Model of steady-state-biofilm kinetics

A steady-state biofilm is defined as one that has neither net growth nor decay over time. The model, developed for steady-state-biofilm kinetics with a single substrate, couples the flux of substrate into a biofilm to the mass (or thickness) of biofilm that would exist at steady-state for a given bulk substrate concentration. Based on kinetic and energetic constraints, this model predicts for a single substrate that a steady-state bulk concentration, S_min, exists below which a steady-state biofilm cannot exist. Thus, in the absence of adsorption of bacteria from the bulk water and for substrate concentration below S_min, substrate flux and biofilm thickness are zero. Equations are provided for calculating the steady-state substrate flux and biofilm thickness for S greater than S_min. An example is provided to demonstrate the use of the steadystate model.     

Steady-state solution of a two-species biofilm problem

Through a thorough investigation of the boundary conditions for a general two-species biofilm model, a simple and fast method for solving the steady-state case is developed and presented. The methods used may be extended to biofilm models in which more than two species are considered. Four different sets of boundary conditions are possible for the two-species biofilm model. Each set is shown to be asymptotically stable. A biofilm model describing the competition between autotrophic and heterotrophic bacteria and a biofilm model considering only Nitrosomonas and Nitrobacter are used for illustration. A parameter L(crit), critical film thickness for bacterial coexistence, is introduced from which criteria on the bulk concentrations for coexistence are derived. From these criteria it is seen that the thinner the biofilm, the more restrictive the conditions are for steady-state coexistence. For thin biofilms there may, in many cases, be no point in considering more than one species in the biofilm model. Furthermore, the gradients of the bacterial concentrations are in many cases negligible in thin biofilms, and the biofilm may then be assumed to be homogeneous. The criteria on the bulk concentrations together with the four sets of boundary conditions provide the necessary information for a direct solution of the steady-state two-species biofilm model by means of an ordinary differential and algebraic equation solver. (c) 1996 John Wiley & Sons, Inc.     

Parameter and process significance in mechanistic modeling of cellulose hydrolysis

A process-based model relevant to landfill and anaerobic digesters was developed, which included a novel approach to biomass transfer between a cellulose-bound biofilm and biomass in the bulk liquid. Model results highlighted the significance of the bacterial colonization of cellulose particles by attachment through contact in solution. Simulations revealed that both enhanced colonization and cellulose degradation are associated with reduced cellulose particle size, increased biomass populations in solution and increased cellulose-binding ability of the biomass. This suggests that transportation of biomass into the system from elsewhere and/or bacterial inoculation of such systems could enhance degradation significantly. A sensitivity analysis of the system parameters revealed the biological rate and yield properties of the hydrolyzing bacteria are most significant with regard to cellulose degradation in the system.     

The impacts of the AOC concentration on biofilm formation under higher shear force condition

The logistic growth model was applied in the study to evaluate the impacts of assimilable organic carbon (AOC) concentration on the growth characteristics of biofilm and bulk bacteria under high flow velocity condition. The experimental results showed that there existed a growth and decline relation between biofilm and bulk bacteria at the low (0.05 mg/L) and medium (0.5 mg/L) AOC levels. Increasing the AOC concentration up to 1.0 mg/L, it resulted in high amounts of biofilm and bulk bacteria simultaneously. Although the carrying capacity of biofilm bacteria at the medium condition of AOC level was substantially reduced, the specific growth rate (GR) of biofilm bacteria was largest at this condition. It showed that the reduction of biofilm bacteria quantity did not represent the suppression of bacterial growth. The quantity of bulk water bacteria was obviously dependent with the quantity of biofilm bacteria and the increase of free bacteria with time in networks was mainly due to the growth and detachment of biofilm bacteria, not due to the growth of free bacteria themselves. The maximum growth rate of biofilm bacteria was increased upon increasing the AOC level. It indicated that the AOC level was an important factor affecting the growth of biofilm bacteria.     

Electrochemical biofilm control: mechanism of action

Although it has been previously demonstrated that an electrical current can be used to control biofilm growth on metal surfaces, the literature results are conflicting and there is no accepted mechanism of action. One of the suggested mechanisms is the production of hydrogen peroxide (H(2)O(2)) on metal surfaces. However, there are literature studies in which H(2)O(2) could not be detected in the bulk solution. This is most likely because H(2)O(2) was produced at a low concentration near the surface and could not be detected in the bulk solution. The goals of this research were (1) to develop a well-controlled system to explain the mechanism of action of the bioelectrochemical effect on 316L stainless steel (SS) surfaces and (2) to test whether the produced H(2)O(2) can reduce cell growth on metal surfaces. It was found that H(2)O(2) was produced near 316L SS surfaces when a negative potential was applied. The H(2)O(2) concentration increased towards the surface, while the dissolved oxygen decreased when the SS surface was polarized to?-600 mV(Ag/AgCl). When polarized and non-polarized surfaces with identical Pseudomonas aeruginosa PAO1 biofilms were continuously fed with air-saturated growth medium, the polarized surfaces showed minimal biofilm growth while there was significant biofilm growth on the non-polarized surfaces. Although there was no detectable H(2)O(2) in the bulk solution, it was found that the surface concentration of H(2)O(2) was able to prevent biofilm growth.     

Storage and growth of denitrifiers in aerobic granules: part I. model development

A mathematical model, based on the Activated Sludge Model No.3 (ASM3), is developed to describe the storage and growth activities of denitrifiers in aerobic granules under anoxic conditions. In this model, mass transfer, hydrolysis, simultaneous anoxic storage and growth, anoxic maintenance, and endogenous decay are all taken into account. The model established is implemented in the well-established AQUASIM simulation software. A combination of completely mixed reactor and biofilm reactor compartments provided by AQUASIM is used to simulate the mass transport and conversion processes occurring in both bulk liquid and granules. The modeling results explicitly show that the external substrate is immediately utilized for storage and growth at feast phase. More external substrates are diverted to storage process than the primary biomass production process. The model simulation indicates that the nitrate utilization rate (NUR) of granules-based denitrification process includes four linear phases of nitrate reduction. Furthermore, the methodology for determining the most important parameter in this model, that is, anoxic reduction factor, is established.     

Impact of flow velocity on the dynamic behaviour of biofilm bacteria

The impact of flow velocity (FV) on the growth dynamics of biofilms and bulk water heterotrophic plate count (HPC) bacteria in drinking water distribution systems was quantified and modeled by combining a logistic growth model with mass balance equations. The dynamic variations in the specific growth and release rates of biofilm bacteria were also quantified. The experimental results showed that the maximum biofilm biomass did not change when flow velocity was increased from 20 to 40 cm s(-1), but was significantly affected when flow velocity was further increased to 60 cm s(-1). Although the concentration of biofilm bacteria was substantially reduced by the higher shear stress, the concentration of bacteria in the bulk fluid was slightly increased. From this it is estimated that the specific growth rate and specific release rate of biofilm bacteria had doubled. The specific release (detachment) rate was dependent on the specific growth rate of the biofilm bacteria.     

Two-Fluid Model of Biofilm Disinfection

We consider a dynamic model of biofilm disinfection in two dimensions. The biofilm is treated as a viscous fluid immersed in a fluid of less viscosity. The bulk fluid moves due to an imposed external parabolic flow. The motion of the fluid is coupled to the biofilm inducing motion of the biofilm. Both the biofilm and the bulk fluid are dominated by viscous forces, hence the Reynolds number is negligible and the appropriate equations are Stokes equations. The governing partial differential equations are recast as boundary integral equations using a version of the Lorenz reciprocal relationship. This allows for robust treatment of the simplified fluid/biofilm motion. The transport of nutrients and antimicrobials, which depends directly on the velocities of the fluid and biofilm, is also included. Disinfection of the bacteria is considered under the assumption that the biofilm growth is overwhelmed by disinfection. Supported by NSF award DMS-0612467.     

Two-dimensional model of biofilm detachment caused by internal stress from liquid flow

A two-dimensional model for biofilm growth and detachment was used to evaluate the effect of detachment on biofilm structures. The detachment process is considered to be due to internal stress created by moving liquid past the biofilm. This model generated a variety of realistic biofilm-formation patterns. It was possible to model in a unified way two different biofilm detachment processes, erosion (small-particle loss), and sloughing (large-biomass-particle removal). The distribution of the fraction from total biomass detached as a function of detached particle mass, gives indications about which of the two mechanisms is dominant. Model simulations indicate that erosion makes the biofilm surface smoother. Sloughing, in contrast, leads to an increased biofilm-surface roughness. Faster growing biofilms have a faster detachment rate than slow-growing biofilms, under similar hydrodynamic conditions and biofilm strength. This is in perfect accordance with the experimental evidence showing that detachment is dependent on both shear- and microbial-growth rates. High growth rates trigger instability in biofilm accumulation and abrupt biomass loss (sloughing). Massive sloughing can be avoided by high liquid shear, combined with low biomass growth rates. As the modeling results show, the causes for sloughing must be sought not only in the biofilm strength, but also in its shape. Several "mushroom-like" biofilm structures like those repeatedly reported in the literature occurred, due to a combined effect of nutrient depletion and breaking at the colony base. A rough carrier surface promotes biofilm development in hydrodynamic conditions in which the biofilm on a flat surface would not form. Although biofilm patches filled completely the cavity in which they started to grow, they were unable to spill over the carrier peaks and to fully colonize the substratum.     

Mathematical simulation of a biofilm process

A mathematical model has been developed for a fixed-film biological process (film flow over a flat plate) that describes bulk liquid transport, diffusional transport of oxygen and organics across a stagnant film, diffusional transport of oxygen and organics into the biofilm, biochemical reactions by the individual cells within the biofilm, biofilm growth, and cell density changes within the biofilm due to cellular decay. Simulation studies are presented to show how contact time and diffusion layer thickness affect process performance.     

Modeling of an anoxic/methanogenic biofilm: effect of pH calculation within the biofilm

The models of anoxic/methanogenic processes in biofilm reactors published until now have supposed that pH does not change between the bulk liquid and biofilm. These assumptions are not necessarily valid for processes in reactors with biofilms. The present work studied an anoxic/methanogenic biofilm reactor incorporating the pH variation in both bulk and biofilm. Two dynamic models, one including the calculation of pH throughout the biofilm, were solved numerically and compared with each other. The results showed that the inclusion of a pH algorithm calculation produces different profiles and efficiencies on an anoxic/methanogenic biofilm system. Values of C/N ratio higher than 20 mg TOC/mg NO₃–N and values of HRT lower than 4.5 h produce differences of up to 46 % with a traditional model that does not include pH calculation inside the biofilm. Thus, the assumption of a constant pH within the biofilm when using the traditional model does not accurately describe the performance of the system under these conditions, and pH calculation inside the biofilm should be included.     

A new method to solve a non-steady-state multispecies biofilm model

A transient multispecies model for quantifying microbial space competition in biofilm is derived from existing models, introducing a new approach to biomass detachment modelling. This model includes inert biomass, substrate diffusion and utilization rate within the biofilm and diffusional layers. It predicts the evolution of biofilm thickness, bulk substrate concentration, species distribution and substrate concentration within the biofilm. A zero-dimensional transient model is described. Its steady-state solution is used to set up initial conditions of the one-dimensional model and case computation towards steady-state solution. Some numerical tools have been developed, enabling fast computation on microcomputers. Simulations show the validity of a zero-dimensional model and perturbated systems are also simulated. Simulations with experimental data give acceptable results.     

Impact of flow velocity on the dynamic behaviour of biofilm bacteria

Abstract

The impact of flow velocity (FV) on the growth dynamics of biofilms and bulk water heterotrophic plate count (HPC) bacteria in drinking water distribution systems was quantified and modeled by combining a logistic growth model with mass balance equations. The dynamic variations in the specific growth and release rates of biofilm bacteria were also quantified. The experimental results showed that the maximum biofilm biomass did not change when flow velocity was increased from 20 to 40 cm s^?1, but was significantly affected when flow velocity was further increased to 60 cm s^?1. Although the concentration of biofilm bacteria was substantially reduced by the higher shear stress, the concentration of bacteria in the bulk fluid was slightly increased. From this it is estimated that the specific growth rate and specific release rate of biofilm bacteria had doubled. The specific release (detachment) rate was dependent on the specific growth rate of the biofilm bacteria.     

Modeling biocide action against biofilms

A phenomenological model of biocide action against microbial biofilms was derived. Processes incorporated in the model include bulk flow in and out of a well-mixed reactor, transport of dissolved species into the biofilm, substrate consumption by bacterial metabolism, bacterial growth, advection of cell mass within the biofilm, cell detachment from the biofilm, cell death, and biocide concentration-dependent disinfection. Simulations were performed to analyze the general behavior of the model and to perform preliminary sensitivity analysis to identify key input parameters. The model captured several general features of antimicrobial agent action against biofilms that have been observed widely by experimenters and practitioners. These included (1) rapid disinfection followed by biofilm regrowth, (2) slower detachment than disinfection, and (3) reduced susceptibility of microorganisms in biofilms. The results support the plausibility of a mechanism of biofilm resistance in which the biocide is neutralized by reaction with biofilm constituents, leading to a reduction in the bulk biocide concentration and, more significantly, biocide concentration gradients within the biofilm. Sensitivity experiments and analyses identified which input parameters influence key response variables. Each of three response variables was sensitive to each of the five input parameters, but they were most sensitive to the initial biofilm thickness and next most sensitive to the biocide disinfection rate coefficient. Statistical regression modeling produced simple equations for approximating the response variables for situations within the range of conditions covered by the sensitivity experiment. The model should be useful as a tool for studying alternative biocide control strategies. For example, the simulations suggested that a good interval between pulses of biocide is the time to minimum thickness. (c) 1996 John Wiley & Sons, Inc.     

Microcolony and biofilm formation as a survival strategy for bacteria

Bacterial communities such as biofilms are widely recognized as being important for survival and persistence of bacteria in harsh environments. Mechanistic models of biofilm growth indicate that the way in which the surface is seeded can effect the morphology of simulated biofilms. Experimental studies indicate that genes which are important for chemotaxis also influence biofilm formation, perhaps by influencing aggregation on a surface. Understanding aggregation and microcolony formation could therefore help clarify factors influencing biofilm formation and illuminate how groups influence the fitness of bacteria. In this paper I develop an individual based model to examine how different behaviors involved in microcolony formation on a surface determine patterns of group sizes and link patterns to bacterial fitness.     

Respirometric assay for biofilm kinetics estimation: parameter identifiability and retrievability

Currently, no fast and accurate methods exist for measuring extant biokinetic parameters for biofilm systems. This article presents a new approach to measure extant biokinetic parameters of biofilms and examines the numerical feasibility of such a method. A completely mixed attached growth bioreactor is subjected to a pulse of substrate, and oxygen consumption is monitored by on-line measurement of dissolved oxygen concentration in the bulk liquid. The oxygen concentration profile is then fit with a mechanistic mathematical model for the biofilm to estimate biokinetic parameters. In this study a transient biofilm model is developed and solved to generate dissolved oxygen profiles in the bulk liquid. Sensitivity analysis of the model reveals that the dissolved oxygen profiles are sufficiently sensitive to the biokinetic parameters-the maximum specific growth rate coefficient (insertion markμ) and the half-saturation coefficient (Ks)-to support parameter estimation if accurate estimates of other model parameters can be obtained. Monte Carlo simulations are conducted with the model to add typical measurement error to the generated dissolved oxygen profiles. Even with measurement error in the dissolved oxygen profile, a pair of biokinetic parameters is always retrievable. The geometric mean of the parameter estimates from the Monte Carlo simulations prove to be an accurate estimator for the true biokinetic values. Higher precision is obtained for insertion markμ estimates than for Ks estimates. In summary, this theoretical analysis reveals that an on-line respirometric assay holds promise for measuring extant biofilm kinetic parameters. Copyright 1998 John Wiley & Sons, Inc.     

An in vitro model for the growth and analysis of chronic wound MRSA biofilms

Aims: To develop an in vitro model (Colony/drip‐flow reactor – C/DFR) for the growth and analysis of methicillin‐resistant Staphylococcus aureus (MRSA) biofilms. Methods and Results: Using the C/DFR model, biofilms were grown on the top of polycarbonate filter membranes inoculated with a clinical isolate of MRSA, placed on absorbent pads in the DFR and harvested after 72 h. The biofilms varied from 256 to 308 μm in thickness with a repeatability standard deviation of 0·22. Testing of antimicrobial agents was also performed where C/DFR biofilms were grown in parallel with conventional colony biofilms. A saline solution (control), 1% silver sulfadiazine solution, and 0·25% Dakin’s solution were used to treat the biofilms for 15 min. Microscopic evaluation of biofilm morphology and thickness was conducted. The Dakins solution in both models produced statistically significantly higher log reductions than silver sulfadiazine treatment. Conclusions: The C/DFR biofilms were thick and repeatable and exhibited higher resistance to Dakins solution than the treated colony biofilms. Significance and Impact of the Study: The C/DFR can be used as a tool for examining complex biofilm physiology as well as for performing comparative experiments that test wound care products and novel antimicrobials.     

Characterization of biofilm growth and biocide susceptibility testing of Mycobacterium phlei using the MBEC assay system

The importance of non-tuberculosis mycobacterial biofilm species in medicine, industry and the environment has recently gained attention. Our objectives were to characterize biofilm growth of Mycobacterium phlei M4, as a model of rapidly growing mycobacteria using the minimal biofilm eradication concentration (MBEC) and to compare biocide susceptibility of planktonic and biofilm organisms. Scanning electron microscopy was also carried out to observe biofilm morphology. With the exception of Sporicidin and Virkon the minimum bactericidal concentration values for all biocides tested were lower than the MBEC values. The MBEC assay system was seen to produce multiple and reproducible biofilms of M. phlei and to be a useful tool for susceptibility studies.     

Multi‐species nitrifying biofilm model (MSNBM) including free ammonia and free nitrous acid inhibition and oxygen limitation

A multi‐species nitrifying biofilm model (MSNBM) is developed to describe nitrite accumulation by simultaneous free ammonia (FA) and free nitrous acid (FNA) inhibition, direct pH inhibition, and oxygen limitation in a biofilm. The MSNBM addresses the spatial gradient of pH with biofilm depth and how it induces changes of FA and FNA speciation and inhibition. Simulations using the MSNBM in a completely mixed biofilm reactor show that influent total ammonia nitrogen (TAN) concentration, bulk dissolved oxygen (DO) concentration, and buffer concentration exert significant control on the suppression of nitrite‐oxidizing bacteria (NOB) and shortcut biological nitrogen removal (SBNR), but the pH in the bulk liquid has a weaker influence. Ammonium oxidation increases the nitrite concentration and decreases the pH, which together can increase FNA inhibition of NOB in the biofilm. Thus, a low buffer concentration can accentuate SBNR. DO and influent TAN concentrations are efficient means to enhance DO limitation, which affects NOB more than ammonia‐oxidizing bacteria (AOB) inside the biofilm. With high influent TAN concentration, FA inhibition is dominant at an early phase, but finally DO limitation becomes more important as TAN degradation and biofilm growth proceed. MSNBM results indicate that oxygen depletion and FNA inhibition throughout the biofilm continuously suppress the growth of NOB, which helps achieve SBNR with a lower TAN concentration than in systems without concentration gradients. Biotechnol. Bioeng. 2010;105: 1115–1130. © 2009 Wiley Periodicals, Inc.     

Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study

A two-dimensional model for quantitative evaluation of the effect of convective and diffusive substrate transport on biofilm heterogeneity was developed. The model includes flow computation around the irregular biofilm surface, substrate mass transfer by convection and diffusion, biomass growth, and biomass spreading. It was found that in the absence of detachment, biofilm heterogeneity is mainly determined by internal mass transfer rate of substrates and by the initial percentage of carrier-surface colonization. Model predictions show that biofilm structures with highly irregular surface develop in the mass transfer-limited regime. As the nutrient availability increases, there is a gradual shift toward compact and smooth biofilms. A smaller fraction of colonized carrier surface leads to a patchy biofilm. Biofilm surface irregularity and deep vertical channels are, in this case, caused by the inability of the colonies to spread over the whole substratum surface. The maximum substrate flux to the biofilm was greatly influenced by both internal and external mass transfer rates, but not affected by the inoculation density. In general, results of the present model were similar to those obtained by a simple diffusion-reaction-growth model.