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The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to continuum methods based on partial differential equations, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for noncrystalline materials, it may still be used as a first-order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to two-dimensional cellular-scale models by assessing the mechanical behavior of model biological tissues, including crystalline (honeycomb) and noncrystalline reference states. The numerical procedure involves applying an affine deformation to the boundary cells and computing the quasistatic position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For center-based cell models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based cell models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete and continuous modeling, adaptation of atom-to-continuum techniques to biological tissues, and model classification. [ABSTRACT FROM AUTHOR]

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport. [ABSTRACT FROM AUTHOR]

In this study, a new technique for three-dimensional imaging of biofilm within porous media using X-ray computed microtomography is presented. Due to the similarity in X-ray absorption coefficients for the porous media (plastic), biofilm and aqueous phase, an X-ray contrast agent is required to image biofilm within the experimental matrix using X-ray computed tomography. The presented technique utilizes a medical suspension of barium sulphate to differentiate between the aqueous phase and the biofilm. Potassium iodide is added to the suspension to aid in delineation between the biofilm and the experimental porous medium. The iodide readily diffuses into the biofilm while the barium sulphate suspension remains in the aqueous phase. This allows for effective differentiation of the three phases within the experimental systems utilized in this study. The behaviour of the two contrast agents, in particular of the barium sulphate, is addressed by comparing two-dimensional images of biofilm within a pore network obtained by (1) optical visualization and (2) X-ray absorption radiography. We show that the contrast mixture provides contrast between the biofilm, the aqueous-phase and the solid-phase (beads). The imaging method is then applied to two three-dimensional packed-bead columns within which biofilm was grown. Examples of reconstructed images are provided to illustrate the effectiveness of the method. Limitations and applications of the technique are discussed. A key benefit, associated with the presented method, is that it captures a substantial amount of information regarding the topology of the pore-scale transport processes. For example, the quantification of changes in porous media effective parameters, such as dispersion or permeability, induced by biofilm growth, is possible using specific upscaling techniques and numerical analysis. We emphasize that the results presented here serve as a first test of this novel approach; issues with accurate segmentation of the images, optimal concentrations of contrast agents and the potential need for use of synchrotron radiation sources need to be addressed before the method can be used for precise quantitative analysis of biofilm geometry in porous media. [ABSTRACT FROM AUTHOR]

Highlights • We study the flow of a shear-thinning fluid flow through porous media. • The nonlinearity in the flow at the pore-scale can lead to a change in the average flow direction compared to the Newtonian case. • We find that increasing disorder in the porous structure reduces the effect of the nonlinearity on the average flow direction. Abstract Modeling the flow of fluids with shear-dependent viscosity through porous media is a challenging fundamental and engineering problem. At continuum-scale, such flows are usually described using modified versions of Darcy's law, which are obtained by considering either an apparent viscosity or an apparent permeability. In the two cases, Darcy's law becomes nonlinear as the apparent viscosity or permeability both depend on the velocity or pressure gradient. The main difference between these two approaches is the impact of non-Newtonian effects on the flow direction. With the apparent viscosity, the flow direction is determined by the standard permeability tensor and unaltered by non-Newtonian effects. On the other hand, with the apparent permeability, the flow direction may be modified by non-Newtonian effects contained in the second-order tensor. Here, we ask the question of whether it is necessary to use a general tensorial correction including changes of flow direction or if the (scalar) apparent viscosity approach is sufficient. To study this, we solve numerically the non-Newtonian flow problem in a variety of isotropic porous structures for a model fluid where the viscosity depends on the shear rate following a power law with a Newtonian cut-off in the limit of low shear rates. We find that the structure of the porous medium plays a fundamental role and that there is a competition between the nonlinearity of the flow, induced by the non-Newtonian rheology, and the disorder of the porous structure. Our main result is that an apparent viscosity is sufficient in cases of sufficiently disordered porous media, as is the case of some sandstones found in petroleum engineering. Fundamentally, this suggests that the disorder in the geometry of the porous structure is mitigating part of the nonlinear effects due to the rheology. [ABSTRACT FROM AUTHOR]

Summary: Optical imaging techniques for biofilm observation, like laser scanning microscopy, are not applicable when investigating biofilm formation in opaque porous media. X‐ray micro‐tomography (X‐ray CMT) might be an alternative but it finds limitations in similarity of X‐ray absorption coefficients for the biofilm and aqueous phases. To overcome this difficulty, barium sulphate was used in Davit et al. (2011) to enable high‐resolution 3D imaging of biofilm via X‐ray CMT. However, this approach lacks comparison with well‐established imaging methods, which are known to capture the fine structures of biofilms, as well as uncertainty quantification. Here, we compare two‐photon laser scanning microscopy (TPLSM) images of Pseudomonas Aeruginosa biofilm grown in glass capillaries against X‐ray CMT using an improved protocol where barium sulphate is combined with low‐gelling temperature agarose to avoid sedimentation. Calibrated phantoms consisting of mono‐dispersed fluorescent and X‐ray absorbent beads were used to evaluate the uncertainty associated with our protocol along with three different segmentation techniques, namely hysteresis, watershed and region growing, to determine the bias relative to image binarization. Metrics such as volume, 3D surface area and thickness were measured and comparison of both imaging modalities shows that X‐ray CMT of biofilm using our protocol yields an accuracy that is comparable and even better in certain respects than TPLSM, even in a nonporous system that is largely favourable to TPLSM. [ABSTRACT FROM AUTHOR]

We use computational fluid dynamics to explore the creeping flow of power-law fluids through isotropic porous media. We find that the flow pattern is primarily controlled by the geometry of the porous structure rather than by the nonlinear effects in the rheology of the fluid. We further highlight a macroscale transition between a Newtonian and a non-Newtonian regime, which is the signature of a coupling between the viscosity of the fluid and the structure of the porous medium. These complex features of the flow can be condensed into an effective length scale, which defines both the non-Newtonian transition and the Newtonian permeability. [ABSTRACT FROM AUTHOR]