Analysis of indentation: implications for measuring mechanical properties with atomic force microscopy.

Indentation using the atomic force microscope (AFM) has potential to measure detailed micromechanical properties of soft biological samples. However, interpretation of the results is complicated by the tapered shape of the AFM probe tip, and its small size relative to the depth of indentation. Finite element models (FEMs) were used to examine effects of indentation depth, tip geometry, and material nonlinearity and heterogeneity on the finite indentation response. Widely applied infinitesimal strain models agreed with FEM results for linear elastic materials, but yielded substantial errors in the estimated properties for nonlinear elastic materials. By accounting for the indenter geometry to compute an apparent elastic modulus as a function of indentation depth, nonlinearity and heterogeneity of material properties may be identified. Furthermore, combined finite indentation and biaxial stretch may reveal the specific functional form of the constitutive law--a requirement for quantitative estimates of material constants to be extracted from AFM indentation data.     

Probing elasticity and adhesion of live cells by atomic force microscopy indentation

Atomic force microscopy (AFM) indentation has become an important technique for quantifying the mechanical properties of live cells at nanoscale. However, determination of cell elasticity modulus from the force–displacement curves measured in the AFM indentations is not a trivial task. The present work shows that these force–displacement curves are affected by indenter-cell adhesion force, while the use of an appropriate indentation model may provide information on the cell elasticity and the work of adhesion of the cell membrane to the surface of the AFM probes. A recently proposed indentation model (Sirghi, Rossi in Appl Phys Lett 89:243118, 2006), which accounts for the effect of the adhesion force in nanoscale indentation, is applied to the AFM indentation experiments performed on live cells with pyramidal indenters. The model considers that the indentation force equilibrates the elastic force of the cell cytoskeleton and the adhesion force of the cell membrane. It is assumed that the indenter-cell contact area and the adhesion force decrease continuously during the unloading part of the indentation (peeling model). Force–displacement curves measured in indentation experiments performed with silicon nitride AFM probes with pyramidal tips on live cells (mouse fibroblast Balb/c3T3 clone A31-1-1) in physiological medium at 37°C agree well with the theoretical prediction and are used to determine the cell elasticity modulus and indenter-cell work of adhesion. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Cell dynamic adhesion and elastic properties probed with cylindrical atomic force microscopy cantilever tips

Cell adhesion is required for essential biological functions such as migration, tissue formation and wound healing, and it is mediated by individual molecules that bind specifically to ligands on other cells or on the extracellular matrix. Atomic force microscopy (AFM) has been successfully used to measure cell adhesion at both single molecule and whole cell levels. However, the measurement of inherent cell adhesion properties requires a constant cell-probe contact area during indentation, a requirement which is not fulfilled in common pyramidal or spherical AFM tips. We developed a procedure using focused ion beam (FIB) technology by which we modified silicon pyramidal AFM cantilever tips to obtain flat-ended cylindrical tips with a constant and known area of contact. The tips were validated on elastic gels and living cells. Cylindrical tips showed a fairly linear force-indentation behaviour on both gels and cells for indentations >200 nm. Cylindrical tips coated with ligands were used to quantify inherent dynamic cell adhesion and elastic properties. Force, work of adhesion and elasticity showed a marked dynamic response. In contrast, the deformation applied to the cells before rupture was fairly constant within the probed dynamic range. Taken together, these results suggest that the dynamic adhesion strength is counterbalanced by the dynamic elastic response to keep a constant cell deformation regardless of the applied pulling rate.     

Imaging soft samples with the atomic force microscope: gelatin in water and propanol.

We have imaged mica coated with thin gelatin films in water, propanol, and mixtures of these two liquids by atomic force microscopy (AFM). The elastic modulus (Young's modulus) can be tuned from 20 kPa to more than 0.1 GPa depending on the ratio of propanol to water. The resolution is best in pure propanol, on the order of 20 nm, and becomes worse for the softer samples. The degradation in resolution can be understood by considering the elastic indentation of the gelatin caused by the AFM tip. This indentation becomes larger and thus the contact area becomes larger the softer the sample is. Therefore this study may be used to estimate the resolution to be expected with an AFM on other soft samples, such as cells. Nondestructive imaging was possible only by imaging at forces < 1 nN. This was difficult to achieve in contact mode because of drift in the zero load deflection of the cantilever, supposedly caused by temperature drift, but straightforward in tapping mode.     

An AFM-based stiffness clamp for dynamic control of rigidity

Atomic force microscopy (AFM) has become a powerful tool for measuring material properties in biology and imposing mechanical boundary conditions on samples from single molecules to cells and tissues. Constant force or constant height can be maintained in an AFM experiment through feedback control of cantilever deflection, known respectively as a ‘force clamp’ or ‘position clamp’. However, stiffness, the third variable in the Hookean relation F = kx that describes AFM cantilever deflection, has not been dynamically controllable in the same way. Here we present and demonstrate a ‘stiffness clamp’ that can vary the apparent stiffness of an AFM cantilever. This method, employable on any AFM system by modifying feedback control of the cantilever, allows rapid and reversible tuning of the stiffness exposed to the sample in a way that can decouple the role of stiffness from force and deformation. We demonstrated the AFM stiffness clamp on two different samples: a contracting fibroblast cell and an expanding polyacrylamide hydrogel. We found that the fibroblast, a cell type that secretes and organizes the extracellular matrix, exhibited a rapid, sub-second change in traction rate (dF/dt) and contraction velocity (dx/dt) in response to step changes in stiffness between 1–100 nN/µm. This response was independent of the absolute contractile force and cell height, demonstrating that cells can react directly to changes in stiffness alone. In contrast, the hydrogel used in our experiment maintained a constant expansion velocity (dx/dt) over this range of stiffness, while the traction rate (dF/dt) changed with stiffness, showing that passive materials can also behave differently in different stiffness environments. The AFM stiffness clamp presented here, which is applicable to mechanical measurements on both biological and non-biological samples, may be used to investigate cellular mechanotransduction under a wide range of controlled mechanical boundary conditions.     

Elastic response, buckling, and instability of microtubules under radial indentation

We tested the mechanical properties of single microtubules by lateral indentation with the tip of an atomic force microscope. Indentations up to approximately 3.6 nm, i.e., 15% of the microtubule diameter, resulted in an approximately linear elastic response, and indentations were reversible without hysteresis. At an indentation force of around 0.3 nN we observed an instability corresponding to an approximately 1-nm indentation step in the taxol-stabilized microtubules, which could be due to partial or complete rupture of a relatively small number of lateral or axial tubulin-tubulin bonds. These indentations were reversible with hysteresis when the tip was retracted and no trace of damage was observed in subsequent high-resolution images. Higher forces caused substantial damage to the microtubules, which either led to depolymerization or, occasionally, to slowly reannealing holes in the microtubule wall. We modeled the experimental results using finite-element methods and find that the simple assumption of a homogeneous isotropic material, albeit structured with the characteristic protofilament corrugations, is sufficient to explain the linear elastic response of microtubules.     

Changes in the hyperelastic properties of endothelial cells induced by tumor necrosis factor-alpha

Mechanical properties of living cells can be determined using atomic force microscopy (AFM). In this study, a novel analysis was developed to determine the mechanical properties of adherent monolayers of pulmonary microvascular endothelial cells (ECs) using AFM and finite element modeling, which considers both the finite thickness of ECs and their nonlinear elastic properties, as well as the large strain induced by AFM. Comparison of this model with the more traditional Hertzian model, which assumes linear elastic behavior, small strains, and infinite cell thickness, suggests that the new analysis can predict the mechanical response of ECs during AFM indentation better than Hertz's model, especially when using force-displacement data obtained from large indentations (>100 nm). The shear moduli and distensibility of ECs were greater when using small indentations (<100 nm) compared to large indentations (>100 nm). Tumor necrosis factor-α induced changes in the mechanical properties of ECs, which included a decrease in the average shear moduli that occurred in all regions of the ECs and an increase in distensibility in the central regions when measured using small indentations. These changes can be modeled as changes in a chain network structure within the ECs.     

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.     

Non-Hertzian approach to analyzing mechanical properties of endothelial cells probed by atomic force microscopy

Detailed measurements of cell material properties are required for understanding how cells respond to their mechanical environment. Atomic force microscopy (AFM) is an increasingly popular measurement technique that uniquely combines subcellular mechanical testing with high-resolution imaging. However, the standard method of analyzing AFM indentation data is based on a simplified "Hertz" theory that requires unrealistic assumptions about cell indentation experiments. The objective of this study was to utilize an alternative "pointwise modulus" approach, that relaxes several of these assumptions, to examine subcellular mechanics of cultured human aortic endothelial cells (HAECs). Data from indentations in 2- to 5-microm square regions of cytoplasm reveal at least two mechanically distinct populations of cellular material. Indentations colocalized with prominent linear structures in AFM images exhibited depth-dependent variation of the apparent pointwise elastic modulus that was not observed at adjacent locations devoid of such structures. The average pointwise modulus at an arbitrary indentation depth of 200 nm was 5.6+/-3.5 kPa and 1.5+/-0.76 kPa (mean+/-SD, n=7) for these two material populations, respectively. The linear structures in AFM images were identified by fluorescence microscopy as bundles of f-actin, or stress fibers. After treatment with 4 microM cytochalasin B, HAECs behaved like a homogeneous linear elastic material with an apparent modulus of 0.89+/-0.46 kPa. These findings reveal complex mechanical behavior specifically associated with actin stress fibers that is not accurately described using the standard Hertz analysis, and may impact how HAECs interact with their mechanical environment.     

Robust strategies for automated AFM force curve analysis--I. Non-adhesive indentation of soft, inhomogeneous materials

The atomic force microscope (AFM) has found wide applicability as a nanoindentation tool to measure local elastic properties of soft materials. An automated approach to the processing of AFM indentation data, namely, the extraction of Young's modulus, is essential to realizing the high-throughput potential of the instrument as an elasticity probe for typical soft materials that exhibit inhomogeneity at microscopic scales. This paper focuses on Hertzian analysis techniques, which are applicable to linear elastic indentation. We compiled a series of synergistic strategies into an algorithm that overcomes many of the complications that have previously impeded efforts to automate the fitting of contact mechanics models to indentation data. AFM raster data sets containing up to 1024 individual force-displacement curves and macroscopic compression data were obtained from testing polyvinyl alcohol gels of known composition. Local elastic properties of tissue-engineered cartilage were also measured by the AFM. All AFM data sets were processed using customized software based on the algorithm, and the extracted values of Young's modulus were compared to those obtained by macroscopic testing. Accuracy of the technique was verified by the good agreement between values of Young's modulus obtained by AFM and by direct compression of the synthetic gels. Validation of robustness was achieved by successfully fitting the vastly different types of force curves generated from the indentation of tissue-engineered cartilage. For AFM indentation data that are amenable to Hertzian analysis, the method presented here minimizes subjectivity in preprocessing and allows for improved consistency and minimized user intervention. Automated, large-scale analysis of indentation data holds tremendous potential in bioengineering applications, such as high-resolution elasticity mapping of natural and artificial tissues.     

Relative microelastic mapping of living cells by atomic force microscopy.

The spatial and temporal changes of the mechanical properties of living cells reflect complex underlying physiological processes. Following these changes should provide valuable insight into the biological importance of cellular mechanics and their regulation. The tip of an atomic force microscope (AFM) can be used to indent soft samples, and the force versus indentation measurement provides information about the local viscoelasticity. By collecting force-distance curves on a time scale where viscous contributions are small, the forces measured are dominated by the elastic properties of the sample. We have developed an experimental approach, using atomic force microscopy, called force integration to equal limits (FIEL) mapping, to produce robust, internally quantitative maps of relative elasticity. FIEL mapping has the advantage of essentially being independent of the tip-sample contact point and the cantilever spring constant. FIEL maps of living Madine-Darby canine kidney (MDCK) cells show that elasticity is uncoupled from topography and reveal a number of unexpected features. These results present a mode of high-resolution visualization in which the contrast is based on the mechanical properties of the sample.     

Investigation of red blood cell mechanical properties using AFM indentation and coarse-grained particle method

Background

Red blood cells (RBCs) deform significantly and repeatedly when passing through narrow capillaries and delivering dioxygen throughout the body. Deformability of RBCs is a key characteristic, largely governed by the mechanical properties of the cell membrane. This study investigated RBC mechanical properties using atomic force microscopy (AFM) with the aim to develop a coarse-grained particle method model to study for the first time RBC indentation in both 2D and 3D. This new model has the potential to be applied to further investigate the local deformability of RBCs, with accurate control over adhesion, probe geometry and position of applied force.

Results

The model considers the linear stretch capacity of the cytoskeleton, bending resistance and areal incompressibility of the bilayer, and volumetric incompressibility of the internal fluid. The model’s performance was validated against force–deformation experiments performed on RBCs under spherical AFM indentation. The model was then used to investigate the mechanisms which absorbed energy through the indentation stroke, and the impact of varying stiffness coefficients on the measured deformability. This study found the membrane’s bending stiffness was most influential in controlling RBC physical behaviour for indentations of up to 200 nm.

Conclusions

As the bilayer provides bending resistance, this infers that structural changes within the bilayer are responsible for the deformability changes experienced by deteriorating RBCs. The numerical model presented here established a foundation for future investigations into changes within the membrane that cause differences in stiffness between healthy and deteriorating RBCs, which have already been measured experimentally with AFM.

     

Nano-mechanical exploration of the surface and sub-surface of hydrated cells of Staphylococcus epidermidis

The surface of hydrated cells of Staphylococcus epidermidis has been probed using an atomic force microscope. While local force measurements over the surface of bacteria reveal a heterogeneous chemical surface, with heterogeneous mechanical properties, different kinds of force curves appear with high frequency, and are thought to provide information on features contributing strongly to the overall mechanical and surface behaviour of the cell. Force curves often present two different mechanical regimes, being the first one (outer) of about 48 nm thick, and presenting a local relative elasticity of about 0.08 N/m, which is about a third of the relative elasticity of the inner part of the cell wall, harder, with a relative elasticity of about 0.24 N/m, in water. Both regimes appears as straight lines in the force versus distance curves (the ‘corresponding’ stress–strain curves in contact mechanics), but hysteresis is observed between the approach and the retraction line in the inner regime, indicating a degree of viscoelasticity. No viscoelasticity is observed in the outer regime, however, which presents quite linear and juxtaposed approach-retraction lines. These kinds of force curves do not present measurable pull-off forces nor snap-in forces, which indicates an almost null interaction between tip and bacterial surface, which could be in agreement with the measured very high hydrophobicity of this strain. Another kind of force curve has been observed recurrently, showing peaks in the retraction curves. Adhesive pull-off forces were measured giving an average of about 2 nN. Interestingly, however, these force curves appear only when quite irregular and wavy retraction curves are present, from the very beginning of its trace (maximum indentation). This leads us to think that these pull-off forces measured by our AFM do not give information on surface forces-unbinding events at the surface of the bacteria, but could be related to events at the sub-surface of the cell surface. Oscillations seen in the retraction curve in the portion corresponding to the contact with the bacteria surface could be due to rupture phenomena within the multilayered cell wall architecture expected in Gram-positive bacteria as Staphylococcus epidermidis, which could result in local irreversible deformations of the cell surface. Imaging with a sharp tip in contact mode sometimes leads to surface damage. Force curves recorded over damaged parts of the cell surface showed a completely different behaviour, in many cases with two well-defined high-adhesion peaks, and also interestingly, with snap-in forces of about 0–2 nN, which seems to indicate a completely different electrical/hydrophobicity state only a few nanometers down from the surface. Similar indentation effects can occur in the contact of a bacterial cell with a solid surface, even when showing only atomic-molecular-scale roughness, thus interacting not only with the very surface of the cell, especially when soft layers are present in the outer. Our results highlight the importance of the cell surface mechanical properties and their interplay with purely surface properties when analyzing cell–material interaction, and show the AFM as a useful method for investigating this.     

Robust strategies for automated AFM force curve analysis-II: adhesion-influenced indentation of soft, elastic materials

In the first of this two-part discourse on the extraction of elastic properties from atomic force microscopy (AFM) data, a scheme for automating the analysis of force-distance curves was introduced and experimentally validated for the Hertzian (i.e., linearly elastic and noninteractive probe-sample pairs) indentation of soft, inhomogeneous materials. In the presence of probe-sample adhesive interactions, which are common especially during retraction of the rigid tip from soft materials, the Hertzian models are no longer adequate. A number of theories (e.g., Johnson-Kendall-Roberts and Derjaguin-Muller-Toporov), covering the full range of sample compliance relative to adhesive force and tip radius, are available for analysis of such data. We incorporated Pietrement and Troyon's approximation (2000, "General Equations Describing Elastic Indentation Depth and Normal Contact Stiffness Versus Load," J. Colloid Interface Sci., 226(1), pp. 166-171) of the Maugis-Dugdale model into the automated procedure. The scheme developed for the processing of Hertzian data was extended to allow for adhesive contact by applying the Pietrement-Troyon equation. Retraction force-displacement data from the indentation of polyvinyl alcohol gels were processed using the customized software. Many of the retraction curves exhibited strong adhesive interactions that were absent in extension. We compared the values of Young's modulus extracted from the retraction data to the values obtained from the extension data and from macroscopic uniaxial compression tests. Application of adhesive contact models and the automated scheme to the retraction curves yielded average values of Young's modulus close to those obtained with Hertzian models for the extension curves. The Pietrement-Troyon equation provided a good fit to the data as indicated by small values of the mean-square error. The Maugis-Dugdale theory is capable of accurately modeling adhesive contact between a rigid spherical indenter and a soft, elastic sample. Pietrement and Troyon's empirical equation greatly simplifies the theory and renders it compatible with the general automation strategies that we developed for Hertzian analysis. Our comprehensive algorithm for automated extraction of Young's moduli from AFM indentation data has been expanded to recognize the presence of either adhesive or Hertzian behavior and apply the appropriate contact model.     

Cell Visco-Elasticity Measured with AFM and Optical Trapping at Sub-Micrometer Deformations

The measurement of the elastic properties of cells is widely used as an indicator for cellular changes during differentiation, upon drug treatment, or resulting from the interaction with the supporting matrix. Elasticity is routinely quantified by indenting the cell with a probe of an AFM while applying nano-Newton forces. Because the resulting deformations are in the micrometer range, the measurements will be affected by the finite thickness of the cell, viscous effects and even cell damage induced by the experiment itself. Here, we have analyzed the response of single 3T3 fibroblasts that were indented with a micrometer-sized bead attached to an AFM cantilever at forces from 30–600 pN, resulting in indentations ranging from 0.2 to 1.2 micrometer. To investigate the cellular response at lower forces up to 10 pN, we developed an optical trap to indent the cell in vertical direction, normal to the plane of the coverslip. Deformations of up to two hundred nanometers achieved at forces of up to 30 pN showed a reversible, thus truly elastic response that was independent on the rate of deformation. We found that at such small deformations, the elastic modulus of 100 Pa is largely determined by the presence of the actin cortex. At higher indentations, viscous effects led to an increase of the apparent elastic modulus. This viscous contribution that followed a weak power law, increased at larger cell indentations. Both AFM and optical trapping indentation experiments give consistent results for the cell elasticity. Optical trapping has the benefit of a lower force noise, which allows a more accurate determination of the absolute indentation. The combination of both techniques allows the investigation of single cells at small and large indentations and enables the separation of their viscous and elastic components.     

Surface structure and nanomechanical properties of Shewanella putrefaciens bacteria at two pH values (4 and 10) determined by atomic force microscopy

The nanomechanical properties of gram-negative bacteria (Shewanella putrefaciens) were investigated in situ in aqueous solutions at two pH values, specifically, 4 and 10, by atomic force microscopy (AFM). For both pH values, the approach force curves exhibited subsequent nonlinear and linear regimens that were related to the progressive indentation of the AFM tip in the bacterial cell wall, including a priori polymeric fringe (nonlinear part), while the linear part was ascribed to compression of the plasma membrane. These results indicate the dynamic of surface ultrastructure in response to changes in pH, leading to variations in nanomechanical properties, such as the Young's modulus and the bacterial spring constant.     

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.     

Dynamic elastic modulus of porcine articular cartilage determined at two different levels of tissue organization by indentation-type atomic force microscopy

Cartilage stiffness was measured ex vivo at the micrometer and nanometer scales to explore structure-mechanical property relationships at smaller scales than has been done previously. A method was developed to measure the dynamic elastic modulus, |E(*)|, in compression by indentation-type atomic force microscopy (IT AFM). Spherical indenter tips (radius = approximately 2.5 microm) and sharp pyramidal tips (radius = approximately 20 nm) were employed to probe micrometer-scale and nanometer-scale response, respectively. |E(*)| values were obtained at 3 Hz from 1024 unloading response curves recorded at a given location on subsurface cartilage from porcine femoral condyles. With the microsphere tips, the average modulus was approximately 2.6 MPa, in agreement with available millimeter-scale data, whereas with the sharp pyramidal tips, it was typically 100-fold lower. In contrast to cartilage, measurements made on agarose gels, a much more molecularly amorphous biomaterial, resulted in the same average modulus for both indentation tips. From results of AFM imaging of cartilage, the micrometer-scale spherical tips resolved no fine structure except some chondrocytes, whereas the nanometer-scale pyramidal tips resolved individual collagen fibers and their 67-nm axial repeat distance. These results suggest that the spherical AFM tip is large enough to measure the aggregate dynamic elastic modulus of cartilage, whereas the sharp AFM tip depicts the elastic properties of its fine structure. Additional measurements of cartilage stiffness following enzyme action revealed that elastase digestion of the collagen moiety lowered the modulus at the micrometer scale. In contrast, digestion of the proteoglycans moiety by cathepsin D had little effect on |E(*)| at the micrometer scale, but yielded a clear stiffening at the nanometer scale. Thus, cartilage compressive stiffness is different at the nanometer scale compared to the overall structural stiffness measured at the micrometer and larger scales because of the fine nanometer-scale structure, and enzyme-induced structural changes can affect this scale-dependent stiffness differently.     

A new device for measuring the viscoelastic properties of hydrated matrix gels

Determinations of the viscoelastic properties of extracellular matrices (ECMs) are becoming increasingly important for accurate predictive modeling of biological systems. Since the interactions of the cells with the ECM and surrounding fluid (e.g., blood, media) each affect cell behavior; it is advantageous to evaluate the ECM's material properties in the presence of the hydrating fluid. Conventional rheometry methods evaluate the bulk material properties of gel materials while displacing the hydrating liquid film. Such systems are therefore nonideal for testing materials such as ECMs, whose properties change with dehydration. The new patent pending, piezoelectrically actuated linear rheometer is designed to eliminate this problem. It uses a single cantilever to apply an oscillating load to the gel and to sense the gel's deflection. Composed of two thin film piezopolymer layers, the cantilever uses one layer as the actuator, and the second piezopolymer layer to measure the lateral movement of its attached probe. The viscoelastic nature of the ECM adds stiffness and damping to the system, resulting in the attenuation and phase shift of the sensor's output voltage. From these parameters, the ECM's shear storage and loss moduli are then determined. Initial tests on the BioMatrix I and type I collagen ECMs reveal that the first prototype of the piezoelectrically actuated linear rheometer is capable of accurately determining the trend and order of magnitude of an ECM's viscoelastic properties. In this paper, details of the rheometer's design and operating principles are described.     

Quasi-linear viscoelastic properties of costal cartilage using atomic force microscopy

Costal cartilage (CC) is one of the load-bearing tissues of the rib cage. Literature on material characterisation of the CC is limited. Atomic force microscopy (AFM) has been extremely successful in characterising the elastic properties of soft biomaterials such as articular cartilage and hydrogels, which are often the material of choice for cartilage models. But AFM data on CC are absent in the literature. In this study, AFM indentations using spherical beaded tips were performed on human CC to isolate the mechanical properties. A novel method was developed for modelling the relaxation indentation experiments based on Fung's quasi-linear viscoelasticity and a continuous relaxation spectrum. This particular model has been popular for uniaxial compression test data analysis. Using the model, the mean Young's modulus of CC was found to be about 2.17, 4.11 and 5.49 MPa for three specimens. A large variation of modulus was observed over the tissue. Also, the modulus values decreased with distance from the costochondral junction.