A new individual-based modelling framework for bacterial biofilm growth applied to cold plasma treatment

Biofilms are colonies of bacteria attached to the surface at a solid-fluid interface. Bacteria in biofilm produce exopolysaccharides (EPS) that form a gel-like matrix in which the bacteria are embedded. Biofilms have numerous consequences in industrial and medical settings, both positive (bioreactors, digestion) and negative (blocking, as corrosive damage of materials/devices, food contamination, clinical infection). The use of antibiotics or mechanical clearing can be effective at removing biofilms, but such treatments are not always effective or appropriate in all situations. Recently, non-thermal atmospheric plasma treatments have been proposed as an alternative (or complementary) form of treatment, that can target sites of infection with minimal damage to the surroundings (e.g. host cells in a clinical setting). These plasmas generate a multitude of chemical species, most of which are very short lived, that can infiltrate and diffuse into the biofilm killing the bacteria within. The aim of this thesis is to develop a multi-dimensional mathematical model to investigate the effect of a non- thermal plasma on biofilms in time and space and to identify key factors that determine effectiveness of the treatment. Most of the chemical products of cold plasmas are too short lived, or too reactive, to be effective in killing the biofilms, it is the longer live species, e.g. ozone, hydrogen peroxide, acid species, that penetrated the biofilm and do the most damage. However, the EPS in biofilms is an effective barrier against ozone and hydrogen peroxide. No published biofilm model combines multi-dimensional growth with a detailed description of EPS production, hence a new mathematical model is developed and applied to simulating plasma treatment. The thesis is split broadly into two parts. The first part presents a new biofilm model framework that simulates growth in response to any number of substrates (e.g. nutrient, oxygen). The model combines an Individual based model (IbM) description of bacteria (individuals or clusters) and substrates are described as a continuum. Novel features of the framework are the assumption that EPS forms a continuum over the domain and the explicit consideration of cellular energy (ATP). Simulations of this model demonstrate the contrast between biofilm grown with topical nutrient sources (forming irregular, bumpy biofilm) and basal nutrient source with topical oxygen such as biofilm grown on agar (forming regular spatially uniform biofilms). The former is in broad agreement with experiments whilst the latter, to our knowledge, has been the subject of very little experimental study. The second part extends the modelling framework to consider the effect of the plasma species. The simulations demonstrate that penetration is a key factor in their effectiveness, for which EPS plays a key role in preventing spread within and beyond the plasma treated zone. The simulations provide estimates of the timescale of equilibration of the main plasma species, predict the effect of combining these species and demonstrate how the constituents of the biofilm can change following treatment. A number of recommended suggestions for future theoretical and experimental study are discussed in the conclusions.