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

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.

Application of molecular tools for in situ monitoring of bacterial growth activity

“…One favours a relatively simple mechanistic model in which structure formation is a direct consequence of nutrient gradients and diffusion rates in the surface community (Wimpenny and Colasanti, 1997). In favour of this idea is the computer-based simulation based on the mathematical cellular automaton model, which creates bio®lm structures in silico similar to those seen in situ (Picioreanu et al, 1998). The other favours a regulated and coordinated multicellular organization based on cell-to-cell communication, which keeps track (and control) of cell proliferation through intercellular chemical signalling.…”

Biofilm dynamics characterization using a novel DO-MEA sensor: mass transport and biokinetics

“…6) was developed to estimate oxygen evolution through biofilm using the one-dimensional diffusionreaction equation (Mitchell et al 2004;Picioreanu et al 1998).…”

Mass transfer in a membrane aerated biofilm

“…Plus le transfert est lent devant la vitesse de consommation bactérienne plus ce gradient est important. Picioreanu et al (1998) montrent par simulation numérique que pour un biofilm de type conventionnel, plus la vitesse de transfert du substrat par rapport à la consommation est faible, plus le biofilm se développe sous forme poreuse, voire filamenteuse ( Figure I-3 La structure du biofilm résulte donc de l'interaction entre plusieurs facteurs (les trois principaux : transfert de matière, force de détachement, vitesse de consommation) qui rendent difficile d'étudier ces facteurs indépendamment les uns des autres.…”