4.2 Article

Modeling and simulation of a bacterial biofilm that is controlled by pH and protonated lactic acids

Journal

Publisher

HINDAWI LTD
DOI: 10.1080/17486700701797922

Keywords

bacterial biofilm; degenerate diffusion; numerical simulation; lactic acids; pH

Funding

  1. Canada's Network Centers
  2. NSERC
  3. Canada Research Chairs Program

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We present a mathematical model for growth and control of facultative anaerobic bacterial biofilms in nutrient rich environments. The growth of the microbial population is limited by protonated lactic acids and the local pH value, which in return are altered as the microbial population changes. The process is described by a non-linear parabolic system of three coupled equations for the dependent variables biomass density, acid concentration and pH. While the equations for the dissolved substrates are semi-linear, the equation for bacterial biomass shows two non-linear diffusion effects, a power law degeneracy as the dependent variable vanishes and a singularity in the diffusion coefficient as the dependent variable approaches its a priori known threshold. The interaction of both effects describes the spatial spreading of the biofilm. The interface between regions where the solution is positive and where it vanishes is the biofilm/bulk interface. We adapt a numerical method to explicitly track this interface in x-t space, based on the weak formulation of the biofilm model in a moving frame. We present numerical simulations of the spatio-temporal biofilm model, applied to a probiotic biofilm control scenario. It is shown that in the biofilm neighbouring regions co-exist in which pathogenic bacterial biomass is produced or killed, respectively. Furthermore, it is illustrated how the augmentation of the bulk with probiotic bacteria leads to an accelerated decay of the pathogenic biofilm.

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