Mathematical modelling of a novel bioactive glass treatment for bacterial biofilms

Abstract

Chronic wounds (principally pressure sores, venous leg ulcers and diabetic foot ulcers) are a drain on global health services and remain a major area of unmet clinical need. Chronic wounds are characterised by a bacterial biofilm (densely aggregated colonies of bacteria encased by a matrix of extracellular polymeric substances), which hinders innate immune response and can prevent wound healing. Bioactive glass (BG) fibres doped with antimicrobial metal ions, such as silver, can offer a promising treatment for chronic wound infections, where silver is well known for its antimicrobial activity against a range of pathogens and is commonly used in wound dressings. We first present a system of non-linear partial differential equations to model the treatment of a chronic wound biofilm infection with BG fibres. The BG fibres are assumed to have two mechanisms of action against the biofilm: physical disruption of the top layers of the biofilm by the BG fibres; and release of antimicrobial silver ions from the BG fibres, which then diffuse into the biofilm and can kill the bacteria. Treatment-associated parameters are estimated from in vitro experimental data using a combination of least-squares minimisation and Approximate Bayesian Computation (ABC). Sensitivity investigations are performed on other parameters that cannot currently be calculated experimentally to investigate their influence on treatment efficacy. We thus predict key parameter regimes that should lead to biofilm eradication, crucially informing the future design of metal-doped BG fibres to maximise treatment efficacy.