Mathematical modeling of biofilm structure with a hybrid differential- discrete cellular automaton approach

Biotechnology and Bioengineering

Volumn 58, Issue 1, 1998, Pages 101-116

  Picioreanu, Cristian ^a   Van Loosdrecht, Mark C M ^a   Heijnen, Joseph J ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Biofilm; Cellular automata; Discrete; Fractal; Modeling; Roughness; Shape; Structure; Surface

Indexed keywords

BIOMASS; CELLULAR NEURAL NETWORKS; DIFFUSION; ENVIRONMENTAL IMPACT; FRACTALS; GROWTH KINETICS; MATHEMATICAL MODELS; POROSITY; SURFACE ROUGHNESS; SURFACE STRUCTURE; TRANSPORT PROPERTIES;

BIOFILM COMPACTNESS; DIFFUSIVE SUBSTRATE TRANSPORT; HYBRID DIFFERENTIAL DISCRETE CELLULAR AUTOMATON; MICROBIAL GROWTH; SURFACE COMPLEXITY;

BIOFILMS;

ARTICLE; BIOFILM; CALCULATION; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; TECHNOLOGY;

AUTOMATION; BIOFILMS; BIOMASS; MODELS, THEORETICAL;

BASIDIOMYCOTA;

EID: 0032485575     PISSN: 00063592     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0290(19980405)58:1<101::AID-BIT11>3.0.CO;2-M     Document Type: Article

References (27)

1. Avnir, D. 1989. The fractal approach to heterogeneous chemistry. John Wiley & Sons, Chichester, UK.
2. Ben-Jacob, E., Schochet, O., Tenenbaum, A., Cohen, I., Czirók, A., Vicsek, T. 1994. Generic modelling of cooperative growth patterns in bacterial colonies. Nature 368: 46-49.
3. Chopard, B., Droz M. 1990. Cellular automata approach to diffusion problems. Springer Proc. Phys. 46: 130-143.
4. 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.
5. Garrido, J. M., van Benthum, W. A. J., van Loosdrecht, M. C. M., Heijnen, J. J. 1997. Influence of dissolved oxygen concentration on nitrite accumulation in a biofilm airlift suspension reactor. Biotechnol. Bioeng. 53: 168-178.
6. Glasbey, C. A., Horgan. G. W. 1994. Image analysis for the biological sciences. John Wiley & Sons, Chichester, UK.
7. Hermanowicz, S. W., Schindler, U., Wilderer, P. 1995. Fractal structure of biofilms: New tools for investigation of morphology. Water Sci. Technol. 32: 99-105.
8. Kaye, B. 1989. A random walk through fractal dimensions. VCH, Weinheim, Germany.
9. Kaandorp, J. A. 1994. Fractal modelling: Growth and form in biology. Springer, Berlin.
10. Kwok, W. K., Picioreanu, C., Ong, S. L., van Loosdrecht, M. C. M., Ng, W. J., Heijnen, J. J. 1997. Influence of biomass production and detachment forces on biofilm structures in a biofilm airlift suspension reactor. Biotechnol. Bioeng. (accepted for publication).
11. Lejeune, R., Baron, G. V. 1997. Simulation of growth of a filamentous fungus in three dimensions. Biotechnol. Bioeng. 53: 139-150.
12. Li, D., Ganczarczyk, J. 1990. Structure of activated sludge floes. Biotechnol. Bioeng. 35: 57-65.
13. Mandelbrot, B. B. 1982. The fractal geometry of nature. W. H. Freeman, San Francisco, CA.
14. Murga, R., Stewart, P. S., Daly, D. 1995. Quantitative analysis of biofilm thickness variability. Biotechnol. Bioeng. 45: 503-510.
15. Obert, M., Pfeifer, P., Sernetz, M. 1990. Microbial growth patterns described by fractal geometry. J. Bacteriol. 172: 1180-1185.
16. Picioreanu, C., van Loosdrecht, M. C. M., Heijnen, J. J. 1997. A new combined differential - discrete cellular automaton approach for biofilm modeling. Biotechnol. Bioeng. 57: 718-731.
17. Sapoval, B., Rosso, M., Gouyet, J.-F. 1985. J. Phys. Lett. (Paris) 46: L149.
18. Savill, N. J., Hogeweg, P. 1997. Modelling morphogenesis: From single cells to crawling slugs. J. Theor. Biol. 184: 229-235.
19. Soddell, J. A., Seviour, R. J. 1994. A comparison of methods for determining the fractal dimensions of colonies of filamentous bacteria. Binary 6: 21-31.
20. Takács, I., Fleit, E. 1995. Modelling of the micromorphology of the activated sludge floc: Low DO, low F/M bulking. Water Sci. Technol. 31: 235-243.
21. Tijhuis, L., van Loosdrecht, M. C. M., Heijnen, J. J. 1994. Formation and growth of heterotrophic aerobic biofilms on small suspended particles in airlift reactors. Biotechnol. Bioeng. 44: 595-608.
22. Toffoli T., Margolus N. 1987. Cellular automata machines; a new environment for modelling. MIT Press, Cambridge, MA.
23. van Loosdrecht, M. C. M., Eikelboom, D., Gjaltema, A., Mulder, A., Tijhuis, L., Heijnen, J. J. 1995. Biofilm structures. Water Sci. Technol. 32: 235-243.
24. van Loosdrecht, M. C. M., Picioreanu, C., Heijnen, J. J. 1997. A more unifying hypothesis for the structure of microbial biofilms. FEMS Microb. Ecol. 24: 181-183.
25. Wijffels, R. H. 1994. Effect of initial biomass concentration on the growth of immobilized Nitrosomonas europaea. Nitrification by immobilized cells. Ph.D. thesis, Wageningen Agricultural University, Wageningen, The Netherlands.
26. Wimpenny, J. W. T., Colasanti, R. 1997. A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models. FEMS Microb. Ecol. 22: 1-16.
27. Wolfram, S. 1986. Theory and applications of cellular automata. World Scientific, Singapore.