Depth-dependent Mechanical Properties Research Articles

A new method for AFM mechanical characterization of heterogeneous samples with finite thickness

ABSTRACT Accurate mathematical expressions have previously been derived for determining the Young's modulus of thin homogeneous samples on rigid substrates when tested using atomic force microscopy. These equations have generally been applied to determine the mechanical properties (in terms of Young's modulus) of thin biological samples bonded to rigid substrates, such as cells. However, biological materials are highly heterogeneous at the nanoscale, so their mechanical properties vary significantly with indentation depth. Consequently, a crucial question is whether these equations are mathematically valid in such cases and if they can lead to reproducible results. In this paper, a rigorous mathematical analysis is used to investigate the validity of equations derived for homogeneous samples with finite thickness when applied to heterogeneous thin samples on rigid substrates. Using the aforementioned analysis, the classical equations are modified to account for depth-dependent mechanical properties. Consequently, the depth-dependent mechanical properties of heterogeneous samples with finite thickness are characterized using appropriate functions instead of single Young's modulus values. Force–indentation data from human fibroblasts and murine breast cancer cells are processed using the method presented in this paper, resulting in accurate and reproducible results.

Depth-dependent mechanical properties of the human cornea by uniaxial extension

The purpose of this study was to investigate the depth-dependent biomechanical properties of the human corneal stroma under uniaxial tensile loading. Human stroma samples were obtained after the removal of Descemet's membrane in the course of Descemet's membrane endothelial keratoplasty (DMEK) transplantation. Uniaxial tensile tests were performed at three different depths: anterior, central, and posterior on 2 × 6 × 0.15 mm strips taken from the central DMEK graft. The measured force-displacement data were used to calculate stress-strain curves and to derive the tangent modulus. The study showed that mechanical strength decreased significantly with depth. The anterior cornea appeared to be the stiffest, with a stiffness approximately 18% higher than that of the central cornea and approximately 38% higher than that of the posterior layer. Larger variations in mechanical response were observed in the posterior group, probably due to the higher degree of alignment of the collagen fibers in the posterior sections of the cornea. This study contributes to a better understanding of the biomechanical tensile properties of the cornea, which has important implications for the development of new treatment strategies for corneal diseases. Accurate quantification of tensile strength as a function of depth is critical information that is lacking in human corneal biomechanics to develop numerical models and new treatment methods.

Determining Spatial Variability of Elastic Properties for Biological Samples Using AFM.

Measuring the mechanical properties (i.e., elasticity in terms of Young's modulus) of biological samples using Atomic Force Microscopy (AFM) indentation at the nanoscale has opened new horizons in studying and detecting various pathological conditions at early stages, including cancer and osteoarthritis. It is expected that AFM techniques will play a key role in the future in disease diagnosis and modeling using rigorous mathematical criteria (i.e., automated user-independent diagnosis). In this review, AFM techniques and mathematical models for determining the spatial variability of elastic properties of biological materials at the nanoscale are presented and discussed. Significant issues concerning the rationality of the elastic half-space assumption, the possibility of monitoring the depth-dependent mechanical properties, and the construction of 3D Young's modulus maps are also presented.

Is it mathematically correct to fit AFM data (obtained on biological materials) to equations arising from Hertzian mechanics?

When testing soft biological samples using the Atomic Force Microscopy (AFM) nanoindentation method, the force-indentation data is usually fitted to the equations provided by Hertzian mechanics. Nevertheless, a significant question remains up to date; is this a correct approach from a mathematical perspective? Biological materials are heterogeneous, so ‘what do we calculate’ when using a classic fitting approach? In this paper, conclusive answers to the abovementioned questions are provided. In addition, a new tool for the nanomechanical characterization of biological samples, the depth-dependent mechanical properties maps, is introduced.

Mechanical size effect and serrated flow of various Zr-based bulk metallic glasses

Despite superior mechanical properties, the cross-scale mechanical properties of Zr-based bulk metallic glasses (BMGs) are urgent to be revealed. Depth-sensitive nanoindentation technique was employed to directly investigate the significant depth-dependent mechanical properties of three kinds of Zr-based BMGs. Specifically, the surface hardness H and elastic modulus E are verified to increase with the decrease of indentation depth while the fracture toughness KIC decreases with the indentation depth. The mechanical size effect is closely related to the evolution of shear bands at various indentation depths, which can be equivalently revealed by the distribution of serrated flow. Based on a relatively shallow indentation depth, the comparatively minor stress gradient established inside the micro-region underneath the indenter tip induces insufficient activation energy of shear bands, which prevents the nucleation of shear bands and further restricts plastic deformation, and ultimately results in enhanced surface hardness and elastic modulus but reduced fracture toughness. In addition, the shear band morphology of residual indentation and the stress distribution obtained from the finite element simulation provide integral evidence in support of the depth-induced mechanical size effect.

Influential parameters on 3-D synthetic ground motions in a sedimentary basin derived from global sensitivity analysis

SUMMARYWhich physical parameters are the most influential when predicting earthquake ground motions in a 3-D sedimentary basin? We answer quantitatively by doing a global sensitivity analysis of two quantities of interest: the peak ground motions (PGMs) and a time–frequency representation (the S transform) of ground motions resulting from the synthetic anelastic responses of the EUROSEISTEST. This domain of interest is modeled by two layers with uncertain depth-dependent mechanical properties and is illuminated by a plane S-wave propagating vertically upward in an uncertain homogeneous elastic bedrock. The global sensitivity analysis is conducted on 800+ physics-based simulations of the EUROSEISTEST requiring 8+ million core-hours (i.e. ≈ 900 yr of mono-core computation). The analysis of the PGMs at the free surface displays the spatial influence of the uncertain input parameters over the entire basin scale, while the analysis of the time–frequency representation shows their influence at a specific location inside the basin. The global sensitivity analysis done on the PGMs points out that their most influential parameter in the middle of the basin is the quality factor QS (it controls up to 80 per cent of the PGMs in certain locations where the sediments thickness is larger than 200 m). On the other hand, the geological layering configuration (here represented by the depth of a geological interface controlling the geological layering) strongly influences the PGMs close to the basin edges, up to 90 per cent. We also found that the shear wave velocity at the free surface of the basin and the one of the bedrock underlying the basin are to be considered on an equal footing, both influencing the PGMs in the middle of the basin and close to its edges. We highlight that the bedrock to basin amplification of the PGMs shows a clear increase with respect to the thickness of the sediments, but this amplification saturates from 200 m of sediments around the value of three and is frequency dependent. This PGMs amplification starts from about one tenth of the mean S-wavelength propagating in the basin. The global sensitivity analysis done on the S transform of the ground motions shows that (i) the own effect of the parameters fully controls the first S-wave train and mostly controls the direct arrival of the basin-induced surfaces waves, (ii) the quality factor QS controls 40–60 per cent of the decay of amplitude of coda waves, the remaining part being mainly controlled by interaction effects due to the coupling effect of several parameters and (iii) the interaction effects between the parameters increases with time, suggesting under the hypotheses of our study that the own effects control the ballistic wave propagation while the interaction effects control the diffusive wave propagation.

The average Young's modulus as a physical quantity for describing the depth-dependent mechanical properties of cells

Hertzian mechanics is a useful theoretical tool for data processing regarding Atomic Force Microscopy (AFM) nanoindentation experiments on cells and other biological samples. A common approach that is usually followed in the literature is to fit the experimentally obtained data to the equations provided by Hertzian analysis. However, there are many different approaches regarding the selection of the maximum indentation depth even for the same biological sample and many of them depend on the experience of the AFM-user. In addition, the results as provided by different research groups on the same sample (e.g. the same cell type) usually vary significantly. Thus, it is crucial to develop novel user-independent methods for assessing the mechanical properties of cells. In this paper a new approach, based on the work done by the indenter, is proposed for data processing. At first, a hypothetical nanoindentation experiment on an elastic half space is assumed in which the maximum indentation depth and the work done by the indenter are equal to the actual experiment. The Young's modulus of the hypothetical ideal material is the actual sample's average Young's modulus. In addition, the function of the average Young's modulus with respect to the indentation depth is introduced to reveal the depth dependent mechanical properties of biological samples. Secondly, the proposed methodology was applied on experimental data from fibroblasts and H4, A172 human glioma cells. The results showed a ‘softening’ of cells as the indentation depth increases. However, for big indentation depths the average Young's modulus always reaches an asymptotic value (the overall average Young's modulus). Thus, the overall average Young's modulus can be used for comparing the results of AFM nanoindentation experiments on cells between different research groups. In addition, the average Young's modulus function can also reveal the maximum value of the indentation depth that should not be surpassed in order to avoid a substrate effect. The analysis proposed by this paper can be applied to any biological sample using conical or spherical indenters. The great advantage of the proposed by this paper technique is that it does not require a linear elastic response of the sample, thus it is appropriate for the mechanical nano-characterization of highly heterogeneous biological materials.

A New Approach for the AFM-Based Mechanical Characterization of Biological Samples.

The AFM nanoindentation technique is a powerful tool for the mechanical characterization of biological samples at the nanoscale. The data analysis of the experimentally obtained results is usually performed using the Hertzian contact mechanics. However, the aforementioned theory can be applied only in cases that the sample is homogeneous and isotropic and presents a linear elastic response. However, biological samples often present depth-dependent mechanical properties, and the Hertzian analysis cannot be used. Thus, in this paper, a different approach is presented, based on a new physical quantity used for the determination of the mechanical properties at the nanoscale. The aforementioned physical quantity is the work done by the indenter per unit volume. The advantages of the presented analysis are significant since the abovementioned magnitude can be used to examine if a sample can be approximated to an elastic half-space. If this approximation is valid, then the new proposed method enables the accurate calculation of Young's modulus. Additionally, it can be used to explore the mechanical properties of samples that are characterized by a depth-dependent mechanical behavior. In conclusion, the proposed analysis presents an accurate yet simple technique for the determination of the mechanical properties of biological samples at the nanoscale that can be also used beyond the Hertzian limit.

Recording microindentation and adhesion tests to analyse the depth-dependent mechanical and adhesive properties of multilayer polymer films as shown for gelatine-coated polyethylene terephthalate and polyethylene films

Further developed methods based on an indenter penetration into a material allow generalised quantitative statements on the composition, the depth-dependent mechanical properties and the delamination behaviour of multilayer polymer films, which is demonstrated on gelatine-coated polyethylene terephthalate and polyethylene films. These highly sensitive polymer testing methods, include the recording microindentation test and the recording adhesion test, describe the material behaviour multi-parametrically and are fast (raw data acquisition within several minutes) and relatively simple, requiring a minimum 1 gram sample depending on the film thickness. Based on the Vickers hardness under load approach, the hardness–depth diagrams calculated from the recording microindentation test provide information about the structure, the thickness and the coating hardness and the substrates. The tangential load vs. tangential path length diagrams from recording adhesion test can detect different scratch processes such as continuous scratching or non-continuous stick-slip layer delamination. Furthermore, they form the basis to quantitatively analyze adhesion, i.e. to determine the critical tangential load and the critical tangential delamination work. Both are highly dependent on the substrate type and treatment.

Optimized Media Volumes Enable Homogeneous Growth of Mesenchymal Stem Cell-Based Engineered Cartilage Constructs.

Despite marked advances in the field of cartilage tissue engineering, it remains a challenge to engineer cartilage constructs with homogeneous properties. Moreover, for engineered cartilage to make it to the clinic, this homogeneous growth must occur in a time-efficient manner. In this study we investigated the potential of increased media volume to expedite the homogeneous maturation of mesenchymal stem cell (MSC) laden engineered constructs over time in vitro. We assessed the MSC-laden constructs after 4 and 8 weeks of chondrogenic culture using bulk mechanical, histological, and biochemical measures. These assays were performed on both the intact total constructs and the construct cores to elucidate region-dependent differences. In addition, local strain transfer was assessed to quantify depth-dependent mechanical properties throughout the constructs. Our findings suggest that increased media volume enhances matrix deposition early in culture and ameliorates unwanted regional heterogeneities at later time points. Taken together, these data support the use of higher media volumes during in vitro culture to hasten tissue maturation and increase the core strength of tissue constructs. These findings will forward the field of cartilage tissue engineering and the translation of tissue engineered constructs.

Recombinant human FGF18 preserves depth-dependent mechanical inhomogeneity in articular cartilage

Articular cartilage is a specialised tissue that has a relatively homogenous endogenous cell population but a diverse extracellular matrix (ECM), with depth-dependent mechanical properties. Repair of this tissue remains an elusive clinical goal, with biological interventions preferred to arthroplasty in younger patients. Osteochondral transplantation (OCT) has emerged for the treatment of cartilage defects and osteoarthritis. Fresh allografts stored at 4 °C have been utilised, though matrix and cell viability loss remains an issue. To address this, several studies have developed media formulations to maintain cartilage explants in vitro. One promising factor for these applications is sprifermin, a human-recombinant fibroblast growth factor-18, which stimulates chondrocyte proliferation and matrix synthesis and is in clinical trials for the treatment of osteoarthritis. The study hypothesis was that addition of sprifermin during storage would maintain the unique depth-dependent mechanical profile of articular cartilage explants, a feature not often evaluated. Explants were maintained for up to 6 weeks with or without a weekly 24 h exposure to sprifermin (100 ng/mL) and the compressive modulus was assessed. Results showed that sprifermin-treated samples maintained their depth-dependent mechanical profile through 3 weeks, whereas untreated samples lost their mechanical integrity over 1 week of culture. Sprifermin also affected ECM balance by maintaining the levels of extracellular collagen and suppressing matrix metalloproteinase production. These findings support the use of sprifermin as a medium additive for OCT allografts during in vitro storage and present a potential mechanism where sprifermin may impact a functional characteristic of articular cartilage in repair strategies.

Bi-layered micro-fibre reinforced hydrogels for articular cartilage regeneration

Articular cartilage has limited capacity for regeneration and when damaged cannot be repaired with currently available metallic or synthetic implants. We aim to bioengineer a microfibre-reinforced hydrogel that can capture the zonal depth-dependent mechanical properties of native cartilage, and simultaneously support neo-cartilage formation. With this goal, a sophisticated bi-layered microfibre architecture, combining a densely distributed crossed fibre mat (superficial tangential zone, STZ) and a uniform box structure (middle and deep zone, MDZ), was successfully manufactured via melt electrospinning and combined with a gelatin–methacrylamide hydrogel. The inclusion of a thin STZ layer greatly increased the composite construct’s peak modulus under both incongruent (3.2-fold) and congruent (2.1-fold) loading, as compared to hydrogels reinforced with only a uniform MDZ structure. Notably, the stress relaxation response of the bi-layered composite construct was comparable to the tested native cartilage tissue. Furthermore, similar production of sulphated glycosaminoglycans and collagen II was observed for the novel composite constructs cultured under mechanical conditioning w/o TGF-ß1 supplementation and in static conditions w/TGF-ß1 supplementation, which confirmed the capability of the novel composite construct to support neo-cartilage formation upon mechanical stimulation. To conclude, these results are an important step towards the design and manufacture of biomechanically competent implants for cartilage regeneration. Statement of SignificanceDamage to articular cartilage results in severe pain and joint disfunction that cannot be treated with currently available implants. This study presents a sophisticated bioengineered bi-layered fibre reinforced cell-laden hydrogel that can approximate the functional mechanical properties of native cartilage. For the first time, the importance of incorporating a viable superficial tangential zone (STZ) – like structure to improve the load-bearing properties of bioengineered constructs, particularly when in-congruent surfaces are compressed, is demonstrated. The present work also provides new insights for the development of implants that are able to promote and guide new cartilaginous tissue formation upon physiologically relevant mechanical stimulation.

Cartilage-on-cartilage contact: effect of compressive loading on tissue deformations and structural integrity of bovine articular cartilage

This study aims to characterize the deformations in articular cartilage under compressive loading and link these to changes in the extracellular matrix constituents described by magnetic resonance imaging (MRI) relaxation times in an experimental model mimicking invivo cartilage-on-cartilage contact. Quantitative MRI images, T1, T2 and T1ρ relaxation times, were acquired at 9.4T from bovine femoral osteochondral explants before and immediately after loading. Two-dimensional intra-tissue displacement and strain fields under cyclic compressive loading (350N) were measured using the displacement encoding with stimulated echoes (DENSE) method. Changes in relaxation times in response to loading were evaluated against the deformation fields. Deformation fields showed consistent patterns among all specimens, with maximal strains at the articular surface that decrease with tissue depth. Axial and transverse strains were maximal around the center of the contact region, whereas shear strains were minimal around the contact center but increased towards contact edges. A decrease in T2 and T1ρ was observed immediately after loading whereas the opposite was observed for T1. No correlations between cartilage deformation patterns and changes in relaxation times were observed. Displacement encoding combined with relaxometry by MRI can noninvasively monitor the cartilage biomechanical and biochemical properties associated with loading. The deformation fields reveal complex patterns reflecting the depth-dependent mechanical properties, but intra-tissue deformation under compressive loading does not correlate with structural and compositional changes. The compacting effect of cyclic compression on the cartilage tissue was revealed by the change in relaxation time immediately after loading.

Mimicking nature: Fabrication of 3D anisotropic electrospun polycaprolactone scaffolds for cartilage tissue engineering applications

There is a growing need to develop strategies capable of engineering the anisotropic cartilaginous fibrous network in vitro and consequently overcome the anatomical and functional restrictions of the standard medical procedures used for cartilage regeneration. In this work, we suggest a fabrication procedure to build 3D anisotropic multi-layered fibrous scaffolds. Polycaprolactone (PCL) was used as bulk material for the different electrospun layers (horizontally, randomly and vertically aligned) that were assembled and then structurally maintained by a biocompatible graphene-oxide-collagen (GO-collagen) microporous network. To validate the resourcefulness of the technique, four PCL-GO-collagen scaffolds with different anisotropic properties were produced and characterized by analysing their depth dependent morphological and mechanical properties.

A compression system for studying depth-dependent mechanical properties of articular cartilage under dynamic loading conditions

The biological activities of chondrocytes are influenced by the mechanical characteristics of their environment. The overall real-time mechanical response of cartilage has been investigated earlier. However, the instantaneous local mechano-biology of cartilage has not been investigated in detail under dynamic loading conditions. In order to address this gap in the literature, we designed a compression testing device and implemented a dual photon microscopy technique with the goal of measuring local mechanical and biological responses of articular cartilage under dynamic loading conditions. The details of the compression system and results of a pilot study are presented here. A 15% ramp compression at a rate of 0.003/s with a subsequent stress relaxation phase was applied to the cartilage explant samples. The extra cellular matrix was imaged throughout the entire thickness of the cartilage sample, and local tissue strains were measured during the compression and relaxation phase. The axial compressive strains in the middle and superficial zones of cartilage were observed to increase during the relaxation phase: this was a new finding, suggesting the importance of further investigations on the real-time local behavior of cartilage. The compression system showed promising results for investigating the dynamic, real-time mechanical response of articular cartilage, and can now be used to reveal the instantaneous mechanical and biological responses of chondrocytes in response to dynamic loading conditions.

Effect of parylene C coating on the antibiocorrosive and mechanical properties of different magnesium alloys

In this paper, parylene C coating with the thickness of 2μm was deposited on different magnesium alloy substrates (AZ31, WE43 and AZ91). The structure and phase composition of parylene C coating was analysed by Fourier transformed infrared (FTIR) spectroscopy and X-ray diffraction (XRD). In addition, extensive surface characterization was done using atomic force microscopy. The corrosion performance of polymer-coated magnesium alloys was investigated by electrochemical measurements in Hanks’ balanced salts solution that simulates bodily fluids at 37±0.5°C. The depth-dependent mechanical properties including Young’s modulus and nanohardness of parylene C films were investigated using nanoindentation technique. The effect of the penetration depth on the properties on nano- and microscale level have been described in detail. The percentage of elastic recovery was used to characterize the elastic properties of the polymeric coatings. The results of XRD showed (020) preferred orientation of the monoclinic unit cell of the alpha phase of parylene C. The parylene C revealed a semicrystalline structure with nanocrystalline blocks of 4.9nm. The parylene C film shows a uniform surface morphology with a higher roughness level at micro and nanoscales compared to magnesium alloy surfaces. All of the uncoated substrates exhibited a low corrosion resistance compared to the coated samples, indicating that the corrosion resistance of the magnesium alloys could be improved by parylene C coating. The resulting average nanohardness and Young’s modulus of the parylene C coatings deposited onto different substrates were in the range of 0.18–0.25GPa and 4.19–5.14GPa, respectively. Furthermore, a higher percentage of elastic recovery of the polymer coating indicated a higher elasticity as compared to the magnesium alloy surface. The polymer coating has revealed the ability to recover elastically. Therefore, parylene C coating can not only improve corrosion resistance, but also provide the ability to recover elastically, expanding the potential applications of this material to include various biointerface platforms.

Enhanced nutrient transport improves the depth-dependent properties of tri-layered engineered cartilage constructs with zonal co-culture of chondrocytes and MSCs.

Articular cartilage is a highly organized tissue driven by zonal heterogeneity of cells, extracellular matrix proteins and fibril orientations, resulting in depth-dependent mechanical properties. Therefore, the recapitulation of the functional properties of native cartilage in a tissue engineered construct requires such a biomimetic design of the morphological organization, and this has remained a challenge in cartilage tissue engineering. This study demonstrates that a layer-by-layer fabrication scheme, including co-cultures of zone-specific articular CHs and MSCs, can reproduce the depth-dependent characteristics and mechanical properties of native cartilage while minimizing the need for large numbers of chondrocytes. In addition, introduction of a porous hollow fiber (combined with a cotton thread) enhanced nutrient transport and depth-dependent properties of the tri-layered construct. Such a tri-layered construct may provide critical advantages for focal cartilage repair. These constructs hold promise for restoring native tissue structure and function, and may be beneficial in terms of zone-to-zone integration with adjacent host tissue and providing more appropriate strain transfer after implantation.

Multi-cycling instrumented nanoindentation of a Ti-23Nb-0.7Ta-2Zr-1.2O alloy in annealed condition

In this study, depth-dependent mechanical properties (i.e. hardness, elastic modulus, and indentation size effect) as well as strain rate sensitivity of a new class of titanium based alloys, Ti-23Nb-0.7Ta-2Zr-1.2O, are considered. To this end, local deformation micro-mechanisms of this alloy are investigated systematically through a constant-strain rate (CSR) instrumented nanoindentation testing technique. The CSR nanoindentation tests were performed at ambient (room) temperature with nominal indentation depths of 100–2000nm and strain rates of 0.005, 0.05, and 0.5s−1 using a Berkovich pyramidal indenter. Nanoindentation is a particularly reliable tool for studying elastic/plastic behavior of metallic alloys. Large strain gradients around the indenter should reveal and help clarify the thermally activated mechanisms contributing to the plastic deformation processes which can quantitatively be interpreted by examining the rate sensitivity index, m, and activation volume. Indentation results show that the strain rate sensitivity and activation volume, Burger’s vector times activation area, are depth-dependent phenomena revealing different controlling plastic deformation mechanisms.

Wear characteristics and inhibition of enamel demineralization by resin-based coating materials.

In this study, wear and inhibition of enamel demineralization by resin-based coating materials were investigated. Seven commercially available coating materials, with and without fillers, were used. A mechanical wear test was performed, and the specimens were then examined with a scanning electron microscope. Hardness and elastic modulus measurements for each material were obtained by nanoindentation testing. Thin layers of each material were applied on human enamel surfaces, which were subjected to alternating immersion in demineralizing and remineralizing solutions. The inhibition ability of enamel demineralization adjacent to the coating was estimated with depth-dependent mechanical properties using the nanoindentation test. The non-filled coating material showed significantly lower hardness, lower elastic modulus, and higher weight loss. There were no significant differences in weight loss among the six filled coating materials. After the alternating immersion protocol, the enamel specimens having application of coating materials with ion-releasing ability were harder than those in the other groups in some locations 1-11 μm from the enamel surface and within 300 μm from the edge of the coating materials. In conclusion, clinical use of the resin-based coating materials with ion-releasing ability may prevent demineralization of exposed enamel adjacent to the coating during treatment.

Computational models for the determination of depth-dependent mechanical properties of skin with a soft, flexible measurement device.

Conformal modulus sensors (CMS) incorporate PZT nanoribbons as mechanical actuators and sensors to achieve reversible conformal contact with the human skin for non-invasive, invivo measurements of skin modulus. An analytic model presented in this paper yields expressions that connect the sensor output voltage to the Young moduli of the epidermis and dermis, the thickness of the epidermis, as well as the material and geometrical parameters of the CMS device itself and its encapsulation layer. Results from the model agree well with invitro experiments on bilayer structures of poly(dimethylsiloxane). These results provide a means to determine the skin moduli (epidermis and dermis) and the thickness of the epidermis from invivo measurements of human skin.