Abstract

Biotechnology and BioengineeringVolume 58, Issue 1 p. 101-116 Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach Cristian Picioreanu, Corresponding Author Cristian Picioreanu [email protected] Delft University of Technology, Department of Biochemical Engineering, Kluyver Laboratory for Biotechnology, Julianalaan 67, 2628 BC Delft, The NetherlandsDelft University of Technology, Department of Biochemical Engineering, Kluyver Laboratory for Biotechnology, Julianalaan 67, 2628 BC Delft, The NetherlandsSearch for more papers by this authorMark C. M. van Loosdrecht, Mark C. M. van Loosdrecht Delft University of Technology, Department of Biochemical Engineering, Kluyver Laboratory for Biotechnology, Julianalaan 67, 2628 BC Delft, The NetherlandsSearch for more papers by this authorJoseph J. Heijnen, Joseph J. Heijnen Delft University of Technology, Department of Biochemical Engineering, Kluyver Laboratory for Biotechnology, Julianalaan 67, 2628 BC Delft, The NetherlandsSearch for more papers by this author Cristian Picioreanu, Corresponding Author Cristian Picioreanu [email protected] Delft University of Technology, Department of Biochemical Engineering, Kluyver Laboratory for Biotechnology, Julianalaan 67, 2628 BC Delft, The NetherlandsDelft University of Technology, Department of Biochemical Engineering, Kluyver Laboratory for Biotechnology, Julianalaan 67, 2628 BC Delft, The NetherlandsSearch for more papers by this authorMark C. M. van Loosdrecht, Mark C. M. van Loosdrecht Delft University of Technology, Department of Biochemical Engineering, Kluyver Laboratory for Biotechnology, Julianalaan 67, 2628 BC Delft, The NetherlandsSearch for more papers by this authorJoseph J. Heijnen, Joseph J. Heijnen Delft University of Technology, Department of Biochemical Engineering, Kluyver Laboratory for Biotechnology, Julianalaan 67, 2628 BC Delft, The NetherlandsSearch for more papers by this author First published: 26 March 2000 https://doi.org/10.1002/(SICI)1097-0290(19980405)58:13.0.CO;2-MCitations: 62AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract A hybrid differential-discrete mathematical model has been used to simulate biofilm structures (surface shape, roughness, porosity) as a result of microbial growth in different environmental conditions. In this study, quantitative two- and three-dimensional models were evaluated by introducing statistical measures to characterize the complete biofilm structure, both the surface structure and volume structure. The surface enlargement, coefficient of roughness, fractal dimension of surface, biofilm compactness, and solids hold-up were found to be good measures of biofilm structure complexity. Among many possible factors affecting the biofilm structure, the influence of biomass growth in relation to the diffusive substrate transport was investigated. Porous biofilms, with many channels and voids between the “finger-like” or “mushroom” outgrowth, were obtained in a substrate-transport-limited regime. Conversely, compact and dense biofilms occurred in systems limited by the biomass growth rate and not by the substrate transfer rate. The surface complexity measures (enlargement, roughness, fractal dimension) all increased with increased transport limitation, whereas the volume measures (compactness, solid hold-up) decreased, showing the change from a compact and dense to a highly porous and open biofilm. © 1998 John Wiley & Sons, Inc. Biotechnol Bioeng 58:101–116, 1998. References Avnir, D. 1989. The fractal approach to heterogeneous chemistry. John Wiley & Sons, Chichester, UK. Google Scholar 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. 10.1038/368046a0 CASPubMedWeb of Science®Google Scholar Chopard, B., Droz, M. 1990. Cellular automata approach to diffusion problems. Springer Proc. Phys. 46: 130–143. 10.1007/978-3-642-75259-9_12 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. 10.1002/bit.260431118 Google Scholar 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. 10.1002/(SICI)1097-0290(19970120)53:23.0.CO;2-M CASPubMedWeb of Science®Google Scholar Glasbey, C. A., Horgan, G. W. 1994. Image analysis for the biological sciences. John Wiley & Sons, Chichester, UK. Google Scholar Hermanowicz, S. W., Schindler, U., Wilderer, P. 1995. Fractal structure of biofilms: New tools for investigation of morphology. Water Sci. Technol. 32: 99–105. 10.1016/0273-1223(96)00013-3 Web of Science®Google Scholar Kaye, B. 1989. A random walk through fractal dimensions. VCH, Weinheim, Germany. Google Scholar Kaandorp, J. A. 1994. Fractal modelling: Growth and form in biology. Springer, Berlin. 10.1007/978-3-642-57922-6 Web of Science®Google Scholar 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). Google Scholar Lejeune, R., Baron, G. V. 1997. Simulation of growth of a filamentous fungus in three dimensions. Biotechnol. Bioeng. 53: 139–150. 10.1002/(SICI)1097-0290(19970120)53:23.0.CO;2-P CASPubMedWeb of Science®Google Scholar Li, D., Ganczarczyk, J. 1990. Structure of activated sludge flocs. Biotechnol. Bioeng. 35: 57–65. 10.1002/bit.260350109 CASPubMedWeb of Science®Google Scholar Mandelbrot, B. B. 1982. The fractal geometry of nature. W. H. Freeman, San Francisco, CA. Web of Science®Google Scholar Murga, R., Stewart, P. S., Daly, D. 1995. Quantitative analysis of biofilm thickness variability. Biotechnol. Bioeng. 45: 503–510. 10.1002/bit.260450607 CASPubMedWeb of Science®Google Scholar Obert, M., Pfeifer, P., Sernetz, M. 1990. Microbial growth patterns described by fractal geometry. J. Bacteriol. 172: 1180–1185. 10.1128/jb.172.3.1180-1185.1990 PubMedWeb of Science®Google Scholar 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. 10.1002/(SICI)1097-0290(19980320)57:63.0.CO;2-O CASPubMedWeb of Science®Google Scholar Sapoval, B., Rosso, M., Gouyet, J.-F. 1985. J. Phys. Lett. (Paris) 46: L149. Web of Science®Google Scholar Savill, N. J., Hogeweg, P. 1997. Modelling morphogenesis: From single cells to crawling slugs. J. Theor. Biol. 184: 229–235. 10.1006/jtbi.1996.0237 PubMedWeb of Science®Google Scholar 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. Web of Science®Google Scholar 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. 10.1016/0273-1223(95)00196-T CASWeb of Science®Google Scholar 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. 10.1002/bit.260440506 CASPubMedWeb of Science®Google Scholar Toffoli, T., Margolus, N. 1987. Cellular automata machines; a new environment for modelling. MIT Press, Cambridge, MA. Google Scholar 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. Web of Science®Google Scholar 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. 10.1016/S0168-6496(97)00064-0 CASWeb of Science®Google Scholar 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. Google Scholar 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. 10.1111/j.1574-6941.1997.tb00351.x CASWeb of Science®Google Scholar Wolfram, S. 1986. Theory and applications of cellular automata. World Scientific, Singapore. Google Scholar Citing Literature Volume58, Issue15 April 1998Pages 101-116 ReferencesRelatedInformation