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A Mathematical Model of Biofilm Growth and Decay

Nassar, David Aziz
http://rave.ohiolink.edu/etdc/view?acc_num=akron1239645901

Abstract Details

2009, Master of Science, University of Akron, Applied Mathematics.
A biofilm is a community of microorganisms embedded in a matrix of proteins, nucleic acids, and polysaccharides. It has been noted that bacteria growing in biofilm conditions are much more resistant to antimicrobials than those bacteria growing in non-biofilm conditions. This paper describes a mathematical model of biofilm growth and decay. The model includes a set of reaction-diffusion equations used to describe the movement of soluble components of the biofilm such as nutrients and antimicrobial agents, and a set of population equations for the description of the particulate components of the biofilm such as forms of bacteria and the component providing structure to the biofilm known as extracellular polymeric substance (EPS). The aim of this paper is to describe a two-dimensional model and the subsequent assumptions made to reduce and solve it as a one-dimensional model. The one-dimensional model that results will be solved using ordinary differential equation solution techniques. From this simplified model, it has been shown that topical treatment with antimicrobial as well as nanosphere delivery for antimicrobial are effective treatment options. Moreover, the modelled mechanism of resistance for bacteria growing in biofilms, ‘persister’ bacteria, was observed. Living bacteria growing with high initial persister populations showed less growth than those living bacteria growing with low initial persister populations. The parametric study between the terms kf and kR (rate of formation of persisters and rate of reversion to living bacteria, respectively) shows that change in these values affects bacterial population sizes, but does not seriouslyaffect the minimum inhibitory concentration (MIC) of the antimicrobial. In conclusion, a summary for calculating proper dosage levels of antimicrobial with nanosphere delivery is performed showing the application of the model to drug-testing.
Gerald Young, PhD (Advisor)
Curtis Clemons, PhD (Advisor)
J. Patrick Wilber, PhD (Advisor)
Biology; Mathematics
biofilm; model; mathematics; continuum; persister; EPS; extracellular polymeric substance; nanosphere; nanoparticle; math

Recommended Citations

Citations

  • Nassar, D. A. (2009). A Mathematical Model of Biofilm Growth and Decay [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1239645901

    APA Style (7th edition)

  • Nassar, David. A Mathematical Model of Biofilm Growth and Decay. 2009. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1239645901.

    MLA Style (8th edition)

  • Nassar, David. "A Mathematical Model of Biofilm Growth and Decay." Master's thesis, University of Akron, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=akron1239645901

    Chicago Manual of Style (17th edition)

akron1239645901
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© 2009, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.