A partial differential equation model of a novel treatment for chronic wound biofilm infections

BACKGROUND: Chronic wounds, such as pressure ulcers, venous leg ulcers, and diabetic foot ulcers, present a significant healthcare challenge due to their prolonged healing times and association with biofilm infections. This study introduces a mathematical model to investigate wound healing dynamics during the proliferative stage, focusing on chronic wound conditions characterised by poor vascularisation, clotting deficiencies, cellular senescence, and bacterial biofilms. METHODS: The model examines the interactions between fibroblasts, keratinocytes, granulation tissue, nutrients, and signalling molecules under normal and impaired healing scenarios. The potential of bioactive glass fibres, doped with antimicrobial and wound healing ions, is also explored. FINDINGS: Model results reflect the impairment of wound healing by biofilm infections, with larger bacterial populations leading to poorer outcomes. Simulations suggest that antimicrobial ions reduce bacterial populations and improve nutrient availability, supporting fibroblast and immune cell activity. Reapplication of bioactive glass fibres enhances ion concentrations, further promoting granulation tissue formation and wound closure under certain conditions. INTERPRETATION: Results identify critical parameters that hinder healing in untreated wounds and demonstrate how bioactive glass fibre design can be optimised to enhance healing outcomes. This work provides a foundation for designing cost-effective treatments for chronic wounds, addressing a significant unmet clinical need.