Microdamage accumulation in bovine trabecular bone in uniaxial compression

In this study we investigated how microdamage accumulated with increasing compressive strain in bovine trabecular bone. We found that little damage is created in the linear elastic region, up to -0.4 percent strain. At an average strain of -0.76 percent +/-0.25 percent, the stress-strain curve became nonlinear, and peaked at -1.91 percent +/-0.55 percent strain. Microdamage increases rapidly during the peak of the stress-strain curve, and a localized band of damage formed. At strains beyond the ultimate strain, the damaged band widened and the density of damage within the band increased. Microdamage occurred as groupings of cracks; the majority of damage occurred as regions of cross-hatching. All microdamage parameters increased with increasing maximum compressive strain. We also observed exponential relationships between crack numerical density and damage (1(o) - (o)Esec/E0) and between crack length density and damage.     

Microdamage propagation in trabecular bone due to changes in loading mode

Microdamage induced by falls or other abnormal loads that cause shear stress in trabecular bone could impair the mechanical properties of the proximal femur or spine. Existing microdamage may also increase the initiation and propagation of further microdamage during subsequent normal, on-axis, loading conditions, resulting in atraumatic or "spontaneous" fractures. Microdamage formation due to shear and compressive strains was studied in 14 on-axis cylindrical bovine tibial trabecular bone specimens. Microdamage was induced by a torsional overload followed by an on-axis compressive overload and quantified microscopically. Fluorescent agents were used to label microdamage and differentiate damage due to the two loading modes. Both the microcrack density and diffuse damage area caused by the torsional overload increased with increasing shear strain from the center to the edge of the specimen. However, the mean microcrack length was uniform across the specimen, suggesting that microcrack length is limited by microstructural features. The mean density of microcracks caused by compressive overloading was slightly higher near the center of the specimen, and the diffuse damage area was uniform across the specimen. Over 20% of the microcracks formed in the initial torsional overloading propagated during compression. Moreover the propagating microcracks were, on average, longer than microcracks formed by a single overload. As such, changes in loading mode can cause propagation of microcracks beyond the microstructural barriers that normally limit the length. Damage induced by in vivo off-axis loads such as falls may similarly propagate during subsequent normal loading, which could affect both remodeling activity and fracture susceptibility.     

Estimation of the effective yield properties of human trabecular bone using nonlinear micro-finite element analyses

Micro-finite element (\(\upmu \)FE) analyses are often used to determine the apparent mechanical properties of trabecular bone volumes. Yet, these apparent properties depend strongly on the applied boundary conditions (BCs) for the limited size of volumes that can be obtained from human bones. To attenuate the influence of the BCs, we computed the yield properties of samples loaded via a surrounding layer of trabecular bone (“embedded configuration”). Thirteen cubic volumes (10.6 mm side length) were collected from \(\upmu \)CT reconstructions of human vertebrae and femora and converted into \(\upmu \)FE models. An isotropic elasto-plastic material model was chosen for bone tissue, and nonlinear \(\upmu \)FE analyses of six uniaxial, shear, and multi-axial load cases were simulated to determine the yield properties of a subregion (5.3 mm side length) of each volume. Three BCs were tested. Kinematic uniform BCs (KUBCs: each boundary node is constrained with uniform displacements) and periodicity-compatible mixed uniform BCs (PMUBCs: each boundary node is constrained with a uniform combination of displacements and tractions mimicking the periodic BCs for an orthotropic material) were directly applied to the subregions, while the embedded configuration was achieved by applying PMUBCs on the larger volumes instead. Yield stresses and strains, and element damage at yield were finally compared across BCs. Our findings indicate that yield strains do not depend on the BCs. However, KUBCs significantly overestimate yield stresses obtained in the embedded configuration (+43.1 ± 27.9%). PMUBCs underestimate (?10.0 ± 11.2%), but not significantly, yield stresses in the embedded situation. Similarly, KUBCs lead to higher damage levels than PMUBCs (+51.0 ± 16.9%) and embedded configurations (+48.4 ± 15.0%). PMUBCs are better suited for reproducing the loading conditions in subregions of the trabecular bone and deliver a fair estimation of their effective (asymptotic) yield properties.     

Multi-axial mechanical properties of human trabecular bone

In the context of osteoporosis, evaluation of bone fracture risk and improved design of epiphyseal bone implants rely on accurate knowledge of the mechanical properties of trabecular bone. A multi-axial loading chamber was designed, built and applied to explore the compressive multi-axial yield and strength properties of human trabecular bone from different anatomical locations. A thorough experimental protocol was elaborated for extraction of cylindrical bone samples, assessment of their morphology by micro-computed tomography and application of different mechanical tests: torsion, uni-axial traction, uni-axial compression and multi-axial compression. A total of 128 bone samples were processed through the protocol and subjected to one of the mechanical tests up to yield and failure. The elastic data were analyzed using a tensorial fabric–elasticity relationship, while the yield and strength data were analyzed with fabric-based, conewise generalized Hill criteria. For each loading mode and more importantly for the combined results, strong relationships were demonstrated between volume fraction, fabric and the elastic, yield and strength properties of human trabecular bone. Despite the reviewed limitations, the obtained results will help improve the simulation of the damage behavior of human bones and bone-implant systems using the finite element method.     

Prediction of trabecular bone principal structural orientation using quantitative ultrasound scanning

Bone has the ability to adapt its structure in response to the mechanical environment as defined as Wolff's Law. The alignment of trabecular structure is intended to adapt to the particular mechanical milieu applied to it. Due to the absence of normal mechanical loading, it will be extremely important to assess the anisotropic deterioration of bone during the extreme conditions, i.e., long term space mission and disease orientated disuse, to predict risk of fractures. The propagation of ultrasound wave in trabecular bone is substantially influenced by the anisotropy of the trabecular structure. Previous studies have shown that both ultrasound velocity and amplitude is dependent on the incident angle of the ultrasound signal into the bone sample. In this work, seven bovine trabecular bone balls were used for rotational ultrasound measurement around three anatomical axes to elucidate the ability of ultrasound to identify trabecular orientation. Both ultrasound attenuation (ATT) and fast wave velocity (UV) were used to calculate the principal orientation of the trabecular bone. By comparing to the mean intercept length (MIL) tensor obtained from μCT, the angle difference of the prediction by UV was 4.45°, while it resulted in 11.67° angle difference between direction predicted by μCT and the prediction by ATT. This result demonstrates the ability of ultrasound as a non-invasive measurement tool for the principal structural orientation of the trabecular bone.     

Microdamage in bone: surface analysis and radiological detection

Microdamage accumulation leads to reduced bone strength and fracture. Intact, damaged and Rose Bengal stained cortical bone specimens were studied using SEM and EDXA imaging. SEM coupled with EDXA studies showed selective labelling of surface damage due to binding of dye at free lattice sites. A series of novel iodinated X-ray contrast agent were synthesised. These agents demonstrated excellent stability, water solubility and lack of atropisomerism. Preliminary imaging studies, using cone-beam mu-CT, demonstrated their ability to provide visible contrast in the solid state on bone surfaces.     

The influence of mechanical stimulation on osteocyte apoptosis and bone viability in human trabecular bone

It has been shown previously using in vivo and ex vivo animal models, that cyclical mechanical stimulation is capable of maintaining osteocyte viability through the control of apoptotic cell death. Here we have studied the effect of mechanical stimulation on osteocyte viability in human trabecular bone maintained in a 3-D bioreactor system. Bone samples, maintained in the bioreactor system for periods of 3, 7 and 27 days, were subjected to either cyclical mechanical stimulation which engendered a maximum of 3,000 microstrain in a waveform corresponding to physiological jumping exercise for 5 minutes daily or control unloading. Unloading resulted in a decrease in osteocyte viability within 3 days that was accompanied by increased levels of cellular apoptosis. Mechanical stimulation significantly reduced apoptosis (p< or =0.032) and improved the maintenance of osteocyte viability in bone from all patient samples. The percentage Alkaline Phosphatase (ALP) labelled bone surface was significantly increased (p< or =0.05) in response to mechanical stimulation in all samples as was the Bone Formation Rate (BFR/BS) (p=0.005) as determined by calcein label incorporation in the 27-day experiment. These data indicate that in this model system, mechanical stimulation is capable of maintaining osteocyte viability in human bone.     

Influence of prostaglandins on electrolyte metabolism of human trabecular bone in vitro

A procedure was developed to investigate the electrolyte metabolism of human trabecular bone and its regulation in vitro, in particular the influence of prostaglandins. Trabecular bone was prepared from femoral heads of patients who had undergone hip replacement surgery for coxarthrosis. 500 mg samples were incubated in modified EAGLE's minimal essential medium. Net electrolyte movements between bone and incubation medium were measured.During 6 hours of incubation PGE₂ caused an increase in the release of calcium and magnesium from bone into incubation medium as compared to controls. The effect of PGE₂ was dose-dependent and comparable to that of human parathyroid hormone 1–34 (hPTH 1–34) whereas hPTH 3–34 had no effect. Human calcitonin (hCT) caused a decrease in the release of calcium and magnesium.PGE₂ was found to be the most potent prostaglandin. PGE₁ and PGE_2α had about 50% and PGE_1α about 40% of the potency of PGE₂. PGA₁ and PGA₂ had no effect.The effect of PGE₂ could be completely inhibited by hCT and was not further enhanced by hPTH 1–34.Magnesium movement was affected in the same way as calcium movement, while phosphate movement and release of alkaline phosphatase and hydroxyproline from bone into incubation medium were not affected by prostaglandins.     

Influence of prostaglandins on electrolyte metabolism of human trabecular bone in vitro

A procedure was developed to investigate the electrolyte metabolism of human trabecular bone and its regulation in vitro, in particular the influence of prostaglandins. Trabecular bone was prepared from femoral heads of patients who had undergone hip replacement surgery for coxarthrosis. 500 mg samples were incubated in modified EAGLE's minimal essential medium. Net electrolyte movements between bone and incubation medium were measured. During 6 hours of incubation PGE2 caused an increase in the release of calcium and magnesium from bone into incubation medium as compared to controls. The effect of PGE2 was dose-dependent and comparable to that of human parathyroid hormone 1-34 (hPTH 1-34) whereas hPTH 3-34 had no effect. Human calcitonin (hCT) caused a decrease in the release of calcium and magnesium. PGE2 was found to be the most potent prostaglandin. PGE1 and PGF2 alpha had about 50% and PGF1 alpha about 40% of the potency of PGE2. PGA1 and PGA2 had no effect. The effect of PGE2 could be completely inhibited by hCT and was not further enhanced by hPTH 1-34. Magnesium movement was affected in the same way as calcium movement, while phosphate movement and release of alkaline phosphatase and hydroxyproline from bone into incubation medium were not affected by prostaglandins.     

Dependence of yield strain of human trabecular bone on anatomic site

Understanding the dependence of human trabecular bone strength behavior on anatomic site provides insight into structure-function relationships and is essential to the increased success of site-specific finite element models of whole bones. To investigate the hypothesis that the yield strains of human trabecular bone depend on anatomic site, the uniaxial tensile and compressive yield properties were compared for cylindrical specimens from the vertebra (n=61), proximal tibia (n=31), femoral greater trochanter (n=23), and femoral neck (n=27) taken from 61 donors (67+/-15years). Test protocols were used that minimized end artifacts and loaded specimens along the main trabecular orientation. Yield strains by site (mean+/-S.D.) ranged from 0.70+/-0.05% for the trochanter to 0.85+/-0.10% for the femoral neck in compression, from 0.61+/-0.05% for the trochanter to 0.70+/-0.05% for the vertebra in tension, and were always higher in compression than tension (p<0.001). The compressive yield strain was higher for the femoral neck than for all other sites (p<0.001), as was the tensile yield strain for the vertebra (p<0.007). Analysis of covariance, with apparent density as the covariate, indicated that inter-site differences existed in yield stress even after adjusting statistically for density (p<0.035). Coefficients of variation in yield strain within each site ranged from only 5-12%, consistent with the strong linear correlations (r(2)=0.94-0.98) found between yield stress and modulus. These results establish that the yield strains of human trabecular bone can differ across sites, but that yield strain may be considered uniform within a given site despite substantial variation in elastic modulus and yield stress.     

Determination of ultrasound phase velocity in trabecular bone using time dependent phase tracking technique

Ultrasound velocity is one of the key acoustic parameters for noninvasive diagnosis of osteoporosis. Ultrasound phase velocity can be uniquely measured from the phase of the ultrasound signal at a specified frequency. Many previous studies used fast Fourier transform (FFT) to determine the phase velocity, which may cause errors due to the limitations of FFT. The new phase tracking technique applied an adaptive tracking algorithm to detect the time dependent phase and amplitude of the ultrasound signal at a specified frequency. This overcame the disadvantages of FFT to ensure the accuracy of the ultrasound phase velocity. As a result, the new method exhibited high accuracy in the measurement of ultrasound phase velocity of two phantom blocks with the error less than 0.4%. 41 cubic trabecular samples from sheep femoral condyles were used in the study. The phase velocity of the samples using the new method had significantly high correlation to the bulk stiffness of the samples (r = 0.84) compared to the phase velocity measured using fast Fourier transform FFT (r = 0.14). In conclusion, the new method provided an accurate measurement of the ultrasound phase velocity in bone.     

A 3D damage model for trabecular bone based on fabric tensors

Motivated by the role of damage in normal and pathological conditions of trabecular bone, a novel 3D constitutive law was developed that describes anisotropic elasticity and the rate-independent degradation in mechanical properties resulting from the growth of cracks or voids in the trabecular tissue. The theoretical model was formulated within the framework of continuum damage mechanics and based on two fabric tensors characterizing the local trabecular morphology. Experimental validation of the model was achieved by uniaxial and torsional testing of waisted bovine trabecular bone specimens. Strong correlations were found between cumulated permanent strain, reduction in elastic moduli and nonlinear postyield stress which support the hypothesis that these variables reflect the same underlying damage process.     

Topographical distribution of trabecular bone strength in the human os calcanei

Mechanical properties of twenty human os calcanei were determined by uniaxial compression testing of bone specimens from facies articularis talaris posterior, facies articularis cuboidea, and tuber calcanei. Specimens were taken oriented perpendicular to the planes of the facies articularis, and in tuber along the presumed loading axis throughout the gait cycle. Young's modulus and strength at facies articularis cuboidea and facies articularis talaris posterior were about three times those at the tuber calcanei. The variation of the relationship between Young's modulus and apparent density indicated differences in the orientation of the trabecula, in relation to the direction of evaluation between these locations. A more detailed analysis of the topographical variation of strength within each location was made using penetration testing of a further nineteen specimens. The results of both types of measurements indicated that the major part of the load during walking is carried by facies articularis talaris posterior and facies articularis cuboidea.     

Heterogeneity of yield strain in low-density versus high-density human trabecular bone

Understanding the off-axis behavior of trabecular yield strains may lend unique insight into the etiology of fractures since yield strains provide measures of failure independent of elastic behavior. We sought to address anisotropy of trabecular yield strains while accounting for variations in both density and anatomic site and to determine the mechanisms governing this behavior. Cylindrical specimens were cored from vertebral bodies (n=22, BV/TV=0.11±0.02) and femoral necks (n=28, BV/TV=0.22±0.06) with the principal trabecular orientation either aligned along the cylinder axis (on-axis, n=22) or at an oblique angle of 15° or 45° (off-axis, n=28). Each specimen was scanned with micro-CT, mechanically compressed to failure, and analysed with nonlinear micro-CT-based finite element analysis. Yield strains depended on anatomic site (p=0.03, ANOVA), and the effect of off-axis loading was different for the two sites (p=0.04)—yield strains increased for off-axis loading of the vertebral bone (p=0.04), but were isotropic for the femoral bone (p=0.66). With sites pooled together, yield strains were positively correlated with BV/TV for on-axis loading (R²=58%, p<0.0001), but no such correlation existed for off-axis loading (p=0.79). Analysis of the modulus-BV/TV and strength-BV/TV relationships indicated that, for the femoral bone, the reduction in strength associated with off-axis loading was greater than that for modulus, while the opposite trend occurred for the vertebral bone. The micro-FE analyses indicated that these trends were due to different failure mechanisms for the two types of bone and the different loading modes. Taken together, these results provide unique insight into the failure behavior of human trabecular bone and highlight the need for a multiaxial failure criterion that accounts for anatomic site and bone volume fraction.     

Effect of boundary conditions on yield properties of human femoral trabecular bone

Trabecular bone plays an important mechanical role in bone fractures and implant stability. Homogenized nonlinear finite element (FE) analysis of whole bones can deliver improved fracture risk and implant loosening assessment. Such simulations require the knowledge of mechanical properties such as an appropriate yield behavior and criterion for trabecular bone. Identification of a complete yield surface is extremely difficult experimentally but can be achieved in silico by using micro-FE analysis on cubical trabecular volume elements. Nevertheless, the influence of the boundary conditions (BCs), which are applied to such volume elements, on the obtained yield properties remains unknown. Therefore, this study compared homogenized yield properties along 17 load cases of 126 human femoral trabecular cubic specimens computed with classical kinematic uniform BCs (KUBCs) and a new set of mixed uniform BCs, namely periodicity-compatible mixed uniform BCs (PMUBCs). In stress space, PMUBCs lead to 7–72 % lower yield stresses compared to KUBCs. The yield surfaces obtained with both KUBCs and PMUBCs demonstrate a pressure-sensitive ellipsoidal shape. A volume fraction and fabric-based quadric yield function successfully fitted the yield surfaces of both BCs with a correlation coefficient \(R^{2} \ge 0.93\). As expected, yield strains show only a weak dependency on bone volume fraction and fabric. The role of the two BCs in homogenized FE analysis of whole bones will need to be investigated and validated with experimental results at the whole bone level in future studies.     

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.     

The sensitivity of nonlinear computational models of trabecular bone to tissue level constitutive model

Microarchitectural finite element models have become a key tool in the analysis of trabecular bone. Robust, accurate, and validated constitutive models would enhance confidence in predictive applications of these models and in their usefulness as accurate assays of tissue properties. Human trabecular bone specimens from the femoral neck (n = 3), greater trochanter (n = 6), and lumbar vertebra (n = 1) of eight different donors were scanned by μ-CT and converted to voxel-based finite element models. Unconfined uniaxial compression and shear loading were simulated for each of three different constitutive models: a principal strain-based model, Drucker–Lode, and Drucker–Prager. The latter was applied with both infinitesimal and finite kinematics. Apparent yield strains exhibited minimal dependence on the constitutive model, differing by at most 16.1%, with the kinematic formulation being influential in compression loading. At the tissue level, the quantities and locations of yielded tissue were insensitive to the constitutive model, with the exception of the Drucker–Lode model, suggesting that correlation of microdamage with computational models does not improve the ability to discriminate between constitutive laws. Taken together, it is unlikely that a tissue constitutive model can be fully validated from apparent-level experiments alone, as the calculations are too insensitive to identify differences in the outcomes. Rather, any asymmetric criterion with a valid yield surface will likely be suitable for most trabecular bone models.     

Fatigue microdamage in bovine trabecular bone

Microdamage, in the form of small cracks, may accumulate in trabecular bone loaded in fatigue. Specimens of bovine trabecular bone were loaded in compressive fatigue at one of four normalized stresses and loading was stopped after the specimens reached one of six maximum strains. Microdamage was identified using a fluorochrome staining technique, and microdamage parameters, including the number of damaged trabeculae and the damaged area fraction, were measured. No microdamage was observed during loading to strains below the yield strain; at higher strains, all microdamage parameters increased with increasing maximum compressive strain. Few significant differences were observed in the type or amount of microdamage accumulation between specimens loaded to the same maximum strain at different normalized stresses; however, more trabecular fractures were observed at high numbers of cycles, which corresponded to low normalized stresses.