Cellular automaton model has been used to describe the formation of microcolonies and biofilms (Ben-Jacob et al., 1991; Wimpenny and Colasanti, 1997; Kreft et al., 2001). The cellular automaton model is defined as spatially and temporally discrete system where the state of an automaton is determined by a set of rules that act locally but apply globally (Wimpenny and Colasanti, 1997). In the model, cellular automata form a class of systems composed of individual units (cells), each with a defined state, and each cell can change its state following the transition rules, which are influenced by its own state and those of other cells (Wimpenny and Colasanti, 1997). This model aims to reproduce a microbial structure under substrate-transfer-limited conditions. Substrate gradients created by local consumption of substrate allow the bacteria situated on "mounds" to have more substrate available than those situated in "valley" (Tolker-Nielsen and Molin, 2000). Thus, the structure of micro-colony or biofilm is related to the availability of resource. Details of the automaton model have been described by Wimpenny and Colasanti (1997).
It had been reported that a simple and practical way towards rapid anaerobic granulation was to increase the organic loading rate based on an 80% reduction of biodegradable chemical oxygen demand with supplementary monitoring of effluent suspended solids washout (de Zeeuw, 1988; Fang and Chui, 1993; Tay and Yan, 1996). The findings are consistent with the prediction of the cellular automaton model which simulates a dynamic development of a microcolony or biofilm under varying environmental conditions. The model can in fact produce a large variety of distinct morphologies in response to changes in growth conditions (Ben-Jacob et al., 1991; Wimpenny and Colasanti, 1997). However, the cellular automaton model does not account for cell mobility towards resource and the role of cell-to-cell communication in the development of spatial organization of microcolony or biofilm, as pointed out by Tolker-Nielsen and Molin (2000).
Recently, based on the cellular automaton theory, a series of multidimensional biofilm models with heterogeneous biomass and substrate distribution in two or three dimensions have been developed (Hermanowicz, 1997; Noguera et al., 1999; Picioreanu et al., 1999, 2001; Kreft et al., 2001). In the multidimensional biofilm models, it is generally assumed that biofilm growth is due to the processes of diffusion, reaction, and growth including biomass growth, division, and spreading. Many studies suggested that the structure of granules is rather similar to the structure of biofilms (MacLeod etal., 1990; Schmidt and Ahring, 1996; Tolker-Nielsen and Molin, 2000), thus the multidimensional models used to explain the spatial organization of bacteria in biofilms could be applied to anaerobic granulation.
It should be pointed out that as models are getting more and more complex, model calibration becomes a challenging task. Without an adequate calibration, quantitative results generated from modeling may become meaningless. Therefore, future study needs to look into the applicability of the multidimensional biofilm models to accommodate anaerobic granulation process.
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