Computational and Mathematical Methods in Medicine

Computational and Mathematical Methods in Medicine / 2008 / Article

Original Article | Open Access

Volume 9 |Article ID 313525 | https://doi.org/10.1080/17486700701797922

Hassan Khassehkhan, Hermann J. Eberl, "Modeling and Simulation of a Bacterial Biofilm That Is Controlled by pH and Protonated Lactic Acids", Computational and Mathematical Methods in Medicine, vol. 9, Article ID 313525, 21 pages, 2008. https://doi.org/10.1080/17486700701797922

Modeling and Simulation of a Bacterial Biofilm That Is Controlled by pH and Protonated Lactic Acids

Received14 Aug 2006
Revised11 Oct 2007
Accepted25 Oct 2007

Abstract

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 xt 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.

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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