An Extension of the Boundary Integral Method Applied to Periodic Disinfection of a Dynamic Biofilm

Several tolerance mechanisms have been introduced to explain how bacterial biofilms are protected from disinfection. One mechanism describes the transition between two subpopulations of bacteria, one of which consumes nutrients, divides, and is susceptible to antimicrobial agents. The other subpopulation consists of dormant bacteria that are insensitive to treatments. It has been shown that the presence of this persister subpopulation can explain experimental observations of bacterial tolerance, at least in simplified domains. This investigation describes the development of a two-dimensional model of an established biofilm immersed in a flowing bulk fluid, where the biofilm influences the fluid dynamics and where the fluid flow can deform the biofilm. We introduce several extensions to this model, including the reaction between the biofilm and the antimicrobial agent, bacterial and exo-polymeric substance production, and persister dynamics. The model and numerical methods are based on the boundary integra...

[1]  P. Stewart,et al.  Adaptive responses to antimicrobial agents in biofilms. , 2005, Environmental microbiology.

[2]  K. Lewis,et al.  Riddle of Biofilm Resistance , 2001, Antimicrobial Agents and Chemotherapy.

[3]  P. Stewart,et al.  Biofilm resistance to antimicrobial agents. , 2000, Microbiology.

[4]  Bruce P. Ayati,et al.  A Multiscale Model of Biofilm as a Senescence-Structured Fluid , 2006, Multiscale Model. Simul..

[5]  I. Klapper,et al.  Description of mechanical response including detachment using a novel particle model of biofilm/flow interaction. , 2007, Water science and technology : a journal of the International Association on Water Pollution Research.

[6]  J. Costerton,et al.  Bacterial biofilms in nature and disease. , 1987, Annual review of microbiology.

[7]  J. Wimpenny,et al.  A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models , 1997 .

[8]  J. Costerton Cystic fibrosis pathogenesis and the role of biofilms in persistent infection. , 2001, Trends in microbiology.

[9]  C. Pozrikidis,et al.  Interfacial dynamics for Stokes flow , 2001 .

[10]  S. Leibler,et al.  Bacterial Persistence as a Phenotypic Switch , 2004, Science.

[11]  D. Allison,et al.  Clonal variation in maximum specific growth rate and susceptibility towards antimicrobials , 2003, Journal of applied microbiology.

[12]  M. R. Brown,et al.  Increasing resistance of planktonic and biofilm cultures of Burkholderia cepacia to ciprofloxacin and ceftazidime during exponential growth. , 1998, The Journal of antimicrobial chemotherapy.

[13]  H. Eberl,et al.  Exposure of biofilms to slow flow fields: the convective contribution to growth and disinfection. , 2008, Journal of theoretical biology.

[14]  D A Stahl,et al.  Use of rRNA fluorescence in situ hybridization for measuring the activity of single cells in young and established biofilms , 1993, Applied and environmental microbiology.

[15]  C. Pozrikidis,et al.  Modeling and Simulation of Capsules and Biological Cells , 2003 .

[16]  Ricardo Cortez,et al.  The Method of Regularized Stokeslets , 2001, SIAM J. Sci. Comput..

[17]  Isaac Klapper,et al.  Finger Formation in Biofilm Layers , 2002, SIAM J. Appl. Math..

[18]  R. LeVeque,et al.  A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources , 2006 .

[19]  Philip S. Stewart,et al.  Modeling Antibiotic Tolerance in Biofilms by Accounting for Nutrient Limitation , 2004, Antimicrobial Agents and Chemotherapy.

[20]  N G Cogan,et al.  Modeling physiological resistance in bacterial biofilms , 2005, Bulletin of mathematical biology.

[21]  N. Cogan HYBRID NUMERICAL TREATMENT OF TWO-FLUID PROBLEMS WITH PASSIVE INTERFACES , 2007 .

[22]  Cory J. Rupp,et al.  Commonality of elastic relaxation times in biofilms. , 2004, Physical review letters.

[23]  C. Pozrikidis Expansion of a compressible gas bubble in Stokes flow , 2001, Journal of Fluid Mechanics.

[24]  Philip S. Stewart,et al.  A Three-Dimensional Computer Model of Four Hypothetical Mechanisms Protecting Biofilms from Antimicrobials , 2006, Applied and Environmental Microbiology.

[25]  Vittorio Cristini,et al.  Drop breakup in three-dimensional viscous flows , 1998 .

[26]  K. Lewis,et al.  Specialized Persister Cells and the Mechanism of Multidrug Tolerance in Escherichia coli , 2004, Journal of bacteriology.

[27]  E Morgenroth,et al.  Biofilm modeling with AQUASIM. , 2004, Water science and technology : a journal of the International Association on Water Pollution Research.

[28]  C. Pozrikidis Boundary Integral and Singularity Methods for Linearized Viscous Flow: Index , 1992 .

[29]  W. G. Characklis,et al.  Activity of Pseudomonas aeruginosa in biofilms: Steady state , 1984, Biotechnology and bioengineering.

[30]  Cory J. Rupp,et al.  Viscoelastic fluid description of bacterial biofilm material properties. , 2002, Biotechnology and bioengineering.

[31]  P. Watnick,et al.  Biofilm, City of Microbes , 2000 .

[32]  P. Stewart,et al.  Role of electrostatic interactions in cohesion of bacterial biofilms , 2002, Applied Microbiology and Biotechnology.

[33]  N. Cogan Incorporating toxin hypothesis into a mathematical model of persister formation and dynamics. , 2007, Journal of theoretical biology.

[34]  P. Stewart,et al.  Modeling biofilm antimicrobial resistance. , 2000, Biotechnology and bioengineering.

[35]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[36]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[37]  J W Wimpenny,et al.  Individual-based modelling of biofilms. , 2001, Microbiology.

[38]  P. Stewart,et al.  Senescence can explain microbial persistence. , 2006, Microbiology.

[39]  J. Thomas Beale,et al.  A Method for Computing Nearly Singular Integrals , 2000, SIAM J. Numer. Anal..

[40]  P. Stewart,et al.  Theoretical aspects of antibiotic diffusion into microbial biofilms , 1996, Antimicrobial agents and chemotherapy.

[41]  M. Loewenberg,et al.  A mathematical formulation of the boundary integral equations for a compressible stokes flow , 2003 .

[42]  Bjarke Bak Christensen,et al.  In Situ Gene Expression in Mixed-Culture Biofilms: Evidence of Metabolic Interactions between Community Members , 1998, Applied and Environmental Microbiology.

[43]  K. Lewis,et al.  Persister cells and tolerance to antimicrobials. , 2004, FEMS microbiology letters.

[44]  W. G. Characklis,et al.  Cellular reporoduction and extracellular polymer formation by Pseudomonas aeruginosa in continuous culture , 1984, Biotechnology and bioengineering.

[45]  J R King,et al.  Modelling antibiotic- and anti-quorum sensing treatment of a spatially-structured Pseudomonas aeruginosa population , 2005, Journal of mathematical biology.

[46]  P. Stewart,et al.  Biofilm penetration and disinfection efficacy of alkaline hypochlorite and chlorosulfamates , 2001, Journal of applied microbiology.

[47]  P. Gilbert,et al.  Microbial Biofilms: Mechanisms of the Protection of Bacterial Biofilms from Antimicrobial Agents , 1995 .

[48]  J. Dockery,et al.  Modelling production of extracellular polymeric substances in a Pseudomonas aeruginosa chemostat culture. , 2001, Water science and technology : a journal of the International Association on Water Pollution Research.

[49]  Anita T. Layton An efficient numerical method for the two-fluid Stokes equations with a moving immersed boundary , 2008 .

[50]  J. Keener,et al.  The role of the biofilm matrix in structural development. , 2004, Mathematical medicine and biology : a journal of the IMA.

[51]  J. Costerton,et al.  Bacterial biofilms: a common cause of persistent infections. , 1999, Science.

[52]  P. Stewart,et al.  Role of Antibiotic Penetration Limitation in Klebsiella pneumoniae Biofilm Resistance to Ampicillin and Ciprofloxacin , 2000, Antimicrobial Agents and Chemotherapy.

[53]  N. Cogan,et al.  Failure of antibiotic treatment in microbial populations , 2008, Journal of mathematical biology.

[54]  W Gujer,et al.  A multispecies biofilm model , 1986, Biotechnology and bioengineering.

[55]  N G Cogan,et al.  Two-Fluid Model of Biofilm Disinfection , 2008, Bulletin of mathematical biology.

[56]  Hal L. Smith,et al.  The pharmacodynamics of antibiotic treatment , 2006 .

[57]  Thomas Y. Hou,et al.  Boundary integral methods for multicomponent fluids and multiphase materials , 2001 .

[58]  Cory J. Rupp,et al.  Biofilm material properties as related to shear-induced deformation and detachment phenomena , 2002, Journal of Industrial Microbiology and Biotechnology.

[59]  B. Levin,et al.  Non-inherited antibiotic resistance , 2006, Nature Reviews Microbiology.

[60]  P. Stewart,et al.  Evidence of bacterial adaptation to monochloramine in Pseudomonas aeruginosa biofilms and evaluation of biocide action model. , 1997, Biotechnology and bioengineering.

[61]  N G Cogan,et al.  Effects of persister formation on bacterial response to dosing. , 2006, Journal of theoretical biology.

[62]  J. King,et al.  Mathematical modelling of therapies targeted at bacterial quorum sensing. , 2004, Mathematical biosciences.

[63]  J J Heijnen,et al.  Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. , 1998, Biotechnology and bioengineering.

[64]  Qi Wang,et al.  Phase Field Models for Biofilms. I. Theory and One-Dimensional Simulations , 2008, SIAM J. Appl. Math..

[65]  L. Fauci,et al.  The method of regularized Stokeslets in three dimensions : Analysis, validation, and application to helical swimming , 2005 .

[66]  D. Davies,et al.  Understanding biofilm resistance to antibacterial agents , 2003, Nature Reviews Drug Discovery.