Mathematical Model of Chronic Dermal Wounds in Diabetes and Obesity
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Mathematical Model of Chronic Dermal Wounds in Diabetes and Obesity Avner Friedman1 · Nourridine Siewe2 Received: 13 January 2020 / Accepted: 27 September 2020 / Published online: 15 October 2020 © Society for Mathematical Biology 2020
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. Keywords Chronic dermal wound · Diabetes · Obesity · M1–M2 blockade · Oxygen blockade
1 Introduction Chronic wounds are wounds that fail to heal within sufficient time period. Chronic dermal wounds (or skin ulcers) account for approximately 6 million skin wounds in the USA WinVivo (2012). Chronic wound patients frequently suffer from type 2 diabetes or obesity Sen et al. (2009); in the USA 95% diabetic cases are type 2 diabetes Hamilton (2013), and in the sequel we often refer to type 2 diabetes shortly as diabetes. More than 2.3 million Americans are treated for diabetes-related skin ulcer each year WinVivo (2012). Approximately 10% of people with diabetes have
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Nourridine Siewe [email protected]
1
Mathematical Biosciences Institute and Department of Mathematics, The Ohio State University, Columbus, OH, USA
2
School of Mathematical Sciences, Rochester Institute of Technology, 1 Lomb Memorial Dr, Rochester, NY 14623, USA
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foot ulcer American Diabetes Associatio (2018). Between 10–15% of diabetes wound ulcers do not heal, and 25% of them will require amputation Azura Vascular Care (2017). With the prevalence of diabetes at 10% among the US population American Diabetes Associatio (2018) and of obesity at 40% Hales et al. (2017), it is becoming urgent to develop a deeper understanding of how diabetes and obesity inhibit or slow the healing process of dermal wounds. The present paper addresses this question with a mathematical model. The process of wound healing can be divided into four somewhat overlapping stages: homeostasis, inflammation, proliferation, and remodeling (Goldberg and Diegelmann 2010; de Oliveira Gonzalez et al. 2016). In homeostasis which starts immediately after injury, clotting factors are delivered by platelets derived factor PDGF which also chemoattracts pro-inflammatory macrophages M1 and fibroblasts (Goldberg and Diegelmann 2010; de Oliveira Gonzalez et
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