Modeling and simulation of a bacterial biofilm that is controlled by pH and protonated lactic acids
type: Item
instance of: scholarly article
title: Modeling and simulation of a bacterial biofilm that is controlled by pH and protonated lactic acids
zbMATH Open document ID: 1145.92002
DOI: 10.1080/17486700701797922
author: Hassan Khassehkhan
author: Hermann J. Eberl
published in: Computational \& Mathematical Methods in Medicine
publication date: 2008-08-15T00:00:00Z
full work available at URL: https://eudml.org/doc/222647
review text: Summary: 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 nonlinear 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 the bacterial biomass shows two nonlinear 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.
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 92C37
Mathematics Subject Classification ID: 65C20
zbMATH DE Number: 5312713
MaRDI profile type: Publication
OpenAlex ID: W2160317018
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description: scientific article; zbMATH DE number 5312713