Multicomponent hydrodynamic model for heterogeneous biofilms: two-dimensional numerical simulations of growth and interaction with flows

Data-driven modeling of heterogeneous viscoelastic biofilms

Biofilms are typically heterogeneous in morphology, structure, and composition, resulting in non-uniform mechanical properties. The distribution of mechanical properties, in turn, determines the biofilm behavior, such as deformation and detachment. Most biofilm models neglect biofilm heterogeneity, especially at the microscale. In this study, an image-based modeling approach was developed to transform two-dimensional optical coherence tomography (OCT) biofilm images to a pixel-scale non-Newtonian viscosity map of the biofilm. The map was calibrated using the bulk viscosity data from rheometer tests, based on assumed maximum and minimum viscosities and a relationship between OCT image intensity signals and non-Newtonian viscosity. While not quantitatively measuring biofilm viscosity for each pixel, it allows a rational spatial allocation of viscosities within the biofilm: areas with lower cell density, e.g., voids, are assigned lower viscosities, and areas with high cell densities are assigned higher viscosities. The spatial distribution of non-Newtonian viscosity was applied in an established Oldroyd-B constitutive model and implemented using the phase-field continuum approach for the deformation and stress analysis. The heterogeneous model was able to predict deformations more accurately than a homogenous one. Stress distribution in the heterogeneous biofilm displayed better characteristics than that in the homogeneous one, because it is highly dependent on the viscosity distribution. This work, using a pixel-scale, image-based approach to map the mechanical heterogeneity of biofilms for computational deformation and stress analysis, provides a novel modeling approach that allows the consideration of biofilm structural and mechanical heterogeneity. Future research should better characterize the relationship between OCT signal and viscosity, and consider other constitutive models for biofilm mechanical behavior. This article is protected by copyright. All rights reserved.

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.

Modeling of Symbiotic Bacterial Biofilm Growth with an Example of the Streptococcus-Veillonella sp. System

We present a multi-dimensional continuum mathematical model for modeling the growth of a symbiotic biofilm system. We take a dual-species namely, the Streptococcus-Veillonella sp. biofilm system as an example for numerical investigations. The presented model describes both the cooperation and competition between these species of bacteria. The coupled partial differential equations are solved by using an integrative finite element numerical strategy. Numerical examples are carried out for studying the evolution and distribution of the bio-components. The results demonstrate that the presented model is capable of describing the symbiotic behavior of the biofilm system. However, homogenized numerical solutions are observed locally. To study the homogenization behavior of the model, numerical investigations regarding on how random initial biomass distribution influences the homogenization process are carried out. We found that a smaller correlation length of the initial biomass distribution leads to faster homogenization of the solution globally, however, shows more fluctuated biomass profiles along the biofilm thickness direction. More realistic scenarios with bacteria in patches are also investigated numerically in this study.

A thin-film extensional flow model for biofilm expansion by sliding motility

In the presence of glycoproteins, bacterial and yeast biofilms are hypothesized to expand by sliding motility. This involves a sheet of cells spreading as a unit, facilitated by cell proliferation and weak adhesion to the substratum. In this paper, we derive an extensional flow model for biofilm expansion by sliding motility to test this hypothesis. We model the biofilm as a two-phase (living cells and an extracellular matrix) viscous fluid mixture, and model nutrient depletion and uptake from the substratum. Applying the thin-film approximation simplifies the model, and reduces it to one-dimensional axisymmetric form. Comparison with Saccharomyces cerevisiae mat formation experiments reveals good agreement between experimental expansion speed and numerical solutions to the model with O ( 1 ) parameters estimated from experiments. This confirms that sliding motility is a possible mechanism for yeast biofilm expansion. Having established the biological relevance of the model, we then demonstrate how the model parameters affect expansion speed, enabling us to predict biofilm expansion for different experimental conditions. Finally, we show that our model can explain the ridge formation observed in some biofilms. This is especially true if surface tension is low, as hypothesized for sliding motility.

Continuum and discrete approach in modeling biofilm development and structure: a review

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

The development of biofilm architecture

We extend the one-dimensional polymer solution theory of bacterial biofilm growth described by Winstanley et al. (2011 Proc. R. Soc. A467, 1449-1467 (doi:10.1098/rspa.2010.0327)) to deal with the problem of the growth of a patch of biofilm in more than one lateral dimension. The extension is non-trivial, as it requires consideration of the rheology of the polymer phase. We use a novel asymptotic technique to reduce the model to a free-boundary problem governed by the equations of Stokes flow with non-standard boundary conditions. We then consider the stability of laterally uniform biofilm growth, and show that the model predicts spatial instability; this is confirmed by a direct numerical solution of the governing equations. The instability results in cusp formation at the biofilm surface and provides an explanation for the common observation of patterned biofilm architectures.

Multicomponent model of deformation and detachment of a biofilm under fluid flow

A novel biofilm model is described which systemically couples bacteria, extracellular polymeric substances (EPS) and solvent phases in biofilm. This enables the study of contributions of rheology of individual phases to deformation of biofilm in response to fluid flow as well as interactions between different phases. The model, which is based on first and second laws of thermodynamics, is derived using an energetic variational approach and phase-field method. Phase-field coupling is used to model structural changes of a biofilm. A newly developed unconditionally energy-stable numerical splitting scheme is implemented for computing the numerical solution of the model efficiently. Model simulations predict biofilm cohesive failure for the flow velocity between [Formula: see text] and [Formula: see text] m s(-1) which is consistent with experiments. Simulations predict biofilm deformation resulting in the formation of streamers for EPS exhibiting a viscous-dominated mechanical response and the viscosity of EPS being less than [Formula: see text]. Higher EPS viscosity provides biofilm with greater resistance to deformation and to removal by the flow. Moreover, simulations show that higher EPS elasticity yields the formation of streamers with complex geometries that are more prone to detachment. These model predictions are shown to be in qualitative agreement with experimental observations.

Biophysics of biofilm infection

This article examines a likely basis of the tenacity of biofilm infections that has received relatively little attention: the resistance of biofilms to mechanical clearance. One way that a biofilm infection persists is by withstanding the flow of fluid or other mechanical forces that work to wash or sweep microorganisms out of the body. The fundamental criterion for mechanical persistence is that the biofilm failure strength exceeds the external applied stress. Mechanical failure of the biofilm and release of planktonic microbial cells is also important in vivo because it can result in dissemination of infection. The fundamental criterion for detachment and dissemination is that the applied stress exceeds the biofilm failure strength. The apparent contradiction for a biofilm to both persist and disseminate is resolved by recognizing that biofilm material properties are inherently heterogeneous. There are also mechanical aspects to the ways that infectious biofilms evade leukocyte phagocytosis. The possibility of alternative therapies for treating biofilm infections that work by reducing biofilm cohesion could (1) allow prevailing hydrodynamic shear to remove biofilm, (2) increase the efficacy of designed interventions for removing biofilms, (3) enable phagocytic engulfment of softened biofilm aggregates, and (4) improve phagocyte mobility and access to biofilm.

DIFFUSION IN BIOFILMS RESPIRING ON ELECTRODES

The goal of this study was to measure spatially and temporally resolved effective diffusion coefficients (D(e)) in biofilms respiring on electrodes. Two model electrochemically active biofilms, Geobacter sulfurreducens PCA and Shewanella oneidensis MR-1, were investigated. A novel nuclear magnetic resonance microimaging perfusion probe capable of simultaneous electrochemical and pulsed-field gradient nuclear magnetic resonance (PFG-NMR) techniques was used. PFG-NMR allowed noninvasive, nondestructive, high spatial resolution in situ D(e) measurements in living biofilms respiring on electrodes. The electrodes were polarized so that they would act as the sole terminal electron acceptor for microbial metabolism. We present our results as both two-dimensional D(e) heat maps and surface-averaged relative effective diffusion coefficient (D(rs)) depth profiles. We found that 1) D(rs) decreases with depth in G. sulfurreducens biofilms, following a sigmoid shape; 2) D(rs) at a given location decreases with G. sulfurreducens biofilm age; 3) average D(e) and D(rs) profiles in G. sulfurreducens biofilms are lower than those in S. oneidensis biofilms-the G. sulfurreducens biofilms studied here were on average 10 times denser than the S. oneidensis biofilms; and 4) halting the respiration of a G. sulfurreducens biofilm decreases the D(e) values. Density, reflected by D(e), plays a major role in the extracellular electron transfer strategies of electrochemically active biofilms.