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Mathematical Model of Chronic Dermal Wounds in Diabetes and Obesity
Avner Friedman1, Nourridine Siewe2
1Mathematical Biosciences Institute and Department of Mathematics, The Ohio State University, Columbus, OH, USA.
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.
Insights
This study identifies four key factors impairing chronic wound healing in diabetic and obese patients: glycation, leukotrienes, stromal derived factor-1 (SDF-1), and insulin resistance. A mathematical model shows these factors hinder wound closure by reducing oxygen flow and macrophage transition.
Area of Science:
- Biomedical Engineering
- Mathematical Biology
- Wound Healing Research
Background:
- Chronic dermal wounds are prevalent in patients with type 2 diabetes and obesity, increasing amputation risk.
- Impaired wound healing in these populations is multifactorial, necessitating a deeper understanding of underlying mechanisms.
Purpose of the Study:
- To identify key factors that impede chronic wound healing in diabetic and obese patients.
- To develop and utilize a mathematical model to analyze the impact of these factors on wound closure.
- To assess potential therapeutic interventions, including insulin injection and oxygen infusion.
Main Methods:
- Identification of four critical factors: excessive glycation, excessive leukotriene production, decreased stromal derived factor-1 (SDF-1) production, and insulin resistance.
- Development of a mathematical model using partial differential equations to simulate wound healing dynamics.
- Analysis of how identified factors affect oxygen flow and macrophage polarization within the wound microenvironment.
Main Results:
- The mathematical model demonstrated that the four identified factors significantly impair wound closure.
- Reduced oxygen flow to the wound area was shown to be a consequence of these factors.
- The transition of pro-inflammatory to anti-inflammatory macrophages was inhibited, further complicating healing.
Conclusions:
- Excessive glycation, leukotrienes, decreased SDF-1, and insulin resistance are critical barriers to chronic wound healing.
- Mathematical modeling provides valuable insights into the mechanisms by which these factors impede healing.
- The model supports the potential efficacy of insulin and oxygen therapies for improving wound healing outcomes.
