Abstract

Citation

Researchers should cite this work as follows:

• Jones, M., Song, B., Thomas, D. (2023). 2004-Jones-Song-Thomas-Controlling wound healing through debridement. SIMIODE, QUBES Educational Resources. doi:10.25334/9904-N236

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Jones, M., B. Song, and D. Thomas. Controlling wound healing through debridement.  Mathematical and Computer Modelling 40(9-10):1057-1064

DOI:10.1016/j.mcm.2003.09.041. Accessed 27 March 2023.

Abstract. The formation of slough (dead tissue) on a wound is widely accepted as an inhibitor to natural wound healing. In this article, a system of differential equations that models slough/wound interaction is developed. We prove a threshold theorem that provides conditions on the amount of slough to guarantee wound healing. As a state-dependent time scale, debridement (the periodic removal of slough) is used as a control. We show that closure of the wound can be reached in infinite time by debriding.

A system of two first order differential equations for the area of the wound and the area of the slough around the wound is developed. The model is modified and studied. Phase plot analysis is rendered and a threshold theorem is developed. The effects of debriding (removal of necrotic tissue to promote wound healing) are discussed.

KEYWORDS: bacteria, wound, healing, system, differential equation, model, isoclines, phase plot, deriding