Quantitative mechanical analysis of indentations on layered, soft elastic materials

Nanorheology and Nanoindentation Revealed a Softening and an Increased Viscous Fluidity of Adherent Mammalian Cells upon Increasing the Frequency

The nanomechanical response of a cell depends on the frequency at which the cell is probed. The components of the cell that contribute to this property and their interplay are not well understood. Here, two force microscopy methods are integrated to characterize the frequency and/or the velocity-dependent properties of living cells. It is shown on HeLa and fibroblasts, that cells soften and fluidize upon increasing the frequency or the velocity of the deformation. This property was independent of the type and values (25 or 1000 nm) of the deformation. At low frequencies (2-10 Hz) or velocities (1-10 µm s-1 ), the response is dominated by the mechanical properties of the cell surface. At higher frequencies (>10 Hz) or velocities (>10 µm s-1 ), the response is dominated by the hydrodynamic drag of the cytosol. Softening and fluidization does not seem to involve any structural remodeling. It reflects a redistribution of the applied stress between the solid and liquid-like elements of the cell as the frequency or the velocity is changed. The data indicates that the quasistatic mechanical properties of a cell featuring a cytoskeleton pathology might be mimicked by the response of a non-pathological cell which is probed at a high frequency.

Inferring mechanical properties of the SARS-CoV-2 virus particle with nano-indentation tests and numerical simulations

The pandemic caused by the SARS-CoV-2 virus has claimed more than 6.5 million lives worldwide. This global challenge has led to accelerated development of highly effective vaccines tied to their ability to elicit a sustained immune response. While numerous studies have focused primarily on the spike (S) protein, less is known about the interior of the virus. Here we propose a methodology that combines several experimental and simulation techniques to elucidate the internal structure and mechanical properties of the SARS-CoV-2 virus. The mechanical response of the virus was analyzed by nanoindentation tests using a novel flat indenter and evaluated in comparison to a conventional sharp tip indentation. The elastic properties of the viral membrane were estimated by analytical solutions, molecular dynamics (MD) simulations on a membrane patch and by a 3D Finite Element (FE)-beam model of the virion's spike protein and membrane molecular structure. The FE-based inverse engineering approach provided a reasonable reproduction of the mechanical response of the virus from the sharp tip indentation and was successfully verified against the flat tip indentation results. The elastic modulus of the viral membrane was estimated in the range of 7-20 MPa. MD simulations showed that the presence of proteins significantly reduces the fracture strength of the membrane patch. However, FE simulations revealed an overall high fracture strength of the virus, with a mechanical behavior similar to the highly ductile behavior of engineering metallic materials. The failure mechanics of the membrane during sharp tip indentation includes progressive damage combined with localized collapse of the membrane due to severe bending. Furthermore, the results support the hypothesis of a close association of the long membrane proteins (M) with membrane-bound hexagonally packed ribonucleoproteins (RNPs). Beyond improved understanding of coronavirus structure, the present findings offer a knowledge base for the development of novel prevention and treatment methods that are independent of the immune system.

Insights and guidelines to interpret forces and deformations at the nanoscale by using a tapping mode AFM simulator: dForce 2.0

Amplitude modulation (tapping mode) AFM is the most versatile AFM mode for imaging surfaces at the nanoscale in air and liquid environments. However, it remains challenging to estimate the forces and deformations exerted by the tip. We introduce a new simulator environment to predict the values of the observables in tapping mode AFM experiments. The relevant feature of dForce 2.0 is the incorporation of contact mechanics models aimed to describe the properties of ultrathin samples. These models were essential to determine the forces applied on samples such as proteins, self-assembled monolayers, lipid bilayers, and few-layered materials. The simulator incorporates two types of long-range magnetic forces. The simulator is written in an open-source code (Python) and it can be run from a personal computer.

Atomic force microscopy-based indentation of cells: modelling the effect of a pericellular coat

A simple analytical model is built up to account for the interface deformation effect in a spherical atomic force microscopy (AFM)-based quasi-static indentation of a living cell covered with a pericellular brush. The compression behaviour of the pericellular coat is described using the Alexander–de Gennes model that allows for nonlinear deformation. An approximate second-order relation between contact force and indenter displacement is obtained in implicit form, using the Hertzian solution as a first-order approximation. A method of fitting the indentation brush/cell model to experimental data is suggested based on the non-dimensionalized version of the displacement–force relation in the parametric form and illustrated with a specific example of AFM raw data taken from the literature.

Nano-structural stiffness measure for soft biomaterials of heterogeneous elasticity

Measuring the structural stiffness aims to reveal the impact of nanostructured components or various physiological circumstances on the elastic response of material to an external indentation. With a pyramidal tip at a nano-scale, we employed the atomic force microscopy (AFM) to indent the surfaces of two compositions of polyacrylamide gels with different softness and seedling roots of Arabidopsis thaliana. We found that the stiffness-depth curve derived from the measured force exhibits a heterogeneous character in elasticity. According to the tendency of stiffness-depth curve, we decomposed the responding force into depth-impact (F_C), Hookean (F_H) and tip-shape (F_S) components, called trimechanic, where F_S and its gradient should be offset at the surface or subsurfaces of the indented material. Thereby, trimechnic theory allows us to observe how the three restoring nanomechanics change with varied depth. Their strengths are represented by the respective spring constants (k_C, k_H, k_S) of three parallel-connected spring (3PCS) analogs to differentiate restoring nanomechansims of indented materials. The effective Young's modulus Ê and the total stiffness k_T (= k_H + k_S) globally unambiguously distinguish the softness between the two gel categories. Data fluctuations were observed in the elasticity parameters of individual samples, reflecting nanostructural variations in the gel matrix. Similar tendencies were found in the results from growing plant roots, though the data fluctuations are expectedly much more dramatic. The zone-wise representation of stiffness by the trimechanic-3PCS framework demonstrates a stiffness measure that reflects beneath nanostructures encountered by deepened depth. The trimechanic-3PCS framework can apply any mechanical model of power-law based force-depth relationship and is compatible with thin layer corrections. It provides a new paradigm for analyzing restoring nanomechanics of soft biomaterials in response to indenting forces.

Indentation of a pressurized silicon stomach model - A non-invasive study of gastric wall stiffness and pressurized gastric content stiffness

BACKGROUND AND AIMS

Evaluation of gastric wall stiffness and intragastric pressure is essential for detailed assessments of gastric accommodation. However, non-invasive assessments are needed for large scale clinical studies and none of the existing methods takes abdominal wall effect into the calculation. This study aimed to assess gastric wall stiffness and gastric content stiffness as a proxy for intragastric pressure using novel mechanical modeling and non-invasive indentation tests on a silicon stomach model.

METHODS

A silicon stomach model (scaling 1:1 with the human stomach) was indented using a pressure algometer at intragastric pressures from 0 to 0.8 kPa. Wall thicknesses and luminal cross-sectional areas along the stomach were measured with ultrasound images. The gastric wall stiffness was compared between measurements from tensile tests on strips cut from the silicon stomach and estimations from a shell indentation model. The pressurized gastric content stiffness was predicted from a bonded two-layer axisymmetric half-space indentation model.

RESULTS

The gastric wall stiffness estimated from the shell indentation model showed no difference to measurements from the mechanical tests on the cutting strips (p = 0.14). The predicted gastric content stiffness was strongly associated with the intragastric pressure (r > 0.83, p < 0.001).

CONCLUSIONS

The mechanical model developed in this study can simultaneously predict the gastric wall stiffness and the pressurized gastric content stiffness. In future studies, the method can be applied to reveal intragastric pressure conditions non-invasively via the pressurized gastric content stiffness during gastric accommodation and emptying such as with magnetic resonance imaging.

Investigating Nanoscale Contact Using AFM-Based Indentation and Molecular Dynamics Simulations

In this work we study nanocontact plasticity in Au thin films using an atomic force microscope based indentation method with the goal of relating the changes in surface morphology to the dislocations created by deformation. This provides a rigorous test of our understanding of deformation and dislocation mechanisms in small volumes. A series of indentation experiments with increasing maximum load was performed. Distinct elastic and plastic regimes were identified in the force-displacement curves, and the corresponding residual imprints were measured. Transmission electron microscope based measured dislocation densities appear to be smaller than the densities expected from the measured residual indents. With the help of molecular dynamics simulations we show that dislocation nucleation and glide alone fail to explain the low dislocation density. Increasing the temperature of the simulations accelerates the rate of thermally activated processes and promotes motion and annihilation of dislocations under the indent while transferring material to the upper surface; dislocation density decreases in the plastic zone and material piles up around the indent. Finally, we discuss why a significant number of cross-slip events is expected beneath the indent under experimental conditions and the implications of this for work hardening during wear.

Biomechanical fracture mechanics of composite layered skin-like materials

Most protective biological tissues are structurally comprised of a stiff and thin outer layer on top of a soft underlying substrate. Examples include mammalian skin, fish scales, crustacean shells, and nut and seed shells. While these composite skin-like tissues are ubiquitous in nature, their mechanics of failure and what potential mechanical advantages their composite structures offer remains unclear. In this work, changes in the puncture mechanics of composite hyperelastic elastomers with differing non-dimensional layer thicknesses are explored. Puncture behavior of these membranes is measured for dull and sharp conical indenters. Membranes with a stiff outer layer of only 1% of the overall composite thickness exhibit a puncture energy comparable to membranes with a stiff outer layer approximately 20 times thicker. This puncture energy, scaled by its flexural capacity, achieves a local maximum when the top layer is approximately 1% of the total membrane, similar to the structure of numerous mammalian species. The mode of failure for these regimes is also investigated. In contrast with puncture directly beneath sharp tips caused by high stress concentrations, a new type of 'coring' type fracture emerges at large indentation depths, resulting from accumulated tensile strain energy along the sides of the divot as the membrane is deformed with a blunt indenter. These results could enhance the durability and robustness of stretchable materials used for products such as surgical gloves, packaging, and flexible electronics.

Accurate Wide-Modulus-Range Nanomechanical Mapping of Ultrathin Interfaces with Bimodal Atomic Force Microscopy

The nanoscale determination of the mechanical properties of interfaces is of paramount relevance in materials science and cell biology. Bimodal atomic force microscopy (AFM) is arguably the most advanced nanoscale method for mapping the elastic modulus of interfaces. Simulations, theory, and experiments have validated bimodal AFM measurements on thick samples (from micrometer to millimeter). However, the bottom-effect artifact, this is, the influence of the rigid support on the determination of the Young's modulus, questions its accuracy for ultrathin materials and interfaces (1-15 nm). Here we develop a bottom-effect correction method that yields the intrinsic Young's modulus value of a material independent of its thickness. Experiments and numerical simulations validate the accuracy of the method for a wide range of materials (1 MPa to 100 GPa). Otherwise, the Young's modulus of an ultrathin material might be overestimated by a 10-fold factor.

Atomic Force Microscopy Nanomechanics of Hard Nanometer-Thick Films on Soft Substrates: Insights into Stretchable Conductors

The nanomechanical properties of ultrathin and nanostructured films of rigid electronic materials on soft substrates are of crucial relevance to realize materials and devices for stretchable electronics. Of particular interest are bending deformations in buckled nanometer-thick films or patterned networks of rigid materials as they can be exploited to compensate for the missing tensile elasticity. Here, we perform atomic force microscopy indentation experiments and electrical measurements to characterize the nanomechanics of ultrathin gold films on a polydimethylsiloxane (PDMS) elastomer. The measured force-indentation data can be analyzed in terms of a simple analytical model describing a bending plate on a semi-infinite soft substrate. The resulting method enables us to quantify the local Young's modulus of elasticity of the nanometer-thick film. Systematic variation of the gold layer thickness reveals the presence of a diffuse interface between the metal film and the elastomer substrate that does not contribute to the bending stiffness. The effect is associated with gold clusters that penetrate the silicone and are not directly connected to the ultrathin film. Only above a critical layer thickness, percolation of the metallic thin film happens, causing a linear increase in bending stiffness and electrical conductivity.

Meso/macro-scale ultra-soft materials' mechanical property evaluation device and testbed

Ultra-soft materials find applications in biomedical devices, sensors and actuators, robotics, and wearable electronics. The mechanical properties of soft materials are often determined using nanoindentation and atomic force microscope techniques, which provide localized properties at a small-scale length. There is a need to evaluate the meso/macro-scale properties of ultra-soft materials to develop integrated devices made of the same. Metallic probes in the existing macroscale equipment cannot be used as they can pierce through the soft materials and fail to capture the associated adhesion forces, resulting in inaccurate values. This study has developed a meso/macro-scale mechanical testing platform to characterize ultra-soft materials accurately. This probe can be adapted to any mechanical testing load frame with a small load cell to capture the adhesion forces during the approach and detachment segments of soft materials' indentation. The integrated camera with the probe enables overcoming the challenge of surface detection and capturing the pull-on and pull-off events. Indentation tests on soft materials with varying stiffness (e.g., high-fat yogurt, chicken breast, aloe Vera, toothpaste, gelatin, and a chocolate bar) were conducted using a 10 mm stiff flat-end polymer probe. A variation of the Johnson-Kendall-Roberts technique was adopted to account for adhesion forces and compute stiffness. Our results suggest that the novel device and methodology can measure mechanical stiffness in the extensive range of 0.5 kPa to a few MPa with high reproducibility at the macro-scale length. The validation was carried out using a commercially available nanoindenter for soft materials.

Coarse-grained elastic network modelling: A fast and stable numerical tool to characterize mesenchymal stem cells subjected to AFM nanoindentation measurements

The knowledge of the mechanical properties is the starting point to study the mechanobiology of mesenchymal stem cells and to understand the relationships linking biophysical stimuli to the cellular differentiation process. In experimental biology, Atomic Force Microscopy (AFM) is a common technique for measuring these mechanical properties. In this paper we present an alternative approach for extracting common mechanical parameters, such as the Young's modulus of cell components, starting from AFM nanoindentation measurements conducted on human mesenchymal stem cells. In a virtual environment, a geometrical model of a stem cell was converted in a highly deformable Coarse-Grained Elastic Network Model (CG-ENM) to reproduce the real AFM experiment and retrieve the related force-indentation curve. An ad-hoc optimization algorithm perturbed the local stiffness values of the springs, subdivided in several functional regions, until the computed force-indentation curve replicated the experimental one. After this curve matching, the extraction of global Young's moduli was performed for different stem cell samples. The algorithm was capable to distinguish the material properties of different subcellular components such as the cell cortex and the cytoskeleton. The numerical results predicted with the elastic network model were then compared to those obtained from hertzian contact theory and Finite Element Method (FEM) for the same case studies, showing an optimal agreement and a highly reduced computational cost. The proposed simulation flow seems to be an accurate, fast and stable method for understanding the mechanical behavior of soft biological materials, even for subcellular levels of detail. Moreover, the elastic network modelling allows shortening the computational times to approximately 33% of the time required by a traditional FEM simulation performed using elements with size comparable to that of springs.

Proof-of-concept for the detection of early osteoarthritis pathology by clinically applicable endomicroscopy and quantitative AI-supported optical biopsy

OBJECTIVE

Clinical trials for osteoarthritis (OA), the leading cause of global disability, are unable to pinpoint the early, potentially reversible disease with clinical technology. Hence, disease-modifying drug candidates cannot be tested early in the disease. To overcome this obstacle, we asked whether early OA-pathology detection is possible with current clinical technology.

METHODS

We determined the relationship between two sensitive early OA markers, atomic force microscopy (AFM)-measured human articular cartilage (AC) surface stiffness, and location-matched superficial zone chondrocyte spatial organizations (SCSOs), asking whether a significant loss of surface stiffness can be detected in early OA SCSO stages. We then tested whether current clinical technology can visualize and accurately diagnose the SCSOs using an approved probe-based confocal laser-endomicroscope and a random forest (RF) model.

RESULTS

We demonstrated a correlation between AC surface stiffness and the SCSO (r_rm = -0.91; 95%CI: -0.97, -0.73), and an extensive loss of surface stiffness specifically in those ACs with early OA-typical SCSO (95%CIs: string SCSO: 269-173 kPa, double string SCSO: 77-46 kPa). This established the SCSO as a visualizable, functionally relevant surrogate marker of early OA AC surface pathology. Moreover, SCSO-based stiffness discrimination worked well in each patient's AC. We then demonstrated feasibility of visualizing the SCSO by clinical laser-endomicroscopy and, importantly, accurate SCSO diagnosis using RF.

CONCLUSION

We present the proof-of-concept of early OA-pathology detection with available clinical technology, introducing a future-oriented, AI-supported, non-destructive quantitative optical biopsy for early disease detection. Operationalizing SCSO recognition, this approach allows testing for correlations between local tissue architectures with other experimental and clinical read-outs, but needs clinical validation and a larger sample size for defining diagnostic thresholds.

Elasticity spectra as a tool to investigate actin cortex mechanics

Background

The mechanical properties of single living cells have proven to be a powerful marker of the cell physiological state. The use of nanoindentation-based single cell force spectroscopy provided a wealth of information on the elasticity of cells, which is still largely to be exploited. The simplest model to describe cell mechanics is to treat them as a homogeneous elastic material and describe it in terms of the Young’s modulus. Beside its simplicity, this approach proved to be extremely informative, allowing to assess the potential of this physical indicator towards high throughput phenotyping in diagnostic and prognostic applications.

Results

Here we propose an extension of this analysis to explicitly account for the properties of the actin cortex. We present a method, the Elasticity Spectra, to calculate the apparent stiffness of the cell as a function of the indentation depth and we suggest a simple phenomenological approach to measure the thickness and stiffness of the actin cortex, in addition to the standard Young’s modulus.

Conclusions

The Elasticity Spectra approach is tested and validated on a set of cells treated with cytoskeleton-affecting drugs, showing the potential to extend the current representation of cell mechanics, without introducing a detailed and complex description of the intracellular structure.

Bottom Effect in Atomic Force Microscopy Nanomechanics

In this work, the influence of the rigid substrate on the determination of the sample Young's modulus, the so-called bottom-effect artifact, is demonstrated by an atomic force microscopy force-spectroscopy experiment. The nanomechanical properties of a one-component supported lipid membrane (SLM) exhibiting areas of two different thicknesses are studied: While a standard contact mechanics model (Sneddon) provides two different elastic moduli for these two morphologies, it is shown that Garcia's bottom-effect artifact correction yields a unique value, as expected for an intrinsic material property. Remarkably, it is demonstrated that the ratio between the contact radius (and not only the indentation) and the sample thickness is the key parameter addressing the relevance of the bottom-effect artifact. The experimental results are validated by finite element method simulations providing a solid support to Garcia's theory. The amphiphilic nature of the investigated material is representative of several kinds of lipids, suggesting that the results have far reaching implications for determining the correct Young's modulus of SLMs. The generality of Garcia's bottom-effect artifact correction allows its application to every kind of supported soft film.

Nanomechanical mapping of soft materials with the atomic force microscope: methods, theory and applications

Fast, high-resolution, non-destructive and quantitative characterization methods are needed to develop materials with tailored properties at the nanoscale or to understand the relationship between mechanical properties and cell physiology. This review introduces the state-of-the-art force microscope-based methods to map at high-spatial resolution the elastic and viscoelastic properties of soft materials. The experimental methods are explained in terms of the theories that enable the transformation of observables into material properties. Several applications in materials science, molecular biology and mechanobiology illustrate the scope, impact and potential of nanomechanical mapping methods.

Nanorheology of living cells measured by AFM-based force-distance curves

Mechanobiology aims to establish functional relationships between the mechanical state of a living a cell and its physiology. The acquisition of force-distance curves with an AFM is by far the dominant method to characterize the nanomechanical properties of living cells. However, theoretical simulations have shown that the contact mechanics models used to determine the Young's modulus from a force-distance curve could be off by a factor 5 from its expected value. The semi-quantitative character arises from the lack of a theory that integrates the AFM data, a realistic viscoelastic model of a cell and its finite-thickness. Here, we develop a method to determine the mechanical response of a cell from a force-distance curve. The method incorporates bottom-effect corrections, a power-law rheology model and the deformation history of the cell. It transforms the experimental data into viscoelastic parameters of the cell as a function of the indentation frequency. The quantitative agreement obtained between the experiments performed on living fibroblast cells and the analytical theory supports the use of force-distance curves to measure the nanorheological properties of cells.

Subsurface Imaging of Cell Organelles by Force Microscopy

The development of high-resolution, label-free, noninvasive, and subsurface microscopy methods of living cells remains a formidable problem. Force-microscopy-based stiffness measurements contribute to our understanding of single-cell nanomechanics. The elastic properties of the cell's outer structures, such as the plasma membrane and actin cytoskeleton, dominate stiffness measurements, which in turns prevents the imaging of intracellular structures. We propose that the above limitation could be overcome by combining 2D sections of the cell's viscoelastic properties. We show the simultaneous imaging of the outer cell's cytoskeleton and the organelles inside the nucleus. The elastic component of interaction force carries information on the cell's outer elements as the cortex and the actin cytoskeleton. The inelastic component is sensitive to the hydrodynamic drag of the inner structures such the nucleoli.