Biofilm Growth Model Research Articles

A Hamilton principle-based model for diffusion-driven biofilm growth.

Dense communities of bacteria, also known as biofilms, are ubiquitous in all of our everyday life. They are not only always surrounding us, but are also active inside our bodies, for example in the oral cavity. While some biofilms are beneficial or even necessary for human life, others can be harmful. Therefore, it is highly important to gain an in-depth understanding of biofilms which can be achieved by in vitro or in vivo experiments. Since these experiments are often time-consuming or expensive, in silico models have proven themselves to be a viable tool in assisting the description and analysis of these complicated processes. Current biofilm growth simulations are using mainly two approaches for describing the underlying models. The volumetric approach splits the deformation tensor into a growth and an elastic part. In this approach, the mass never changes, unless some additional constraints are enforced. The density-based approach, on the other hand, uses an evolution equation to update the growing tissue by adding mass. Here, the density stays constant, and no pressure is exerted. The in silico model presented in this work combines the two approaches. Thus, it is possible to capture stresses inside of the biofilm while adding mass. Since this approach is directly derived from Hamilton's principle, it fulfills the first and second law of thermodynamics automatically, which other models need to be checked for separately. In this work, we show the derivation of the model as well as some selected numerical experiments. The numerical experiments show a good phenomenological agreement with what is to be expected from a growing biofilm. The numerical behavior is stable, and we are thus capable of solving complicated boundary value problems. In addition, the model is very reactive to different input parameters, thereby different behavior of various biofilms can be captured without modifying the model.

Residual cells and nutrient availability guide wound healing in bacterial biofilms.

Biofilms are multicellular heterogeneous bacterial communities characterized by social-like division of labor, and remarkable robustness with respect to external stresses. Increasingly often an analogy between biofilms and arguably more complex eukaryotic tissues is being drawn. One illustrative example of where this analogy can be practically useful is the process of wound healing. While it has been extensively studied in eukaryotic tissues, the mechanism of wound healing in biofilms is virtually unexplored. Combining experiments in Bacillus subtilis bacteria, a model organism for biofilm formation, and a lattice-based theoretical model of biofilm growth, we studied how biofilms recover after macroscopic damage. We suggest that nutrient gradients and the abundance of proliferating cells are key factors augmenting wound closure. Accordingly, in the model, cell quiescence, nutrient fluxes, and biomass represented by cells and self-secreted extracellular matrix are necessary to qualitatively recapitulate the experimental results for damage repair. One of the surprising experimental findings is that residual cells, persisting in a damaged area after removal of a part of the biofilm, prominently affect the healing process. Taken together, our results outline the important roles of nutrient gradients and residual cells on biomass regrowth on macroscopic scales of the whole biofilm. The proposed combined experiment-simulation framework opens the way to further investigate the possible relation between wound healing, cell signaling and cell phenotype alternation in the local microenvironment of the wound.

Spatiotemporal succession of phosphorous accumulating biofilms during the first year of establishment.

Many wastewater treatment plants are dependent on the utilization of microorganisms in biofilms. Our knowledge about the establishment of these biofilms is limited, particular with respect to biofilms involved in enhanced biological phosphorus removal (EBPR). These biofilms rely on polyphosphate-accumulating organisms (PAOs), requiring alternating oxic and anaerobic conditions for phosphorous uptake. This challenge has been solved using the Hias process, which combines moving-bed biofilm-reactor (MBBR) technology with physical transfer of biofilm-carriers from oxic to anaerobic zones. We combined biofilm fractionation with temporal analyses to unveil the establishment in the Hias process. A stable phosphorous removal efficiency of >95% was reached within 16 weeks of operation. Phosphorus removal, however, was not correlated with the establishment of known PAOs. The biofilms seemed associated with an outer microbiota layer with rapid turnover and an inner layer with a slow expansion. The inner layer showed an overrepresentation of known PAOs. In conclusion, our spatiotemporal analyses of phosphorous accumulating biofilm establishment lead to a new model for biofilm growth, while the mechanisms for phosphorous removal remain largely unresolved.

Microorganism Carrier-Surface Method as an Efficient Model for Microscopic Characterization of Biofilm Structure and Dispersion in Dairy Associated Spore-Forming Bacteria

Dispersion, defined as the release of planktonic cells is the final stage of biofilm development and of major significance in clinical and industrial settings. Currently, biofilm dispersion is considered as a promising avenue for biofilm control and an important topic research. However, a problem facing such research projects is how to induce planktonic life in a biofilm. Numerous systems are used for the investigation of biofilm dispersion, including dynamic continuous or static batch systems. This mini-review describes the usefulness of the microorganism carrier-surface method as a simple biofilm growth model which successfully allowed microscopic characterization of biofilm structure and dispersion in dairy-associated spore-forming bacteria and should be an efficient model for studying dispersion process.

Simulation of various biofilm fractal morphologies by agent-based model

Biofilms are clusters of bacteria wrapped in extracellular matrix and polymers. The study of biofilm morphological transformation has been around for a long time and has attracted widespread attention. In this paper, we present a model for biofilm growth based on the interaction force, in which bacteria are treated as tiny particles and locations of particles are updated by calculating the repulsive forces among particles. We adapt a continuity equation to indicate nutrient concentration variation in the substrate. Based on the above, we study the morphological transformation of biofilms. We find that nutrient concentration and nutrient diffusion rate dominate different biofilm morphological transition processes, in which biofilms would grow into fractal morphology under the conditions of low nutrient concentration and nutrient diffusivity. At the same time, we expand our model by introducing a second particle to mimic extracellular polymeric substances (EPS) in biofilms. We find that the interaction between different particles can lead to phase separation patterns between cells and EPSs, and the adhesion effect of EPS can attenuate this phenomenon. In contrast to single particle system models, branches are inhibited due to EPS filling in dual particle system models, and this invalidation is boosted by the enhancement of the depletion effect.

Inverse problems for a model of biofilm growth

Abstract A bacterial biofilm is an aggregate of micro-organisms growing fixed onto a solid surface, rather than floating freely in a liquid. Biofilms play a major role in various practical situations such as surgical infections and water treatment. We consider a non-linear partial differential equation (PDE) model of biofilm growth subject to initial and Dirichlet boundary conditions, and the inverse coefficient problem of recovering the unknown parameters in the model from extra measurements of quantities related to the biofilm and substrate. By addressing and analysing this inverse problem, we provide reliable and robust reconstructions of the primary physical quantities of interest represented by the diffusion coefficients of substrate and biofilm, the biomass spreading parameters, the maximum specific consumption and growth rates, the biofilm decay rate and the half saturation constant. We give particular attention to the constant coefficients involved in the leading-part non-linearity, and present a uniqueness proof and some numerical results. In the course of the numerical investigation, we have identified extra data information that enables improving the reconstruction of the eight-parameter set of physical quantities associated to the model of biofilm growth.

Compartmental Modeling of Biofouling in Industrial Cooling Circuits

AbstractIndustrial cooling circuits with wet cooling towers use raw water to remove residual heat from industrial processes. These circuits are very prone to fouling and particularly biofouling. This work proposes a compartmental model built from a full hydrodynamic characterization (using computational fluid dynamics and experimental, local, and system data) of an industrial cooling circuit and implemented with a biofilm growth model which considers kinetic (temperature, concentrations) as well as hydrodynamic (internal and external transfer) limitations. It can therefore predict the biofouling growth per surface unit in the different part of the circuit, considering the various hydrodynamic conditions, while taking only a few minutes to simulate a full year considering season variation of temperature and water quality.

Predicting tubular heat exchanger efficiency reduction caused by marine biofilm adhesion using CFD simulations

A novel efficiency reduction model to tubular heat exchanger based on heat transfer losses by biofilm adhesion is proposed, which included a modified equation based on the real data-dependent time, seawater, hydrodynamics and heat transfer resistance using computational fluid dynamics (CFD). The biofilm growth model based on Verhulst model and experimental data has been obtained and simulated in a CFD software tool to analyze the tubular heat exchanger performance prediction cooled by seawater. The biofilm CFD model with appropriate fit, and the correlation coefficient (R2) values are between 0.97 and 0.99, was validated by experimental data obtained at different flow velocity. The final results of in/outlet difference temperatures were from 3.9 °C to 2.2 °C for different flow velocity with R2 > 0.97. The simulation results demonstrate that the novel CFD model is capable of predicting the efficiency losses during the development period of biofilm growth in in open-loop cooling seawater systems.

Permeable Biofilms Can Support Persistent Hyporheic Anoxic Microzones

AbstractExperimental observations reveal the existence of anoxic microzones within oxygen‐rich aquatic sediments. The microzones are hotspots of enhanced removal of nitrate and production of greenhouse gas nitrous oxide. Here we established a new microscale flow, reactive transport and biofilm growth model and explore how anoxic microzones form and evolve within hyporheic zones under dynamic interactions among pore‐scale flow, reactive transport and biofilm growth. The microzones can form and evolve by two patterns as streambeds are progressively clogged due to biofilm growth: (a) physical and biogeochemical conditions‐dependent perennial microzones for permeable biofilms, and (b) physical and biogeochemical conditions‐independent ephemeral microzones for low permeability biofilms. During biofilm growth, persistent transport‐dominated systems sustain for the former, whereas the transformation of transport‐dominated to reaction‐dominated systems occurs for the latter. These findings are significantly different from previous single pattern of ephemeral microzones.

Thin-film lubrication model for biofilm expansion under strong adhesion.

Understanding microbial biofilm growth is important to public health because biofilms are a leading cause of persistent clinical infections. In this paper, we develop a thin-film model for microbial biofilm growth on a solid substratum to which it adheres strongly. We model biofilms as two-phase viscous fluid mixtures of living cells and extracellular fluid. The model explicitly tracks the movement, depletion, and uptake of nutrients and incorporates cell proliferation via a nutrient-dependent source term. Notably, our thin-film reduction is two dimensional and includes the vertical dependence of cell volume fraction. Numerical solutions show that this vertical dependence is weak for biologically feasible parameters, reinforcing results from previous models in which this dependence was neglected. We exploit this weak dependence by writing and solving a simplified one-dimensional model that is computationally more efficient than the full model. We use both the one- and two-dimensional models to predict how model parameters affect expansion speed and biofilm thickness. This analysis reveals that expansion speed depends on cell proliferation, nutrient availability, cell-cell adhesion on the upper surface, and slip on the biofilm-substratum interface. Our numerical solutions provide a means to qualitatively distinguish between the extensional flow and lubrication regimes, and quantitative predictions that can be tested in future experiments.

A mathematical model of discrete attachment to a cellulolytic biofilm using random DEs.

We propose a new mathematical framework for the addition of stochastic attachment to biofilm models, via the use of random ordinary differential equations. We focus our approach on a spatially explicit model of cellulolytic biofilm growth and formation that comprises a PDE-ODE coupled system to describe the biomass and carbon respectively. The model equations are discretized in space using a standard finite volume method. We introduce discrete attachment events into the discretized model via an impulse function with a standard stochastic process as input. We solve our model with an implicit ODE solver. We provide basic simulations to investigate the qualitative features of our model. We then perform a grid refinement study to investigate the spatial convergence of our model. We investigate model behaviour while varying key attachment parameters. Lastly, we use our attachment model to provide evidence for a stable travelling wave solution to the original PDE-ODE coupled system.

Modeling microbial growth of dynamic membrane in a biohydrogen production bioreactor

Biohydrogen is renewable and has a huge potential to replace fossil fuels. Understanding mechanisms of controlling microbial processes of the dynamic membrane is critical for effective dark fermentative biohydrogen production in a dynamic membrane bioreactor (DMBR). This paper aims to develop a sophisticated model of biofilm growth, dynamic membrane formation, and dark fermentative hydrogen production within a platform of coupled lattice Boltzmann and cellular automata. The model was validated against the experimental data available and then was applied for the investigation of biohydrogen production in bioreactors under different membrane structures and inlet velocities. The results showed that porous twisted channels in the dynamic membrane could significantly affect biohydrogen extraction and biofilm patterns. In all cases, the dynamic membrane formation has three phases: the initial bacteria deposit, stable biofilm growth, and stable maximum biofilm biomass. The biohydrogen production could increase by 16.4% by optimizing the porous structure and increase 30%–40% of the hydrogen extraction. Inlet velocity also affects biohydrogen extraction in a range of −28.3%–71.2%. Both porous structure and inlet velocity would be critical operational parameters for continuous biohydrogen production. The present model demonstrated its capability to investigate dark fermentative hydrogen production and its potential applications to porous bioreactors.

Cell position fates and collective fountain flow in bacterial biofilms revealed by light-sheet microscopy.

Bacterial biofilms represent a basic form of multicellular organization that confers survival advantages to constituent cells. The sequential stages of cell ordering during biofilm development have been studied in the pathogen and model biofilm-former Vibrio cholerae It is unknown how spatial trajectories of individual cells and the collective motions of many cells drive biofilm expansion. We developed dual-view light-sheet microscopy to investigate the dynamics of biofilm development from a founder cell to a mature three-dimensional community. Tracking of individual cells revealed two distinct fates: one set of biofilm cells expanded ballistically outward, while the other became trapped at the substrate. A collective fountain-like flow transported cells to the biofilm front, bypassing members trapped at the substrate and facilitating lateral biofilm expansion. This collective flow pattern was quantitatively captured by a continuum model of biofilm growth against substrate friction. Coordinated cell movement required the matrix protein RbmA, without which cells expanded erratically. Thus, tracking cell lineages and trajectories in space and time revealed how multicellular structures form from a single founder cell.

Bacterial biofilms in infective endocarditis: an in vitro model to investigate emerging technologies of antimicrobial cardiovascular device coatings

ObjectiveIn spite of the progress in antimicrobial and surgical therapy, infective endocarditis (IE) is still associated with a high morbidity and mortality. IE is characterized by bacterial biofilms of the endocardium, especially of the aortic and mitral valve leading to their destruction. About one quarter of patients with formal surgery indication cannot undergo surgery. This group of patients needs further options of therapy, but due to a lack of models for IE prospects of research are low. Therefore, the purpose of this project was to establish an in vitro model of infective endocarditis to allow growth of bacterial biofilms on porcine aortic valves, serving as baseline for further research.Methods and resultsA pulsatile two-chamber circulation model was constructed that kept native porcine aortic valves under sterile, physiologic hemodynamic and temperature conditions. To create biofilms on porcine aortic valves the system was inoculated with Staphylococcus epidermidis PIA 8400. Aortic roots were incubated in the model for increasing periods of time (24 h and 40 h) and bacterial titration (1.5 × 104 CFU/mL and 1.5 × 105 CFU/mL) with 5 L cardiac output per minute. After incubation, tissue sections were analysed by fluorescence in situ hybridization (FISH) for direct visualization of the biofilms. Pilot tests for biofilm growth showed monospecies colonization consisting of cocci with time- and inocula-dependent increase after 24 h and 40 h (n = 4). In n = 3 experiments for 24 h, with the same inocula, FISH visualized biofilms with ribosome-containing, and thus metabolic active cocci, tissue infiltration and similar colonization pattern as observed by the FISH in human IE heart valves infected by S. epidermidis.ConclusionThese results demonstrate the establishment of a novel in vitro model for bacterial biofilm growth on porcine aortic roots mimicking IE. The model will allow to identify predilection sites of valves for bacterial adhesion and biofilm growth and it may serve as baseline for further research on IE therapy and prevention, e.g. the development of antimicrobial transcatheter approaches to IE.Graphic abstract

Biofilm and Planktonic Bacteria Differentially Express a Small Molecule (<3kD), Heat‐Stable, Protease‐Resistant Factor that Affects Bovine Neutrophil Function in a NF‐Kappa β‐Independent Mechanism

IntroductionChronic bacterial infections and the associated inflammation have a significant impact in both veterinary and human medicine. Bacterial biofilms are a major cause of the persistent inflammation observed in chronic infections and nearly 80% of all infections involve biofilms. Biofilms are typically polymicrobial in composition and many of these mixed‐infections involve anaerobic bacteria. Recent evidence demonstrates that immune cells often disregard the signals released from biofilm bacteria, and ineffectual clearance of biofilms may explain the chronicity of this sort of infection. A mixed‐species model of anaerobic biofilm growth was developed to evaluate medically relevant biofilms and their interactions with bovine neutrophils.AimsTo generate mixed‐species bacterial biofilms composed of the two opportunistic pathogens Fusobacterium necrophorum and Porphyromonas levii, and to employ the in vitro system to investigate factors associated with biofilms that may limit neutrophil functional ability.MethodsMixed‐species biofilm formation was verified with SEM, CLSM and viable cell counts. Neutrophil oxidative burst was assessed with a fluorescent microplate assay for hydrogen peroxide. Chemotaxis was measured with a Transwell transmigration assay. Extracellular factors released from planktonic cultures and biofilms were assessed by size‐exclusion filtration, lipopolysaccharide (LPS) removal, protease and heat treatment. Mechanistic experiments to study neutrophil responses to these supernatants were conducted with specific inhibitors of function, such as NF‐κβ signaling (BAY‐11) and inflammasome activation (glyburide).ResultsNeutrophils exposed to planktonic bacterial supernatants showed significantly elevated oxidative (4‐fold increase in fluorescence) and chemotactic responses compared to neutrophils exposed to biofilm products from identical bacteria. LPS plays a significant role in the stimulation of neutrophils; in this experiment biofilms produced substantially more LPS than planktonic bacteria despite inducing less neutrophil response. Removal of LPS resulted in similar neutrophil responses to planktonic and biofilm supernatants.Size‐exclusion filtration of bacterial supernatants and subsequent exposure to neutrophils revealed that the active stimulatory molecule is below 3 kD and is released strictly from planktonic cultures. Intensive heat and protease treatment of the <3kD fractions did not alter neutrophil functional responses. Treatment with a NF‐κβ inhibitor demonstrated that neutrophils respond specifically to planktonic supernatants independently of NF‐κβ signaling.ConclusionsWe describe a heat‐stable, protease‐resistant, non‐LPS, small (<3kD) factor produced by in vitro planktonic cultures of F. necrophorum and P. levii that activates bovine neutrophils. Neutrophils did not exhibit the same oxidative and chemotactic responses upon exposure to in vitro generated biofilm supernatants and these differential responses are the result of a NF‐κβ independent mechanism, perhaps through an inflammasome‐mediated process.Support or Funding InformationFunding provided by the University of Calgary Grant 10002461 to DW Morck.

A Dimensionally Reduced Model of Biofilm Growth Within a Flow Cell

Biofilms are colonies of bacteria attached to surfaces. They play a critical role in many engineering and medical applications. Scientists study biofilm growth in flow cells but often have limited direct knowledge of the environmental conditions in the apparatus. Using fully resolved, numerical simulations to estimate conditions within a flow cell is computationally expensive. In this paper, we use asymptotic analysis to create a simulation of a biofilm system that has one growth-limiting substrate, and we show that this method runs quickly while maintaining similar accuracy to prior models. These equations can provide a better understanding of the environmental conditions in experiments and can establish the boundary conditions for further smaller-scale numerical simulations.

Hybrid Model of Bacterial Biofilm Growth.

Bacterial biofilms play a critical role in environmental processes, water treatment, human health, and food processing. They exhibit highly complex dynamics due to the interactions between the bacteria and the extracellular polymeric substance (EPS), water, and nutrients and minerals that make up the biofilm. We present a hybrid computational model in which the dynamics of discrete bacterial cells are simulated within a multiphase continuum, consisting of EPS and water as separate interacting phases, through which nutrients and minerals diffuse. Bacterial cells in our model consume water and nutrients in order to grow, divide, and produce EPS. Consequently, EPS flows outward from the bacterial colony, while water flows inward. The model predicts bacterial colony formation as a treelike structure. The distribution of bacterial growth and EPS production is found to be sensitive to the pore spacing between bacteria and the consumption of nutrients within the bacterial colony. Forces that are sometimes neglected in biofilm simulations, such as lubrication force between nearby bacterial cells and osmotic (swelling) pressure force resulting from gradients in EPS concentration, are observed to have an important effect on biofilm growth via their influence on bacteria pore spacing and associated water/nutrient percolation into the bacterial colony.

Ex vivo biofilm-forming ability of dermatophytes using dog and cat hair: an ethically viable approach for an infection model

The aim of this study was to establish an ex vivo model for dermatophyte biofilm growth, using hair from dogs and cats. Strains of Microsporum canis, M. gypseum, Trichophyton mentagrophytes and T. tonsurans were assessed for in vitro and ex vivo biofilm production. All T. mentagrophytes and T. tonsurans isolates and 8/12 M. canis and 1/7 M. gypseum isolates formed biofilms in vitro, while all tested isolates presented biofilm growth on ex vivo models. T. mentagrophytes and M. canis formed more homogeneous and better-structured biofilms with greater biomass production on cat hair but T. tonsurans formed more biofilm on dog hair. Confocal and scanning electron microscopy demonstrated fungal hyphae colonizing and perforating the hair shaft, abundant fungal conidia, biofilm extracellular matrix and biofilm water channels. The present study demonstrated an ex vivo model for the performance of studies on biofilm formation by dermatophytes, using dog and cat hair.

Interaction between biofilm growth and NAPL remediation: A pore-scale study

In this paper, we introduce a pore-scale model to study the interaction between biofilm growth and non-aqueous-phase-liquid (NAPL) dissolution. Liquid flow and dissolved NAPL transport are coupled with a biofilm growth model to correctly describe the complex dynamics of the processes including fluid flow, NAPL dissolution/biodegradation and biofilm growth. Fluid flow is simulated using an immersed boundary-lattice Boltzmann (IB-LB) model; while solute transport is solved by a cut-cell finite volume method (FVM). A uniform dissolution approach is also adopted to capture the temporal evolution of trapped blobs. Spatio-temporal distributions of the biomass are investigated using a cellular automaton algorithm combined with the immersed boundary method (IBM). Simulations focused on NAPL dissolution in both abiotic and biotic conditions are conducted to assess the capability of the model. In abiotic conditions, we analyze the effects of the hydrodynamic regimes and the spatial distribution of NAPL blobs on the dissolution rate under different assumptions (i.e., blob size and Péclet number). In biotic conditions, a series of impact factors are also investigated (i.e., spatial distribution, reaction kinetics and NAPL-induced toxicity). Finally, the current model is used to evaluate the pore scale relevance of a local equilibrium assumption between fluid phase and biofilm phase in the vicinity of the NAPL source.

Biofilm modeling in evolving porous media with Beavers‐Joseph condition

AbstractIn this article, we derive an effective model for biofilm growth in a saturated porous medium. Several experimental investigations found out that biomass is in general very heterogeneous and contains in particular channels filled with fluid. These channels facilitate the transport of nutritive substances within the biofilm by advection. Referring to this, we model the biofilm itself at the pore‐scale as a porous medium. Hence the starting point at the pore‐scale is a Darcy‐Stokes system, where the Beavers‐Joseph boundary condition at the corresponding interface is proposed. By formal periodic homogenization we derive an averaged model describing the process via Darcy's law and upscaled transport equations with effective coefficients given by the evolving microstructure. Based on the assumption of uniform evolve of the underlying pore geometry, solvability in a weak sense global in time or at least up to a possible clogging phenomenon is stated.