A multicomponent model for biofilm-drug interaction

Brandon Lindley; Qi Wang; Tianyu Zhang

doi:10.3934/dcdsb.2011.15.417

Article Contents

2011, Volume 15, Issue 2: 417-456. Doi: 10.3934/dcdsb.2011.15.417

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A multicomponent model for biofilm-drug interaction

1.
US Naval Research Laboratory, 4555 Overlook Ave. Southwest, Washington, DC 20375
2.
Department of Mathematics & NanoCenter, University of South Carolina, Columbia, SC 29208
3.
Department of Mathematical Sciences, Montana State University, P.O. Box 172400, Bozeman, MT 59717-2400

Received: November 30, 2009

Revised: February 28, 2010

Published: August 2011

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Abstract

We develop a tri-component model for the biofilm and solvent mixture, in which the extracellular polymeric substance (EPS) network, bacteria and effective solvent consisting of the solvent, nutrient, drugs etc. are modeled explicitly. The tri-component mixture is assumed incompressible as a whole while inter-component mixing, dissipation, and conversion are allowed. A linear stability analysis is conducted on constant equilibria revealing up to two unstable modes corresponding to possible bacterial growth induced by the bacterial and EPS production and dependent upon the regime of the model parameters. A 1-D transient simulation is carried out to investigate the nonlinear dynamics of the EPS network, bacteria distribution, drug and nutrient distribution in a channel with and without shear. Finally, the transient biofilm dynamics are studied with respect to a host of diffusive properties of the drug and nutrient present in the biofilm.

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Mathematics Subject Classification: Primary: 92C05, 92C15; Secondary: 92B05.

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