Two-Fluid Model of Biofilm Disinfection

Abstract We consider a dynamic model of biofilm disinfection in two dimensions. The biofilm is treated as a viscous fluid immersed in a fluid of less viscosity. The bulk fluid moves due to an imposed external parabolic flow. The motion of the fluid is coupled to the biofilm inducing motion of the biofilm. Both the biofilm and the bulk fluid are dominated by viscous forces, hence the Reynolds number is negligible and the appropriate equations are Stokes equations. The governing partial differential equations are recast as boundary integral equations using a version of the Lorenz reciprocal relationship. This allows for robust treatment of the simplified fluid/biofilm motion. The transport of nutrients and antimicrobials, which depends directly on the velocities of the fluid and biofilm, is also included. Disinfection of the bacteria is considered under the assumption that the biofilm growth is overwhelmed by disinfection.

[1]  H G Othmer,et al.  A mathematical model for outgrowth and spatial patterning of the vertebrate limb bud. , 1999, Journal of theoretical biology.

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

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

[4]  S. Kjelleberg,et al.  Attenuation of Pseudomonas aeruginosa virulence by quorum sensing inhibitors , 2003, The EMBO journal.

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

[6]  C Bozzi,et al.  Measurements of CP-violating asymmetries in B0-->K(0)(s)pi(0) decays. , 2004, Physical review letters.

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

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

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

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

[11]  B. M. Veeregowda,et al.  Biofilms: A survival strategy of bacteria , 2003 .

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

[13]  M. Loosdrecht,et al.  Evaluating 3-D and 1-D mathematical models for mass transport in heterogeneous biofilms , 2000 .

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

[15]  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 .

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

[17]  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.

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

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

[20]  P. Stewart,et al.  Role of dose concentration in biocide efficacy against Pseudomonas aeruginosa biofilms , 2002, Journal of Industrial Microbiology and Biotechnology.

[21]  William H. Press,et al.  Numerical recipes in C , 2002 .

[22]  J J Heijnen,et al.  A theoretical study on the effect of surface roughness on mass transport and transformation in biofilms. , 2000, Biotechnology and bioengineering.

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

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

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

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

[27]  Anita Mayo,et al.  Fast High Order Accurate Solution of Laplace’s Equation on Irregular Regions , 1985 .

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

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

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

[31]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

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

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

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

[35]  Gianluca Iaccarino,et al.  IMMERSED BOUNDARY METHODS , 2005 .

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

[37]  J. J. Heijnen,et al.  A three-dimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms , 2000 .

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

[39]  Randall J. LeVeque,et al.  Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension , 1997, SIAM J. Sci. Comput..

[40]  Anita T. Layton.  Modeling Water Transport across Elastic Boundaries Using an Explicit Jump Method , 2006, SIAM J. Sci. Comput..

[41]  Khellil Sefiane,et al.  Experimental investigation of self-induced thermocapillary convection for an evaporating meniscus in capillary tubes using micro-PIV , 2005 .

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

[43]  E. Greenberg,et al.  Chelator-Induced Dispersal and Killing of Pseudomonas aeruginosa Cells in a Biofilm , 2006, Applied and Environmental Microbiology.