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Kinetic theories for biofilms
1. | Department of Mathematics and NanoCenter at USC, University of South Carolina, Columbia, SC 29208 |
2. | Department of Mathematical Sciences, Montana State University, P.O. Box 172400, Bozeman, MT 59717-2400 |
References:
[1] |
E. Alpkvist and I. Klapper, A multidimensional multispecies continuum model for heterogeneous biofilm development, Bull. Math. Biol., 69 (2007), 765-789. |
[2] |
A. N. Beris and B. Edwards, "Thermodynamics of Flowing Systems with Internal Microstructure,'' Oxford Engineering Science Series, 36, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1994. |
[3] |
R. B. Bird, R. C. Armstrong and O. Hassager, "Dynamics of Polymeric Liquids,'' Vol. 1 & 2, John Wiley & Sons, New York, 1987. |
[4] |
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I: Interfacial free energy, J. Chem. Phys., 28 (1958), 258-267.
doi: 10.1063/1.1744102. |
[5] |
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. III: Nucleation in a 2-component incompressible fluid, J. Chem. Phys., 31 (1959), 688-699.
doi: 10.1063/1.1730447. |
[6] |
P. M. Chaikin and T. C. Lubensky, "Principles of Condensed Matter Physics,'' Cambridge University Press, Cambridge, 1995. |
[7] |
Chen Chen, Mingming Ren, Ashok Srinivasan and Qi Wang, 3-D simulations of biofilm-solvent interaction, East Asian Journal on Applied Mathematics, 1 (2011), 197-214. |
[8] |
N. G. Cogan and J. Keener, Channel formation in gels, SIAM J. Applied Math., 65 (2005), 1839-1854.
doi: 10.1137/040605515. |
[9] |
N. Cogan and J. Keener, The role of biofilm matrix in structural development, Mathematical Medicine and Biology, 21 (2004), 147-166.
doi: 10.1093/imammb/21.2.147. |
[10] |
J. W. Costerton, Z. Lewandowski, D. E. Caldwell, D. R. Korber and H. M. Lappin-Scott, Microbial biofilms, Annu. Rev. Microbiol., 49 (1995), 711-745.
doi: 10.1146/annurev.mi.49.100195.003431. |
[11] |
B. Costerton, "Medical Biofilm Microbiology: The Role of Microbial Biofilms in Disease, Chronic Infections, and Medical Device Failure," CD-ROM, Montana State University, 2003. |
[12] |
M. E. Davey and G. A. O'toole, Microbial biofilms: From ecology to molecular genetics, Microbiology and Molecular Biology Reviews, 64 (2000), 847-867.
doi: 10.1128/MMBR.64.4.847-867.2000. |
[13] |
E. De Lancey Pulcini, Bacterial biofilms: A review of current research, Nephrologie, 22 (2001), 439-441. |
[14] |
J. Dockery and I. Klapper, Finger formation in biofilm layers, SIAM J. Appl. Math., 62 (2001/02), 853-869. |
[15] |
M. Doi and S. F. Edwards, "The Theory of Polymer Dynamics,'' Oxford Science Publications, Oxford, 1986. |
[16] |
M. Doi, "Introduction to Polymer Physics,'' Oxford Science Publications, Oxford, 1995. |
[17] |
P. J. Flory, "Principles of Polymer Chemistry,'' Cornell University Press, Ithaca, NY, 1953. |
[18] |
D. J. Hassett, P. A. Limbach, R. F. Hennigan, K. E. Klose, R. E. Hancock, M. D. Platt and D. F. Hunt, Bacterial biofilms of importance to medicine and bioterrorism: Proteomic techniques to identify novel vaccine components and drug targets, Expert Opin. Biol. Ther., 3 (2003), 1201-1207.
doi: 10.1517/14712598.3.8.1201. |
[19] |
I. Klapper, Effect of heterogeneous structure in mechanically unstressed biofilms on overall growth, Bulletin of Mathemstical Biology, 66 (2004), 809-824.
doi: 10.1016/j.bulm.2003.11.008. |
[20] |
I. Klapper, C. J. Rupp, R. Cargo, B. Purvedorj and P. Stoodley, Viscoelastic fluid description of bacterial biofilm material properties, Biotechnology and Bioengineering, 80 (2002), 289-296.
doi: 10.1002/bit.10376. |
[21] |
I. Klapper and J. Dockery, Role of cohesion in the material description of biofilms, Phys. Rev. E (3), 74 (2006), 031902, 8 pp. |
[22] |
R. G. Larson, "The Rheology of Complex Fluids,'' Oxford University Press, New York, 1998. |
[23] |
C. S. Laspidou and B. E. Rittmann, Modeling biofilm complexity by including active and inert biomass and extracelluar polymeric substances, Biofilm, 1 (2004), 285-291. |
[24] |
C. A. A. Lima, R. Ribeiro, E. Foresti and M. Zaiat, Morphological study of biomass during the start-up period of a fixed-bed anaerobic reactor treating domestic sewage, Brazilian Archives of Biology and Technology. |
[25] |
J. Lowengrub and L. Truskinovsky, Quasi-incompressible Cahn-Hilliard fluids and topological transitions, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 454 (1998), 2617-2654. |
[26] |
S. T. Milner, Dynamical theory of concentration fluctuations in polymer solutions under shear, Phys. Rev. E, 48 (1993), 3674-3691.
doi: 10.1103/PhysRevE.48.3674. |
[27] |
G. O'Toole, H. B. Kaplan and R. Kolter, Biofilm formation as microbial development, Annual Review of Microbiology, 54 (2000), 49-79. |
[28] |
C. Picioreanu, M. van Loosdrecht and J. Heijnen, Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach, Biotech. Bioeng., 58 (1998), 101-116.
doi: 10.1002/(SICI)1097-0290(19980405)58:1<101::AID-BIT11>3.0.CO;2-M. |
[29] |
C. Picioreanu, M. van Loosdrecht and J. Heijnen, Multidimensional modelling of biofilm structure, in "Biotech. Microbial Biosystems: New Frontiers" (eds. C. R. Bell, M. Brylinsky and P. Johnson-Green), Proceedings of the 8th International Symposium on Microbial Ecology, Atlantic Canada Society for Microbial Ecology, Halifax, Canada, 1999. |
[30] |
C. Picioreanu, M. J.-U. Kreft and M. van Loosdrecht, Particle-based multidimensional multispecies biofilm models, Applied and Envrionmental Microbiology, 70 (2004), 3024-3040.
doi: 10.1128/AEM.70.5.3024-3040.2004. |
[31] |
C. Picioreanu, J. B. Xavier and M. van Loosdrecht, Advances in mathematical modeling of biofilm structure, Biofilm, 1 (2004), 337-349. |
[32] |
P. Stoodley, Z. Lewandowski, J. D. Boyle and H. M. Lappin-Scott, The formation of migratory ripples in a mixed species bacterial biofilm growing in turbulent flows, Environ. Microbiol., 1 (1999), 447-457.
doi: 10.1046/j.1462-2920.1999.00055.x. |
[33] |
H. Tanaka, Viscoelastic model of phase separation, Phys. Rev. E, 56 (1997), 4451-4462.
doi: 10.1103/PhysRevE.56.4451. |
[34] |
C. Wolgemuth, E. Hoiczyk, D. Kaiser and G. Oster, How myxobacteria glide, Current Biology, 12 (2002), 369-377.
doi: 10.1016/S0960-9822(02)00716-9. |
[35] |
Pengtao Yue, James J. Feng, Chun Liu and Jie Shen, A diffuse-interface method for simulating two-phase flows of complex fluids, J. Fluid Mech., 515 (2004), 293-317. |
[36] |
Pengtao Yue, James J. Feng, Chun Liu and Jie Shen, Viscoelastic effects on drop deformation in steady shear, J. Fluid Mech., 540 (2005), 427-437.
doi: 10.1017/S0022112005006166. |
[37] |
T. Zhang, N. Cogan and Q. Wang, Phase-field models for biofilms. I. Theory and one-dimensional simulations, SIAM J. Appl. Math., 69 (2008), 641-669.
doi: 10.1137/070691966. |
[38] |
T. Zhang, N. Cogan and Q. Wang, Phase-field models for biofilms. II. 2-D numerical simulations of biofilm-blow interaction, Communications in Computational Physics, 4 (2008), 72-101. |
show all references
References:
[1] |
E. Alpkvist and I. Klapper, A multidimensional multispecies continuum model for heterogeneous biofilm development, Bull. Math. Biol., 69 (2007), 765-789. |
[2] |
A. N. Beris and B. Edwards, "Thermodynamics of Flowing Systems with Internal Microstructure,'' Oxford Engineering Science Series, 36, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1994. |
[3] |
R. B. Bird, R. C. Armstrong and O. Hassager, "Dynamics of Polymeric Liquids,'' Vol. 1 & 2, John Wiley & Sons, New York, 1987. |
[4] |
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I: Interfacial free energy, J. Chem. Phys., 28 (1958), 258-267.
doi: 10.1063/1.1744102. |
[5] |
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. III: Nucleation in a 2-component incompressible fluid, J. Chem. Phys., 31 (1959), 688-699.
doi: 10.1063/1.1730447. |
[6] |
P. M. Chaikin and T. C. Lubensky, "Principles of Condensed Matter Physics,'' Cambridge University Press, Cambridge, 1995. |
[7] |
Chen Chen, Mingming Ren, Ashok Srinivasan and Qi Wang, 3-D simulations of biofilm-solvent interaction, East Asian Journal on Applied Mathematics, 1 (2011), 197-214. |
[8] |
N. G. Cogan and J. Keener, Channel formation in gels, SIAM J. Applied Math., 65 (2005), 1839-1854.
doi: 10.1137/040605515. |
[9] |
N. Cogan and J. Keener, The role of biofilm matrix in structural development, Mathematical Medicine and Biology, 21 (2004), 147-166.
doi: 10.1093/imammb/21.2.147. |
[10] |
J. W. Costerton, Z. Lewandowski, D. E. Caldwell, D. R. Korber and H. M. Lappin-Scott, Microbial biofilms, Annu. Rev. Microbiol., 49 (1995), 711-745.
doi: 10.1146/annurev.mi.49.100195.003431. |
[11] |
B. Costerton, "Medical Biofilm Microbiology: The Role of Microbial Biofilms in Disease, Chronic Infections, and Medical Device Failure," CD-ROM, Montana State University, 2003. |
[12] |
M. E. Davey and G. A. O'toole, Microbial biofilms: From ecology to molecular genetics, Microbiology and Molecular Biology Reviews, 64 (2000), 847-867.
doi: 10.1128/MMBR.64.4.847-867.2000. |
[13] |
E. De Lancey Pulcini, Bacterial biofilms: A review of current research, Nephrologie, 22 (2001), 439-441. |
[14] |
J. Dockery and I. Klapper, Finger formation in biofilm layers, SIAM J. Appl. Math., 62 (2001/02), 853-869. |
[15] |
M. Doi and S. F. Edwards, "The Theory of Polymer Dynamics,'' Oxford Science Publications, Oxford, 1986. |
[16] |
M. Doi, "Introduction to Polymer Physics,'' Oxford Science Publications, Oxford, 1995. |
[17] |
P. J. Flory, "Principles of Polymer Chemistry,'' Cornell University Press, Ithaca, NY, 1953. |
[18] |
D. J. Hassett, P. A. Limbach, R. F. Hennigan, K. E. Klose, R. E. Hancock, M. D. Platt and D. F. Hunt, Bacterial biofilms of importance to medicine and bioterrorism: Proteomic techniques to identify novel vaccine components and drug targets, Expert Opin. Biol. Ther., 3 (2003), 1201-1207.
doi: 10.1517/14712598.3.8.1201. |
[19] |
I. Klapper, Effect of heterogeneous structure in mechanically unstressed biofilms on overall growth, Bulletin of Mathemstical Biology, 66 (2004), 809-824.
doi: 10.1016/j.bulm.2003.11.008. |
[20] |
I. Klapper, C. J. Rupp, R. Cargo, B. Purvedorj and P. Stoodley, Viscoelastic fluid description of bacterial biofilm material properties, Biotechnology and Bioengineering, 80 (2002), 289-296.
doi: 10.1002/bit.10376. |
[21] |
I. Klapper and J. Dockery, Role of cohesion in the material description of biofilms, Phys. Rev. E (3), 74 (2006), 031902, 8 pp. |
[22] |
R. G. Larson, "The Rheology of Complex Fluids,'' Oxford University Press, New York, 1998. |
[23] |
C. S. Laspidou and B. E. Rittmann, Modeling biofilm complexity by including active and inert biomass and extracelluar polymeric substances, Biofilm, 1 (2004), 285-291. |
[24] |
C. A. A. Lima, R. Ribeiro, E. Foresti and M. Zaiat, Morphological study of biomass during the start-up period of a fixed-bed anaerobic reactor treating domestic sewage, Brazilian Archives of Biology and Technology. |
[25] |
J. Lowengrub and L. Truskinovsky, Quasi-incompressible Cahn-Hilliard fluids and topological transitions, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 454 (1998), 2617-2654. |
[26] |
S. T. Milner, Dynamical theory of concentration fluctuations in polymer solutions under shear, Phys. Rev. E, 48 (1993), 3674-3691.
doi: 10.1103/PhysRevE.48.3674. |
[27] |
G. O'Toole, H. B. Kaplan and R. Kolter, Biofilm formation as microbial development, Annual Review of Microbiology, 54 (2000), 49-79. |
[28] |
C. Picioreanu, M. van Loosdrecht and J. Heijnen, Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach, Biotech. Bioeng., 58 (1998), 101-116.
doi: 10.1002/(SICI)1097-0290(19980405)58:1<101::AID-BIT11>3.0.CO;2-M. |
[29] |
C. Picioreanu, M. van Loosdrecht and J. Heijnen, Multidimensional modelling of biofilm structure, in "Biotech. Microbial Biosystems: New Frontiers" (eds. C. R. Bell, M. Brylinsky and P. Johnson-Green), Proceedings of the 8th International Symposium on Microbial Ecology, Atlantic Canada Society for Microbial Ecology, Halifax, Canada, 1999. |
[30] |
C. Picioreanu, M. J.-U. Kreft and M. van Loosdrecht, Particle-based multidimensional multispecies biofilm models, Applied and Envrionmental Microbiology, 70 (2004), 3024-3040.
doi: 10.1128/AEM.70.5.3024-3040.2004. |
[31] |
C. Picioreanu, J. B. Xavier and M. van Loosdrecht, Advances in mathematical modeling of biofilm structure, Biofilm, 1 (2004), 337-349. |
[32] |
P. Stoodley, Z. Lewandowski, J. D. Boyle and H. M. Lappin-Scott, The formation of migratory ripples in a mixed species bacterial biofilm growing in turbulent flows, Environ. Microbiol., 1 (1999), 447-457.
doi: 10.1046/j.1462-2920.1999.00055.x. |
[33] |
H. Tanaka, Viscoelastic model of phase separation, Phys. Rev. E, 56 (1997), 4451-4462.
doi: 10.1103/PhysRevE.56.4451. |
[34] |
C. Wolgemuth, E. Hoiczyk, D. Kaiser and G. Oster, How myxobacteria glide, Current Biology, 12 (2002), 369-377.
doi: 10.1016/S0960-9822(02)00716-9. |
[35] |
Pengtao Yue, James J. Feng, Chun Liu and Jie Shen, A diffuse-interface method for simulating two-phase flows of complex fluids, J. Fluid Mech., 515 (2004), 293-317. |
[36] |
Pengtao Yue, James J. Feng, Chun Liu and Jie Shen, Viscoelastic effects on drop deformation in steady shear, J. Fluid Mech., 540 (2005), 427-437.
doi: 10.1017/S0022112005006166. |
[37] |
T. Zhang, N. Cogan and Q. Wang, Phase-field models for biofilms. I. Theory and one-dimensional simulations, SIAM J. Appl. Math., 69 (2008), 641-669.
doi: 10.1137/070691966. |
[38] |
T. Zhang, N. Cogan and Q. Wang, Phase-field models for biofilms. II. 2-D numerical simulations of biofilm-blow interaction, Communications in Computational Physics, 4 (2008), 72-101. |
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