Microscale consolidation analysis of relaxation behavior of single living chondrocytes subjected to varying strain-rates

Besides the elastic stiffness, the relaxation behavior of single living cells is also of interest of various researchers when studying cell mechanics. It is hypothesized that the relaxation response of the cells is governed by both intrinsic viscoelasticity of the solid phase and fluid-solid interactions mechanisms. There are a number of mechanical models have been developed to investigate the relaxation behavior of single cells. However, there is lack of model enable to accurately capture both of the mechanisms. Therefore, in this study, the porohyperelastic (PHE) model, which is an extension of the consolidation theory, combined with inverse Finite Element Analysis (FEA) technique was used at the first time to investigate the relaxation response of living chondrocytes. This model was also utilized to study the dependence of relaxation behavior of the cells on strain-rates. The stress-relaxation experiments under the various strain-rates were conducted with the Atomic Force Microscopy (AFM). The results have demonstrated that the PHE model could effectively capture the stress-relaxation behavior of the living chondrocytes, especially at intermediate to high strain-rates. Although this model gave some errors at lower strain-rates, its performance was acceptable. Therefore, the PHE model is properly a promising model for single cell mechanics studies. Moreover, it has been found that the hydraulic permeability of living chondrocytes reduced with decreasing of strain-rates. It might be due to the intracellular fluid volume fraction and the fluid pore pressure gradients of chondrocytes were higher when higher strain-rates applied.

A multiscale study on the structural and mechanical properties of the luffa sponge from Luffa cylindrica plant

Cellular materials that are often observed in biological systems exhibit excellent mechanical properties at remarkably low densities. Luffa sponge is one of such materials with a complex interconnecting porous structure. In this paper, we studied the relationship between its structural and mechanical properties at different levels of its hierarchical organization from a single fiber to a segment of whole sponge. The tensile mechanical behaviors of three single fibers were examined by an Instron testing machine and the ultrastructure of a fractured single fiber was observed in a scanning electronic microscope. Moreover, the compressive mechanical behaviors of the foam-like blocks from different locations of the sponge were examined. The difference of the compressive stress-strain responses of four sets of segmental samples were also compared. The result shows that the single fiber is a porous composite material mainly consisting of cellulose fibrils and lignin/hemicellulose matrix, and its Young's modulus and strength are comparable to wood. The mechanical behavior of the block samples from the hoop wall is superior to that from the core part. Furthermore, it shows that the influence of the inner surface on the mechanical property of the segmental sample is stronger than that of the core part; in particular, the former's Young's modulus, strength and strain energy absorbed are about 1.6 times higher. The present work can improve our understanding of the structure-function relationship of the natural material, which may inspire fabrication of new biomimetic foams with desirable mechanical efficiency for further applications in anti-crushing devices and super-light sandwich panels.

Nonlinear mechanical property of tracheal cartilage: A theoretical and experimental study

Background: Despite being the stiffest airway of the bronchial tree, the trachea undergoes significant deformation due to intrathoracic pressure during breathing. The mechanical properties of the trachea affect the flow in the airway and may contribute to the biological function of the lung. Method: A Fung-type strain energy density function was used to investigate the nonlinear mechanical behavior of tracheal cartilage. A bending test on pig tracheal cartilage was performed and a mathematical model for analyzing the deformation of tracheal cartilage was developed. The constants included in the strain energy density function were determined by fitting the experimental data. Result: The experimental data show that tracheal cartilage is a nonlinear material displaying higher strength in compression than in tension. When the compression forces varied from -0.02 to -0.03 N and from -0.03 to -0.04 N, the deformation ratios were 11.03±2.18% and 7.27±1.59%, respectively. Both were much smaller than the deformation ratios (20.01±4.49%) under tension forces of 0.02 to 0.01 N. The Fung-type strain energy density function can capture this nonlinear behavior very well, whilst the linear stress-strain relation cannot. It underestimates the stability of trachea by exaggerating the displacement in compression. This study may improve our understanding of the nonlinear behavior of tracheal cartilage and it may be useful for the future study on tracheal collapse behavior under physiological and pathological conditions.

Development of a biaxial compression device for biological samples : preliminary experimental results for a closed cell foam

Biological tissues are subjected to complex loading states in vivo and in order to define constitutive equations that effectively simulate their mechanical behaviour under these loads, it is necessary to obtain data on the tissue's response to multiaxial loading. Single axis and shear testing of biological tissues is often carried out, but biaxial testing is less common. We sought to design and commission a biaxial compression testing device, capable of obtaining repeatable data for biological samples. The apparatus comprised a sealed stainless steel pressure vessel specifically designed such that a state of hydrostatic compression could be created on the test specimen while simultaneously unloading the sample along one axis with an equilibrating tensile pressure. Thus a state of equibiaxial compression was created perpendicular to the long axis of a rectangular sample. For the purpose of calibration and commissioning of the vessel, rectangular samples of closed cell ethylene vinyl acetate (EVA) foam were tested. Each sample was subjected to repeated loading, and nine separate biaxial experiments were carried out to a maximum pressure of 204 kPa (30 psi), with a relaxation time of two hours between them. Calibration testing demonstrated the force applied to the samples had a maximum error of 0.026 N (0.423% of maximum applied force). Under repeated loading, the foam sample demonstrated lower stiffness during the first load cycle. Following this cycle, an increased stiffness, repeatable response was observed with successive loading. While the experimental protocol was developed for EVA foam, preliminary results on this material suggest that this device may be capable of providing test data for biological tissue samples. The load response of the foam was characteristic of closed cell foams, with consolidation during the early loading cycles, then a repeatable load-displacement response upon repeated loading. The repeatability of the test results demonstrated the ability of the test device to provide reproducible test data and the low experimental error in the force demonstrated the reliability of the test data.

Plantar enthesopathy : thickening of the enthesis is correlated with energy dissipation of the plantar fat pad during walking

Background: The enthesis of the plantar fascia is thought to play an important role in stress dissipation. However, the potential link between entheseal thickening characteristic of enthesopathy and the stress-dissipating properties of the intervening plantar fat pad have not been investigated. Purpose: This study was conducted to identify whether plantar fat pad mechanics explain variance in the thickness of the fascial enthesis in individuals with and without plantar enthesopathy. Study Design: Case-control study; Level of evidence, 3. Methods: The study population consisted of 9 patients with unilateral plantar enthesopathy and 9 asymptomatic, individually matched controls. The thickness of the enthesis of the symptomatic, asymptomatic, and a matched control limb was acquired using high-resolution ultrasound. The compressive strain of the plantar fat pad during walking was estimated from dynamic lateral radiographs acquired with a multifunction fluoroscopy unit. Peak compressive stress was simultaneously acquired via a pressure platform. Principal viscoelastic parameters were estimated from subsequent stress-strain curves. Results: The symptomatic fascial enthesis (6.7 ± 2.0 mm) was significantly thicker than the asymptomatic enthesis (4.2 ± 0.4 mm), which in turn was thicker than the enthesis (3.3 ± 0.4 mm) of control limbs (P < .05). There was no significant difference in the mean thickness, peak stress, peak strain, or secant modulus of the plantar fat pad between limbs. However, the energy dissipated by the fat pad during loading and unloading was significantly lower in the symptomatic limb (0.55 ± 0.17) when compared with asymptomatic (0.69 ± 0.13) and control (0.70 ± 0.09) limbs (P < .05). The sonographic thickness of the enthesis was correlated with the energy dissipation ratio of the plantar fat pad (r = .72, P < .05), but only in the symptomatic limb. Conclusion: The energy-dissipating properties of the plantar fat pad are associated with the sonograpic appearance of the enthesis in symptomatic limbs, providing a previously unidentified link between the mechanical behavior of the plantar fat pad and enthesopathy.

The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elasto-plastic constitutive properties. However, all but one FE study to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6 m and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E=13.56GPa and Poisson‟s ratio f 0.3. Plasticity was incorporated using both Drucker-Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force-indentation curve for both von Mises and Drucker-Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27 to 0.11 m with a von Mises model, and from 0.09 to 0.02 m with Drucker-Prager plasticity. We conclude that it is potentially important to include friction in nanoindentation simulations of bone if pile-up is used to compare simulation results with experiment.

Load-unloading response of intact and artificially degraded articular cartilage correlated with near infrared (NIR) absorption spectra

The conventional mechanical properties of articular cartilage, such as compressive stiffness, have been demonstrated to be limited in their capacity to distinguish intact (visually normal) from degraded cartilage samples. In this paper, we explore the correlation between a new mechanical parameter, namely the reswelling of articular cartilage following unloading from a given compressive load, and the near infrared (NIR) spectrum. The capacity to distinguish mechanically intact from proteoglycan-depleted tissue relative to the "reswelling" characteristic was first established, and the result was subsequently correlated with the NIR spectral data of the respective tissue samples. To achieve this, normal intact and enzymatically degraded samples were subjected to both NIR probing and mechanical compression based on a load-unload-reswelling protocol. The parameter δ(r), characteristic of the osmotic "reswelling" of the matrix after unloading to a constant small load in the order of the osmotic pressure of cartilage, was obtained for the different sample types. Multivariate statistics was employed to determine the degree of correlation between δ(r) and the NIR absorption spectrum of relevant specimens using Partial Least Squared (PLS) regression. The results show a strong relationship (R(2)=95.89%, p<0.0001) between the spectral data and δ(r). This correlation of δ(r) with NIR spectral data suggests the potential for determining the reswelling characteristics non-destructively. It was also observed that δ(r) values bear a significant relationship with the cartilage matrix integrity, indicated by its proteoglycan content, and can therefore differentiate between normal and artificially degraded proteoglycan-depleted cartilage samples. It is therefore argued that the reswelling of cartilage, which is both biochemical (osmotic) and mechanical (hydrostatic pressure) in origin, could be a strong candidate for characterizing the tissue, especially in regions surrounding focal cartilage defects in joints.

First steps towards modeling a multi-scale Earth system

Recent advances in computational geodynamics are applied to explore the link between Earth’s heat, its chemistry and its mechanical behavior. Computational thermal-mechanical solutions are now allowing us to understand Earth patterns by solving the basic physics of heat transfer. This approach is currently used to solve basic convection patterns of terrestrial planets. Applying the same methodology to smaller scales delivers promising similarities between observed and predicted structures which are often the site of mineral deposits. The new approach involves a fully coupled solution to the energy, momentum and continuity equations of the system at all scales, allowing the prediction of fractures, shear zones and other typical geological patterns out of a randomly perturbed initial state. The results of this approach are linking a global geodynamic mechanical framework over regional-scale mineral deposits down to the underlying micro-scale processes. Ongoing work includes the challenge of incorporating chemistry into the formulation.

Fabrication and microstructure of mechanically alloyed Mg-Al-Nd alloys

In this work, nanocrystalline Mg-Al-Nd alloys were fabricated using mechanical alloying method. Phase structure of the extrided rods was examined using X-ray diffraction (XRD) and the microstructures were observed using transmission electronic microscopy (TEM). High yield strength was obtained in the alloys with a high Nd content due to grain refinement and Nd rich precipitate phase.

Numerical investigation of motion and deformation of a single red blood cell in a stenosed capillary

It is generally assumed that influence of the red blood cells (RBCs) is predominant in blood rheology. The healthy RBCs are highly deformable and can thus easily squeeze through the smallest capillaries having internal diameter less than their characteristic size. On the other hand, RBCs infected by malaria or other diseases are stiffer and so less deformable. Thus it is harder for them to flow through the smallest capillaries. Therefore, it is very important to critically and realistically investigate the mechanical behavior of both healthy and infected RBCs which is a current gap in knowledge. The motion and the steady state deformed shape of the RBCs depend on many factors, such as the geometrical parameters of the capillary through which blood flows, the membrane bending stiffness and the mean velocity of the blood flow. In this study, motion and deformation of a single two-dimensional RBC in a stenosed capillary is explored by using smoothed particle hydrodynamics (SPH) method. An elastic spring network is used to model the RBC membrane, while the RBC's inside fluid and outside fluid are treated as SPH particles. The effect of RBC's membrane stiffness (kb), inlet pressure (P) and geometrical parameters of the capillary on the motion and deformation of the RBC is studied. The deformation index, RBC's mean velocity and the cell membrane energy are analyzed when the cell passes through the stenosed capillary. The simulation results demonstrate that the kb, P and the geometrical parameters of the capillary have a significant impact on the RBCs' motion and deformation in the stenosed section.

Photo-cross-linked poly(D,L-lactide)-based networks. Structural characterization by HR-MAS NMR spectroscopy and hydrolytic degradation behavior

To date, biodegradable networks and particularly their kinetic chain lengths have been characterized by analysis of their degradation products in solution. We characterize the network itself by NMR analysis in the solvent-swollen state under magic angle spinning conditions. The networks were prepared by photoinitiated cross-linking of poly(dl-lactide)−dimethacrylate macromers (5 kg/mol) in the presence of an unreactive diluent. Using diffusion filtering and 2D correlation spectroscopy techniques, all network components are identified. By quantification of network-bound photoinitiator fragments, an average kinetic chain length of 9 ± 2 methacrylate units is determined. The PDLLA macromer solution was also used with a dye to prepare computer-designed structures by stereolithography. For these networks structures, the average kinetic chain length is 24 ± 4 methacrylate units. In all cases the calculated molecular weights of the polymethacrylate chains after degradation are maximally 8.8 kg/mol, which is far below the threshold for renal clearance. Upon incubation in phosphate buffered saline at 37 °C, the networks show a similar mass loss profile in time as linear high-molecular-weight PDLLA (HMW PDLLA). The mechanical properties are preserved longer for the PDLLA networks than for HMW PDLLA. The initial tensile strength of 47 ± 2 MPa does not decrease significantly for the first 15 weeks, while HMW PDLLA lost 85 ± 5% of its strength within 5 weeks. The physical properties, kinetic chain length, and degradation profile of these photo-cross-linked PDLLA networks make them most suited materials for orthopedic applications and use in (bone) tissue engineering.

Interfacial debonding behavior of composite beam/plates with PZT patch

This paper studies interfacial debonding behavior of composite beams which include piezoelectric materials, adhesive and host beam. The focus is put on crack initiation and growth of the piezoelectric adhesive interface. Closed-form solutions of interface stresses and energy release rates are obtained for adhesive layer in the piezoelectric composite beams. Finite element analyses have been carried out to study the initiation and growth of interfaces crack for piezoelectric beams with interface element by ANSYS, in which the interface element of FE model is based on the cohesive zone models to characterize the fracture behavior of the interfacial debonding. The results have been compared with analystical solution, and the influence of different geometry and material parameters on the interfacial behavior of piezoelectric composite beams have been discussed.

Long-term effects of hydrogel properties on human chondrocyte behavior

Hydrogels provide a 3-dimensional network for embedded cells and offer promise for cartilage tissue engineering applications. Nature-derived hydrogels, including alginate, have been shown to enhance the chondrocyte phenotype but are variable and not entirely controllable. Synthetic hydrogels, including polyethylene glycol (PEG)-based matrices, have the advantage of repeatability and modularity; mechanical stiffness, cell adhesion, and degradability can be altered independently. In this study, we compared the long-term in vitro effects of different hydrogels (alginate and Factor XIIIa-cross-linked MMP-sensitive PEG at two stiffness levels) on the behavior of expanded human chondrocytes and the development of construct properties. Monolayer-expanded human chondrocytes remained viable throughout culture, but morphology varied greatly in different hydrogels. Chondrocytes were characteristically round in alginate but mostly spread in PEG gels at both concentrations. Chondrogenic gene (COL2A1, aggrecan) expression increased in all hydrogels, but alginate constructs had much higher expression levels of these genes (up to 90-fold for COL2A1), as well as proteoglycan 4, a functional marker of the superficial zone. Also, chondrocytes expressed COL1A1 and COL10A1, indicative of de-differentiation and hypertrophy. After 12 weeks, constructs with lower polymer content were stiffer than similar constructs with higher polymer content, with the highest compressive modulus measured in 2.5% PEG gels. Different materials and polymer concentrations have markedly different potency to affect chondrocyte behavior. While synthetic hydrogels offer many advantages over natural materials such as alginate, they must be further optimized to elicit desired chondrocyte responses for use as cartilage models and for development of functional tissue-engineered articular cartilage.

Application of machine learning in fault diagnostics of mechanical systems

A diagnostic method based on Bayesian Networks (probabilistic graphical models) is presented. Unlike conventional diagnostic approaches, in this method instead of focusing on system residuals at one or a few operating points, diagnosis is done by analyzing system behavior patterns over a window of operation. It is shown how this approach can loosen the dependency of diagnostic methods on precise system modeling while maintaining the desired characteristics of fault detection and diagnosis (FDD) tools (fault isolation, robustness, adaptability, and scalability) at a satisfactory level. As an example, the method is applied to fault diagnosis in HVAC systems, an area with considerable modeling and sensor network constraints.