1887

Chapter 13 : Modeling Biofilms

MyBook is a cheap paperback edition of the original book and will be sold at uniform, low price.

Ebook: Choose a downloadable PDF or ePub file. Chapter is a downloadable PDF file. File must be downloaded within 48 hours of purchase

Buy this Chapter
Digital (?) $15.00

Preview this chapter:
Zoom in
Zoomout

Modeling Biofilms, Page 1 of 2

| /docserver/preview/fulltext/10.1128/9781555817718/9781555818944_Chap13-1.gif /docserver/preview/fulltext/10.1128/9781555817718/9781555818944_Chap13-2.gif

Abstract:

Because all levels of biofilm models are useful depending on the application, this chapter describes and discusses biofilm modeling starting from the simple, homogeneous case to the more complex, structurally and functionally heterogeneous cases. Obviously, the complexity of the model is reduced when a single-species biofilm is modeled (i.e., a functionally homogeneous but structurally heterogeneous biofilm); thus, the discussions in the chapter focus on this simplified problem. In the cellular automata (CA) biofilm model, there are two superimposed lattices, one of them containing information on the location of food particles (substrate lattice) and the other one describing the location of microbial particles (microbial lattice). The simulation of biofilm activity is done by evaluating these stochastic processes over a series of time steps. A section describes the fundamental rules for these stochastic processes and their relation to the physical and biological parameters that represent the biofilm system. Biofilm erosion at the surface, another possible process controlling biofilm growth, can be implemented by selecting a maximum biofilm height, beyond which any microbial outgrowth will be removed from the biofilm. The evolution of biofilm modeling from the 1970s until now shows different approaches to the mathematical abstraction of the biofilm problem, but it is evident that the conceptual basis for all the models is similar and relies on mathematically coupling substrate diffusion with substrate utilization, microbial growth, and microbial decay or detachment.

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Highlighted Text: Show | Hide
Loading full text...

Full text loading...

Figures

Image of FIGURE 1
FIGURE 1

Schematic representation of a homogeneous biofilm system.

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Permissions and Reprints Request Permissions
Download as Powerpoint
Image of FIGURE 2
FIGURE 2

Discretization of a 1D biofilm problem and corresponding explicit finite difference approximation of equations 2 to 4.

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Permissions and Reprints Request Permissions
Download as Powerpoint
Image of FIGURE 3
FIGURE 3

The evaluation of growth and decay in a biofilm model produces an uneven distribution of the size of biofilm elements. A reevaluation of the boundaries between elements restores the equally sized element configuration.

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Permissions and Reprints Request Permissions
Download as Powerpoint
Image of FIGURE 4
FIGURE 4

Periodic boundaries in a 2D domain are illustrated by bending the planar domain to form a cylinder in which the left-most elements overlap with the right-most elements (i.e., elements in column 1 = elements in column ).

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Permissions and Reprints Request Permissions
Download as Powerpoint
Image of FIGURE 5
FIGURE 5

Schematic representation of the mixing and transport steps in the CA diffusion rule. During mixing, all food particles change layers (shown in this figure is a 180° directional change). During the transport step, the particles are moved according to the layer in which they are located (e.g., north, east, south, or west, for the layers shown).

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Permissions and Reprints Request Permissions
Download as Powerpoint
Image of FIGURE 6
FIGURE 6

Schematic representation of evaluation of connectivity and sloughing. Light squares represent microbial particles without an identified connection to the substratum. Dark squares represent connected microbial particles. Connectivity “flows” through microbial cells (steps 1 to 8) and unconnected cells are sloughed off (step 9).

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Permissions and Reprints Request Permissions
Download as Powerpoint
Image of FIGURE 7
FIGURE 7

Flowchart of algorithm used to simulate biofilm dynamics with the quantitative CA biofilm model.

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Permissions and Reprints Request Permissions
Download as Powerpoint
Image of FIGURE 8
FIGURE 8

Simulation of a functionally homogeneous and structurally heterogeneous biofilm using the CA model. The typical cycle includes growth, decay, and sloughing processes.

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Permissions and Reprints Request Permissions
Download as Powerpoint
Image of FIGURE 9
FIGURE 9

Substrate flux (A) and biofilm thickness (B) during the simulation of a functionally homogeneous and structurally heterogeneous biofilm using the quantitative CA biofilm model.

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Permissions and Reprints Request Permissions
Download as Powerpoint
Image of FIGURE 10
FIGURE 10

Simulation of growth of a heterogeneous biofilm using the quantitative CA biofilm model. The biofilm has two microbial species, heterotrophs (dark areas) and nitrifiers (white areas).

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Permissions and Reprints Request Permissions
Download as Powerpoint
Image of FIGURE 11
FIGURE 11

Average concentration of microbial species (A) and chemical species (B) throughout the biofilm matrix at day 18 of the simulation.

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Permissions and Reprints Request Permissions
Download as Powerpoint

References

/content/book/10.1128/9781555817718.chap13
1. Atkinson, B.,, and I. J. Davies. 1974. The overall rate of substrate uptake (reaction) by microbial films. Part I. A biological rate equation. Trans. Inst. Chem. Eng. 52:248259.
2. Ben-Jacob, E.,, O. Schochet,, A. Tenenbaum,, I. Cohen,, A. Czirok,, and T. Vicsek. 1994. Generic modelling of cooperative growth patterns in bacterial colonies. Nature 368:4649.
3. Brieger, L.,, and E. Bonomi. 1991. A stochastic cellular automaton simulation of the non-linear diffusion equation. Physica D 47:159168.
4. Caldwell, D. E.,, D. R. Korber,, and J. R. Lawrence,. 1992. Confocal laser microscopy and digital image analysis in microbial ecology, p. 167. In K. C. Marshall (ed.) , Advances in Microbial Ecology. Plenum Press, New York, N.Y.
5. Chopard, B.,, and M. Droz. 1991. Cellular automata model for the diffusion equation. J. Stat. Phys. 64:859892.
6. Chopard, B.,, and M. Droz. 1999. Cellular Automata Modeling of Physical Systems. Cambridge University Press, New York, N.Y..
7. Colasanti, R. 1992. Cellular automata models of microbial colonies. Binary 4:191193.
8. Costerton, J. W.,, Z. Lewandowski,, D. E. Caldwell,, D. R. Korber,, and H. M. Lappin-Scott. 1995. Microbial Biofilms. Annu. Rev. Microbiol. 79:711745.
9. Dab, D.,, and J.-P. Boon,. 1990. Cellular automata approach to reaction-diffusion systems, p. 257273. In P. Manneville, , N. Boccara, , G. Y. Vichniac, , and R. Bidaux (ed.), Cellular Automata and Modeling of Complex Systems. Springer-Verlag, Berlin, Germany.
10. de Beer, D.,, P. Stoodley,, and Z. Lewandowski. 1996. Liquid flow and mass transport in heterogeneous biofilms. Water Res. 30:27612765.
11. D’Souza, R. M.,, and N. H. Margolus. 1999. A thermodynamically reversible generalization of diffusion limited aggregation. Phys. Rev. E 60:264274.
12. Eberl, H. J.,, E. Morgenroth,, M. C. M. van Loosdrecht,, D. R. Noguera,, C. Picioreanu,, B. E. Rittmann,, A. O. Schwarz,, and O. Wanner. 2003. Modelling a spatially heterogeneous biofilm and the bulk fluid: selected results from benchmark problem 2 (BM2). Proceedings of the IWA Biofilms Conference, Cape Town, South Africa. IWA Publishing, London, United Kingdom.
13. Eberl, H. J.,, C. Picioreanu,, J. J. Heijnen,, and M. C. M. van Loosdrecht. 2000. A threedimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms. Chem. Eng. Sci. 55:62096222.
14. Edelstein-Keshet, L. 1988. Mathematical Models in Biology. Random House, New York, N.Y.
15. Ermentrout, G. B.,, and L. Edelstein-Keshet. 1993. Cellular automata approaches to biological modeling. J. Theor. Biol. 160:97133.
16. Harris, N. P.,, and G. S. Hansford. 1976. A study of substrate removal in a microbial film reactor. Water Res. 10:935943.
17. Heath, M. S.,, S. A. Wirtel,, and B. E. Rittmann. 1990. Simplified design of biofilm processes using normalized loading curves. Res. J. Water Pollut. Control Fed. 62:185192.
18. Hermanowicz, S. 1997. A model of two-dimensional biofilm morphology, p. 521524. Proceedings of the Second International Conference of Microorganisms in Activated Sludge and Biofilm Processes, Berkeley, Calif. IAWQ Publishing, London, United Kingdom.
19. Kaandorp, J. A.,, C. P. Lowe,, D. Frenkel,, and P. M. A. Sloot. 1996. Effect of nutrient diffusion and flow on coral morphology. Phys. Rev. Lett. 77:23282331.
20. Kaandorp, J. A.,, and P. M. A. Sloot. 1997. Parallel simulation of accretive growth and form in three dimensions. BioSystems 44:181192.
21. Kissel, J. C.,, P. L. McCarty,, and R. L. Street. 1984. Numerical simulation of mixed-culture biofilm. J. Environ. Eng. 110:393411.
22. Kreft, J.-U.,, C. Picioreanu,, J. W. T. Wimpenny,, and M. C. M. van Loosdrecht. 2001. Individualbased modelling of biofilms. Microbiology 147:28972912.
23. Lawrence, J. R.,, D. R. Korber,, B. D. Hoyle,, J. W. Costerton,, and D. E. Calswell. 1991. Optical sectioning of microbial biofilms. J. Bacteriol. 173:65586567.
24. Massol-Deyá, A. A.,, J. Whallon,, R. F. Hickey,, and J. M. Tiedje. 1995. Channel structures in aerobic biofilms of fixed-film reactors treating contaminated groundwater. Appl. Environ. Microbiol. 61:769777.
25. Matsushita, M.,, and H. Fujikawa. 1990. Diffusion-limited growth in bacterial colony formation. Physica A 168:498506.
26. Morgenroth, E.,, H. J. Eberl,, M. C. M. van Loosdrecht,, D. R. Noguera,, G. E. Pizarro,, C. Picioreanu,, B. E. Rittmann,, A. O. Schwarz,, and O. Wanner. 2003. Results from the single species benchmark problem (BM1). Proceedings of the IWA Biofilm Conference, Cape Town, South Africa. IWA Publishing, London, United Kingdom.
27. Noguera, D. R.,, and E. Morgenroth. 2003. Introduction to the IWA Task Group on Biofilm Modeling. Proceedings of the IWA Biofilm Conference, Cape Town, South Africa. IWA Publishing, London, United Kingdom.
28. Noguera, D. R.,, S. Okabe,, and C. Picioreanu. 1999a. Biofilm modeling: present status and future directions. Water Sci. Technol. 39:273278.
29. Noguera, D. R.,, G. E. Pizarro,, D. A. Stahl,, and B. E. Rittmann. 1999b. Simulation of multispecies biofilm development in three dimensions. Water Sci. Technol. 39:123130.
30. Picioreanu, C.,, M. C. M. van Loosdrecht,, and J. J. Heijnen. 1998a. Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotechnol. Bioeng. 58:101116.
31. Picioreanu, C.,, M. C. M. van Loosdrecht,, and J. J. Heijnen. 1998b. A new combined differentialdiscrete cellular automaton approach for biofilm modeling: application for growth in gel beads. Biotechnol. Bioeng. 57:718731.
32. Pizarro, G. E. 2001. Quantitative modeling of heterogeneous biofilms using cellular automata. Ph.D. dissertation. University of Wisconsin, Madison, Wisc.
33. Pizarro, G. E.,, D. Griffeath,, and D. R. Noguera. 2001. Quantitative cellular automaton model for biofilms. J. Environ. Eng. ASCE 127:782789.
34. Press, W. H.,, S. A. Teukolsky,, W. T. Vetterling,, and B. P. Flannery. 1992. Numerical Recipes in C: the Art of Scientific Computing. Cambridge University Press, New York, N.Y.
35. Rittmann, B. E.,, and P. L. McCarty. 2001. Environmental Biotechnology: Principles and Applications. McGraw-Hill, New York, N.Y.
36. Rittmann, B. E.,, A. O. Schwarz,, H. J. Eberl,, E. Morgenroth,, J. Perez,, M. C. M. van Loosdrecht,, and O. Wanner. 2003. Results from the multi-species benchmark problem (BM3) using one-dimensional models. Proceedings of the IWA Biofilms Conference, Cape Town, South Africa. IWA Publishing, London, United Kingdom.
37. Rittmann, B. E.,, D. Stilwell,, and A. Ohashi. 2002. The transient-state, multiple-species biofilm model for biofiltration processes. Water Res. 36: 23422356.
38. Rothmann, D. H.,, and S. Zaleski. 1997. Lattice-Gas Cellular Automata. Simple Models of Complex Hydrodynamics. Cambridge University Press, Cambridge, United Kingdom.
39. Sáez, P. B.,, and B. E. Rittmann. 1988. Improved pseudoanalytical solution for steady-state biofilm kinetics. Biotechnol. Bioeng. 32:379385.
40. Sáez, P. B.,, and B. E. Rittmann. 1992. Accurate pseudoanalytical solution for steady-state biofilms. Biotechnol. Bioeng. 39:790793.
41. Schindler, J.,, and L. Rovensky. 1994. A model of intrinsic growth of a Bacillus colony. Binary 6:105108.
42. Stewart, P. S. 1998. A review of experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms. Biotechnol. Bioeng. 59:261272.
43. Stewart, P. S.,, M. A. Hamilton,, B. R. Goldstein,, and B. T. Schneider. 1996. Modeling biocide action against biofilms. Biotechnol. Bioeng. 49:445455.
44. Stoodley, P.,, Z. Lewandowski,, J. D. Boyle,, and H. M. Lappin-Scott. 1999. The formation of migratory ripples in a mixed species bacterial biofilm growing in turbulent flow. Environ. Microbiol. 1:447455.
45. Strikwerda, J. C. 1989. Finite Difference Schemes and Partial Differential Equations. Chapman & Hall, New York, N.Y.
46. Toffoli, T. 1984. Cellular automata as an alternative to (rather than an approximation of ) differential equations in modeling physics. Physica D 10:117127.
47. Toffoli, T.,, and N. Margolus. 1987. Cellular Automata Machines. The MIT Press, Cambridge, Mass.
48. Wanner, O.,, and W. Gujer. 1986. A multispecies biofilm model. Biotechnol. Bioeng. 28:314328.
49. Wanner, O.,, and P. Reichert. 1996. Mathematical modeling of mixed-culture biofilms. Biotechnol. Bioeng. 49:172184.
50. Williamson, K.,, and P. L. McCarty. 1976. A model of substrate utilization by bacterial films.J. Water Pollut. Control Fed. 48:924.
51. Wimpenny, J. W. T.,, and R. Colasanti. 1997. A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models. FEMS Microbiol. Ecol. 22:116.
52. Wirtel, S. A.,, D. R. Noguera,, D. T. Kampmeier,, M. S. Heath,, and B. R. Rittmann. 1992. Explaining widely varying biofilm-process performance with normalized loading curves. Water Environ. Res. 64:706711.

Tables

Generic image for table
TABLE 1

Notation used in this chapter

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Generic image for table
TABLE 2

Step-by-step instructions for using the pseudoanalytical model of Saéz and Rittmann

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Generic image for table
TABLE 3

Parameters used for the simulation of a functionally homogeneous, structurally heterogeneous biofilm presented in example 1

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Generic image for table
TABLE 4

Calculation of parameters for the quantitative CA biofilm model (example 1)

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Generic image for table
TABLE 5

Summary of parameters for microbial species in example 2, the functionally heterogeneous CA biofilm model

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13
Generic image for table
TABLE 6

Summary of parameters for microbial species in example 2, the functionally heterogeneous CA biofilm model

Citation: Noguera D, Pizarro G, Regan J. 2004. Modeling Biofilms, p 222-249. In Ghannoum M, O'Toole G (ed), Microbial Biofilms. ASM Press, Washington, DC. doi: 10.1128/9781555817718.ch13

This is a required field
Please enter a valid email address
Please check the format of the address you have entered.
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error