Two-dimensional cellular automaton model for mixed-culture biofilm

Transcription

1 Two-dimensional cellular automaton model for mixed-culture biofilm G.E. Pizarro*, C. García*, R. Moreno** and M.E. Sepúlveda** * Department of Hydraulic and Environmental Engineering, Pontificia Universidad Católica de Chile, Casilla 36 Correo 22, Santiago, Chile ( gpizarro@ing.puc.cl; cpgarcia@puc.cl) ** Department of Computer Science, Pontificia Universidad Católica de Chile, Casilla 36 Correo 22, Santiago, Chile ( ramoreno@puc.cl; marcos@ing.puc.cl) Abstract Structural and microbial heterogeneity occurs in almost any type of biofilm system. General approaches for the design of biofilm systems consider biofilms as homogeneous and of constant thickness. In order to improve the design of biofilms systems, models need to incorporate structural heterogeneity and the effect of inert microbial mass. We have improved a 2D biofilm model based on cellular automata (CA) and used it to simulate multidimensional biofilms with active and inert biomass including a self-organizing development. Results indicate that the presence of inert biomass within biofilm structures does not change considerably the substrate flux into the biofilm because the active biomass is located at the surface of the biofilm. Long-term simulations revealed that although the biofilm system is highly heterogeneous and the microstructure is continuously changing, the biofilm reaches a dynamic steady-state with prediction of biofilm thickness and substrate flux stabilizing on a delimited range. Keywords Biofilm modeling; cellular automata; dynamic steady-state; multidimensional model; selforganization Introduction It has been demonstrated that heterogeneity (physical and microbial) occurs in almost any type of biofilm system (Hermanowicz, 22; Massol-Deyá et al., 1995; Stoodley et al., 1999). General approaches for the design of biofilm systems consider biofilms as homogeneous and of constant thickness (Sáez and Rittmann, 1992; Williamson and McCarty, 1976). More developed models incorporate microbial heterogeneity but still assume a onedimensional (1D) biofilm (Rittmann and Manem, 1992; Wanner and Gujer, 1986; Wanner and Reichert, 1996). In order to improve the design of biofilms systems, models need to also incorporate structural heterogeneity. An important factor for a structurally heterogeneous biofilm model is the detachment process. For the 1D model, detachment is assumed as a first order term added to the maintenance decay coefficient. This way of representing detachment does not take into account the location of specific cells within the biofilm. A structurally heterogeneous biofilm model can represent detachment as a natural consequence of the decay of bacteria that form the biofilm and does not need a detachment coefficient (Pizarro, 21). One of the important features of the multi-species models is the incorporation of the fate of decayed biomass in the form of inert biomass. For the 1D models, this process results in the accumulation of inert biomass closer to the substratum while active biomass remains at the surface (Rittmann and Manem, 1992; Wanner and Gujer, 1986; Wanner and Reichert, 1996). Since the detachment coefficient applies to all cells within the biofilm, steady-state biofilms with maximum thickness can be obtained. For the structurally heterogeneous biofilm model, where detachment is modeled only as the loss of connectivity of the cells of the biofilm to the substratum, when inert biomass is incorporated the result is a biofilm that increases its thickness continually because there is no mechanism to remove the inactive Water Science and Technology Vol 49 No pp IWA Publishing

2 G.E. Pizarroet al. 194 cells that remain close to the substratum. Using experimental techniques, researchers have elucidated some implications of the death/lysis process: decreasing the biofilm density in deep biofilm layers (Bishop et al., 1995) and biofilm shrinking and cavity formation (Ohashi and Harada, 1996). This suggests that inert biomass has to lose its mechanical properties and at some point leave the deep layers of the biofilm open and allow sloughing to occur. Thus, the main modeling advances presented here are to incorporate the formation of inert biomass within a structurally heterogeneous biofilm, to incorporate mechanisms for the decay (in terms of its mechanical properties) of the inert biomass and to include a self-organizing development of the biofilm structure. This is attained with a 2D biofilm model based on cellular automata (CA) (Pizarro et al., 21). Mathematical model The CA biofilm model used here describes substrate and biomass as discrete particles existing and interacting in a specified 2D physical domain. Substrate particles move by random walks, simulating molecular diffusion. The concentration of substrate at a given location is represented by the density of substrate particles in the neighborhood of that location. Active microorganisms in the biofilm can grow attached to a surface or to other microbial particles, consume substrate particles, and duplicate if a sufficient amount of substrate is consumed. Inert microbial particles do not consume substrate and can serve as support for active microbial particles. The dynamics of the system are simulated using stochastic processes that represent the occurrence of specific events, such as substrate diffusion, substrate utilization, biofilm growth, and biofilm decay (active and inert). Detachment (or sloughing) is a natural consequence of the dynamics of the simulation and is determined by evaluating the connectivity of the cells to the substratum. Diffusion and reaction events are separated from growth and decay events using the concept of characteristic times (Kissel et al., 1984). Model Assumptions: The model considers only one limiting substrate. The biofilm is composed of two types of bacteria, active and inert. When an active biomass particle decays, it has a probability to change into an inert particle or to disappear from the physical domain. Inert biomass particles have a probability to disappear from the physical domain. The probability of a substrate particle being consumed depends on the concentration of substrate particles in the neighborhood. A boundary layer is assumed to be parallel to the substratum, and to have a defined minimum thickness, which is measured from the bulk liquid to the maximum height of the simulated biofilm. Sloughing occurs only when biofilm cells lose connectivity to the substratum and are assumed to leave the domain. Detailed description of the CA biofilm model, the definition of the boundary conditions and the relationships with the kinetic and physical parameters can be found elsewhere (Noguera et al., in press; Pizarro, 21). Model results Simulations were run using typical parameters for heterotrophic biofilms (Sáez and Rittmann, 1992), shown in Table 1. The formation of inert biomass considered the fraction of active biomass not biodegradable (1-f d ) (Laspidou and Rittmann, 22). Part of the decayed biomass will form inert biomass at a rate r inert_f (Eq. (1)), where b is the decay coefficient and X f is the active biomass density. To incorporate the loss of structural resistance of inert biomass we introduced a decay rate of inert biomass (b inac ), which considers that

3 Table 1 Parameters used for the simulation of a structurally heterogeneous biofilm Parameter Value Units qˆ 8. mg/mg-day K s 1. mg/l Y.5 mg/mg b.1 day 1 D l.8 cm 2 /day D f.64 cm 2 /day part of this inert biomass will disappear from the system at a rate r inert_d (Eq. (2)), where X i is the inert biomass density. The net inert biomass accumulation is represented by Eq. (3). G.E. Pizarroet al. ( ) r = b 1 f X inert _ f d f r = b X inert _ d inac i dxi = r _ r dt inert f inert _ d (1) (2) (3) Three kinds of simulations were performed with values for the formation of inert biomass and the decay of inert biomass. The values of the parameters used are presented in Table 2 for the three cases analyzed. Case A includes only endogenous decay and thus active biomass disappears from the domain and there is no inert biomass formation. Case B considers that part of the decayed biomass will form inert biomass (at a rate r inert_f ) and part of this inert biomass will disappear from the system (at a rate r inert_d ). Finally, Case C also considers the formation of biomass but inert biomass will accumulate since there is no disappearance from the system. Results show that the steady state substrate flux predictions of the three model simulations A, B, and C are very similar. This similarity is due to the heterogeneous structures and the distribution of active biomass on the external part of the biofilm. However, the pattern for biofilm sloughing changes. Figure 1 shows snapshots of the three cases for two bulk substrate concentrations, 2 and 4 mg/l at 5 days of simulation. It was observed that the distribution of the biomass with biofilm depth changes as the time increases. Figure 1 also shows the normalized density of active and inert biomass with biofilm depth at 5 days of simulation. As for previous results (Pizarro et al., 21), long-term simulations revealed that although the biofilm system is highly heterogeneous and the microstructure is continuously changing, the biofilm reaches a dynamic steady-state with prediction of biofilm thickness and substrate flux stabilizing on a delimited range (Figure 2 after 5 days of simulation). Note that this is not the case for simulation C, where b inac is zero, even though the substrate flux into the biofilm remains fairly constant, biofilm thickness increases continuously. Table 2 Values for parameters f d and b inac for the three simulations analyzed Parameter Case A Case B Case C f d b inac (d 1 ).1 195

4 G.E. Pizarroet al. Figure 1 Snapshots of biofilm structure after 5 days of simulation for a bulk substrate concentration (S b ) of 2 and 4 mg/l with A) no inert biomass production; B) inert biomass production and loss and C) inert biomass production and accumulation. Normalized density of biomass at different depths of the biofilm is shown at the right side of each panel. Light color represents active cells while dark represents inert cells 196 Discussion and conclusions The CA model presented confirms the concept of dynamic steady-state and the importance of self-organization in biofilm structure formation. The results of the simulations demonstrated that the presence of inert biomass within biofilm structures does not change considerably the substrate flux into the biofilm because the active biomass is located mainly at the surface of the biofilm. Table 3 presents the values for the density of biomass per unit area (M act and M inert ) and mean biofilm thickness (L f ) for active and inert biomass for cases A, B, and C for two bulk substrate concentrations. It can be noted that the mass of active cells in the three cases is very similar, what changes is the amount of inert biomass. For the structurally heterogeneous biofilm model, the way of obtaining a finite biofilm

5 Thickness (µm) A Thickness (µm) B Thickness (µm) C Substrate Flux (mg/cm2-d) A Substrate Flux (mg/cm2-d) B Figure 2 Average biofilm thickness and substrate flux over time for S b = 4 mg/l. Cases A) with no inert biomass production; B) with inert biomass production and loss, and C) with inert biomass production and accumulation Substrate Flux (mg/cm2-d) C G.E. Pizarroet al. Table 3 Steady-state values for parameters in simulations of cases A, B, and C for S b = 2 and 4 mg/l Substrate Sb= 2 mg/l Sb= 4 mg/l Parameter A B C A B C J b (mg/cm 2 d) L f (µm) M act (mg/cm 2 ) M inert (mg/cm 2 ) thickness is allowing detachment to occur. Given the assumptions of the 2D CA model presented here, detachment was obtained by adding a new first order parameter, b inac, to represent the loss of structural resistance of inert biomass, allowing sloughing to occur. In this way, biofilms can reach a dynamic steady-state with substrate fluxes similar to simulations without inactive biomass formation and with finite biofilm thickness. Biofilm density varies with the biofilm depth according to the observations made by Bishop and colleagues (Bishop et al., 1995) even though it changes continuously as sloughing events take place. Acknowledgements This research was funded by a grant from FONDECYT (National Fund for the Development of Science and Technology, project 12736) and by a grant for young researchers from Fundación Andes (C-1376). References Bishop, P.L., Zhang, T.C. and Fu, Y.-C. (1995). Effects of biofilm structure, microbial distributions and mass transport on biodegradation processes. Water Science and Technology, 31(1), Hermanowicz, S.W. (22). Biofilm structure: An interplay of models and experiments. In: Biofilms in Wastewater Treatment: an Interdisciplinary Approach, S. Wuertz, P.A. Wilderer, and P. L. Bishop (eds), IWA Publishing. Kissel, J.C., McCarty, P.L. and Street, R.L. (1984). Numerical Simulation of Mixed-Culture Biofilm. Journal of Environmental Engineering, 11(2), Laspidou, C.S. and Rittmann, B.E. (22). Non-steady state modeling of extracellular polymeric substances, soluble microbial products, and active and inert biomass. Water Research, 36(8), Massol-Deyá, A.A., Whallon, J., Hickey, R.F. and Tiedje, J.M. (1995). Channel structures in aerobic 197

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