Mathematical modelling of biofilm structures

Antonie van Leeuwenhoek, International Journal of General and Molecular Microbiology

Volumn 81, Issue 1-4, 2002, Pages 245-256

  Van Loosdrecht, M C M ^a   Heijnen, J J ^a   Eberl, H ^b   Kreft, J ^c   Picioreanu, C ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b INSTITUTE OF EPIDEMIOLOGY   (Germany)

^c UNIVERSITY OF BONN   (Germany)

Author keywords

Biofilm; Detachment; Mathematical model; Morphology; Transport

Indexed keywords

BIOFILM; MATHEMATICAL ANALYSIS; MODELING; MORPHOLOGY;

ARTICLE; BIOFILM; BIOFILM REACTOR; BIOMASS DISTRIBUTION; CHEMICAL REACTION KINETICS; CONTROLLED STUDY; DIFFUSION; EROSION; MATHEMATICAL MODEL; MORPHOLOGY; NONHUMAN; PRIORITY JOURNAL; SHEAR STRESS; STRAIN DIFFERENCE; THERMODYNAMICS;

BACTERIA; BIOFILMS; BIOREACTORS; MODELS, BIOLOGICAL;

EID: 0036423439     PISSN: 00036072     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020527020464     Document Type: Article

References (39)

1. Ben-Jacob E, Schochet O, Tenenbaum A, Cohen I, Czirok A & Vicsek T (1994) Generic modelling of cooperative growth patterns in bacterial colonies. Nature 368: 46-49.
2. Beyenal H & Lewandowski Z (2002) Internal and external mass transfer in biofilms grown at various flow velocities. Biotechn. Progr. 18: 55-61.
3. Caldwell DE, Korber JR & Lawrence DR (1993). Analysis of biofilm formation using 2D vs 3D digital imaging. J. Appl. Bacteriol. 74: S52-S66.
4. Characklis WG & Marshall KC (1989) Biofilms. John Wiley & Sons, New York.
5. Debus O, Baumgaertl H & Sekoulov-I (1994) Influence of fluid velocities on the degradation of volatile aromatic compounds in membrane bound biofilms. Water Sci. Techn. 29(10-11): 253-262.
6. De Beer D, Stoodley P, Roe F & Lewandowski Z (1994). Effects of biofilm structures on oxygen distribution and mass transport. Biotechnol. Bioeng. 43: 1131-1138.
7. Eberl H, Picioreanu C & van Loosdrecht MCM (1999) Modelling geometrical heterogeneity in biofilms. In: Proceedings of The 13th International Conference of High Performance Computing Systems & Applications, June 1999, Kingston, Canada.
8. Eberl HJ, Picioreanu C, Heijnen JJ & van Loosdrecht MCM (2000) Three-dimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms. Chem. Eng. Sci. 55: 6209-6222.
9. Eberl HJ, Parker DF & van Loosdrecht MCM (2001) A new deterministic spatio-temporal continuum model for biofilm development. J. Theor. Med. 3: 161-175.
10. Gjaltema A, Arts PAM, van Loosdrecht MCM, Kuenen JG & Heijnen JJ (1994) Heterogeneity of biofilms in rotating annular reactors: Occurrence, structure and consequences. Biotechnol. Bioeng. 44: 194-204.
11. Gjaltema A, Tijhuis L, van Loosdrecht MCM & Heijnen JJ (1995) Detachment of biomass from suspended nongrowing spherical biofilms in airlift reactors. Biotechnol. Bioeng. 46: 258-269.
12. Hermanowicz SW (1998) A model of two-dimensional biofilm morphology. Water Sci. Tech. 37: 219-222.
13. Korstgens V, Flemming HC, Wingender J & Borchard W (2001) Uniaxial compression measurement device for investigation of the mechanical stability of biofilms. J. Microbiol. Meth. 46 (1): 9-17.
14. Kugaprasatham S, Nagaoka H & Ohgaki S (1992) Effect of turbulence on nitrifying biofilms at non-limiting substrate conditions. Water Res. 26:(12) 1629-1638.
15. Kwok WK, Picioreanu C, Ong SL, van Loosdrecht MCM, Ng WJ & Heijnen JJ (1998) Influence of biomass production and detachment forces on biofilm structures in a biofilm airlift suspension reactor. Biotechnol. Bioeng. 58: 400-407.
16. Kreft JU, Booth G & Wimpenny JWT (1998). BacSim, a simulator for individual-based modelling of bacterial colony growth. Microbiology 144: 3275-3287.
17. Kreft JU, Picioreanu C, Wimpenny JWT & van Loosdrecht MCM (2001) Individual-based modelling of biofilms. Microbiology 147: 2897-2912.
18. Kreft JU & Wimpenny JWT (2001) Effect of EPS on biofilm structure and function as revealed by an individual-based model of biofilm growth. Water Sci. Tech. 43(6): 135-141.
19. Noguera DR, Pizzaro G, Stahl DA & Rittmann BE (1999) Simulation of multispecies biofilm development in three dimensions Water Sci. Techn. 39:(7) 123-130.
20. Ohashi A, Koyama T, Syutsubo K & Harada H (1999) A novel method for evaluation of biofilm tensile strength resisting erosion. Water Sci. Technol. 39(7): 261-268.
21. Picioreanu C, van Loosdrecht MCM & Heijnen JJ (1998) Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotechnol. Bioeng. 58(1): 101-116.
22. Picioreanu C, van Loosdrecht MCM & Heijnen JJ (2000a) A theoretical study on the effect of surface roughness on mass transport and transformation in biofilms. Biotechnol. Bioeng. 68(4): 355-369.
23. Picioreanu C, van Loosdrecht MCM & Heijnen JJ (2000b) Effect of diffusive and convective substrate transport on biofilm structure formation: a 2-D modeling study. Biotechnol. Bioeng. 69(5): 504-515.
24. Picioreanu C, van Loosdrecht MCM & Heijnen JJ (2000c) Modelling and predicting biofilm structure. In: Allison DG, Gilbert P, Lappin-Scott HM & Wilson M (Ed) Community Structure and Co-operation in Biofilms (pp 129-166). Cambridge University Press, 2000, ISBN 0 521 79302 5.
25. Picioreanu C, Van Loosdrecht MCM & Heijnen JJ (2001) Two-dimensional model of biofilm detachment caused by internal stress from liquid flow. Biotechnol. Bioeng. 72(2): 205-218.
26. Picioreanu C & Van Loosdrecht MCM (2002) A mathematical model for initiation of microbiologically influenced corrosion by differential aeration. J. Electrochem. Soc. 149(6): B211-B223.
27. Rittmann B-E, Matthew P, Reeves Howard W & Stahl DA (1999) How biofilm clusters affect substrate flux and ecological selection. Water Sci. Techn. 39(7): 99-105.
28. Stoodley P, Lewandowski Z, Boyle JD & Lappin-Scott HM (1998) Oscillation characteristics of biofilm streamers in turbulent flowing water as related to drag and pressure drop. Biotechnol. Bioeng. 57(5): 536-544.
29. Stoodley P, Boyle JD, De Beer D & Lappin-Scott HM (1999b) Evolving perspectives of biofilm structure. Biofouling 14(1): 75-90.
30. Stoodley P, Wilson S, Hall-Stoodley L, Boyle JD, Lappin-Scott HM & Costerton JW (2001) Growth and detachment of cell clusters from mature mixed-species biofilms. Appl. Env. Microbiol. 67: 5608-5613.
31. Tijhuis L, Hijman B, van Loosdrecht MCM & Heijnen JJ (1996) Influence of detachment, substrate loading and reactor scale on the formation of biofilms in airlift reactors. Appl. Microbiol. Biotechnol. 45: 7-17.
32. Van Loosdrecht MCM, Eikelboom D, Gjaltema A, Mulder A, Tijhuis L & Heijnen JJ (1995) Biofilm structures. Water Sci. Technol. 32(8): 35-43.
33. Van Loosdrecht MCM, Picioreanu C & Heijnen JJ.(1997) A more unifying hypothesis for the structure of microbial biofilms. FEMS Microb. Ecol. 24: 181-183.
34. Verschuren PG & van den Heuvel JC (2002) Substrate controlled development of anaerobic acidifying aggregates at different shear rates in a gas lift reactor. Biotech. Bioeng. 77: 306-315.
35. Villaseñor JC, van Loosdrecht MCM, Picioreanu C & Heijnen JJ (2000) Influence of different substrates on the formation of biofilms in a biofilm airlift suspension reactor. Water Sci. Techn. 41(4-5): 323-330.
36. Wanner O & Gujer W (1986) A multispecies biofilm model. Biotechnol. Bioeng. 28: 314-328.
37. Wanner O (1996) Modelling of biofilms. Biofouling 10: 31-41.
38. Wasche S, Horn H & Hempel DC (2000) Mass transfer phenomena in biofilm systems. Water Sci. Techn. 41(4): 357-360.
39. Wimpenny JWT & Colasanti (1997) A unifying hypothesis for the structure of microbial biofilms based on cellular automata. FEMS Microb. Ecol. 22: 1-16.