Skip to main content

Mathematical modelling of biofilm structures

Antonie van Leeuwenhoek volume 81, pages 245–256 (2002)Cite this article

Abstract

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Beyenal H & Lewandowski Z (2002) Internal and external mass transfer in biofilms grown at various flow velocities. Biotechn. Progr. 18: 55–61.

    Article  CAS  Google Scholar 

  • 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 

  • Characklis WG & Marshall KC (1989) Biofilms. John Wiley & Sons, New York.

    Google Scholar 

  • 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.

    CAS  Google Scholar 

  • 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.

    Article  CAS  PubMed  Google Scholar 

  • 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.

  • 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.

    Article  CAS  Google Scholar 

  • 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 

  • 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.

    Article  CAS  PubMed  Google Scholar 

  • 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.

    Article  CAS  PubMed  Google Scholar 

  • Hermanowicz SW (1998) A model of two-dimensional biofilm morphology. Water Sci. Tech. 37: 219–222.

    Article  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • Kugaprasatham S, Nagaoka H & Ohgaki S (1992) Effect of turbulence on nitrifying biofilms at non-limiting substrate conditions. Water Res. 26:(12) 1629–1638.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Kreft JU, Booth G & Wimpenny JWT (1998). BacSim, a simulator for individual-based modelling of bacterial colony growth. Microbiology 144: 3275–3287.

    Article  PubMed  CAS  Google Scholar 

  • Kreft JU, Picioreanu C, Wimpenny JWT & van Loosdrecht MCM (2001) Individual-based modelling of biofilms. Microbiology 147: 2897–2912.

    PubMed  CAS  Google Scholar 

  • 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.

    CAS  Google Scholar 

  • Noguera DR, Pizzaro G, Stahl DA & Rittmann BE (1999) Simulation of multispecies biofilm development in three dimensions Water Sci. Techn. 39:(7) 123–130.

    Article  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Stoodley P, Boyle JD, De Beer D & Lappin-Scott HM (1999b) Evolving perspectives of biofilm structure. Biofouling 14(1): 75–90.

    Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • Van Loosdrecht MCM, Eikelboom D, Gjaltema A, Mulder A, Tijhuis L & Heijnen JJ (1995) Biofilm structures. Water Sci. Technol. 32(8): 35–43.

    Article  CAS  Google Scholar 

  • Van Loosdrecht MCM, Picioreanu C & Heijnen JJ.(1997) A more unifying hypothesis for the structure of microbial biofilms. FEMS Microb. Ecol. 24: 181–183.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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 

  • Wanner O & Gujer W (1986) A multispecies biofilm model. Biotechnol. Bioeng. 28: 314–328.

    Article  CAS  PubMed  Google Scholar 

  • Wanner O (1996) Modelling of biofilms. Biofouling 10: 31–41.

    Article  CAS  Google Scholar 

  • Wasche S, Horn H & Hempel DC (2000) Mass transfer phenomena in biofilm systems. Water Sci. Techn. 41(4): 357–360.

    CAS  Google Scholar 

  • Wimpenny JWT & Colasanti (1997) A unifying hypothesis for the structure of microbial biofilms based on cellular automata. FEMS Miccrob. Ecol. 22: 1–16.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kluyverlaboratory for Biotechnology, Delft University of Technology, Julianalaan 67, 2628 BC, Delft, The Netherlands

    M.C.M. van Loosdrecht, J.J. Heijnen & C. Picioreanu

  2. GSF, Inst. For Biomathematics and Biometry, pf 1129, 85758, Neuherberg, Germany

    H. Eberl

  3. Abteilung Theoretische Biologie, Botanisches Institut der Universität Bonn, Kirschallee 1, D-53115, Bonn, Germany

    J. Kreft

Authors
  1. M.C.M. van Loosdrecht
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J.J. Heijnen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Eberl
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Kreft
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. C. Picioreanu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M.C.M. van Loosdrecht.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

van Loosdrecht, M., Heijnen, J., Eberl, H. et al. Mathematical modelling of biofilm structures. Antonie Van Leeuwenhoek 81, 245–256 (2002). https://doi.org/10.1023/A:1020527020464

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020527020464

  • biofilm
  • detachment
  • mathematical model
  • morphology
  • transport