Dehomogenized Elastic Properties of Heterogeneous Layered Materials in AFM Indentation Experiments

Atomic force microscopy (AFM) is used to study mechanical properties of biological materials at submicron length scales. However, such samples are often structurally heterogeneous even at the local level, with different regions having distinct mechanical properties. Physical or chemical disruption can isolate individual structural elements but may alter the properties being measured. Therefore, to determine the micromechanical properties of intact heterogeneous multilayered samples indented by AFM, we propose the Hybrid Eshelby Decomposition (HED) analysis, which combines a modified homogenization theory and finite element modeling to extract layer-specific elastic moduli of composite structures from single indentations, utilizing knowledge of the component distribution to achieve solution uniqueness. Using finite element model-simulated indentation of layered samples with micron-scale thickness dimensions, biologically relevant elastic properties for incompressible soft tissues, and layer-specific heterogeneity of an order of magnitude or less, HED analysis recovered the prescribed modulus values typically within 10% error. Experimental validation using bilayer spin-coated polydimethylsiloxane samples also yielded self-consistent layer-specific modulus values whether arranged as stiff layer on soft substrate or soft layer on stiff substrate. We further examined a biophysical application by characterizing layer-specific microelastic properties of full-thickness mouse aortic wall tissue, demonstrating that the HED-extracted modulus of the tunica media was more than fivefold stiffer than the intima and not significantly different from direct indentation of exposed media tissue. Our results show that the elastic properties of surface and subsurface layers of microscale synthetic and biological samples can be simultaneously extracted from the composite material response to AFM indentation. HED analysis offers a robust approach to studying regional micromechanics of heterogeneous multilayered samples without destructively separating individual components before testing.     

Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone consists of mineral platelet with nanometer size embedded in a protein matrix, it is similar to the microstructure of soft matrix nanocomposites reinforced with hard nanostructures. Considering a representative volume element (RVE) of the microstructure of bone as the microscale problem in our hierarchical multiscale modeling scheme, the global behavior of bone is obtained under various macroscopic loading conditions. This scheme may be suitable for modeling arbitrary bone geometries subjected to a variety of loading conditions. Using the presented method, mechanical properties of cortical bone including elastic moduli and Poisson's ratios in two major directions and shear modulus is obtained for different mineral volume fractions.     

Influence of biomass production and detachment forces on biofilm structures in a biofilm airlift suspension reactor

The influence of process conditions (substrate loading rate and detachment force) on the structure of biofilms grown on basalt particles in a Biofilm Airlift Suspension (BAS) reactor was studied. The structure of the biofilms (density, surface shape, and thickness) and microbial characteristics (biomass yield) were investigated at substrate loading rates of 5, 10, 15, and 20 kg COD/m3. day with basalt concentrations of 60 g/L, 150 g/L, and 250 g/L. The basalt concentration determines the number of biofilm particles in steady state, which is the main determining factor for the biofilm detachment in these systems. In total, 12 experimental runs were performed. A high biofilm density (up to 67 g/L) and a high biomass concentration was observed at high detachment forces. The higher biomass content is associated with a lower biomass substrate loading rate and therefore with a lower biomass yield (from 0.4 down to 0.12 gbiomass/gacetate). Contrary to general beliefs, the observed biomass detachment decreased with increasing detachment force. In addition, smoother (fewer protuberances), denser and thinner compact biofilms were obtained when the biomass surface production rate decreased and/or the detachment force increased. These observations confirmed a hypothesis, postulated earlier by Van Loosdrecht et al. (1995b), that the balance between biofilm substrate surface loading (proportional to biomass surface production rate, when biomass yield is constant) and detachment force determines the biofilm structure. When detachment forces are relatively high only a patchy biofilm will develop, whereas at low detachment forces, the biofilm becomes highly heterogeneous with many pores and protuberances. With the right balance, smooth, dense and stable biofilms can be obtained. Copyright 1998 John Wiley & Sons, Inc.     

Macroscale versus microscale methods for physiological analysis of biofilms formed in 96-well microtiter plates

Microtiter plates with 96 wells have become one of the preferred platforms for biofilm studies mainly because they enable high-throughput assays. In this work, macroscale and microscale methods were used to study the impact of hydrodynamic conditions on the physiology and location of Escherichia coli JM109(DE3) biofilms formed in microtiter plates. Biofilms were formed in shaking and static conditions, and two macroscale parameters were assayed: the total amount of biofilm was measured by the crystal violet assay and the metabolic activity was determined by the resazurin assay. From the macroscale point of view, there were no statistically significant differences between the biofilms formed in static and shaking conditions. However, at a microscale level, the differences between both conditions were revealed using scanning electron microscopy (SEM). It was observed that biofilm morphology and spatial distribution along the wall were different in these conditions. Simulation of the hydrodynamic conditions inside the wells at a microscale was performed by computational fluid dynamics (CFD). These simulations showed that the shear strain rate was unevenly distributed on the walls during shaking conditions and that regions of higher shear strain rate were obtained closer to the air/liquid interface. Additionally, it was shown that wall regions subjected to higher shear strain rates were associated with the formation of biofilms containing cells of smaller size. Conversely, regions with lower shear strain rate were prone to have a more uniform spatial distribution of adhered cells of larger size. The results presented on this work highlight the wealth of information that may be gathered by complementing macroscale approaches with a microscale analysis of the experiments.     

Versatile and inexpensive Hall-Effect force sensor for mechanical characterization of soft biological materials

Mismatch of hierarchical structure and mechanical properties between tissue-engineered implants and native tissue may result in signal cues that negatively impact repair and remodeling. With bottom-up tissue engineering approaches, designing tissue components with proper microscale mechanical properties is crucial to achieve necessary macroscale properties in the final implant. However, characterizing microscale mechanical properties is challenging, and current methods do not provide the versatility and sensitivity required to measure these fragile, soft biological materials. Here, we developed a novel, highly sensitive Hall-Effect based force sensor that is capable of measuring mechanical properties of biological materials over wide force ranges (μN to N), allowing its use at all steps in layer-by-layer fabrication of engineered tissues. The force sensor design can be easily customized to measure specific force ranges, while remaining easy to fabricate using inexpensive, commercial materials. Although we used the force sensor to characterize mechanics of single-layer cell sheets and silk fibers, the design can be easily adapted for different applications spanning larger force ranges (>N). This platform is thus a novel, versatile, and practical tool for mechanically characterizing biological and biomimetic materials.     

Mechanical property determination of bone through nano- and micro-indentation testing and finite element simulation

Measurement of the mechanical properties of bone is important for estimating the stresses and strains exerted at the cellular level due to loading experienced on a macro-scale. Nano- and micro-mechanical properties of bone are also of interest to the pharmaceutical industry when drug therapies have intentional or non-intentional effects on bone mineral content and strength. The interactions that can occur between nano- and micro-indentation creep test condition parameters were considered in this study, and average hardness and elastic modulus were obtained as a function of indentation testing conditions (maximum load, load/unload rate, load-holding time, and indenter shape). The results suggest that bone reveals different mechanical properties when loading increases from the nano- to the micro-scale range (microN to N), which were measured using low- and high-load indentation testing systems. A four-parameter visco-elastic/plastic constitutive model was then applied to simulate the indentation load vs. depth response over both load ranges. Good agreement between the experimental data and finite element model was obtained when simulating the visco-elastic/plastic response of bone. The results highlight the complexity of bone as a biological tissue and the need to understand the impact of testing conditions on the measured results.     

Tools for studying and modulating (cardiac muscle) cell mechanics and mechanosensing across the scales

Cardiomyocytes generate force for the contraction of the heart to pump blood into the lungs and body. At the same time, they are exquisitely tuned to the mechanical environment and react to e.g. changes in cell and extracellular matrix stiffness or altered stretching due to reduced ejection fraction in heart disease, by adapting their cytoskeleton, force generation and cell mechanics. Both mechanical sensing and cell mechanical adaptations are multiscale processes. Receptor interactions with the extracellular matrix at the nanoscale will lead to clustering of receptors and modification of the cytoskeleton. This in turn alters mechanosensing, force generation, cell and nuclear stiffness and viscoelasticity at the microscale. Further, this affects cell shape, orientation, maturation and tissue integration at the microscale to macroscale. A variety of tools have been developed and adapted to measure cardiomyocyte receptor-ligand interactions and forces or mechanics at the different ranges, resulting in a wealth of new information about cardiomyocyte mechanobiology. Here, we take stock at the different tools for exploring cardiomyocyte mechanosensing and cell mechanics at the different scales from the nanoscale to microscale and macroscale.     

Stress and strain localization in stretched collagenous tissues via a multiscale modelling approach

Mechanobiology of cells in soft collagenous tissues is highly affected by both tissue response at the macroscale and stress/strain localization mechanisms due to features at lower scales. In this paper, the macroscale mechanical behaviour of soft collagenous tissues is modelled by a three-level multiscale approach, based on a multi-step homogenisation technique from nanoscale up to the macroscale. Nanoscale effects, related to both intermolecular cross-links and collagen mechanics, are accounted for, together with geometric nonlinearities at the microscale. Moreover, an effective submodelling procedure is conceived in order to evaluate the local stress and strain fields at the microscale, which is around and within cells. Numerical results, obtained by using an incremental finite element formulation and addressing stretched tendinous tissues, prove consistency and accuracy of the model at both macroscale and microscale, confirming also the effectiveness of the multiscale modelling concept for successfully analysing physiopathological processes in biological tissues.     

Homogenization of Pseudomonas aeruginosa PAO1 biofilms visualized by freeze‐substitution electron microscopy

A knowledge of the mechanical properties of bacterial biofilms is required to more fully understand the processes of biofilm formation such as initial adhesion or detachment. The main contribution of this article is to demonstrate the use of homogenization techniques to compute mechanical parameters of Pseudomonas aeruginosa PAO1 biofilms. For this purpose, homogenization techniques are used to analyze freeze substitution electron micrographs of the biofilm cross‐sections. The concept of a representative volume element and the study about his representativeness allows us to determine the optimal size in order to analyze these biofilm images. Results demonstrate significant heterogeneities with respect to stiffness and these can be explained by varying cell density distribution throughout the bacterial biofilms. These stiffness variations lead to different mechanical properties along the height of the biofilm. Moreover, a numerical shear stress test shows the impact of these heterogeneities on the detachment process. Several modes of detachment are highlighted according to the local strain energy in the different parts of the biofilm. Knowing where, and how, a biofilm may detach will allow better prediction of accumulation and biomass detachment. Biotechnol. Bioeng. 2013; 110: 1405–1418. © 2012 Wiley Periodicals, Inc.     

Direct measurement of the mechanical properties of lipid phases in supported bilayers

Biological membranes define not only the cell boundaries but any compartment within the cell. To some extent, the functionality of membranes is related to the elastic properties of the lipid bilayer and the mechanical and hydrophobic matching with functional membrane proteins. Supported lipid bilayers (SLBs) are valid biomimetic systems for the study of membrane biophysical properties. Here, we acquired high-resolution topographic and quantitative mechanics data of phase-separated SLBs using a recent atomic force microscopy (AFM) imaging mode based on force measurements. This technique allows us to quantitatively map at high resolution the mechanical differences of lipid phases at different loading forces. We have applied this approach to evaluate the contribution of the underlying hard support in the determination of the elastic properties of SLBs and to determine the adequate indentation range for obtaining reliable elastic moduli values. At ~200 pN, elastic forces dominated the force-indentation response and the sample deformation was <20% of the bilayer thickness, at which the contribution of the support was found to be negligible. The obtained Young's modulus (E) of 19.3 MPa and 28.1 MPa allowed us to estimate the area stretch modulus (k(A)) as 106 pN/nm and 199 pN/nm and the bending stiffness (k(c)) as 18 k(B)T and 57 k(B)T for the liquid and gel phases, respectively.     

Carchesium stalk fibrillar matrix as a highly filled polymer network.

Glycerolated stalks of the sessile peritrich ciliate Carchesium sp. were treated with 10(-6) g ion/1 Ca2+ to disrupt the contractile spasmoneme. The resulting preparation consisted primarily of the fibrillar matrix, a dense extra-cellular meshwork of microfibrils. Some mechanical properties of this preparation have been investigated. The matrix tensile force-extension ratio relation for an initial stretch was characteristic of a soft, swollen polymer network, elastic modulus in young stalks 1.7 X 10(5) Nm-2, in mature stalks 4.0 X 10(5) Nm-2. The higher elastic modulus in mature stalks implies an increase in the interchain cross-link frequency. In young stalks, elastic modulus was found to be independent of the ambient Ca2+ concentration in the threshold range for spasmonemal contraction. Stalk relaxation was pronouncedly irreversible, showing stress softening and permanent hysteresis on repeated loading. Hysteresis was time independent and stiffness was not recovered after four hours at zero strain. Hysteresis was enhanced by repeated loading to the same tensile force. Stress-strain hysteresis at a low extension is characteristic of highly filled polymer networks in which polymer chains are interconnected via rigid filler particles as well as directly cross-linked.     

Detachment forces and their influence on the structure and metabolic behaviour of biofilms

The biofilm reactor has been frequently applied in wastewater treatment. The formation, structure and metabolic activity of the biofilms are closely associated with the detachment forces in the reactors. This paper reviews the essential role of detachment forces in the biofilm process. A more compact, stable and denser biofilm can be formed at a relatively higher detachment force. The detachment force has significant influence on the structure, mass transfer, production of exopolysaccharides, metabolic and genetic properties of the biofilm. In an engineering sense, the detachment forces can be manipulated, as a control parameter, to produce a more stable and compact biofilm for use in wastewater treatment. The molecular and genetic mechanisms responsible for the detachment force-associated phenomena are not yet fully understood.     

Indentation and adhesive probing of a cell membrane with AFM: theoretical model and experiments

In probing adhesion and cell mechanics by atomic force microscopy (AFM), the mechanical properties of the membrane have an important if neglected role. Here we theoretically model the contact of an AFM tip with a cell membrane, where direct motivation and data are derived from a prototypical ligand-receptor adhesion experiment. An AFM tip is functionalized with a prototypical ligand, SIRPalpha, and then used to probe its native receptor on red cells, CD47. The interactions prove specific and typical in force, and also show in detachment, a sawtooth-shaped disruption process that can extend over hundreds of nm. The theoretical model here that accounts for both membrane indentation as well as membrane extension in tip retraction incorporates membrane tension and elasticity as well as AFM tip geometry and stochastic disruption. Importantly, indentation depth proves initially proportional to membrane tension and does not follow the standard Hertz model. Computations of detachment confirm nonperiodic disruption with membrane extensions of hundreds of nm set by membrane tension. Membrane mechanical properties thus clearly influence AFM probing of cells, including single molecule adhesion experiments.     

On the calculation of the elastic modulus of a biofilm streamer

Biofilm mechanical properties are essential in quantifying the rate of microbial detachment, a key process in determining the function and structure of biofilm systems. Although properties such as biofilm elastic moduli, yield stress and cohesive strength have been studied before, a wide range of values for the biofilm Young's modulus that differ by several orders of magnitude are reported in the literature. In this article, we use experimental data reported in Stoodley et al. [Stoodley et al., Biotechnol Bioeng (1999): 65(1):83-92] and present a methodology for the calculation of Young's modulus, which partially explains the large difference between the values reported in the literature.     

The significance of calcium ions on Pseudomonas fluorescens biofilms – a structural and mechanical study

The purpose of this study was to investigate the effects of calcium ions on the structural and mechanical properties of Pseudomonas fluorescens biofilms grown for 48?h. Advanced investigative techniques such as confocal laser scanning microscopy and atomic force spectroscopy were employed to characterize biofilm structure as well as biofilm mechanical properties following growth at different calcium concentrations. The presence of calcium during biofilm development led to higher surface coverage with distinct structural phenotypes in the form of a granular and heterogeneous surface, compared with the smoother and homogeneous biofilm surface in the absence of calcium. The presence of calcium also increased the adhesive nature of the biofilm, while reducing its elastic properties. These results suggest that calcium ions could have a functional role in biofilm development and have practical implications, for example, in analysis of biofouling in membrane-based water-treatment processes such as nanofiltration or reverse osmosis where elevated calcium concentrations may occur at the solid–liquid interface.     

Micromechanical model of a surrogate for collagenous soft tissues: development, validation and analysis of mesoscale size effects

Aligned, collagenous tissues such as tendons and ligaments are composed primarily of water and type I collagen, organized hierarchically into nanoscale fibrils, microscale fibers and mesoscale fascicles. Force transfer across scales is complex and poorly understood. Since innervation, the vasculature, damage mechanisms and mechanotransduction occur at the microscale and mesoscale, understanding multiscale interactions is of high importance. This study used a physical model in combination with a computational model to isolate and examine the mechanisms of force transfer between scales. A collagen-based surrogate served as the physical model. The surrogate consisted of extruded collagen fibers embedded within a collagen gel matrix. A micromechanical finite element model of the surrogate was validated using tensile test data that were recorded using a custom tensile testing device mounted on a confocal microscope. Results demonstrated that the experimentally measured macroscale strain was not representative of the microscale strain, which was highly inhomogeneous. The micromechanical model, in combination with a macroscopic continuum model, revealed that the microscale inhomogeneity resulted from size effects in the presence of a constrained boundary. A sensitivity study indicated that significant scale effects would be present over a range of physiologically relevant inter-fiber spacing values and matrix material properties. The results indicate that the traditional continuum assumption is not valid for describing the macroscale behavior of the surrogate and that boundary-induced size effects are present.     

Microscale frictional response of bovine articular cartilage from atomic force microscopy

The objective of this study was to compare micro- and macroscale friction coefficients of bovine articular cartilage. Microscale measurements were performed using standard atomic force microscopy (AFM) techniques, using a 5 microm spherical probe tip. Twenty-four cylindrical osteochondral plugs were harvested in pairs from adjacent positions in six fresh bovine humeral heads (4-6 months old), and divided into two groups for AFM and macroscopic friction measurements. AFM measurements of friction were observed to be time-independent, whereas macroscale measurements demonstrated the well-documented time-dependent increase from a minimum to an equilibrium value. The microscale AFM friction coefficient (mu(AFM), 0.152+/-0.079) and macroscale equilibrium friction coefficient (mu(eq), 0.138+/-0.036) exhibited no statistical differences (p=0.50), while the macroscale minimum friction coefficient (mu(min), 0.004+/-0.001) was significantly smaller than mu(eq) and mu(AFM) (p<0.0001). Variations in articular surface roughness (Rq= 462+/-216 nm) did not correlate significantly with mu(AFM), mu(eq) or mu(min). The effective compressive modulus determined from AFM indentation tests using a Hertz contact analysis was E*=45.8+/-18.8 kPa. The main finding of this study is that mu(AFM) is more representative of the macroscale equilibrium friction coefficient, which represents the frictional response in the absence of cartilage interstitial fluid pressurization. These results suggest that AFM measurements may be highly suited for exploring the role of boundary lubricants in diarthrodial joint lubrication independently of the confounding effect of fluid pressurization to provide greater insight into articular cartilage lubrication.     

Investigating various many-body force fields for their ability to predict reduction in elastic modulus due to vacancies using molecular dynamics simulations

ABSTRACT

Molecular dynamics simulations are more frequently being utilised to predict macroscale mechanical properties as a result of atomistic defects. However, the interatomic force field can significantly affect the resulting mechanical properties. While several studies exist which demonstrate the ability of various force fields to predict mechanical properties, the investigation into which is most accurate for the investigation of vacancies is limited. To obtain meaningful predictions of mechanical properties, a clear understanding of force field parameterisation is required. As such, the current study evaluates various many-body force fields to demonstrate the reduction in mechanical properties of iron and iron–chromium due to the presence of vacancies while undergoing room temperature atomistic uniaxial tension. Reduction was normalised in each case with the zero-vacancy elastic modulus, removing the need to predict an accurate nominal elastic modulus. Comparisons were made to experimental data and an empirical model from literature. It was demonstrated that accurate fitting to vacancy formation and migration energy allowed for accurate predictions. In addition, bond-order based force fields showed enhanced predictions regardless of fitting procedure. Overall, these findings highlight the need to understand capabilities and limitations of available force fields, as well as the need for enhanced parameterisation of force fields.     

Influence of detachment,substrate loading and reactor scale on the formation of biofilms in airlift reactors

 For a stable and reliable operation of the biofilm airlift suspension reactor (BAS reactor) means to control biomass concentration, biofilm thickness and biofilm morphology are required. For this reason, the influence of applied detachment forces and surface substrate loading on the formation of heterotrophic biofilms in laboratory-scale BAS reactors was studied. Detachment forces were altered by variation of the initial bare carrier concentration or the superficial air velocity. In addition, the dynamics of biofilm formation during start-up of a full scale BAS reactor (300 m³) was monitored and compared with the laboratory-scale start-up (3 l). This study shows that the biofilm morphology and strength were influenced to a large extent by the surface substrate loading and applied detachment forces. A moderate surface substrate loading and a high detachment force yielded smooth and strong biofilms. The combination of a high surface substrate loading and low detachment forces did lead to rough biofilms, but did not lead to the expected high amount of biomass on the carrier, apparently because of the formation of weaker biofilms. The strength of the bio-films appeared to be related to the detachment forces applied during biofilm formation, in combination with the surface substrate loading. The biofilm morphology and biomass on carrier in the BAS reactor can be controlled using the carrier concentration, substrate loading rate and the superficial air velocity as parameters. The dynamics of biofilm formation during the start-up of a full-scale BAS reactor proved to be similar to heterotrophic biofilm formation in laboratory-scale reactors. This indicates that a model system on the laboratory scale can successfully be applied to predict dynamic phenomena in the full-scale reactor. Received: 31 March 1995/Received revision: 11 August 1995/Accepted: 22 August 1995     

3D finite element model of biofilm detachment using real biofilm structures from CLSM data

In this work, a three‐dimensional model of fluid–structure interactions (FSI) in biofilm systems is developed in order to simulate biofilm detachment as a result of mechanical processes. Therein, fluid flow past the biofilm surface results in a mechanical load on the structure which in turn causes internal stresses in the biofilm matrix. When the strength of the matrix is exceeded parts of the structure are detached. The model is used to investigate the influence of several parameters related to the mechanical strength of the biofilm matrix, Young's modulus, Reynolds number, and biofilm structure on biofilm detachment. Variations in biofilm strength and flow conditions significantly influence the simulation outcome. With respect to structural properties the model is widely independent from a change of Young's modulus. A further result of this work indicates that the change of biofilm structure due to growth or other processes will significantly change the stress distribution in the biofilm and thereby the detachment rate. An increase of the mechanical load by increasing fluid flow results in a flat surface of the remaining biofilm structure. It is concluded that the change of structure during biofilm development is the key determinant in terms of the detachment behavior. Biotechnol. Bioeng. 2009;103: 177–186. © 2008 Wiley Periodicals, Inc.