Mechanical property determination of bone through nano- and micro-indentation testing and finite element simulation

Measurement of the mechanical properties of bone is important for estimating the stresses and strains exerted at the cellular level due to loading experienced on a macro-scale. Nano- and micro-mechanical properties of bone are also of interest to the pharmaceutical industry when drug therapies have intentional or non-intentional effects on bone mineral content and strength. The interactions that can occur between nano- and micro-indentation creep test condition parameters were considered in this study, and average hardness and elastic modulus were obtained as a function of indentation testing conditions (maximum load, load/unload rate, load-holding time, and indenter shape). The results suggest that bone reveals different mechanical properties when loading increases from the nano- to the micro-scale range (microN to N), which were measured using low- and high-load indentation testing systems. A four-parameter visco-elastic/plastic constitutive model was then applied to simulate the indentation load vs. depth response over both load ranges. Good agreement between the experimental data and finite element model was obtained when simulating the visco-elastic/plastic response of bone. The results highlight the complexity of bone as a biological tissue and the need to understand the impact of testing conditions on the measured results.     

Nanoindentation response of nickel surface using molecular dynamics simulation

The mechanisms of dislocation nucleation on a nickel (Ni) (001) surface under nanoindentation behaviours are investigated using molecular dynamics simulation. The characteristic mechanisms include the molecular models of a thermal layer (TL) and thermal with a free layer (TFL), multi-step load/unload cycles, tilt angles and shapes of the indenter, and slip vectors. The model of a TL has higher reaction force than a TFL. The maximum forces of nanoindentation decrease with increasing time of the multi-step load/unload cycle. The indenter with the tilt angle has larger force to act on the molecular model than the indenter along the normal direction. The effect of the indentation shape is presented such that the conical tip has larger load force to act on the molecular model. The defects along Shockley partials on the (111) plane are produced during nanoindentation involving nucleation, glide and slip.     

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

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

Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response

Anisotropy is one of the most peculiar aspects of cortical bone mechanical behaviour, and the numerical approach can be successfully used to investigate aspects of bone tissue mechanics that analytical methods solve in approximate way or do not cover. In this work, nanoindentation experimental tests and finite element simulations were employed to investigate the elastic-inelastic anisotropic mechanical properties of cortical bone. The model allows for anisotropic elastic and post-yield behaviour of the tissue. A tension-compression mismatch and direction-dependent yield stresses are allowed for. Indentation experiments along the axial and transverse directions were simulated with the purpose to predict the indentation moduli and hardnesses along multiple orientations. Results showed that the experimental transverse-to-axial ratio of indentation moduli, equal to 0.74, is predicted with a ～3% discrepancy regardless the post-yield material behaviour; whereas, the transverse-to-axial hardness ratio, equal to 0.86, can be correctly simulated (discrepancy ～6% w.r.t. the experimental results) only employing an anisotropic post-elastic constitutive model. Further, direct comparison between the experimental and simulated indentation tests evidenced a good agreement in the loading branch of the indentation curves and in the peak loads for a transverse-to-axial yield stress ratio comparable to the experimentally obtained transverse-to-axial hardness ratio. In perspective, the present work results strongly support the coupling between indentation experiments and FEM simulations to get a deeper knowledge of bone tissue mechanical behaviour at the microstructural level. The present model could be used to assess the effect of variations of constitutive parameters due to age, injury, and/or disease on bone mechanical performance in the context of indentation testing.     

Percussive Foraging: Stimuli for Prey Location by Aye-Ayes (Daubentonia madagascariensis)

Aye-ayes (Daubentonia madagascariensis) use the thin middle finger to tap on wood in search of subsurface cavities containing insect larvae. When a cavity is located, they gnaw away wood until the prey can be extracted. Previous researchers suggested that acoustical cues reveal cavity location. We designed five studies to identify the cavity features that provide acoustical cues. When cavities were backfilled with gelatin or acoustical foam, excavation was still successful, suggesting that the reverberation of sound in air-filled cavities is not necessary for detection. Moreover, when the density of cavity content was varied, there was no difference in excavation frequency. On the other hand, a one-dimensional break in the subsurface wood was an effective stimulus for excavation. These studies suggest that a simple interface beneath the surface is sufficient to elicit excavation and that neither prey nor cavity nor even small air pockets are necessary to elicit the behavior. These results raise provocative questions as to how the aye-aye manages to forage efficiently.     

Nanoindentation as a Probe of Nanoscale Residual Stresses: Atomistic Simulation Results

Abstract

Results from two sets of molecular dynamics simulations are reported. In the first set of simulations a nanoscale tip was used to indent single-crystal gold lattices subjected to external strains. These were carried out to explore possible relationships between nanoindentation curves and elastic properties of uniformly strained films. The changes in the slope of the loading curves reflect the stress state of the sample. In the second set of simulations the use of shallow nanoindentation for mapping nonuniform residual surface stress near a dislocation intersecting a surface was tested. Correlation between the maximum force on the tip and the initial local stresses at the point of indentation were observed. Preliminary atomistic simulations indicate that atomic-force microscopy can be used as a nondestructive, nanoscale probe of the surface stress distributions.     

The effect of holding time on nanoindentation measurements of creep in bone

Viscoelasticity may affect both the elastic and fracture characteristics of bone. Nanoindentation can be used to measure the creep behavior of bone by fitting the depth vs. time data at constant load to rheological models. However, the creep data may be influenced by latent effects arising during the loading phase of indentation. As such, the loading protocol, particularly the holding time, may affect the measured creep time constants. To characterize the effect of holding time on the measures, four cortical bone samples were prepared from four bovine femora and subjected to nanoindentation to measure the creep behavior. The creep time constants were found by fitting the indentation depth vs. time curve to three different rheological models: the standard linear solid, Burgers model, and a two-dashpot Kelvin model. All three models provided good fits to the data, which were relatively insensitive to the initial parameter estimates. The calculated creep time constants increased monotonically with increasing holding time for all three models. However, the relative differences between measurements within a single osteon, within a single sample, and between samples were maintained for creep holding times over 16s. Hence, while the creep time constants measured by nanoindentation with hold times up to 30s may not provide accurate property measurements, comparisons between samples are valid if all are assessed at the same holding time. Considering the long-term viscosity of bone tissue, Burgers model provided the best performance in terms of stability and goodness of fit, and is recommended for future studies.     

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.     

Kinetic analysis of root growth and georeaction

The kinetics of growth and georeaction of horizontal or vertical maize (cv. ORLA 264) apical root segments were analysed. Elongation and curvature data were fitted to a mathematical function and the effect of both light and decapitation reported. Elongation of horizontal segments was found to be more sensitive to light than to decapitation. A light treatment or the decapitation presented several effects on the shape of the growth curves. Growth of vertical segments was affected much more by decapitation than by light treatment. The shape of the curves was clearly different for decapitated and intact segments.
Curvature is affected both by light and decapitation but the shape of the bending curves is modified principally by decapitation.
Under the present conditions used, growth and georeaction of root segments do not seem to be strictly correlated.     

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.     

Simulation of bone strain by orthodontic implants using the finite element method]

Load direction of applied forces, implant geometry and other biomechanical parameters lead to varying reactions in the surrounding bone structure. Three types of endosseous implant measuring 9 mm in length and 3.3 mm in diameter with and without superperiosteal step, and a threaded surface were investigated with the aid of a finite element method using the COSMOS/M 2.5 program. The load on the implant was investigated under vertical, horizontal, and diagonal forces of between 0.01 N and 100 N. Vertical loading of simple implants caused bone deformation of more than 600 mu eps. The application of the superperiosteal step clearly reduced the deformation. The largest deformations under vertical loading were observed in the trabecular bone with all 3 implant geometries. On horizontal loading the deformation shifted from the trabecular to the cortical bone and was particularly marked at the transition between the two. The smallest deformations, less than 300 mu eps, were measured at implants with a superperiosteal step under diagonal loading. The thread did not improve loading capacity. Implants with a superperiosteal step are recommended since they contribute to more rapid healing and strengthening of the bone.     

Temperature Dependent Mechanical Property of PZT Film: An Investigation by Nanoindentation

Load-depth curves of an unpoled Lead Zirconate Titanate (PZT) film composite as a function of temperature were measured by nanoindentation technique. Its reduce modulus and hardness were calculated by the typical Oliver-Pharr method. Then the true modulus and hardness of the PZT film were assessed by decoupling the influence of substrate using methods proposed by Zhou et al. and Korsunsky et al., respectively. Results show that the indentation depth and modulus increase, but the hardness decreases at elevated temperature. The increasing of indentation depth and the decreasing of hardness are thought to be caused by the decreasing of the critical stress needed to excite dislocation initiation at high temperature. The increasing of true modulus is attributed to the reducing of recoverable indentation depth induced by back-switched domains. The influence of residual stress on the indentation behavior of PZT film composite was also investigated by measuring its load-depth curves with pre-load strains.     

A guest molecule-host cavity fitting algorithm to mine PDB for small molecule targets

Inhaled anesthetic molecule occupancy of a protein internal cavity depends in part on the volumes of the guest molecule and the host site. Current algorithms to determine volume and surface area of cavities in proteins whose structures have been determined and cataloged make no allowance for shape or small degrees of shape adjustment to accommodate a guest. We developed an algorithm to determine spheroid dimensions matching cavity volume and surface area and applied it to screen the cavities of 6,658 nonredundant structures stored in the Protein Data Bank (PDB) for potential targets of halothane (2-bromo-2-chloro-1,1,1-trifluoroethane). Our algorithm determined sizes of prolate and oblate spheroids matching dimensions of each cavity found. If those spheroids could accommodate halothane (radius 2.91 A) as a guest, we determined the packing coefficient. 394,766 total cavities were identified. Of 58,681 cavities satisfying the fit criteria for halothane, 11,902 cavities had packing coefficients in the range of 0.46-0.64. This represents 20.3% of cavities large enough to hold halothane, 3.0% of all cavities processed, and found in 2,432 protein structures. Our algorithm incorporates shape dependence to screen guest-host relationships for potential small molecule occupancy of protein cavities. Proteins with large numbers of such cavities are more likely to be functionally altered by halothane.     

Precision of nanoindentation protocols for measurement of viscoelasticity in cortical and trabecular bone

Nanoindentation has recently gained attention as a characterization technique for mechanical properties of biological tissues, such as bone, on the sub-micron level. However, optimal methods to characterize viscoelastic properties of bones are yet to be established. This study aimed to compare the time-dependent viscoelastic properties of bone tissue obtained with different nanoindentation methods. Bovine cortical and trabecular bone samples (n=8) from the distal femur and proximal tibia were dehydrated, embedded and polished. The material properties determined using nanoindentation were hardness and reduced modulus, as well as time-dependent parameters based on creep, loading-rate, dissipated energy and semi-dynamic testing under load control. Each loading protocol was repeated 160 times and the reproducibility was assessed based on the coefficient of variation (CV). Additionally, three well-characterized polymers were tested and CV values were calculated for reference.The employed methods were able to characterize time-dependent viscoelastic properties of bone. However, their reproducibility varied highly (CV 9–40%). The creep constant increased with increasing dwell time. The reproducibility was best with a 30 s creep period (CV 18%). The dissipated energy was stable after three repeated load cycles, and the reproducibility improved with each cycle (CV 23%). The viscoelastic properties determined with semi-dynamic test increased with increase in frequency. These measurements were most reproducible at high frequencies (CV 9–10%). Our results indicate that several methods are feasible for the determination of viscoelastic properties of bone material. The high frequency semi-dynamic test showed the highest precision within the tested nanoindentation protocols.     

On the nature of cavities on protein surfaces: application to the identification of drug-binding sites

In this article we introduce a new method for the identification and the accurate characterization of protein surface cavities. The method is encoded in the program SCREEN (Surface Cavity REcognition and EvaluatioN). As a first test of the utility of our approach we used SCREEN to locate and analyze the surface cavities of a nonredundant set of 99 proteins cocrystallized with drugs. We find that this set of proteins has on average about 14 distinct cavities per protein. In all cases, a drug is bound at one (and sometimes more than one) of these cavities. Using cavity size alone as a criterion for predicting drug-binding sites yields a high balanced error rate of 15.7%, with only 71.7% coverage. Here we characterize each surface cavity by computing a comprehensive set of 408 physicochemical, structural, and geometric attributes. By applying modern machine learning techniques (Random Forests) we were able to develop a classifier that can identify drug-binding cavities with a balanced error rate of 7.2% and coverage of 88.9%. Only 18 of the 408 cavity attributes had a statistically significant role in the prediction. Of these 18 important attributes, almost all involved size and shape rather than physicochemical properties of the surface cavity. The implications of these results are discussed. A SCREEN Web server is available at http://interface.bioc.columbia.edu/screen.     

Modeling and simulation of the mechanical response from nanoindentation test of DNA-filled viral capsids

Viruses can be described as biological objects composed mainly of two parts: a stiff protein shell called a capsid, and a core inside the capsid containing the nucleic acid and liquid. In many double-stranded DNA bacterial viruses (aka phage), the volume ratio between the liquid and the encapsidated DNA is approximately 1:1. Due to the dominant DNA hydration force, water strongly mediates the interaction between the packaged DNA strands. Therefore, water that hydrates the DNA plays an important role in nanoindentation experiments of DNA-filled viral capsids. Nanoindentation measurements allow us to gain further insight into the nature of the hydration and electrostatic interactions between the DNA strands. With this motivation, a continuum-based numerical model for simulating the nanoindentation response of DNA-filled viral capsids is proposed here. The viral capsid is modeled as large- strain isotropic hyper-elastic material, whereas porous elasticity is adopted to capture the mechanical response of the filled viral capsid. The voids inside the viral capsid are assumed to be filled with liquid, which is modeled as a homogenous incompressible fluid. The motion of a fluid flowing through the porous medium upon capsid indentation is modeled using Darcy’s law, describing the flow of fluid through a porous medium. The nanoindentation response is simulated using three-dimensional finite element analysis and the simulations are performed using the finite element code Abaqus. Force-indentation curves for empty, partially and completely DNA-filled capsids are directly compared to the experimental data for bacteriophage λ. Material parameters such as Young’s modulus, shear modulus, and bulk modulus are determined by comparing computed force-indentation curves to the data from the atomic force microscopy (AFM) experiments. Predictions are made for pressure distribution inside the capsid, as well as the fluid volume ratio variation during the indentation test.     

Nanostructure and nanomechanics of live Phaeodactylum tricornutum morphotypes

The ultrastructure and mechanical properties of the fusiform, triradiate and ovoid morphotypes of Phaeodactylum tricornutum were investigated using atomic force microscopy. Using topographic imaging, we showed that the surface of the ovoid form is rougher than those of the two other specimens, and coated with an outer layer of extracellular polymers. Using spatially resolved force–indentation curves, we found that the valve of the ovoid form is about five times stiffer (Young modulus of ∼500 kPa) than those of the other forms (∼100 kPa), a finding fully consistent with the fact that only the ovoid form has a silica valve, whereas the valves in the other two consist mostly of organic material. Notably, the girdle region of both fusiform and ovoid forms was five times softer than the valve, suggesting that this region is poor in silica and enriched in organic material. For the triradiate form, we showed the arms to be softer than the core region, presumably as a result of organelle localization. Last, we observed mucilaginous footprints of moderate stiffness (∼100 kPa) in the vicinity of ovoid diatoms, which we believe are secreted extracellular polymers.     

Roost characteristics as indicators for heterothermic behavior of forest-dwelling bats

Many forest-dwelling bats spend their diurnal inactivity period in tree cavities. During this time bats can save energy through heterothermy. A heterothermic response (torpor) is characterized by a lowered body temperature, reduced metabolic rate, and reduction of other physiological processes, and can be influenced by the microclimatic conditions of roost cavities. The thermal and physical characteristics of roosts used by the sympatric, ecologically, and morphologically similar bat species Myotis bechsteinii, M. nattereri, and Plecotus auritus were compared. These three species differ in their heterothermic behavior, with the lowest skin temperatures observed for P. auritus. Therefore, we hypothesized that roosts occupied by the three species should differ in roost characteristics and microclimatic conditions, whereby P. auritus should select colder and thermally less stable roosts. The results showed that horizontal depth of the cavity, diameter of the roost tree, and microclimatic conditions within roosts differed among species. Roosts of P. auritus had the lowest horizontal depth, lowest thermal stability, and lowest mean minimum roost temperatures. Height of the roost, diameter of the roost tree, and vertical depth were also shown to influence microclimatic conditions. With increasing diameter of the tree and increasing horizontal depth, mean minimum roost temperature increased and thermal stability improved. Furthermore, with ascending height above ground insulation and mean roost temperatures increased. Our results imply that species such as P. auritus, which use pronounced torpor as a primary energy saving strategy, prefer colder cavities that support their heterothermic strategy.