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.     

Post-yield nanomechanics of human cortical bone in compression using synchrotron X-ray scattering techniques

The ultrastructural response to applied loads governs the post-yield deformation and failure behavior of bone, and is correlated with bone fragility fractures. Combining a novel progressive loading protocol and synchrotron X-ray scattering techniques, this study investigated the correlation of the local deformation (i.e., internal strains of the mineral and collagen phases) with the bulk mechanical behavior of bone. The results indicated that the internal strains of the longitudinally oriented collagen fibrils and mineral crystals increased almost linearly with respect to the macroscopic strain prior to yielding, but markedly decreased first and then gradually leveled off after yielding. Similar changes were also observed in the applied stress before and after yielding of bone. However, the collagen to mineral strain ratio remained nearly constant throughout the loading process. In addition, the internal strains of longitudinal mineral and collagen phases did not exhibit a linear relationship with either the modulus loss or the plastic deformation of bulk bone tissue. Finally, the time-dependent response of local deformation in the mineral phase was observed after yielding. Based on the results, we speculate that the mineral crystals and collagen fibrils aligned with the loading axis only partially explain the post-yield deformation, suggesting that shear deformation involving obliquely oriented crystals and fibrils (off axis) is dominant mechanism of yielding for human cortical bone in compression.     

Probabilistic failure analysis of bone using a finite element model of mineral–collagen composites

Microdamage accumulation is a major pathway for energy dissipation during the post-yield deformation of bone. In this study, a two-dimensional probabilistic finite element model of a mineral–collagen composite was developed to investigate the influence of the tissue and ultrastructural properties of bone on the evolution of microdamage from an initial defect in tension. The probabilistic failure analyses indicated that the microdamage progression would be along the plane of the initial defect when the debonding at mineral–collagen interfaces was either absent or limited in the vicinity of the defect. In this case, the formation of a linear microcrack would be facilitated. However, the microdamage progression would be scattered away from the initial defect plane if interfacial debonding takes place at a large scale. This would suggest the possible formation of diffuse damage. In addition to interfacial debonding, the sensitivity analyses indicated that the microdamage progression was also dependent on the other material and ultrastructural properties of bone. The intensity of stress concentration accompanied with microdamage progression was more sensitive to the elastic modulus of the mineral phase and the nonlinearity of the collagen phase, whereas the scattering of failure location was largely dependent on the mineral to collagen ratio and the nonlinearity of the collagen phase. The findings of this study may help understanding the post-yield behavior of bone at the ultrastructural level and shed light on the underlying mechanism of bone fractures.     

The relative contributions of non-enzymatic glycation and cortical porosity on the fracture toughness of aging bone

The risk of fracture increases with age due to the decline of bone mass and bone quality. One of the age-related changes in bone quality occurs through the formation and accumulation of advanced glycation end-products (AGEs) due to non-enzymatic glycation (NEG). However as a number of other changes including increased porosity occur with age and affect bone fragility, the relative contribution of AGEs on the fracture resistance of aging bone is unknown. Using a high-resolution nonlinear finite element model that incorporate cohesive elements and micro-computed tomography-based 3d meshes, we investigated the contribution of AGEs and cortical porosity on the fracture toughness of human bone. The results show that NEG caused a 52% reduction in propagation fracture toughness (R-curve slope). The combined effects of porosity and AGEs resulted in an 88% reduction in propagation toughness. These findings are consistent with previous experimental results. The model captured the age-related changes in the R-curve toughening by incorporating bone quantity and bone quality changes, and these simulations demonstrate the ability of the cohesive models to account for the irreversible dynamic crack growth processes affected by the changes in post-yield material behavior. By decoupling the matrix-level effects due to NEG and intracortical porosity, we are able to directly determine the effects of NEG on fracture toughness. The outcome of this study suggests that it may be important to include the age-related changes in the material level properties by using finite element analysis towards the prediction of fracture risk.     

Prediction of microdamage formation using a mineral-collagen composite model of bone

Age-related changes in bone quality are mainly manifested in the reduced toughness. Since the post-yield deformation of bone is realized through microdamage formation (e.g., microcracking and diffuse damage), it is necessary to understand the mechanism of microdamage formation in bone in order to elucidate underlying mechanisms of age-related bone fractures. In this study, a two-dimensional shear lag model was developed to predict stress concentration fields around an initial crack in a mineral-collagen composite. In this model, non-linear elasticity was assumed for the collagen phase, and linear elasticity for the mineral. Based on the pattern of the stress concentration fields, the condition for microdamage formation was discussed. The results of our analyses indicate that: (1) an initial crack formed in mineral phase may cause stress concentration in the adjacent mineral layers; (2) the pattern of stress concentration fields depends not only on the spatial but also mechanical properties of the collagen and mineral phases; (3) the pattern of the stress concentration fields could determine either coalescence or scattering of nano cracks around the initial crack.     

Raloxifene Prevents Skeletal Fragility in Adult Female Zucker Diabetic Sprague-Dawley Rats

Fracture risk in type 2 diabetes is increased despite normal or high bone mineral density, implicating poor bone quality as a risk factor. Raloxifene improves bone material and mechanical properties independent of bone mineral density. This study aimed to determine if raloxifene prevents the negative effects of diabetes on skeletal fragility in diabetes-prone rats. Adult Zucker Diabetic Sprague-Dawley (ZDSD) female rats (20-week-old, n = 24) were fed a diabetogenic high-fat diet and were randomized to receive daily subcutaneous injections of raloxifene or vehicle for 12 weeks. Blood glucose was measured weekly and glycated hemoglobin was measured at baseline and 12 weeks. At sacrifice, femora and lumbar vertebrae were harvested for imaging and mechanical testing. Raloxifene-treated rats had a lower incidence of type 2 diabetes compared with vehicle-treated rats. In addition, raloxifene-treated rats had blood glucose levels significantly lower than both diabetic vehicle-treated rats as well as vehicle-treated rats that did not become diabetic. Femoral toughness was greater in raloxifene-treated rats compared with both diabetic and non-diabetic vehicle-treated ZDSD rats, due to greater energy absorption in the post-yield region of the stress-strain curve. Similar differences between groups were observed for the structural (extrinsic) mechanical properties of energy-to-failure, post-yield energy-to-failure, and post-yield displacement. These results show that raloxifene is beneficial in preventing the onset of diabetes and improving bone material properties in the diabetes-prone ZDSD rat. This presents unique therapeutic potential for raloxifene in preserving bone quality in diabetes as well as in diabetes prevention, if these results can be supported by future experimental and clinical studies.     

Constitutive relationship of tissue behavior with damage accumulation of human cortical bone

Microdamage accumulation has been identified as a major conduit for bone tissues to absorb fracture energy. Due to the poor understanding of its underlying mechanism, however, an adequate constitutive relationship between damage accumulation and the mechanical behavior of bone has not yet been established. In this study, the constitutive relationship between the damage accumulation induced by overload and the evolution of mechanical properties of bone with incremental deformation was established based on the experimental results obtained from a novel progressive loading protocol developed in our laboratory. First, a decayed exponential model was proposed to capture the damage accumulation (modulus loss) with increase in applied strain. Next, a power law function was proposed to represent the progression of plastic deformation with damage accumulation. Finally, a linear combination of the Kohlrausch–Williams–Watts (KWW) and the Debye functions was used to depict the viscoelastic behavior of bone associated with damage accumulation. The results of this study may help in developing a constitutive model for predicting the mechanical behavior of cortical bone tissues.     

Indirect determination of trabecular bone effective tissue failure properties using micro-finite element simulations

Trabecular bone strength is marked not only by the onset of local yielding, but also by post-yield behavior. To study and predict trabecular bone elastic and yield properties, micro-finite element (micro-FE) models were successfully applied. However, trabecular bone strength predictions require micro-FE models incorporating post-yield behavior of trabecular bone tissue. Due to experimental difficulties, such data is currently not available. Here we used micro-FE modeling to determine failure behavior of trabecular bone tissue indirectly, by iteratively fitting FE simulation to experimental results. Failure parameters were fitted to an isotropic plasticity model based on Hill's yield function, using materially and geometrically nonlinear micro-FE models of seven bovine trabecular bone specimens. The predictive value of the averaged effective tissue properties was subsequently tested. The results showed that compression softening had to be included on the tissue level in order to accurately describe the apparent-level behavior of the bone specimens. A sensitivity study revealed that the simulated response was less sensitive to variations in the post-yield properties of the bone tissue than variations in the elastic and yield properties. Due to fitting of the tissue properties, apparent-level behavior could be accurately reproduced for each specimen separately. Predictions based on the averaged and fixed tissue properties were less accurate, due to inter-specimen variations in the tissue properties.     

N-Phenacylthiazolium Bromide Reduces Bone Fragility Induced by Nonenzymatic Glycation

Nonenzymatic glycation (NEG) describes a series of post-translational modifications in the collagenous matrices of human tissues. These modifications, known as advanced glycation end-products (AGEs), result in an altered collagen crosslink profile which impacts the mechanical behavior of their constituent tissues. Bone, which has an organic phase consisting primarily of type I collagen, is significantly affected by NEG. Through constant remodeling by chemical resorption, deposition and mineralization, healthy bone naturally eliminates these impurities. Because bone remodeling slows with age, AGEs accumulate at a greater rate. An inverse correlation between AGE content and material-level properties, particularly in the post-yield region of deformation, has been observed and verified. Interested in reversing the negative effects of NEG, here we evaluate the ability of n-phenacylthiazolium bromide (PTB) to cleave AGE crosslinks in human cancellous bone. Cancellous bone cylinders were obtained from nine male donors, ages nineteen to eighty, and subjected to one of six PTB treatments. Following treatment, each specimen was mechanically tested under physiological conditions to failure and AGEs were quantified by fluorescence. Treatment with PTB showed a significant decrease in AGE content versus control NEG groups as well as a significant rebound in the post-yield material level properties (p<0.05). The data suggest that treatment with PTB could be an effective means to reduce AGE content and decrease bone fragility caused by NEG in human bone.     

Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure

It is difficult to define the 'physiological' mechanical properties of bone. Traumatic failures in-vivo are more likely to be orders of magnitude faster than the quasistatic tests usually employed in-vitro. We have reported recently [Hansen, U., Zioupos, P., Simpson, R., Currey, J.D., Hynd, D., 2008. The effect of strain rate on the mechanical properties of human cortical bone. Journal of Biomechanical Engineering/Transactions of the ASME 130, 011011-1-8] results from tests on specimens of human femoral cortical bone loaded in tension at strain rates (epsilon ) ranging from low (0.08s(-1)) to high (18s(-1)). Across this strain rate range the modulus of elasticity generally increased, stress at yield and failure and strain at failure decreased for rates higher than 1s(-1), while strain at yield was invariant for most strain rates and only decreased at rates higher than 10s(-1). The results showed that strain rate has a stronger effect on post-yield deformation than on initiation of macroscopic yielding. In general, specimens loaded at high strain rates were brittle, while those loaded at low strain rates were much tougher. Here, a post-test examination of the microcracking damage reveals that microcracking was inversely related to the strain rate. Specimens loaded at low strain rates showed considerable post-yield strain and also much more microcracking. Partial correlation and regression analysis suggested that the development of post-yield strain was a function of the amount of microcracking incurred (the cause), rather than being a direct result of the strain rate (the excitation). Presumably low strain rates allow time for microcracking to develop, which increases the compliance of the specimen, making them tougher. This behaviour confirms a more general rule that the degree to which bone is brittle or tough depends on the amount of microcracking damage it is able to sustain. More importantly, the key to bone toughness is its ability to avoid a ductile-to-brittle transition for as long as possible during the deformation. The key to bone's brittleness, on the other hand, is the strain and damage localisation early on in the process, which leads to low post-yield strains and low-energy absorption to failure.     

A novel scratching approach for measuring age-related changes in the in situ toughness of bone

A scratch test using a nanoindentation system was proposed in this study to assess the age-related changes in the in situ toughness of bone matrix at ultrastructural levels. A tissue removal energy density (u(r)) was defined and estimated as the work done by the scratch (U(T)) divided by the total volume of the scratch groove (u(s)). The value of u(s) was used as a relative measure of the in situ toughness of the tissue. Human cortical bone specimens obtained from middle-aged (between 49 and 59 years old) and elderly groups (over 69 years old) were tested using this technique. A significant difference in the estimated removal energy density (u(s)) in the secondary osteons was found between the middle-aged and elderly groups (5.49+/-0.696 vs. 4.09+/-1.30 N/mm(2), respectively).     

Energy dissipation of osteopontin at a HAp mineral interface: Implications for bone biomechanics

Osteopontin (OPN) is a one of the most abundant non-collagenous proteins in the bone's organic matrix. OPN is responsible for mediating bonding at mineral interfaces in the extrafibrillar space and recent evidence shows that it is a major contributor to bone's fracture resistance. While several experimental studies have identified an important role for calcium ions in mediating energy dissipation in OPN protein networks, the underlying molecular mechanisms remain largely unknown. In the current study, the role of calcium ions on energy dissipation at OPN interface with hydroxyapatite (HAp) as the main bone mineral was investigated. For the first time, the three-dimensional structure of OPN proteins were predicted, and it was found that calcium ions greatly influenced the final protein configuration and energy dissipation performance. Under small deformation, the compact cOPN structure, resulting from calcium ions presence, facilitated greater energy dissipation through sacrificial bond breaking and mechanisms mediated by the surface-bound calcium. At larger deformation, the compact structure also enabled cOPN to dissipate higher energy. Moreover, it was found that phosphorylation of OPN played an important role in energy dissipation. While previous studies have shown that OPN dissipated energy by forming aggregate networks, this study also showed that network formation is not necessary and that individual OPN proteins can dissipate large amounts of energy at HAp interfaces.     

Alterations in damage processes in dense cancellous bone following gamma-radiation sterilization

Structurally intact cancellous bone allograft is an attractive tissue form because its high porosity can provide space for delivery of osteogenic factors and also allows for more rapid and complete in-growth of host tissues. Gamma radiation sterilization is commonly used in cancellous bone allograft to prevent disease transmission. Commonly used doses of gamma radiation sterilization (25–35 kGy) have been shown to modify cortical bone post-yield properties and crack propagation but have not been associated with changes in cancellous bone material properties. The purpose of this study was to determine the effects of irradiation on the elastic and yield properties and microscopic tissue damage processes in dense cancellous bone. Cancellous bone specimens (13 control, 14 irradiated to 30 kGy) from bovine proximal tibiae were tested in compression to 1.3% apparent strain and examined for microscopic tissue damage. The yield strain in irradiated specimens (0.93±0.11%, mean±SD) did not differ from that in control specimens (0.90±0.11%, p=0.44). No differences in elastic modulus were observed between groups after accounting for differences in bone volume fraction. However, irradiated specimens showed greater residual strain (p=0.01), increased number of microfractures (p=0.02), and reduced amounts of cross-hatching type damage (p<0.01). Although gamma radiation sterilization at commonly used dosing (30 kGy) does not modify elastic or yield properties of dense cancellous bone, it does cause modifications in damage processes, resulting in increased permanent deformation following isolated overloading.     

Age-related differences in the morphology of microdamage propagation in trabecular bone

Microdamage density has been shown to increase with age in trabecular bone and is associated with decreased fracture toughness. Numerous studies of crack propagation in cortical bone have been conducted, but data in trabecular bone is lacking. In this study, propagation of severe, linear, and diffuse damage was examined in trabecular bone cores from the femoral head of younger (61.3±3.1 years) and older (75.0±3.9 years) men and women. Using a two-step mechanical testing protocol, damage was first initiated with static uniaxial compression to 0.8% strain then propagated at a normalized stress level of 0.005 to a strain endpoint of 0.8%. Coupling mechanical testing with a dual-fluorescent staining technique, the number and length/area of propagating cracks were quantified. It was found that the number of cycles to the test endpoint was substantially decreased in older compared to younger samples (younger: 77,372±15,984 cycles; older: 34,944±11,964 cycles, p=0.06). This corresponded with a greater number of severely damaged trabeculae expanding in area during the fatigue test in the older group. In the younger group, diffusely damaged trabeculae had a greater damage area, which illustrates an efficient energy dissipation mechanism. These results suggest that age-related differences in fatigue life of human trabecular bone may be due to differences in propagated microdamage morphology.     

Tonic finite element model of the lower limb

It is widely admitted that muscle bracing influences the result of an impact, facilitating fractures by enhancing load transmission and reducing energy dissipation. However, human numerical models used to identify injury mechanisms involved in car crashes hardly take into account this particular mechanical behavior of muscles. In this context, in this work we aim to develop a numerical model, including muscle architecture and bracing capability, focusing on lower limbs. The three-dimensional (3-D) geometry of the musculoskeletal system was extracted from MRI images, where muscular heads were separated into individual entities. Muscle mechanical behavior is based on a phenomenological approach, and depends on a reduced number of input parameters, i.e., the muscle optimal length and its corresponding maximal force. In terms of geometry, muscles are modeled with 3-D viscoelastic solids, guided in the direction of fibers with a set of contractile springs. Validation was first achieved on an isolated bundle and then by comparing emergency braking forces resulting from both numerical simulations and experimental tests on volunteers. Frontal impact simulation showed that the inclusion of muscle bracing in modeling dynamic impact situations can alter bone stresses to potentially injury-inducing levels.     

Strain rate dependence of the mechanical properties of reindeer antler and the cumulative damage model of bone fracture

Carter and Caler have produced a 'cumulative damage' model for the fracture of bone, based on creep experiments on human bone, which has been corroborated by monotonic tensile tests on bone, loaded at various strain rates. Monotonic tensile tests on reindeer's antler, which has a lower modulus of elasticity than human bone, produce very similar results. Unlike human bone, reindeer antler always shows a large post-yield strain, and it is possible to distinguish pre-yield and post-yield behaviour. The 'final stiffness' (ultimate stress/ultimate strain) is invariant with strain rate. This is confirmation that bone fractures when a certain amount of damage has accumulated. However, reindeer antler shows a considerable post-yield increase in stress. This is difficult to accommodate in a cumulative damage model.     

Modeling the tensile mechanical behavior of bone along the longitudinal direction

The tensile stress-strain behavior of bone along its longitudinal axis is modeled by using a simple shear-lag theory, wherein, stresses and strains in a unit cell consisting of an organic matrix reinforced by overlapped mineral platelets are computed. It is assumed that loads are transferred between overlapped mineral-platelets by shear in the organic matrix. The mechanical behavior of bone in which the matrix partially or completely debonds from the sides of the overlapped mineral platelets (after an ultimate interfacial shear stress value is exceeded) is modeled. It is shown that the tensile mechanical behavior of bone can be modeled only by assuming little or no debonding of the organic from the mineral. A physical phenomenon that explains the tensile behavior of bone is, after the interfacial shear stress has reached a constant value over the length of the mineral platelets, the collagen molecules/microfibrils (with the associated mineral platelets) move relative to one another. The tensile stress-strain curve of bovine bone is modeled using this model. The theory predicts the mechanical behavior of the tissue in the elastic, yield and post-yield region. The ultimate strain and strengths are not predicted in the present model.     

Bone toughening through stress-induced non-collagenous protein denaturation

Bone toughness emerges from the interaction of several multiscale toughening mechanisms. Recently, the formation of nanoscale dilatational bands and hence the accumulation of submicron diffuse damage were suggested as an important energy dissipation processes in bone. However, a detailed mechanistic understanding of the effect of this submicron toughening mechanism across multiple scales is lacking. Here, we propose a new three-dimensional ultrastructure volume element model showing the formation of nanoscale dilatational bands based on stress-induced non-collagenous protein denaturation and quantify the total energy released through this mechanism in the vicinity of a propagating crack. Under tensile deformation, large hydrostatic stress develops at the nanoscale as a result of local confinement. This tensile hydrostatic stress supports the denaturation of non-collagenous proteins at organic–inorganic interfaces, which leads to energy dissipation. Our model provides new fundamental understanding of the mechanism of dilatational bands formation and its contribution to bone toughness.     

Biomechanical characterization of cartilages by a novel approach of blunt impact testing

The present article introduces a novel method of characterizing the macromechanical cartilage properties based on dynamic testing. The proposed approach of instrumented impact testing shows the possibility of more detailed investigation of the acting dynamic forces and corresponding deformations within the wide range of strain rates and loads, including the unloading part of stress-strain curves and hysteresis loops. The presented results of the unconfined compression testing of both the native joint cartilage tissues and potential substitute materials outlined the opportunity to measure the dissipation energy and thus to identify the initial mechanical deterioration symptoms and to introduce a better definition of material damage. Based on the analysis of measured specimen deformation, the intact and pathologically changed cartilage tissue can be distinguished and the differences revealed.     

Diurnal variation and age-related changes of bone turnover markers in female Göttingen minipigs

We investigated diurnal variation and age-related changes in bone turnover markers in female Gottingen minipigs. Ten females, 6-9 months of age, were used for confirmation of diurnal variation. Blood was collected at 3 h intervals for 24 h, and bone-specific alkaline phosphatase and intact osteocalcin (OC) levels were determined by enzyme immunoassay and radioimmunoassay, respectively. Urine was collected at 3 h intervals for 24 h using a tray attached to the bottom of the cage. The levels of N-terminal telopeptide of type I collagen (NTX) were determined by enzyme immunoassay. Pyridinoline and deoxypyridinoline were measured by high performance liquid chromatography. OC and NTX exhibited diurnal variation (Kruskal-Wallis test, P < 0.05), with the highest and lowest levels at 18:00 h (76.7 +/- 26.2 ng/ml) and 06:00 h (44.3 +/- 10.3 ng/ml), and at 03:00-05:59 h (550.4 +/- 82.4 nmol/micromol Cr) and 12:00-14:59 h (297.8 +/- 152.5 nmol/micromol Cr), respectively. In the study of age-related changes, blood and urine samples from 66 females (age range, 3-76 months) were examined to determine the bone turnover markers. All markers showed high correlations with age (0.569 < R(2) < 0.818). High levels of bone turnover markers were observed in young animals, decreasing with age (Kruskal-Wallis test, P < 0.01). The diurnal variation and age-related changes revealed in the present study will be useful in studies of bone diseases using female Gottingen minipigs.