The role of mineral content in determining the micromechanical properties of discrete trabecular bone remodeling packets

In trabecular bone, each remodeling event results in the resorption and/or formation of discrete structural units called ‘packets’. These remodeling packets represent a fundamental level of bone’s structural hierarchy at which to investigate composition and mechanical behaviors. The objective of this study was to apply the complementary techniques of quantitative backscattered electron microscopy (qBSEM) and nanoindentation to investigate inter-relationships between packet mineralization, elastic modulus, contact hardness and plastic deformation resistance. Indentation arrays were performed across nine trabecular spicules from 3 human donors; these spicules were then imaged using qBSEM, and discretized into their composite remodeling packets (127 in total). Packets were classified spatially as peripheral or central, and mean contact hardness, plastic deformation resistance, elastic modulus and calcium content calculated for each. Inter-relationships between measured parameters were analysed using linear regression analyses, and dependence on location assessed using Student’s t-tests. Significant positive correlations were found between all mechanical parameters and calcium content. Elastic modulus and contact hardness were significantly correlated, however elastic modulus and plastic deformation resistance were not. Calcium content, contact hardness and elastic modulus were all significantly higher for central packets than for peripheral, confirming that packet mineral content contributes to micromechanical heterogeneity within individual trabecular spicules. Plastic deformation resistance, however, showed no such regional dependence, indicating that the plastic deformation properties in particular, are determined not only by mineral content, but also by the organic matrix and interactions between these two components.     

Mechanical behavior of intact and low-grade degenerated cartilage.

Young's modulus, elastic and plastic deformation, mechanical hardness and load at failure were determined for low-grade degenerated hyaline cartilage in a porcine model. Osteochondral plugs from the medial condyle of 30 female pigs were used. Cartilage defects were classified using the International Cartilage Repair Society (ICRS) protocol. Mechanical hardness was measured using a Shore A testing device. Total stiffness and plastic deformation was evaluated in the range 50-200 N using a 5-mm indenter. The load at failure was then determined. ICRS grade I specimens showed significantly lower stiffness than grade 0 specimens. ICRS grade 0 specimen showed no significant plastic deformation within the load range 25-100 N. In degenerated cartilage, plastic deformation started at a significantly lower load (50 N). The Young's modulus at 25 N in ICRS grade 0 specimens (18.8 MPa) was significantly higher than in grade I (11.1 MPa) or grade II (10.5 MPa) specimens. Intact cartilage showed significantly higher tension at failure and mechanical Shore A hardness. Young's modulus and tension at failure showed strong correlation. Cartilage degeneration is associated with a significant loss of elasticity and mechanical stress resistance. Shore hardness measurement is an adequate method for rapid biomechanical evaluation of cartilage specimens.     

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.     

Elastic energy storage in unmineralized and mineralized extracellular matrices (ECMs): a comparison between molecular modeling and experimental measurements

In order to facilitate locomotion and limb movement many animals store energy elastically in their tendons. In the turkey, much of the force generated by the gastrocnemius muscle is stored as elastic energy during tendon deformation and not within the muscle. As limbs move, the tendons are strained causing the collagen fibers in the extracellular matrices to be strained. During growth, avian tendons mineralize in the portions distal to the muscle and show increased tensile strength, modulus, and energy stored per unit strain as a result. In this study the energy stored in unmineralized and mineralized collagen fibers was measured and compared to the amount of energy stored in molecular models. Elastic energy storage values calculated using the molecular model were slightly higher than those obtained from collagen fibers, but display the same increases in slope as the fiber data. We hypothesize that these increases in slope are due to a change from the stretching of flexible regions of the collagen molecule to the stretching of less flexible regions. The elastic modulus obtained from the unmineralized molecular model correlates well with elastic moduli of unmineralized collagen from other studies. This study demonstrates the potential importance of molecular modeling in the design of new biomaterials.     

Progressive post-yield behavior of human cortical bone in compression for middle-aged and elderly groups

In this study, a progressive loading regimen (load–dwell–unloading–dwell–reloading) was applied on bone samples to examine the compressive post-yield response of bone at increasing strain levels. Cortical bone specimens from human tibiae of two age groups (middle-aged group: 53±2 years, 4 females and 4 males, elderly group: 83±6 years, 4 females and 4 males) were loaded in compression using the progressive loading scheme. Modulus degradation, plastic deformation, viscous response, and energy dissipation of bone during post-yield deformation were assessed. Although initial modulus was not significantly different between the two age groups, the degradation of modulus with the applied strain in the elderly group was faster than in the middle-aged group. The modulus loss (or microdamage accumulation) of bone occurred prior to plastic deformation. Plastic strain had a similar linear relationship with the applied strain for both middle-aged and the elderly group although middle-aged bone yielded at a greater strain. The viscoelastic time constant changed similarly with increasing strain for the two groups, whereas a higher magnitude of stress relaxation was observed in the middle-aged group. Energy dissipation was investigated through three pathways: elastic release strain energy, hysteresis energy, and plastic strain energy. The middle-aged group had significantly greater capacity of energy dissipation than the elderly group in all three pathways. The information obtained may provide important insights in age-related effects on bone fragility.     

Influence of microstructure on deformation anisotropy of mineralized cuticle from the lobster Homarus americanus

The exoskeleton of the American lobster Homarus americanus is a hierarchically organized nano-composite material consisting of organic chitin-protein fibers associated with inorganic calcium carbonate. The presence of a well-developed and periodically arranged pore canal system leads to a honeycomb-like structure. The concomitant presence of the twisted plywood arrangement of the mineralized chitin-protein fibers alters the elastic properties, the deformation behavior, and fracture behavior compared to classical honeycomb structures. By performing compression tests in various directions of the cuticle we examined the anisotropic elastic-plastic deformation and fracture behavior of mineralized parts of the exoskeleton. By applying digital image correlation during compression testing, the evolution of the elastic-plastic deformation at the microscopic scale was observed with high resolution and simultaneously global stress and strain data were acquired. Shear tests were performed in order to determine the fracture energy for different shear planes and directions. The investigation of the microstructure after plastic deformation revealed the underlying deformation mechanisms of lobster endocuticle from the claws under different loading conditions. For evaluating the effect of hydration the samples were tested both in the dry and in the wet state.     

ORAL ASSESSMENT OF HARDNESS BETWEEN ELASTIC AND PLASTIC PRODUCTS

This study examined how people compare the hardness of different materials. Simple models with either elastic or plastic behavior were prepared and controlled mechanically. Six elastomers were compared to 29 plastic dental waxes of different hardness. For each elastic sample, a psychophysical staircase method was used to determine its perceived hardness in comparison to the plastic samples. Single bites were performed and the forces were recorded by a small load-cell placed between the sample and the teeth. Nine subjects. free of dental pathology, participated in this study. Subjects were able to match samples of both materials with a specific stress ratio which depended on the hardness of the elastic samples. Results indicated that people do not use the same sensory cues and, in this case, no clear role of the bite force was established.     

Br-rich tips of calcified crab claws are less hard but more fracture resistant: A comparison of mineralized and heavy-element biological materials

We find that the spoon-like tips of the chelipeds (large claws) of the crab Pachygrapsus crassipes differ from the rest of the claw in that they are not calcified, but instead contain about 1% bromine—thus they represent a new example of a class of structural biological materials that contain heavy elements such as Zn, Mn, Fe, Cu, and Br bound in an organic matrix. X-ray absorption spectroscopy data suggest that the bromine is bound to phenyl rings, possibly in tyrosine. We measure a broad array of mechanical properties of a heavy-element biological material for the first time (abrasion resistance, coefficient of kinetic friction, energy of fracture, hardness, modulus of elasticity and dynamic mechanical properties), and we make a direct comparison with a mineralized tissue. Our results suggest that the greatest advantage of bromine-rich cuticle over calcified cuticle is resistance to fracture (the energy of fracture is about an order of magnitude greater than for calcified cuticle). The greatest advantage relative to unenriched cuticle, represented by ant mandible cuticle, is a factor of about 1.5 greater hardness and modulus of elasticity. The spoon-like tips gain additional fracture resistance from the orientation of the constituent laminae and from the viscoelasticity of the material. We suggest that fracture resistance is of greater importance in smaller organisms, and we speculate that one function of heavy elements in structural biological materials is to reduce molecular resonant frequencies and thereby increase absorption of energy from impacts.     

Effects of age on elastic moduli of human lungs.

The model of the lung as an elastic continuum undergoing small distortions from a uniformly inflated state has been used to describe many lung deformation problems. Lung stress-strain material properties needed for this model are described by two elastic moduli: the bulk modulus, which describes a uniform inflation, and the shear modulus, which describes an isovolume deformation. In this study we measured the bulk modulus and shear modulus of human lungs obtained at autopsy at several fixed transpulmonary pressures (Ptp). The bulk modulus was obtained from small pressure-volume perturbations on different points of the deflation pressure-volume curve. The shear modulus was obtained from indentation tests on the lung surface. The results indicated that, at a constant Ptp, both bulk and shear moduli increased with age, and the increase was greater at higher Ptp values. The micromechanical basis for these changes remains to be elucidated.     

Elastic characterization of transversely isotropic soft materials by dynamic shear and asymmetric indentation

The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isotropic soft material. A soft gel with controlled anisotropy was obtained by polymerizing a mixture of fibrinogen and thrombin solutions in a high field magnet (B?=?11.7 T); fibrils in the resulting gel were predominantly aligned parallel to the magnetic field. Aligned fibrin gels were subject to dynamic (20-40 Hz) shear deformation in two orthogonal directions. The shear storage modulus was 1.08?±?0. 42 kPa (mean?±?std. dev.) for shear in a plane parallel to the dominant fiber direction, and 0.58?±?0.21 kPa for shear in the plane of isotropy. Gels were indented by a rectangular tip of a large aspect ratio, aligned either parallel or perpendicular to the normal to the plane of transverse isotropy. Aligned fibrin gels appeared stiffer when indented with the long axis of a rectangular tip perpendicular to the dominant fiber direction. Three-dimensional numerical simulations of asymmetric indentation were used to determine the relationship between direction-dependent differences in indentation stiffness and material parameters. This approach enables the estimation of a complete set of parameters for an incompressible, transversely isotropic, linear elastic material.     

Nanoindentation and whole-bone bending estimates of material properties in bones from the senescence accelerated mouse SAMP6

The senescence accelerated mouse, strain P6 (SAMP6) has been described as a model of senile osteoporosis. Recent results from whole-bone bending tests indicate that, despite having increased moments of inertia, SAMP6 long bones are weak and brittle compared to SAMR1 controls. In the current study we determined material properties of cortical bone from SAMP6 and SAMR1 femora and tibiae by two methods-nanoindentation and whole-bone bending tests combined with simple beam theory. We hypothesized that: (1) SAMP6 mice have reduced cortical bone material properties compared to SAMR1 controls; and (2) modulus estimated from whole-bone bending tests correlates well with modulus determined by nanoindentation. Results from nanoindentation indicated that modulus and hardness are approximately 10% higher in SAMP6 mice compared to SAMR1 controls (p<0.001), a finding consistent with slightly higher mineralization in SAMP6 bones. Despite their superior elastic and hardness properties, the bending failure properties of SAMP6 bones were markedly inferior--ultimate stress and toughness were reduced by 40% and 60%, respectively (p<0.001). Comparisons between the two testing methods for determining modulus showed poor agreement. Modulus estimated from whole-bone bending tests was not correlated with modulus determined by nanoindentation (p=0.054; r2=0.03) and the absolute values differed by a factor of five between the two methods (bending [wet], 6GPa; nanoindentation [dry], 31GPa). Moreover, relative differences between groups were inconsistent between the two methods. We conclude: (1) cortical bone from the SAMP6 mouse has increased modulus and hardness but poor material strength and toughness, which underscores the relevance of the SAMP6 mouse for studies of skeletal fragility, and (2) values of elastic modulus of bone tissue estimated using simple beam theory and bending tests of mouse femora and tibiae are inaccurate and should be interpreted with caution.     

Stress wave velocities in bovine patellar tendon.

The velocity of longitudinal stress waves in an elastic body is given by the square root of the ratio of its elastic modulus to its density. In tendinous and ligamentous tissue, the elastic modulus increases with strain and with strain rate. Therefore, it was postulated that stress wave velocity would also increase with increasing strain and strain rate. The purpose of this study was to determine the velocity of stress waves in tendinous tissue as a function of strain and to compare these values to those predicted using the elastic modulus derived from quasi-static testing. Five bovine patellar tendons were harvested and potted as bone-tendon-bone specimens. Quasi-static mechanical properties were determined in tension at a deformation rate of 100 mm/s. Impact loading was employed to determine wave velocity at various strain levels, achieved by preloading the tendon. Following impact, there was a measurable delay in force transmission across the specimen and this delay decreased with increasing tendon strain. The wave velocities at tendon strains of 0.0075, 0.015, and 0.0225 were determined to be 260 +/- 52 m/s, 360 +/- 71 m/s, and 461 +/- 94 m/s, respectively. These velocities were significantly (p < 0.01) faster than those predicted using elastic moduli derived from the quasi-static tests by 52, 45, and 41 percent, respectively. This study has documented that stress wave velocity in patellar tendon increases with increasing strain and is underestimated with a modulus estimated from quasi-static testing.     

The temperature dependence of the deformation of bone

The deformation characteristics of compact bone have been measured as a function of temperature in the range from −58 to 90°C. At temperatures below 25°C elastic, anelastic and plastic contributions to the strain could be distinguished. The Young's modulus increased as the temperature was reduced, while the nonelastic component was approximately independent of temperature. An interpretation of these results is made in terms of an idealised hydroxyapatite-collagen composite. At temperatures higher than 50°C the deformation was compounded by non-equilibrium recovery and an irreversible change in the structure of bone.     

Sensitivity analysis and parametric study of elastic properties of an unidirectional mineralized bone fibril-array using mean field methods

The key parameters determining the elastic properties of an unidirectional mineralized bone fibril-array decomposed in two further hierarchical levels are investigated using mean field methods. Modeling of the elastic properties of mineralized micro- and nanostructures requires accurate information about the underlying topology and the constituents’ material properties. These input data are still afflicted by great uncertainties and their influence on computed elastic constants of a bone fibril-array remains unclear. In this work, mean field methods are applied to model mineralized fibrils, the extra-fibrillar matrix and the resulting fibril-array. The isotropic or transverse isotropic elastic constants of these constituents are computed as a function of degree of mineralization, mineral distribution between fibrils and extra-fibrillar matrix, collagen stiffness and fibril volume fraction. The linear sensitivity of the elastic constants was assessed at a default set of the above parameters. The strain ratios between the constituents as well as the axial and transverse indentation moduli of the fibril-array were calculated for comparison with experiments. Results indicate that the degree of mineralization and the collagen stiffness dominate fibril-array elasticity. Interestingly, the stiffness of the extra-fibrillar matrix has a strong influence on transverse and shear moduli of the fibril-array. The axial strain of the intra-fibrillar mineral platelets is 30–90% of the applied fibril strain, depending on mineralization and collagen stiffness. The fibril-to-fibril-array strain ratio is essentially ~1. This study provides an improved insight in the parameters, which govern the fibril-array stiffness of mineralized tissues such as bone.     

Effects of non-linearity on cell–ECM interactions

Filamentous biopolymers such as F-actin, vimentin, fibrin and collagen that form networks within the cytoskeleton or the extracellular matrix have unusual rheological properties not present in most synthetic soft materials that are used as cell substrates or scaffolds for tissue engineering. Gels formed by purified filamentous biopolymers are often strain stiffening, with an elastic modulus that can increase an order of magnitude at moderate strains that are relevant to cell and tissue deformation in vivo. This review summarizes some experimental studies of non-linear rheology in biopolymer gels, discusses possible molecular mechanisms that account for strain stiffening, and explores the possible relevance of non-linear rheology to the interactions between cell and extracellular matrices.     

A model for predicting growth responses in plants to changes in external water potential: Zea mays primary roots

In response to osmotic step changes, three distinct phases have been noted in the growth response of Zea mays primary roots. They are cessation or slowing of growth over a period of 15–20 minutes, tissue contraction, and a damped oscillatory return to nearly normal growth rate, all within a period of about one hour. A system model of the tissue response is presented to explain such behavior and to serve in a predictive capacity to govern future experiments.It is supposed that for turgor pressure in excess of a cell wall yield threshold, plastic flow is the major component of wall deformation, and that when turgor falls below yield threshold, elastic deformation is dominant. The equations of the model describe growth rate as a function of time in terms of the following properties; plastic flow, elastic deformation, permeability to water, and solute uptake. They are derived from basic equations of feedback interactions between internal osmotic pressure and growth rate, and between wall softening, turgor and growth rate.The model predicts oscillatory growth rate regulation, and phase and amplitude relationships between turgor pressure and growth rate. The simplest model which accounts for all observations is that of biphasic deformation, two modes of wall softening, and a dual feedback system involving osmotic and yield threshold control of growth rate.It should be noted that to predict the time course of turgor pressure, osmotic pressure, yield pressure, and growth rate, two initial conditions and six system parameter values are sufficient. So far only the initial values of growth rate and its derivative can be obtained for Zea mays primary roots. However, values for wall softening and hardening coefficients (including the strain and turgor independent component), plastic extensibility, water permeability and dilution rate coefficients have not been obtained as yet for Zea roots. Values for some of these parameters have been obtained for other roots, coleoptiles, and giant algal cells.Lest the reader despair, it should be pointed out that experimental observations coupled with simulation studies will help establish restricted ranges of values that the system parameters might assume. These can then be compared with known values in the literature and values experimentally obtained in the future.     

Analytical and numerical analysis of human dental occlusal contact

The knowledge of contact forces in teeth surfaces during mastication or para-functional movements can help to understand processes related to friction and wear of human dental enamel. The development of a numerical model for analysis of the occlusal contact between two antagonistic teeth is proposed, which includes three basic steps: the characterisation of the surface roughness, its homogenisation using an assumed distribution function and the numerical determination of the resulting forces. Finite element strain results for the main different asperities are statistically combined, deriving the predicted macroscopic behaviour of the interface. Axisymmetric and 3D numerical models with an elasto-plastic constitutive law are used to simulate micro-indentations and micro-contacts, respectively. The contact is allowed to occur locally in planes not necessarily parallel to the surface's mean plane, a problem for which there is no analytical solution. The three identified parameters, homogenised surface hardness (3.68 GPa), surface yield stress (3.08 GPa) and static friction coefficient (0.23), agree with the experimental values reported in the literature.     

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.     

Osteoblast response to the elastic strain of metallic support

It is known that metallic elements of joint endoprostheses undergo elastic strain due to their mechanical function. This is one of the factors which may be responsible for the loosening of endoprostheses. Since mechanisms involved in it remain unclear, it seems valuable to verify if cells responsible for bone regeneration are affected by a strain of the implant. Our experiment examines the influence of elastic strain applied to Ti6Al4V samples on osteoblasts cultured on their surface in vitro. Human bone-derived cells are observed in contact with metallic plates. Titanium alloy was chosen as a support since it is one of the most commonly used materials for stems in joint endoprostheses. Cyclic elastic deformation of 0.1% was applied to the support once daily for 7 days. Two thousand cycles were applied each time. Samples which were not subject to strain served as control. After the observation period XTT assay was performed, alkaline phosphatase activity as well as osteocalcin concentration and nitric oxide secretion were determined and compared with the results obtained in the control group. It was found that the number of viable cells in the mechanically stimulated population was significantly higher than in control, while both alkaline phosphatase activity and osteocalcin concentration were significantly lower in the experimental group. Nitric oxide secretion was found in the culture which was subject to elastic strain, but not in the control. The possible clinical implication is that elastic strain of the metallic endoprostheses may influence osteoblasts which are in contact with the implant in vivo.     

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

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