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)58:1<101::AID-BIT11>3.0.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. 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