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Mathematical Model of Chronic Dermal Wounds in Diabetes and Obesity

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Abstract

Chronic dermal-wound patients frequently suffer from diabetes type 2 and obesity; without treatment or early intervention, these patients are at risk of amputation. In this paper, we identified four factors that impair wound healing in these populations: excessive production of glycation, excessive production of leukotrient, decreased production of stromal derived factor (SDF-1), and insulin resistance. We developed a mathematical model of wound healing that includes these factors. The model consists of a system of partial differential equations, and it demonstrates how these four factors impair the closure of the wound, by reducing the oxygen flow into the wound area and by blocking the transition from pro-inflammatory macrophages to anti-inflammatory macrophages. The model is used to assess treatment by insulin injection and by oxygen infusion.

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  • 07 January 2021

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Acknowledgements

This research was supported by the Mathematical Biosciences Institute of The Ohio State University. This work was conducted while Nourridine Siewe was a Postdoctoral Fellow at the University of British Columbia, Okanagan.

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  1. Mathematical Biosciences Institute and Department of Mathematics, The Ohio State University, Columbus, OH, USA

    Avner Friedman

  2. School of Mathematical Sciences, Rochester Institute of Technology, 1 Lomb Memorial Dr, Rochester, NY, 14623, USA

    Nourridine Siewe

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Friedman, A., Siewe, N. Mathematical Model of Chronic Dermal Wounds in Diabetes and Obesity. Bull Math Biol 82, 137 (2020). https://doi.org/10.1007/s11538-020-00815-x

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