Antonie van Leeuwenhoek

, Volume 81, Issue 1–4, pp 245–256 | Cite as

Mathematical modelling of biofilm structures

  • M.C.M. van Loosdrecht
  • J.J. Heijnen
  • H. Eberl
  • J. Kreft
  • C. Picioreanu


The morphology of biofilms received much attention in the last years. Several concepts to explain the development of biofilm structures have been proposed. We believe that biofilm structure formation depends on physical as well as general and specific biological factors. The physical factors (e.g. governing substrate transport) as well as general biological factors such as growth yield and substrate conversion rates are the basic factors governing structure formation. Specific strain dependent factors will modify these, giving a further variation between different biofilm systems. Biofilm formation seems to be primarily dependent on the interaction between mass transport and conversion processes. When a biofilm is strongly diffusion limited it will tend to become a heterogeneous and porous structure. When the conversion is the rate-limiting step, the biofilm will tend to become homogenous and compact. On top of these two processes, detachment processes play a significant role. In systems with a high detachment (or shear) force, detachment will be in the form of erosion, giving smoother biofilms. Systems with a low detachment force tend to give a more porous biofilm and detachment occurs mainly by sloughing. Biofilm structure results from the interplay between these interactions (mass transfer, conversion rates, detachment forces) making it difficult to study systems taking only one of these factors into account.

biofilm detachment mathematical model morphology transport 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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.PubMedCrossRefGoogle Scholar
  2. Beyenal H & Lewandowski Z (2002) Internal and external mass transfer in biofilms grown at various flow velocities. Biotechn. Progr. 18: 55–61.CrossRefGoogle Scholar
  3. Caldwell DE, Korber JR & Lawrence DR (1993). Analysis of biofilm formation using 2D vs 3D digital imaging. J. Appl. Bacteriol. 74: S52–S66.Google Scholar
  4. Characklis WG & Marshall KC (1989) Biofilms. John Wiley & Sons, New York.Google Scholar
  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.Google Scholar
  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.CrossRefPubMedGoogle Scholar
  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.Google Scholar
  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.CrossRefGoogle Scholar
  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.Google Scholar
  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.CrossRefPubMedGoogle Scholar
  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.CrossRefPubMedGoogle Scholar
  12. Hermanowicz SW (1998) A model of two-dimensional biofilm morphology. Water Sci. Tech. 37: 219–222.CrossRefGoogle Scholar
  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.CrossRefGoogle Scholar
  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.CrossRefGoogle Scholar
  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.PubMedCrossRefGoogle Scholar
  16. Kreft JU, Booth G & Wimpenny JWT (1998). BacSim, a simulator for individual-based modelling of bacterial colony growth. Microbiology 144: 3275–3287.PubMedCrossRefGoogle Scholar
  17. Kreft JU, Picioreanu C, Wimpenny JWT & van Loosdrecht MCM (2001) Individual-based modelling of biofilms. Microbiology 147: 2897–2912.PubMedGoogle Scholar
  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.Google Scholar
  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.CrossRefGoogle Scholar
  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.CrossRefGoogle Scholar
  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.PubMedCrossRefGoogle Scholar
  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.PubMedCrossRefGoogle Scholar
  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.PubMedCrossRefGoogle Scholar
  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.Google Scholar
  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.PubMedCrossRefGoogle Scholar
  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.CrossRefGoogle Scholar
  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.CrossRefGoogle Scholar
  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.PubMedCrossRefGoogle Scholar
  29. Stoodley P, Boyle JD, De Beer D & Lappin-Scott HM (1999b) Evolving perspectives of biofilm structure. Biofouling 14(1): 75–90.Google Scholar
  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.CrossRefGoogle Scholar
  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.CrossRefGoogle Scholar
  32. Van Loosdrecht MCM, Eikelboom D, Gjaltema A, Mulder A, Tijhuis L & Heijnen JJ (1995) Biofilm structures. Water Sci. Technol. 32(8): 35–43.CrossRefGoogle Scholar
  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.CrossRefGoogle Scholar
  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.CrossRefGoogle Scholar
  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.Google Scholar
  36. Wanner O & Gujer W (1986) A multispecies biofilm model. Biotechnol. Bioeng. 28: 314–328.CrossRefPubMedGoogle Scholar
  37. Wanner O (1996) Modelling of biofilms. Biofouling 10: 31–41.CrossRefGoogle Scholar
  38. Wasche S, Horn H & Hempel DC (2000) Mass transfer phenomena in biofilm systems. Water Sci. Techn. 41(4): 357–360.Google Scholar
  39. Wimpenny JWT & Colasanti (1997) A unifying hypothesis for the structure of microbial biofilms based on cellular automata. FEMS Miccrob. Ecol. 22: 1–16.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • M.C.M. van Loosdrecht
    • 1
  • J.J. Heijnen
    • 1
  • H. Eberl
    • 2
  • J. Kreft
    • 3
  • C. Picioreanu
    • 1
  1. 1.Kluyverlaboratory for BiotechnologyDelft University of TechnologyDelftThe Netherlands
  2. 2.GSF, Inst. For Biomathematics and BiometryNeuherbergGermany
  3. 3.Abteilung Theoretische BiologieBotanisches Institut der Universität BonnBonnGermany

Personalised recommendations