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A multicomponent model for biofilm-drug interaction
1. | US Naval Research Laboratory, 4555 Overlook Ave. Southwest, Washington, DC 20375, United States |
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, United States |
References:
[1] |
G. C. Barker and M. J. Grimson, A cellular automaton model of microbial growth, Binary Comput. Microbiol., 5 (1993), 132-137. |
[2] |
E. Ben-Jacob, O. Schochet, A. Tenenbaum, I. Cohen, A. Czirok and V. Tamas, Generic modelling of cooperative growth patterns in bacterial colonies, Nature(London), 368 (1994), 46-49.
doi: 10.1038/368046a0. |
[3] |
A. N. Beris and B. Edwards, "Thermodynamics of Flowing System," Oxford University Press, 1994. |
[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] |
N. G. Cogan and J. P. Keener, The role of the biofilm matrix in structural development, Math. Med. Biol., 21 (2004), 147-166.
doi: 10.1093/imammb/21.2.147. |
[7] |
R. L. Colasanti, Cellular automata models of microbial colonies, Binary Comput. Microbiol., 4 (1992), 191. |
[8] |
J. D. Dockery and I. Klapper, Finger formation in biofilm layers, SIAM. J. Appl. Math., 62 (2001), 853-869. |
[9] |
H. J. Eberl, D. F. Parker and M. C. M. van Loosdrecht, A new deterministic spatio-temporal continuum model for biofilm development, J. Theor. Mde., 3 (2001), 161-175.
doi: 10.1080/10273660108833072. |
[10] |
P. J. Flory, "Principles of Polymer Chemistry," Cornell University Press, Ithaca, NY, 1953. |
[11] |
D. R. Noguera G. Pizarro and D. Griffeath, Quantative cellular automaton model for biofilms, J. Environ. Eng., 127 (2001), 782-789.
doi: 10.1061/(ASCE)0733-9372(2001)127:9(782). |
[12] |
S. W. Hermanowicz, A simple 2d biofilm model yields a variety of morphological features, Math. Biosci., 169 (2001), 1-14.
doi: 10.1016/S0025-5564(00)00049-3. |
[13] |
R. K. Hinson and W. M. Kocher, Model for effective diffusivities in aerobic biofilms, Journal of Environmental Engineering, (1996), 1023-1030.
doi: 10.1061/(ASCE)0733-9372(1996)122:11(1023). |
[14] |
J. C. Kissel, P. L. McCarty and R. L. Street, Numerical simulation of mixed-culture biofilm, J. Environ. Eng., 110 (1984), 393-411.
doi: 10.1061/(ASCE)0733-9372(1984)110:2(393). |
[15] |
I. Klapper and J. Dockery, Role of cohesion in material description of biofilms, Phys. Rev. E, 74 (2006), 031902.
doi: 10.1103/PhysRevE.74.031902. |
[16] |
C. Picioreanu, M. C. Loosdrecht and J. J. Heijnen, Discrete-differential modelling of biofilm structure, Wat. Sci. Tech., 39 (1999), 115-122.
doi: 10.1016/S0273-1223(99)00158-4. |
[17] |
C. Picioreanu, M. C. Loosdrecht and J. J. Heijnen, Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study, Biotech. Bioeng., 69 (2000), 504-515.
doi: 10.1002/1097-0290(20000905)69:5<504::AID-BIT5>3.0.CO;2-S. |
[18] |
C. Picioreanu, M. C. Loosdrecht and J. J. Heijnen, Two-dimensional model of biofilm detachment caused by internal stress from liquid flow, Biotech. Bioeng., 72 (2001), 205-218.
doi: 10.1002/1097-0290(20000120)72:2<205::AID-BIT9>3.0.CO;2-L. |
[19] |
C. Picioreanu, M. C. M. Loosdrecht and J. J. Heijnen, A new combined differential-discrete cellular automaton approach for biofilm modeling: Application for growth in gel beads, Biotech. Bioeng., 57 (1998), 718-731.
doi: 10.1002/(SICI)1097-0290(19980320)57:6<718::AID-BIT9>3.0.CO;2-O. |
[20] |
G. Pizarro, R. Moreno C. Garcia and M. E. Sepulveda, Two-dimensional cellular automaton model for mixed-culture biofilm, Wat. Sci. Tech., 49 (2004), 193-198. |
[21] |
B. E. Rittmann, The effect of shear stress on biofilm loss rate, Biotech. Bioeng., 24 (1982), 501-506.
doi: 10.1002/bit.260240219. |
[22] |
B. E. Rittmann and P. L. McCarty, Evaluation of steady-state biofilm kinetics, Biotech. Bioeng., 22 (1980), 2359-2373.
doi: 10.1002/bit.260221111. |
[23] |
B. E. Rittmann and P. L. McCarty, Model of steady-state-biofilm kinetics, Biotech. Bioeng., 22 (1980), 2243-2357. |
[24] |
Q. Wang and T. Zhang, Review of mathematical models for biofilms, Communication in Solid State Physics, 2010. |
[25] |
O. Wanner and W. Gujer, Competition in biofilms, Wat. Sci. Tech., 17 (1984), 27-44. |
[26] |
O. Wanner and W. Gujer, A multispecies biofilm model, Wat. Sci. Tech., 28 (1986), 314-328. |
[27] |
J. W. T. Wimpenny and R. Colasanti, A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models, FEMS Micro. Ecol., 22 (1997), 1-16.
doi: 10.1111/j.1574-6941.1997.tb00351.x. |
[28] |
T. Zhang, N. Cogan and Q. Wang, Phase-field models for biofilms I. theory and simulations, SIAM, J. Appl. Math., 69 (2008), 641-669.
doi: 10.1137/070691966. |
[29] |
T. Zhang, N. Cogan and Q. Wang, Phase-field models for biofilms II. 2-d numerical simulations of biofilm-flow interaction, Commun. Comput. Phys., 4 (2008), 72-101. |
show all references
References:
[1] |
G. C. Barker and M. J. Grimson, A cellular automaton model of microbial growth, Binary Comput. Microbiol., 5 (1993), 132-137. |
[2] |
E. Ben-Jacob, O. Schochet, A. Tenenbaum, I. Cohen, A. Czirok and V. Tamas, Generic modelling of cooperative growth patterns in bacterial colonies, Nature(London), 368 (1994), 46-49.
doi: 10.1038/368046a0. |
[3] |
A. N. Beris and B. Edwards, "Thermodynamics of Flowing System," Oxford University Press, 1994. |
[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] |
N. G. Cogan and J. P. Keener, The role of the biofilm matrix in structural development, Math. Med. Biol., 21 (2004), 147-166.
doi: 10.1093/imammb/21.2.147. |
[7] |
R. L. Colasanti, Cellular automata models of microbial colonies, Binary Comput. Microbiol., 4 (1992), 191. |
[8] |
J. D. Dockery and I. Klapper, Finger formation in biofilm layers, SIAM. J. Appl. Math., 62 (2001), 853-869. |
[9] |
H. J. Eberl, D. F. Parker and M. C. M. van Loosdrecht, A new deterministic spatio-temporal continuum model for biofilm development, J. Theor. Mde., 3 (2001), 161-175.
doi: 10.1080/10273660108833072. |
[10] |
P. J. Flory, "Principles of Polymer Chemistry," Cornell University Press, Ithaca, NY, 1953. |
[11] |
D. R. Noguera G. Pizarro and D. Griffeath, Quantative cellular automaton model for biofilms, J. Environ. Eng., 127 (2001), 782-789.
doi: 10.1061/(ASCE)0733-9372(2001)127:9(782). |
[12] |
S. W. Hermanowicz, A simple 2d biofilm model yields a variety of morphological features, Math. Biosci., 169 (2001), 1-14.
doi: 10.1016/S0025-5564(00)00049-3. |
[13] |
R. K. Hinson and W. M. Kocher, Model for effective diffusivities in aerobic biofilms, Journal of Environmental Engineering, (1996), 1023-1030.
doi: 10.1061/(ASCE)0733-9372(1996)122:11(1023). |
[14] |
J. C. Kissel, P. L. McCarty and R. L. Street, Numerical simulation of mixed-culture biofilm, J. Environ. Eng., 110 (1984), 393-411.
doi: 10.1061/(ASCE)0733-9372(1984)110:2(393). |
[15] |
I. Klapper and J. Dockery, Role of cohesion in material description of biofilms, Phys. Rev. E, 74 (2006), 031902.
doi: 10.1103/PhysRevE.74.031902. |
[16] |
C. Picioreanu, M. C. Loosdrecht and J. J. Heijnen, Discrete-differential modelling of biofilm structure, Wat. Sci. Tech., 39 (1999), 115-122.
doi: 10.1016/S0273-1223(99)00158-4. |
[17] |
C. Picioreanu, M. C. Loosdrecht and J. J. Heijnen, Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study, Biotech. Bioeng., 69 (2000), 504-515.
doi: 10.1002/1097-0290(20000905)69:5<504::AID-BIT5>3.0.CO;2-S. |
[18] |
C. Picioreanu, M. C. Loosdrecht and J. J. Heijnen, Two-dimensional model of biofilm detachment caused by internal stress from liquid flow, Biotech. Bioeng., 72 (2001), 205-218.
doi: 10.1002/1097-0290(20000120)72:2<205::AID-BIT9>3.0.CO;2-L. |
[19] |
C. Picioreanu, M. C. M. Loosdrecht and J. J. Heijnen, A new combined differential-discrete cellular automaton approach for biofilm modeling: Application for growth in gel beads, Biotech. Bioeng., 57 (1998), 718-731.
doi: 10.1002/(SICI)1097-0290(19980320)57:6<718::AID-BIT9>3.0.CO;2-O. |
[20] |
G. Pizarro, R. Moreno C. Garcia and M. E. Sepulveda, Two-dimensional cellular automaton model for mixed-culture biofilm, Wat. Sci. Tech., 49 (2004), 193-198. |
[21] |
B. E. Rittmann, The effect of shear stress on biofilm loss rate, Biotech. Bioeng., 24 (1982), 501-506.
doi: 10.1002/bit.260240219. |
[22] |
B. E. Rittmann and P. L. McCarty, Evaluation of steady-state biofilm kinetics, Biotech. Bioeng., 22 (1980), 2359-2373.
doi: 10.1002/bit.260221111. |
[23] |
B. E. Rittmann and P. L. McCarty, Model of steady-state-biofilm kinetics, Biotech. Bioeng., 22 (1980), 2243-2357. |
[24] |
Q. Wang and T. Zhang, Review of mathematical models for biofilms, Communication in Solid State Physics, 2010. |
[25] |
O. Wanner and W. Gujer, Competition in biofilms, Wat. Sci. Tech., 17 (1984), 27-44. |
[26] |
O. Wanner and W. Gujer, A multispecies biofilm model, Wat. Sci. Tech., 28 (1986), 314-328. |
[27] |
J. W. T. Wimpenny and R. Colasanti, A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models, FEMS Micro. Ecol., 22 (1997), 1-16.
doi: 10.1111/j.1574-6941.1997.tb00351.x. |
[28] |
T. Zhang, N. Cogan and Q. Wang, Phase-field models for biofilms I. theory and simulations, SIAM, J. Appl. Math., 69 (2008), 641-669.
doi: 10.1137/070691966. |
[29] |
T. Zhang, N. Cogan and Q. Wang, Phase-field models for biofilms II. 2-d numerical simulations of biofilm-flow interaction, Commun. Comput. Phys., 4 (2008), 72-101. |
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