Molecular dynamics study on deformation and mechanics of nanoscale Au/Cu multilayers under indentation

The effects of individual layer thickness, indentation velocity, and temperature on the mechanical properties and mechanics of nanoscale Au/Cu multilayers under indentation were studied using molecular dynamics simulations based on the many-body embedded-atom potential. The simulation results show that layer interfaces act as strong barriers that resist the propagation of dislocations, even at an extremely small individual layer thickness of 3 nm. The number of dislocations increases significantly and the growth of dislocations decreases with decreasing individual layer thickness. There is no clear relationship between the magnitude of the required indentation force and the number of film layers; however, the average required indentation force increases with increasing indentation velocity and decreasing temperature. During indentation at a relatively low velocity, dislocation propagation is more significant; the number of disordered atoms significantly increases at a relatively high indentation velocity.     

Nanoindentation measurements of biomechanical properties in mature and newly formed bone tissue surrounding an implant

The characterization of the biomechanical properties of newly formed bone tissue around implants is important to understand the osseointegration process. The objective of this study is to investigate the evolution of the hardness and indentation modulus of newly formed bone tissue as a function of healing time. To do so, a nanoindentation device is employed following a multimodality approach using histological analysis. Coin-shaped implants were placed in vivo at a distance of 200 μm from the cortical bone surface, leading to an initially empty cavity of 200 μm * 4.4 mm. Three New Zealand White rabbits were sacrificed after 4, 7, and 13 weeks of healing time. The bone samples were embedded and analyzed using histological analyses, allowing to distinguish mature and newly formed bone tissue. The bone mechanical properties were then measured in mature and newly formed bone tissue. The results are within the range of hardness and apparent Young's modulus values reported in previous literature. One-way ANOVA test revealed a significant effect of healing time on the indentation modulus (p < 0.001, F = 111.24) and hardness (p < 0.02, F = 3.47) of bone tissue. A Tukey-Kramer analysis revealed that the biomechanical properties of newly formed bone tissue (4 weeks) were significantly different from those of mature bone tissue. The comparison with the results obtained in Mathieu et al. (2011, "Micro-Brillouin Scattering Measurements in Mature and Newly Formed Bone Tissue Surrounding an Implant," J. Biomech. Eng., 133, 021006). shows that bone mass density increases by approximately 13.5% between newly formed bone (7 weeks) and mature bone tissue.     

The nanoindentation responses of nickel surfaces with different crystal orientations

Molecular dynamics (MD) simulations are applied to elucidate the anisotropic characteristics in the material responses for crystallographic nickel substrates with (100), (110) and (111) surface orientations during nanoindentation, compensating for the experimental limitation of nanoindentation—particularly for pure nickel substrates of three crystallographic orientations. This study examines several factors under indentation: three-dimensional phases of plastic deformation which correspond to atomic stress distributions, pile-up patterns at maximum indentation depth, and extracted material properties at different crystallographic orientations. The present results reveal that the strain energy of the substrate exerted by the tip is stored by the formation of the homogeneous nucleation, and is dissipated by the dislocation sliding of the {111} plane. The steep variations of the indentation curve from the local peak to the local minimums are affected by the numbers of slip angle of {111} sliding plane. The pile-up patterns of the three nickel substrates prove that the crystalline nickel materials demonstrate the pile-up phenomenon from nanoindentation on the nano-scale. The three crystallographic nickel substrates exhibit differing amounts of pile-up dislocation spreading at different crystallographic orientations. Finally, the effects of surface orientation in material properties of FCC nickel material on the nano-scale are observable through the slip angle numbers of {111} sliding planes which influence hardness values, as well as the cohesive energy of different crystallographic surfaces that indicate Young's modulus.     

Investigation into the biphasic properties of a hydrogel for use in a cushion form replacement joint.

A hydrogel with potential applications in the role of a cushion form replacement joint bearing surface material has been investigated. The material properties are required for further development and design studies and have not previously been quantified. Creep indentation experiments were therefore performed on samples of the hydrogel. The biphasic model developed by Mow and co-workers (Mak et al., 1987; Mow et al., 1989a) was used to curve-fit the experimental data to theoretical solutions in order to extract the three intrinsic biphasic material properties of the hydrogel (aggregate modulus, HA, Poisson's ratio, Vs, and permeability, k). Ranges of material properties were determined: aggregate modulus was calculated to be between 18.4 and 27.5 MPa, Poisson's ratio 0.0-0.307, and permeability 0.012-7.27 x 10(-17) m4/Ns. The hydrogel thus had a higher aggregate modulus than values published for natural normal articular cartilage, the Poisson's ratios were similar to articular cartilage, and finally the hydrogel was found to be less permeable than articular cartilage. The determination of these values will facilitate further numerical analysis of the stress distribution in a cushion form replacement joint.     

Probing softness of the parietal pleural surface at the micron scale

The pleural surfaces of the chest wall and lung slide against each other, lubricated by pleural fluid. During sliding motion of soft tissues, shear induced hydrodynamic pressure deforms the surfaces, promoting uniformity of the fluid layer thickness, thereby reducing friction. To assess pleural deformability at length scales comparable to pleural fluid thickness, we measured the modulus of the parietal pleura of rat chest wall using atomic force microscopy (AFM) to indent the pleural surface with spheres (radius 2.5 and 5 μm). The pleura exhibited two distinct indentation responses depending on location, reflecting either homogeneous or significantly heterogeneous tissue properties. We found an elastic modulus of 0.38-0.95 kPa, lower than the values measured using flat-ended cylinders >100 μm radii (Gouldstone et al., 2003, Journal of Applied Physiology 95, 2345-2349). Interestingly, the pleura exhibited a three-fold higher modulus when probed using 2.5 vs. 5 μm spherical tips at the same normalized depth, confirming depth dependent inhomogeneous elastic properties. The observed softness of the pleura supports the hypothesis that unevenness of the pleural surface on this scale is smoothed by local hydrodynamic pressure.     

High biobased content epoxy-anhydride thermosets from epoxidized sucrose esters of Fatty acids

Novel highly functional biobased epoxy compounds, epoxidized sucrose esters of fatty acids (ESEFAs), were cross-linked with a liquid cycloaliphatic anhydride to prepare polyester thermosets. The degree of cure or conversion was studied using differential scanning calorimetry (DSC), and the sol content of the thermosets was determined using solvent extraction. The mechanical properties were studied using tensile testing to determine Young's modulus, tensile stress, and elongation at break. Dynamic mechanical analysis (DMA) was used to determine glass-transition temperature, storage modulus, and cross-link density. The nanomechanical properties of the surfaces were studied using nanoindentation to determine reduced modulus and indentation hardness. The properties of coatings on steel substrates were studied to determine coating hardness, adhesion, solvent resistance, and mechanical durability. Compared with the control, epoxidized soybean oil, the anhydride-cured ESEFAs have high modulus and are hard and ductile, high-performance thermoset materials while maintaining a high biobased content (71-77% in theory). The exceptional performance of the ESEFAs is attributed to the unique structure of these macromolecules: well-defined compact structures with high epoxide functionality. These biobased thermosets have potential uses in applications such as composites, adhesives, and coatings.     

Mechanical properties of DNA films

The Young's dynamical modulus (E) and the DNA film logarithmic decrement (theta) at frequencies from 50 Hz to 20 kHz are measured. These values are investigated as functions of the degree of hydration and temperature. Isotherms of DNA film hydration at 25 degrees C are measured. The process of film hydration changing with temperature is studied. It is shown that the Young's modulus for wet DNA films (E = 0.02-0.025 GN m-2) strongly increases with decreasing hydration and makes E = 0.5-0.7 GN m-2. Dependence of E on hydration is of a complex character. Young's modulus of denatured DNA films is larger than that of native ones. All peculiarities of changing of E and theta of native DNA films (observed at variation of hydration) vanish in the case of denatured ones. The native and denatured DNA films isotherms are different and depend on the technique of denaturation. The Young's modulus of DNA films containing greater than 1 g H2O/g dry DNA is found to decrease with increasing temperature, undergoing a number of step-like changes accompanied by changes in the film hydration. At low water content (less than 0.3 g H2O/g dry DNA), changing of E with increasing temperature takes place smoothly. The denaturation temperature is a function of the water content.     

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.     

Creep contributes to the fatigue behavior of bovine trabecular bone.

Repetitive, low-intensity loading from normal daily activities can generate fatigue damage in trabecular bone, a potential cause of spontaneous fractures of the hip and spine. Finite element models of trabecular bone (Guo et al., 1994) suggest that both creep and slow crack growth contribute to fatigue failure. In an effort to characterize these damage mechanisms experimentally, we conducted fatigue and creep tests on 85 waisted specimens of trabecular bone obtained from 76 bovine proximal tibiae. All applied stresses were normalized by the previously measured specimen modulus. Fatigue tests were conducted at room temperature; creep tests were conducted at 4, 15, 25, 37, 45, and 53 degrees C in a custom-designed apparatus. The fatigue behavior was characterized by decreasing modulus and increasing hysteresis prior to failure. The hysteresis loops progressively displaced along the strain axis, indicating that creep was also involved in the fatigue process. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates. Strong and highly significant power-law relationships were found between cycles-to-failure, time-to-failure, steady-state creep rate, and the applied loads. Creep analyses of the fatigue hysteresis loops also generated strong and highly significant power law relationships for time-to-failure and steady-state creep rate. Lastly, the products of creep rate and time-to-failure were constant for both the fatigue and creep tests and were equal to the measured failure strains, suggesting that creep plays a fundamental role in the fatigue behavior of trabecular bone. Additional analysis of the fatigue strain data suggests that creep and slow crack growth are not separate processes that dominate at high and low loads, respectively, but are present throughout all stages of fatigue.     

Effect of indenter size on elastic modulus of cartilage measured by indentation

Our preliminary indentation experiments showed that the equilibrium elastic modulus of murine tibial cartilage increased with decreasing indenter size: flat-ended 60 deg conical tips with end diameters of 15 microm and 90 microm gave 1.50+/-0.82 MPa (mean+/-standard deviation) and 0.55+/-0.11 MPa, respectively (p<0.01). The goal of this paper is to determine if the dependence on tip size is an inherent feature of the equilibrium elastic modulus of cartilage as measured by indentation. Since modulus values from nonindentation tests are not available for comparison for murine cartilage, bovine cartilage was used. Flat-ended conical or cylindrical tips with end diameters ranging from 5 microm to 4 mm were used to measure the equilibrium elastic modulus of bovine patellar cartilage. The same tips were used to test urethane rubber for comparison. The equilibrium modulus of the bovine patellar cartilage increased monotonically with decreasing tip size. The modulus obtained from the 2 mm and 4 mm tips (0.63+/-0.21 MPa) agreed with values reported in the literature; however, the modulus measured by the 90 microm tip was over two and a half times larger than the value obtained from the 1000 microm tip. In contrast, the elastic modulus of urethane rubber obtained using the same 5 microm-4 mm tips was independent of tip size. The equilibrium elastic modulus of bovine patellar cartilage measured by indentation depends on tip size. This appears to be an inherent feature of indentation of cartilage, perhaps due to its inhomogeneous structure.     

Stiffness and heterogeneity of the pulmonary endothelial glycocalyx measured by atomic force microscopy

The mechanical properties of endothelial glycocalyx were studied using atomic force microscopy with a silica bead (diameter ～18 μm) serving as an indenter. Even at indentations of several hundred nanometers, the bead exerted very low compressive pressures on the bovine lung microvascular endothelial cell (BLMVEC) glycocalyx and allowed for an averaging of stiffness in the bead-cell contact area. The elastic modulus of BLMVEC glycocalyx was determined as a pointwise function of the indentation depth before and after enzymatic degradation of specific glycocalyx components. The modulus-indentation depth profiles showed the cells becoming progressively stiffer with increased indentation. Three different enzymes were used: heparinases III and I and hyaluronidase. The main effects of heparinase III and hyaluronidase enzymes were that the elastic modulus in the cell junction regions increased more rapidly with the indentation than in BLMVEC controls, and that the effective thickness of glycocalyx was reduced. Cytochalasin D abolished the modulus increase with the indentation. The confocal profiling of heparan sulfate and hyaluronan with atomic force microscopy indentation data demonstrated marked heterogeneity of the glycocalyx composition between cell junctions and nuclear regions.     

An application of nanoindentation technique to measure bone tissue Lamellae properties

Measuring the microscopic mechanical properties of bone tissue is important in support of understanding the etiology and pathogenesis of many bone diseases. Knowledge about these properties provides a context for estimating the local mechanical environment of bone related cells thait coordinate the adaptation to loads experienced at the whole organ level. The objective of this study was to determine the effects of experimental testing parameters on nanoindentation measures of lamellar-level bone mechanical properties. Specifically, we examined the effect of specimen preparation condition, indentation depth, repetitive loading, time delay, and displacement rate. The nanoindentation experiments produced measures of lamellar elastic moduli for human cortical bone (average value of 17.7 +/- 4.0 GPa for osteons and 19.3 +/- 4.7 GPa for interstitial bone tissue). In addition, the hardness measurements produced results consistent with data in the literature (average 0.52 +/- 0.15 GPa for osteons and 0.59 +/- 0.20 GPa for interstitial bone tissue). Consistent modulus values can be obtained from a 500-nm-deep indent. The results also indicated that the moduli and hardnesses of the dry specimens are significantly greater (22.6% and 56.9%, respectively) than those of the wet and wet and embedded specimens. The latter two groups were not different. The moduli obtained at a 5-nm/s loading rate were significantly lower than the values at the 10- and 20-nm/s loading rates while the 10- and 20-nm/s rates were not significantly different. The hardness measurements showed similar rate-dependent results. The preliminary results indicated that interstitial bone tissue has significantly higher modulus and hardness than osteonal bone tissue. In addition, a significant correlation between hardness and elastic modulus was observed.     

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.     

Patterns of cartilage stiffness on normal and degenerate human femoral heads

Using the apparatus and technique described in an earlier paper, (Kempson et al. 1971), indentation tests were performed on areas of cartilage of 0·125 in dia., in situ on, and distributed evenly over, the cartilage surface of the human femoral head. Curves of indentation vs. time were plotted for a physiological stress of approximately 400 lbf/in². (28·2 kgf/cm², 2·36 MN/m²). The stiffness of each area of cartilage was calculated from the appropriate indentation value, in the form of a creep modulus at 2 sec, using the equations described in the previous paper (see Appendix). Layered maps and histograms showing the variation of both cartilage stiffness and indentation are presented.     

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.     

Characterization of the mechanical properties of skin by inverse analysis combined with the indentation test

This study proposes a new method to determine the mechanical properties of human skin by the use of the indentation test [Pailler-Mattei, 2004. Caractérisation mécanique et tribologique de la peau humaine in vivo, Ph.D. Thesis, ECL-no. 2004-31; Pailler-Mattei, Zahouani, 2004. Journal of Adhesion Science and Technology 18, 1739-1758]. The principle of the measurements consists in applying an in vivo compressive stress [Zhang et al., 1994. Proceedings of the Institution of Mechanical Engineers 208, 217-222; Bosboom et al., 2001. Journal of Biomechanics 34, 1365-1368; Oomens et al., 1984. Selected Proceedings of Meetings of European Society of Biomechanics, pp. 227-232; Oomens et al., 1987. Journal of Biomechanics 20(9), 877-885] on the skin tissue of an individual's forearm. These measurements show an increase in the normal contact force as a function of the indentation depth. The interpretation of such results usually requires a long and tedious phenomenological study. We propose a new method to determine the mechanical parameters which control the response of skin tissue. This method is threefold: experimental, numerical, and comparative. It consists combining experimental results with a numerical finite elements model in order to find out the required parameters. This process uses a scheme of extended Kalman filters (EKF) [Gu et al., 2003. Materials Science and Engineering A345, 223-233; Nakamura et al., 2000. Acta Mater 48, 4293-4306; Leustean and Rosu, 2003. Certifying Kalman filters. RIACS Technical Report 03.02, 27pp. http://gureni.cs.uiuc.edu/~grosu/download/luta + leo.pdf; Welch and Bishop, An introduction to Kalman filter, University of North Carolina at Chapel Hill, 16p. http://www.cs.unc.edu/~welch/kalman/]. The first results presented in this study correspond to a simplified numerical modeling of the global system. The skin is assumed to be a semi-infinite layer with an isotropic linear elastic mechanical behavior [Zhang et al., 1994. Proceedings of the Institution of Mechanical Engineers 208, 217-222] This analysis will be extended to more realistic models in further works.     

Effect of pericellular matrix formation by chondrocytes cultured in agarose gel on the viscoelastic properties of agarose gel matrix

The viscoelasticity of chondrocyte-seeded agarose gel (AGC0) and that of chondrocyte-seeded agarose gel after 21 days of cultivation (AGC3) were investigated. In AGC3, pericellular matrix (PCM)-like material around each chondrocyte was found to be constructed, which was confirmed by an optical micrograph in conjunction with toluidine blue staining. The relaxation modulus of each of the chondrocyte-agarose gel composite systems was measured by a non-constrained indentation method. Stress-strain curves for all of the specimens examined had a toe region followed by a linear region terminated by specimen fracture. The slope of the linear region of AGC0 was smaller than that of AG, while the SS curve of AGC0 was indistinguishable from that of AGC3. All of the relaxation curves studied were typical of gels, having a fast relaxation process up to 10³ s followed by a plateau. The relaxation modulus of AGC0 was smaller than that of agarose gel (AG), the decrement in relaxation modulus from AG to AGC0 being attributed to the seeding of chondrocytes that have a smaller modulus than that of agarose gels. However, the relaxation modulus of AGC3 was increased at the early viscoelastic region in particular, as compared with that of AGC0. The increments in the relaxation modulus in AGC3 were attributed to the PCM-like material produced by chondrocytes, where the produced material may provide crosslink points and reinforce the agarose gel.     

Indentation as a technique to assess the mechanical properties of fallback foods

A number of living primates feed part-year on seemingly hard food objects as a fallback. We ask here how hardness can be quantified and how this can help understand primate feeding ecology. We report a simple indentation methodology for quantifying hardness, elastic modulus, and toughness in the sense that materials scientists would define them. Suggested categories of fallback foods—nuts, seeds, and root vegetables—were tested, with accuracy checked on standard materials with known properties by the same means. Results were generally consistent, but the moduli of root vegetables were overestimated here. All these properties are important components of what fieldworkers mean by hardness and help understand how food properties influence primate behavior. Hardness sensu stricto determines whether foods leave permanent marks on tooth tissues when they are bitten on. The force at which a food plastically deforms can be estimated from hardness and modulus. When fallback foods are bilayered, consisting of a nutritious core protected by a hard outer coat, it is possible to predict their failure force from the toughness and modulus of the outer coat, and the modulus of the enclosed core. These forces can be high and bite forces may be maximized in fallback food consumption. Expanding the context, the same equation for the failure force for a bilayered solid can be applied to teeth. This analysis predicts that blunt cusps and thick enamel will indeed help to sustain the integrity of teeth against contacts with these foods up to high loads. Am J Phys Anthropol 140:643–652, 2009. © 2009 Wiley-Liss, Inc.     

High-resolution spatial mapping of shear properties in cartilage

Structural properties of articular cartilage such as proteoglycan content, collagen content and collagen alignment are known to vary over length scales as small as a few microns (Bullough and Goodfellow, 1968; Bi et al., 2006). Characterizing the resulting variation in mechanical properties is critical for understanding how the inhomogeneous architecture of this tissue gives rise to its function. Previous studies have measured the depth-dependent shear modulus of articular cartilage using methods such as particle image velocimetry (PIV) that rely on cells and cell nuclei as fiducial markers to track tissue deformation (Buckley et al., 2008; Wong et al., 2008a). However, such techniques are limited by the density of trackable markers, which may be too low to take full advantage of optical microscopy. This limitation leads to noise in the acquired data, which is often exacerbated when the data is manipulated. In this study, we report on two techniques for increasing the accuracy of tissue deformation measurements. In the first technique, deformations were tracked in a grid that was photobleached on each tissue sample (Bruehlmann et al., 2004). In the second, a numerical technique was implemented that allowed for accurate differentiation of optical displacement measurements by minimizing the propagated experimental error while ensuring that truncation error associated with local averaging of the data remained small. To test their efficacy, we employed these techniques to compare the depth-dependent shear moduli of neonatal bovine and adult human articular cartilage. Using a photobleached grid and numerical optimization to gather and analyze data led to results consistent with those reported previously (Buckley et al., 2008; Wong et al., 2008a), but with increased spatial resolution and characteristic coefficients of variation that were reduced up to a factor of 3. This increased resolution allowed us to determine that the shear modulus of neonatal bovine and adult human tissue both exhibit a global minimum at a depth z of around 100 μm and plateau at large depths. The consistency of the depth dependence of |G*|(Z) for adult human and neonatal bovine tissue suggests a functional advantage resulting from this behavior.     

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.