Examination of local variations in viscous, elastic, and plastic indentation responses in healing bone

Quality assessment of regenerated bone in intraosseous and intramuscular scaffolds by spectroscopy and nanoindentation

The efficiency of synthetic bone grafts can be evaluated either in osseous sites, to analyze osteoconduction or ectopically, in intramuscular or subcutaneous sites, to assess osteoinduction. Bone regeneration is usually evaluated in terms of the presence and quantity of newly formed bone, but little information is normally provided on the quality of this bone. Here, we propose a novel approach to evaluate bone quality by the combined use of spectroscopy techniques and nanoindentation. Calcium phosphate scaffolds with different architectures, either foamed or 3D-printed, that were implanted in osseous or intramuscular defects in Beagle dogs for 6 or 12 weeks were analyzed. ATR-FTIR and Raman spectroscopy were performed, and mineral-to-matrix ratio, crystallinity, and mineral and collagen maturity were calculated and mapped for the newly regenerated bone and the mature cortical bone from the same specimen. For all the parameters studied, the newly-formed bone showed lower values than the mature host bone. Hardness and elastic modulus were determined by nanoindentation and, in line with what was observed by spectroscopy, lower values were observed in the regenerated bone than in the cortical bone. While, as expected, all techniques pointed to an increase in the maturity of the newly-formed bone between 6 and 12 weeks, the bone found in the intramuscular samples after 12 weeks presented lower mineralization than the intraosseous counterparts. Moreover, scaffold architecture also played a role in bone maturity, with the foamed scaffolds showing higher mineralization and crystallinity than the 3D-printed scaffolds after 12 weeks.

Different Passive Viscoelastic Properties Between the Left and Right Ventricles in Healthy Adult Ovine

Ventricle dysfunction is the most common cause of heart failure, which leads to high mortality and morbidity. The mechanical behavior of the ventricle is critical to its physiological function. It is known that the ventricle is anisotropic and viscoelastic. However, the understanding of ventricular viscoelasticity is much less than that of its elasticity. Moreover, the left and right ventricles (LV&RV) are different in embryologic origin, anatomy, and function, but whether they distinguish in viscoelastic properties is unclear. We hypothesized that passive viscoelasticity is different between healthy LVs and RVs. Ex vivo cyclic biaxial tensile mechanical tests (1, 0.1, 0.01 Hz) and stress relaxation (strain of 3, 6, 9, 12, 15%) were performed for ventricles from healthy adult sheep. Outflow track direction was defined as the longitudinal direction. Hysteresis stress-strain loops and stress relaxation curves were obtained to quantify the viscoelastic properties. We found that the RV had more pronounced frequency-dependent viscoelastic changes than the LV. Under the physiological frequency (1 Hz), the LV was more anisotropic in the elasticity and stiffer than the RV in both directions, whereas the RV was more anisotropic in the viscosity and more viscous than the LV in the longitudinal direction. The LV was quasi-linear viscoelastic in the longitudinal but not circumferential direction, and the RV was nonlinear viscoelastic in both directions. This study is the first to investigate passive viscoelastic differences in healthy LVs and RVs, and the findings will deepen the understanding of biomechanical mechanisms of ventricular function.

Intrinsic properties of osteomalacia bone evaluated by nanoindentation and FTIRM analysis

Osteomalacia is a pathological bone condition consisting in a deficient primary mineralization of the matrix, leading to an accumulation of osteoid tissue and reduced bone mechanical strength. The amounts, properties and organization of bone constituents at tissue level, are known to influence its mechanical properties. It is then important to investigate the relationship between mechanical behavior and tissue composition at this scale in order to provide a better understanding of bone fragility mechanisms associates with this pathology. Our purpose was to analyze the links between ultra-structural properties and the mechanical behavior of this pathological bone tissue (osteomalacia) at tissue level (mineral and osteoid separately, or global). Four bone biopsies were taken from patients with osteomalacia, and subsequently embedded, sectioned, and polished. Then nanoindentation tests were performed to determine local elastic modulus E, contact hardness Hc and true hardness H for both mineralized and organic bone phases and for the global bone. The creep of the bone was also studied using a special indentation procedure in order to assess visco-elasto-plastic (creep) bone behavior. This allowed a detailed study of the rheological models adapted to the bone and to calculate the parameters associated to a Burgers model. Ultra-structural parameters were measured by Fourier Transform InfraRed Microspectroscopy (FTIRM) on the same position as the indents. The use of rheological models confirmed a significant contribution from the organic phase on the viscous character of bone tissue. The elastic E and the elasto-plastic H_c deformation were correlated to both collagen maturity and Mineral/Matrix. The pure plastic deformation H was only correlated to the mineral phase. Our data show that mineral phase greatly affects mechanical variables (moduli and viscosities) and that organic phase (as illustrated in osteoid tissue) may play an important role in the creep behavior of bone. In conclusion, this study brings mechanical and physicochemical values for osteoid and mineral phases.

The relationship of whole human vertebral body creep to geometric, microstructural, and material properties

Creep, the time dependent deformation of a structure under load, is an important viscoelastic property of bone and may play a role in the development of permanent deformity of the vertebrae in vivo leading to clinically observable spinal fractures. To date, creep properties and their relationship to geometric, microstructural, and material properties have not been described in isolated human vertebral bodies. In this study, a range of image-based measures of vertebral bone geometry, bone mass, microarchitecture and mineralization were examined in multiple regression models in an effort to understand their contribution to creep behavior. Several variables, such as measures of mineralization heterogeneity, average bone density, and connectivity density persistently appeared as significant effects in multiple regression models (adjusted r²: 0.17-0.56). Although further work is needed to identify additional tissue properties to fully describe the portion of variability not explained by these models, these data are expected to help understand mechanisms underlying creep and improve prediction of vertebral deformities that eventually progress to a clinically observable fracture.

Mechanical properties of bone tissues surrounding dental implant systems with different treatments and healing periods

OBJECTIVES

The objective of the current study was to examine whether the nanoindentation parameters can assess the alteration of bone quality resulting from different degrees of bone remodeling between bone tissue ages around the dental implant interface with different treatments and healing periods.

MATERIALS AND METHODS

Dental implants were placed in mandibles of six male dogs. Treatment groups included: resorbable blast media-treated titanium (Ti) implants, alumina-blasted zirconia implants (ATZ), alumina-blasted zirconia implants applied with demineralized bone matrix (ATZ-D), and alumina-blasted zirconia implants applied with rhBMP-2 (ATZ-B). Nanoindentation modulus (E), hardness (H), viscosity (η), and viscoelastic creep (Creep/P _max) were measured for new and old bone tissues adjacent to the implants at 3 and 6 weeks of post-implantation. A total of 945 indentations were conducted for 32 implant systems.

RESULTS

Significantly lower E, H, and η but higher Creep/P _max were measured for new bone tissues than old bone tissues, independent of treatments at both healing periods (p < 0.001). All nanoindentation parameters were not significantly different between healing periods (p > 0.568). ATZ-D and ATZ-B implants had the stiffer slope of correlation between E and Creep/P _max of the new bone tissue than Ti implant (p < 0.039).

CONCLUSIONS

Current results indicated that, in addition to elastic modulus and plastic hardness, measurement of viscoelastic properties of bone tissue surrounding the implant can provide more detailed information to understand mechanical behavior of an implant system.

CLINICAL RELEVANCE

Ability of energy absorption in the interfacial bone tissue can play a significant role in the long-term success of a dental implant system.

An inverse method for determining the spatially resolved properties of viscoelastic-viscoplastic three-dimensional printed materials

A method using experimental nanoindentation and inverse finite-element analysis (FEA) has been developed that enables the spatial variation of material constitutive properties to be accurately determined. The method was used to measure property variation in a three-dimensional printed (3DP) polymeric material. The accuracy of the method is dependent on the applicability of the constitutive model used in the inverse FEA, hence four potential material models: viscoelastic, viscoelastic–viscoplastic, nonlinear viscoelastic and nonlinear viscoelastic–viscoplastic were evaluated, with the latter enabling the best fit to experimental data. Significant changes in material properties were seen in the depth direction of the 3DP sample, which could be linked to the degree of cross-linking within the material, a feature inherent in a UV-cured layer-by-layer construction method. It is proposed that the method is a powerful tool in the analysis of manufacturing processes with potential spatial property variation that will also enable the accurate prediction of final manufactured part performance.

Characterization of the elastic and viscoelastic properties of dentin by a nanoindentation creep test

Dentin is the main supporting structure of teeth, but its mechanical properties may be adversely affected by pathological demineralization. The purposes of this study were to develop a quantitative approach to characterize the viscoelastic properties of dentin after de- and re-mineralization, and to examine the elastic properties using a nanoindentation creep test. Dentin specimens were prepared to receive both micro- and nano-indentation tests at wet and dry states. These tests were repeatedly performed after demineralization (1% citric acid for 3 days) and remineralization (artificial saliva immersion for 28 days). The nanoindentation test was executed in a creep mode, and the resulting displacement-time responses were disintegrated into primary (transient) and secondary (viscous) creep. The structural changes and mineral densities of dentin were also examined under SEM and microCT, respectively. The results showed that demineralization removed superficial minerals of dentin to the depth of 400 μm, and affected its micro- and nano-hardness, especially in the hydrate state. Remineralization only repaired the minerals at the surface layer, and partially recovered the nanohardness. Both the primary the secondary creep increased in the demineralized dentin, while the hydration further enhanced creep deformation of untreated and remineralized dentin. Remineralization reduced the primary creep of dentin, but did not effectively increase the viscosity. In conclusion, water plasticization increases the transient and viscous creep strains of demineralized dentin and reduces load sustainability. The nanoindentation creep test is capable of analyzing the elastic and viscoelastic properties of dentin, and reveals crucial information about creep responses.

Ultra-structural defects cause low bone matrix stiffness despite high mineralization in osteogenesis imperfecta mice

Bone is a complex material with a hierarchical multi-scale organization from the molecule to the organ scale. The genetic bone disease, osteogenesis imperfecta, is primarily caused by mutations in the collagen type I genes, resulting in bone fragility. Because the basis of the disease is molecular with ramifications at the whole bone level, it provides a platform for investigating the relationship between structure, composition, and mechanics throughout the hierarchy. Prior studies have individually shown that OI leads to: 1. increased bone mineralization, 2. decreased elastic modulus, and 3. smaller apatite crystal size. However, these have not been studied together and the mechanism for how mineral structure influences tissue mechanics has not been identified. This lack of understanding inhibits the development of more accurate models and therapies. To address this research gap, we used a mouse model of the disease (oim) to measure these outcomes together in order to propose an underlying mechanism for the changes in properties. Our main finding was that despite increased mineralization, oim bones have lower stiffness that may result from the poorly organized mineral matrix with significantly smaller, highly packed and disoriented apatite crystals. Using a composite framework, we interpret the lower oim bone matrix elasticity observed as the result of a change in the aspect ratio of apatite crystals and a disruption of the crystal connectivity.

Viscoelastic properties of human cortical bone tissue depend on gender and elastic modulus

Bone exhibits rate-dependent failure behavior, suggesting that viscoelasticity is a factor in the damage and fracture of bone. Microdamage initiates at scales below the macroscopic porosity in bone, and, as such, is affected by the intrinsic viscoelasticity of the bone tissue. The viscoelasticity of the bone tissue can be measured by nanoindentation and recording the creep behavior at constant load. The viscoelastic properties have been used to assess differences in tissue behavior with respect to fracture healing, aging, and mouse strains. In this study, we compared the viscoelastic behavior of human cortical bone between genders by using nanoindentation at a fixed load of 10 mN to measure the creep time constant. Bones from females had a significantly greater time constant, indicating slower creep and relaxation, than bones from males. The creep time constants decreased with increasing tissue modulus. The mineralization, collagen content, and collagen cross-link density, which were bulk measurements, were analyzed to determine if the differences in viscoelastic behavior were explained by compositional differences in the bone. However, none of the parameters differed between genders, nor were they correlated to the viscoelastic time constant. As such, the difference must depend on other matrix proteins that we did not assess or differences in the microstructural organization. This is one of the only intrinsic bone material properties that has been found to differ between males and females, and it may be important for assessing differences in fracture risk, since crack propagation is generally sensitive to viscoelastic properties.

Bone micromechanical properties are compromised during long-term alendronate therapy independently of mineralization

In the treatment of postmenopausal osteoporosis (PMOP), the use of alendronate (ALN) leads to a decrease in the risk of vertebral and nonvertebral fractures. To explore the possible adverse effects of prolonged ALN therapy, we studied the effects of 8 ± 2 years (6-10 years) of ALN treatment on the iliac cortical bone mineral and collagen quality and micromechanical properties; by design, our study examined these parameters, independent of the degree of mineralization. From six ALN-treated and five age-matched untreated PMOP women, 153 bone structural units have been chosen according their degree of mineralization to obtain the same distribution in each group. In those bone structural units, Fourier transform infrared spectroscopy, quantitative microradiography, and nanoindentation were used to assess bone quality. Irrespective of the degree of mineralization, ALN treatment was associated with higher collagen maturity (+7%, p < 0.001, c.v. = 13% and 16% in treated and untreated women, respectively) and lower mineral crystallinity than that observed in the untreated PMOP group (-2%, p < 0.0001, c.v. = 3% in both groups). Bone matrix from ALN-treated women also had lower elastic modulus (-12%, p < 0.0001, c.v. = 14% in both groups) and, contact hardness (-6%, p < 0.05, c.v. = 14% in both groups) than that of untreated women. Crystallinity (which reflects the size and perfection of crystals) was associated with both elastic modulus and contact hardness in treated women exclusively (r = 0.43 and r = 0.54, p < 0.0001, respectively), even after adjustment for the amount of mineral. We infer that long-term ALN treatment compromises micromechanical properties of the bone matrix as assessed ex vivo. The strength deficits are in part related to difference in crystallinity, irrespective of the mineral amount and mineral maturity. These novel findings at local levels of bone structure will have to be taken into account in the study of the pathophysiology of bone fragilities associated with prolonged ALN treatment.

Indentation experiments and simulation of ovine bone using a viscoelastic-plastic damage model

Indentation methods have been widely used to study bone at the micro- and nanoscales. It has been shown that bone exhibits viscoelastic behavior with permanent deformation during indentation. At the same time, damage due to microcracks is induced due to the stresses beneath the indenter tip. In this work, a simplified viscoelastic-plastic damage model was developed to more closely simulate indentation creep data, and the effect of the model parameters on the indentation curve was investigated. Experimentally, baseline and 2-year postovariectomized (OVX-2) ovine (sheep) bone samples were prepared and indented. The damage model was then applied via finite element analysis to simulate the bone indentation data. The mechanical properties of yielding, viscosity, and damage parameter were obtained from the simulations. The results suggest that damage develops more quickly for OVX-2 samples under the same indentation load conditions as the baseline data.

Direct comparison of nanoindentation and macroscopic measurements of bone viscoelasticity

Nanoindentation has become a standard method for measuring mechanical properties of bone, especially within microstructural units such as individual osteons or trabeculae. The use of nanoindentation to measure elastic properties has been thoroughly studied and validated. However, it is also possible to assess time dependent properties of bone by nanoindentation. The goal of this study was to compare time dependent mechanical properties of bone measured at the macroscopic level with those measured by nanoindentation. Twelve samples were prepared from the posterior distal femoral cortex of young cows. Initially, dogbone samples were prepared and subjected to torsional stress relaxation in a saline bath at 37 °C. A 5 mm thick disk was subsequently sectioned from the gage length, and subjected to nanoindentation. Nanoindentation was performed on hydrated samples using a standard protocol with 20 indents performed in 20 different osteons in each sample. Creep and stress relaxation data were fit to a Burgers four parameter rheological model, a five parameter generalized Maxwell model, and a three parameter standard linear solid. For Burgers viscoelastic model, the time constants measured by nanoindentation and torsion were weakly negatively correlated, while for the other two models the time constants were uncorrelated. The results support the notion that the viscoelastic behavior of bone at the macroscopic scale is primarily due to microstructural features, interfaces, or fluid flow, rather than viscous behavior of the bone tissue. As viscoelasticity affects the fatigue behavior of materials, the microscale properties may provide a measure of bone quality associated with initial damage formation.

Respective roles of organic and mineral components of human cortical bone matrix in micromechanical behavior: an instrumented indentation study

Bone is a multiscale composite material made of both a type I collagen matrix and a poorly crystalline apatite mineral phase. Due to remodeling activity, cortical bone is made of Bone Structural Units (BSUs) called osteons. Since osteon represents a fundamental level of structural hierarchy, it is important to investigate the relationship between mechanical behavior and tissue composition at this scale for a better understanding of the mechanisms of bone fragility. The aim of this study is to analyze the links between ultrastructural properties and the mechanical behavior of bone tissue at the scale of osteon. Iliac bone biopsies were taken from untreated postmenopausal osteoporotic women, embedded, sectioned and microradiographed to assess the degree of mineralization of bone (DMB). On each section, BSUs of known DMB were indented with relatively high load (~500 mN) to determine local elastic modulus (E), contact hardness (H(c)) and true hardness (H) of several bone lamellae. Crystallinity and collagen maturity were measured by Fourier Transform InfraRed Microspectroscopy (FTIRM) on the same BSUs. Inter-relationships between mechanical properties and ultrastructural components were analyzed using multiple regression analysis. This study showed that elastic deformation was only explained by DMB whereas plastic deformation was more correlated with collagen maturity. Contact hardness, reflecting both elastic and plastic behaviors, was correlated with both DMB and collagen maturity. No relationship was found between crystallinity and mechanical properties at the osteon level.

Biomechanical evaluation of regenerating long bone by nanoindentation

It is crucial to measure the mechanical function of regenerating bone in order to assess the mechanical performance of the regenerating portion as well as the efficiency of the regeneration methods. In this study, nanoindentation was applied to regenerating and intact rabbit ulnae to determine the material properties of hardness and elasticity; viscoelasticity was also investigated to precisely evaluate the material properties. Both intact and regenerating bones exhibited remarkable viscoelasticity manifested as a creep behavior during load hold at the maximum load, and the creep was significantly greater in the regenerating bone than the intact bone. The creep resulted in an overestimation of the hardness and Young's modulus. Hence, during nanoindentation testing of bones, the effect of creep should be eliminated. Moreover, the regenerating bone had lower hardness and Young's modulus than the intact bone. The nanoindentation technique proved to be a powerful approach for understanding the mechanical properties of regenerating bone.

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.

Indentation of Nonlinearly Viscoelastic Solids

Much recent attention has been focused on the indentation of linearly viscoelastic solids, and analysis techniques have been developed for polymeric material characterization. However, there has been relatively little progress made in the development of analytical approaches for indentation of nonlinearly viscoelastic materials. Soft biological tissues tend to exhibit responses which are nonlinearly viscoelastic and are frequently modeled using a decomposition of the relaxation or creep function into a product of two functions, one time-dependent and the other stress- or strain-level dependent. Consideration here is for soft biological tissue-like responses, exhibiting approximately quadratic stress-strain behavior, which can be alternatively cast as linear dependence of elastic modulus on strain level. An analytical approach is considered in the context of indentation problems with flat punch, spherical and conical indenter shapes. Hereditary integral expressions are developed and solved for typical indentation experimental conditions including indentation creep, load-relaxation and monotonic constant load- or displacement-rate tests. Primary emphasis is on the deconvolution of material and geometrical nonlinearities during an indentation experiment. The simple analytical expressions that result from this analysis can be implemented for indentation characterization of soft biological tissues without the need for computationally- intensive inverse finite element approaches.

Transplantation of human fetal blood stem cells in the osteogenesis imperfecta mouse leads to improvement in multiscale tissue properties

Osteogenesis imperfecta (OI or brittle bone disease) is a disorder of connective tissues caused by mutations in the collagen genes. We previously showed that intrauterine transplantation of human blood fetal stem/stromal cells in OI mice (oim) resulted in a significant reduction of bone fracture. This work examines the cellular mechanisms and mechanical bone modifications underlying these therapeutic effects, particularly examining the direct effects of donor collagen expression on bone material properties. In this study, we found an 84% reduction in femoral fractures in transplanted oim mice. Fetal blood stem/stromal cells engrafted in bones, differentiated into mature osteoblasts, expressed osteocalcin, and produced COL1a2 protein, which is absent in oim mice. The presence of normal collagen decreased hydroxyproline content in bones, altered the apatite crystal structure, increased the bone matrix stiffness, and reduced bone brittleness. In conclusion, expression of normal collagen from mature osteoblast of donor origin significantly decreased bone brittleness by improving the mechanical integrity of the bone at the molecular, tissue, and whole bone levels.

Relationships of Viscosity With Contact Hardness and Modulus of Bone Matrix Measured by Nanoindentation

Creep is an active form of time-dependent viscoelastic deformation that occurs in bone tissue during daily life. Recent findings indicate bone mineralization, which is involved in determining the elastic and plastic properties of bone matrix, can also contribute in controlling its viscoelastic property. Nanoindentation viscosity was used as a direct measure for the capacity of a material to resist viscous-like flow under loading. The objectives of this study were to examine (1) whether the nanoindentation viscosity obtained using the traditional viscoelastic Voigt model can describe creep response of bone matrix and (2) how the nanoindentation viscosity is related to contact hardness and elastic modulus. The Voigt model accurately described the creep behavior of bone matrix (r2>0.96, p<0.001). The nanoindentation viscosity had strong relationships with nanoindentation contact hardness (r2=0.94, p<0.001) and modulus (r2=0.83, p<0.001) independent of tissue ages of osteonal bone matrix. The strong positive relationships of nanoindentation viscosity with contact hardness and modulus can be interpreted as increases in the mineral portion of bone matrix may limit the interfibril motion of collagen while enhancing the mechanical stability of bone. We suggest that previous nanoindentation results can be reanalyzed to characterize the viscoelastic creep using the Voigt model.

A practical guide for analysis of nanoindentation data

Mechanical properties of biological materials are increasingly explored via nanoindentation testing. This paper reviews the modes of deformation found during indentation: elastic, plastic, viscous and fracture. A scheme is provided for ascertaining which deformation modes are active during a particular indentation test based on the load-displacement trace. Two behavior maps for indentation are presented, one in the viscous-elastic-plastic space, concerning homogeneous deformation, and one in the plastic versus brittle space, concerning the transition to fracture behavior when the threshold for cracking is exceeded. Best-practice methods for characterizing materials are presented based on which deformation modes are active; the discussion includes both nanoindentation experimental test options and appropriate methods for analyzing the resulting data.