A Mathematical Model for Lymphangiogenesis in Normal and Diabetic Wounds

TL;DR

This paper presents a new mathematical model using differential equations to describe lymphangiogenesis in wounds, highlighting key factors like TGF-$\beta$ and VEGF, and suggesting potential therapeutic strategies for diabetic wound healing.

Contribution

A novel five-equation model specifically for lymphangiogenesis in wounds, with parameter estimation and sensitivity analysis for therapeutic insights.

Findings

Balance of TGF-$\beta$ and VEGF is crucial for lymphangiogenesis.

Lowering macrophage activation of TGF-$\beta$ may enhance healing.

Increasing basal lymphatic endothelial cell growth could be beneficial.

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-$\beta$ 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-$\beta$ and increasing the basal lymphatic endothelial cell growth rate, \emph{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.