Bianchi
authors.affiliation: Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, Scotland, EH14 4AS, UK.
authors.forename: Kevin J
authors.initials: KJ
authors.lastname: Painter
authors.affiliation: Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, Scotland, EH14 4AS, UK.
authors.forename: Jonathan A
authors.initials: JA
authors.lastname: Sherratt
mesh_terms: D003920:Diabetes Mellitus / Q000378:metabolism / Q000503:physiopathology*; D006801:Humans; D042583:Lymphangiogenesis / Q000502:physiology*; D042601:Lymphatic Vessels; D008264:Macrophages / Q000502:physiology; D008954:Models, Biological; D012867:Skin / Q000293:injuries; D016212:Transforming Growth Factor beta / Q000378:metabolism; D042461:Vascular Endothelial Growth Factor A / Q000378:metabolism; D014945:Wound Healing / Q000502:physiology*
chemical_list: D016212:Transforming Growth Factor beta; C467484:VEGFA protein, human; D042461:Vascular Endothelial Growth Factor A
keywords: Diabetes; Lymphatics; Modelling; Wound healing