Small oscillatory accelerations, independent of matrix deformations, increase osteoblast activity and enhance bone morphology

A range of tissues have the capacity to adapt to mechanical challenges, an attribute presumed to be regulated through deformation of the cell and/or surrounding matrix. In contrast, it is shown here that extremely small oscillatory accelerations, applied as unconstrained motion and inducing negligible deformation, serve as an anabolic stimulus to osteoblasts in vivo. Habitual background loading was removed from the tibiae of 18 female adult mice by hindlimb-unloading. For 20 min/d, 5 d/wk, the left tibia of each mouse was subjected to oscillatory 0.6 g accelerations at 45 Hz while the right tibia served as control. Sham-loaded (n = 9) and normal age-matched control (n = 18) mice provided additional comparisons. Oscillatory accelerations, applied in the absence of weight bearing, resulted in 70% greater bone formation rates in the trabeculae of the metaphysis, but similar levels of bone resorption, when compared to contralateral controls. Quantity and quality of trabecular bone also improved as a result of the acceleration stimulus, as evidenced by a significantly greater bone volume fraction (17%) and connectivity density (33%), and significantly smaller trabecular spacing (-6%) and structural model index (-11%). These in vivo data indicate that mechanosensory elements of resident bone cell populations can perceive and respond to acceleratory signals, and point to an efficient means of introducing intense physical signals into a biologic system without putting the matrix at risk of overloading. In retrospect, acceleration, as opposed to direct mechanical distortion, represents a more generic and safe, and perhaps more fundamental means of transducing physical challenges to the cells and tissues of an organism.     

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.     

Wing and leg bone microstructure reflects migratory demands in resident and migrant populations of the Dark-eyed Junco (Junco hyemalis)

Migration is the primary strategy that temperate birds use to avoid overwintering under harsh conditions. As a consequence, migratory birds have evolved specific morphological features in their wings and skeleton. However, in addition to varying in overall shape and size, bone can also change at the microstructural level by, for example, increasing its thickness. Such changes are critical to preventing fracture and damage under repeated loading (fatigue), yet it is not known whether migratory behaviour influences bone microstructure. To address this gap in the literature, we performed micro-computed tomography on skeletons of resident and migrant subspecies of the Dark-eyed Junco Junco hyemalis. We investigated the differences in the major wing bone, the humerus, and the major leg bone, the femur. In each bone, we studied the microarchitecture of the two types of bone tissue: cortical bone, the thick outer layer of bone; and trabecular bone, which is the porous network of bone tissue at the ends of long bones. We used linear models to quantify morphological features with respect to body mass and migratory behaviour. Humeri from migratory birds were thinner, wider and had higher overall geometric stiffness, i.e. a higher polar moment of inertia, relative to humeri from resident birds. These features may help keep their bones stiff to maintain their increased body mass during migration. In contrast, migrant femora were shorter, thinner and had lower geometric stiffness than femora of residents, potentially to reduce total body mass. Tissue mineral density was lower in both the humerus and the femur of migratory birds. In addition, migratory subspecies had less trabecular bone (lower bone volume fraction) due primarily to a loss of trabecular thickness. Migratory behaviour may thus select for improved stiffness and fatigue resistance in the wing bones and reduced mass of leg bones. Our work demonstrates how important insights into morphological adaptation can be obtained by investigating bone microstructure.     

Trabecular eccentricity and bone adaptation

It is well established that bones functionally adapt by mechanisms that control tissue density, whole bone geometry, and trabecular orientation. In this study, we propose the existence of another such powerful mechanism, namely, trabecular eccentricity, i.e. non-central placement of trabecular bone within a cortical envelope. In the human femoral neck, trabecular eccentricity results in a thicker cortical shell on the inferior than superior aspect. In an overall context of expanding understanding of bone adaptation, the goal of this study was to demonstrate the biomechanical significance of, and provide a mechanistic explanation for, the relationship between trabecular eccentricity and stresses in the human femoral neck. Using composite beam theory, we showed that the biomechanical effects of eccentricity during a habitual loading situation were to increase the stress at the superior aspect of the neck and decrease the stress at the inferior aspect, resulting in an overall protective effect. Further, increasing eccentricity had a stress-reducing effect equivalent to that of increasing cortical thickness or increasing trabecular modulus. We conclude that an asymmetric placement of trabecular bone within a cortical bone envelope represents yet another mechanism by which whole bones can adapt to mechanical demands.     

Tissue stresses and strain in trabeculae of a canine proximal femur can be quantified from computer reconstructions

A quantitative assessment of bone tissue stresses and strains is essential for the understanding of failure mechanisms associated with osteoporosis, osteoarthritis, loosening of implants and cell- mediated adaptive bone-remodeling processes. According to Wolff's trajectorial hypothesis, the trabecular architecture is such that minimal tissue stresses are paired with minimal weight. This paradigm at least suggests that, normally, stresses and strains should be distributed rather evenly over the trabecular architecture. Although bone stresses at the apparent level were determined with finite element analysis (FEA), by assuming it to be continuous, there is no data available on trabecular tissue stresses or strains of bones in situ under physiological loading conditions. The objectives of this project were to supply reasonable estimates of these quantities for the canine femur, to compare trabecular-tissue to apparent stresses, and to test Wolff's hypothesis in a quantitative sense. For that purpose, the newly developed method of large-scale micro-FEA was applied in conjunction with micro-CT structural measurements. A three-dimensional high-resolution computer reconstruction of a proximal canine femur was made using a micro-CT scanner. This was converted to a large-scale FE-model with 7.6 million elements, adequately refined to represent individual trabeculae. Using a special-purpose FE-solver, analyses were conducted for three different orthogonal hip-joint loading cases, one of which represented the stance-phase of walking. By superimposing the results, the tissue stress and strain distributions could also be calculated for other force directions. Further analyses of results were concentrated on a trabecular volume of interest (VOI) located in the center of the head. For the stance phase of walking an average tissue principal strain in the VOI of 279 strain was found, with a standard deviation of 212 microstrain. The standard deviation depended not only on the hip-force magnitude, but also on its direction. In more than 95% of the tissue volume the principal stresses and strains were in a range from zero to three times the averages, for all hip-force directions. This indicates that no single load creates even stress or strain distributions in the trabecular architecture. Nevertheless, excessive values occurred at few locations only, and the maximum tissue stress was approximately half the value reported for the tissue fatigue strength. These results thus indicate that trabecular bone tissue has a safety factor of approximately two for hip-joint loads that occur during normal activities.     

The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques

Acoustic microscopy (30-60 microm resolution) and nanoindentation (1-5 microm resolution) are techniques that can be used to evaluate the elastic properties of human bone at a microstructural level. The goals of the current study were (1) to measure and compare the Young's moduli of trabecular and cortical bone tissues from a common human donor, and (2) to compare the Young's moduli of bone tissue measured using acoustic microscopy to those measured using nanoindentation. The Young's modulus of cortical bone in the longitudinal direction was about 40% greater than (p<0.01) the Young's modulus in the transverse direction. The Young's modulus of trabecular bone tissue was slightly higher than the transverse Young's modulus of cortical bone, but substantially lower than the longitudinal Young's modulus of cortical bone. These findings were consistent for both measurement methods and suggest that elasticity of trabecular tissue is within the range of that of cortical bone tissue. The calculation of Young's modulus using nanoindentation assumes that the material is elastically isotropic. The current results, i.e., the average anisotropy ratio (E(L)/E(T)) for cortical bone determined by nanoindentation was similar to that determined by the acoustic microscope, suggest that this assumption does not limit nanoindentation as a technique for measurement of Young's modulus in anisotropic bone.     

Tissue stresses and strain in trabeculae of a canine proximal femur can be quantified from computer reconstructions

A quantitative assessment of bone tissue stresses and strains is essential for the understanding of failure mechanisms associated with osteoporosis, osteoarthritis, loosening of implants and cell-mediated adaptive bone-remodeling processes. According to Wolff's trajectorial hypothesis, the trabecular architecture is such that minimal tissue stresses are paired with minimal weight. This paradigm at least suggests that, normally, stresses and strains should be distributed rather evenly over the trabecular architecture. Although bone stresses at the apparent level were determined with finite element analysis (FEA), by assuming it to be continuous, there is no data available on trabecular tissue stresses or strains of bones in situ under physiological loading conditions. The objectives of this project were to supply reasonable estimates of these quantities for the canine femur, to compare trabecular-tissue to apparent stresses, and to test Wolff's hypothesis in a quantitative sense. For that purpose, the newly developed method of large-scale micro-FEA was applied in conjunction with micro-CT structural measurements. A three-dimensional high-resolution computer reconstruction of a proximal canine femur was made using a micro-CT scanner. This was converted to a large-scale FE-model with 7.6 million elements, adequately refined to represent individual trabeculae. Using a special-purpose FE-solver, analyses were conducted for three different orthogonal hip-joint loading cases, one of which represented the stance-phase of walking. By superimposing the results, the tissue stress and strain distributions could also be calculated for other force directions. Further analyses of results were concentrated on a trabecular volume of interest (VOI) located in the center of the head. For the stance phase of walking an average tissue principal strain in the VOI of 279 strain was found, with a standard deviation of 212 microstrain. The standard deviation depended not only on the hip-force magnitude, but also on its direction. In more than 95% of the tissue volume the principal stresses and strains were in a range from zero to three times the averages, for all hip-force directions. This indicates that no single load creates even stress or strain distributions in the trabecular architecture. Nevertheless, excessive values occurred at few locations only, and the maximum tissue stress was approximately half the value reported for the tissue fatigue strength. These results thus indicate that trabecular bone tissue has a safety factor of approximately two for hip-joint loads that occur during normal activities.     

Adaptations to free-fall impact are different in the shafts and bone ends of rat forelimbs.

Impact exercise can have beneficial effects on the growing skeleton. To understand what changes it promotes in the shafts and ends of weight-bearing bones, we measured the effects of impact from repetitive free falls in growing rats. Fischer 344 female rats, 6.5 wk old, were assigned to one of three groups (n = 10 each). Controls were not dropped, whereas those subjected to impact were dropped from 30 or 60 cm. Rats in both free-fall groups were dropped 10 times per day for 8 wk. Leg bones were mechanically tested, and their cross-sectional area (CSA), cross-sectional moments of inertia, and volumetric bone mineral density (BMD) were measured by peripheral quantitative computed tomography. In the shafts of the forelimbs, but not the hindlimbs, free-fall impact resulted in greater ultimate breaking force, minimum and maximum second moments of area, and CSA but not BMD. In the bone ends of the forelimb and tibial bones, trabecular BMD increased but CSA did not. Landing from 30 and 60 cm produced peak impact forces of 12.0 and 16.7 times the standing forefoot weight for each front leg and of 4.5 and 7.7 times the standing hind foot weight for each hind foot. Overall, free-fall impact affected the forelimbs by increasing trabecular bone density in the bone ends and improving the strength at the shaft as a result of geometric improvements. These results indicate that adaptation to impact may occur by different mechanisms in bone end and shaft regions.     

Trabecular shear stress in human vertebral cancellous bone: intra- and inter-individual variations

Correlation of the mean and standard deviation of trabecular stresses has been proposed as a mechanism by which a strong relationship between the apparent strength and stiffness of cancellous bone can be achieved. The current study examined whether the relationship between the mean and standard deviation of trabecular von Mises stresses can be generalized for any group of cancellous bone. Cylindrical human vertebral cancellous bone specimens were cut in the infero-superior direction from T12 of 23 individuals (inter-individual group). Thirty nine additional specimens were prepared similarly from the T4-T12 and L2-L5 vertebrae of a 63 year old male (intra-individual group). The specimens were scanned by micro-computed tomography (microCT) and trabecular von Mises stresses were calculated using finite element modeling. The expected value, standard deviation and coefficient of variation of the von Mises stress were calculated form a three-parameter Weibull function fitted to von Mises stress data from each specimen. It was found that the average and standard deviation of trabecular von Mises shear stress were: (i) correlated with each other, supporting the idea that high correlation between the apparent strength and stiffness of cancellous bone can be achieved through controlling the trabecular level shear stress variations, (ii) dependent on anatomical site and sample group, suggesting that the variation of stresses are correlated to the mean stress to different degrees between vertebrae and individuals, and (iii) dependent on bone volume fraction, consistent with the idea that shear stress is less well controlled in bones with low BV/TV. The conversion of infero-superior loading into trabecular von Mises stresses was maximum for the tissue at the junction of the thoracic and lumbar spine (T12-L1) consistent with this junction being a common site of vertebral fracture.     

Stress-concentrating effect of resorption lacunae in trabecular bone

Analyses of the distributions of stress and strain within individual bone trabeculae have not yet been reported. In this study, four trabeculae were imaged and finite elements models were generated in an attempt to quantify the variability of stress/strain in real trabeculae. In three of these trabeculae, cavities were identified with depths comparable to values reported for resorption lacunae ( approximately 50 microm)-although we cannot be certain, it is most probable that they are indeed resorption lacunae. A tensile load was applied to each trabeculum to simulate physiological loading and to ensure that bending was minimized. The force carried by each trabecula was calculated from this value using the average cross sectional area of each trabecula. The analyses predict that very high stresses (>100 MPa) existed within bone trabecular tissue. Stress and strain distributions were highly heterogeneous in all cases, more so in trabeculae with the presumptive resorption lacunae where at least 30% of the tissue had a strain greater than 4000 micoepsilon in all cases. Stresses were elevated at the pit of the lacunae, and peak stress concentrations were located in the longitudinal direction ahead of the lacunae. Given these high strains, we suggest that microdamage is inevitable around resorption lacunae in trabecular bone, and may cause the bone multicellular unit to proceed to resorb a packet of bone in the trabeculum rather than just resorb whatever localized area was initially targeted.     

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.     

Gender specific LRP5 influences on trabecular bone structure and strength

A mutation in LRP5 (low-density lipoprotein receptor-related protein 5) has been shown to increase bone mass and density in humans and animals. Transgenic mice expressing the LRP5 mutation (G171V) demonstrate an increase in bone mass as compared to non-transgenic (NTG) littermates. This study evaluated LRP5 gene and gender-related influences on the structural and biomechanical strength properties of trabecular and cortical bone in femurs and vertebrae (L5) of 17-week-old mice. Micro-computed tomography was used to evaluate the trabecular bone structure of distal femurs and vertebrae ex vivo. Mechanical testing of the trabecular bone in the distal femur was done to determine biomechanical strength. Differences due to genotype and gender were tested using two-way ANOVA at a significance level of p<0.05. Trabecular bone structural parameters (BV/TV, trabecular thickness, number, etc.) at the distal femur, femoral neck, and vertebral body sites were greater in the transgenic as compared to the NTG mice. In addition, vertebral cortical thickness and trabecular strength parameters (ultimate and yield loads, stiffness, ultimate and yield stresses) in the distal femur were greater in the transgenic mice as compared to NTG. The increasing trends of cortical thickness were also noted in the transgenic mice as compared to NTG. Within LRP5 (G171V) mutant mice, there were significant gender-related differences in some of the trabecular bone structural parameters at all the sites (distal femur, femoral neck, and vertebral body). However, unlike trabecular structural parameters, the gender-specific differences were not found in the trabecular strength of LRP5 transgenic mice. In summary, these findings suggest that the LRP5 (G171V) mutation results in greater trabecular bone structure and strength at both the distal femurs and vertebral bodies as compared to NTG. In addition, only the trabecular structure parameters were affected by gender within the LRP5 (G171V) mutation.     

Trabecular angle of the human talus is associated with the level of cartilage degeneration

The architecture of bone trabeculae is based on the direction of stresses applied to the bone. The human talar dome receives compressive forces from the tibia and, to a much lesser extent, the fibula when standing, walking, and running, and transmits the force downward to the calcaneus through the talar body and anterior to the navicular via the talar head. As a result, the body of the talus has predominately vertical trabeculae. However, here we hypothesize that cartilage degeneration at the articular surface is associated with trabecular angle within the associated bone, as a reflection of joint alignment and/or biomechanics (stability, congruence, angulation, etc). Through measurement of trabecular angle with Fast Fourier Transform Analysis, we show a positive correlation between the cartilage degeneration score of the articular surface of the talar dome and the angle of trabecular deviation from the perpendicular axis of the dome (right talus R=0.75, p<0.01; left talus R=0.79, p<0.01).     

Lead concentrations in cortical and trabecular bones in deceased smelter workers

The aim of the study was to compare bone lead concentrations in cortical and trabecular bones in long-term exposed primary copper and lead smelter workers, and to relate the measured concentrations to the previous lead exposure of the workers. Lead concentrations in seven bones (trabecular: sternum, vertebrae, iliac crest, rib; cortical: femur, left forefinger, and temporal bone) were determined by electrothermal atomic absorption spectrometry in 32 male, long-term exposed copper and lead smelter workers, and compared with levels in 10 male occupationally unexposed reference persons. A time-integrated blood lead index (cumulative blood lead index, CBLI) was calculated for each worker. The lead levels in the seven studied bones were all significantly higher in active and retired lead workers as compared with the reference group (p相似文献   

Optimum stiffness for leg bones

A limb bone will be lighter if it is made thinner. However, thinner bones are more flexible (for given length and shape of cross-section) so their muscles must shorten more to move the distal end of the bone against a resisting force. To shorten more, a muscle needs longer muscle fibres and so must be heavier. Thus a particular thickness for the bone will enable the combined mass of bone plus muscle to be minimized. Peak stresses due to bending moments, in bones that were optimized according to this criterion, would be about ±70 MPa. Stresses of about this magnitude have been found in leg bones of various mammals, in strenuous activities such as running and jumping. However, similar stresses might be predicted on grounds of strength requirements, to give adequate factors of safety.     

The effect of the loading condition corresponding to functional shoulder activities on trabecular architecture of glenoid

There is little information on bone morphology as it relates to shoulder activities. This study investigated how loads corresponding to functional shoulder activities affect the trabecular architecture of the glenoid. Two different protocols were used. Protocol 1 investigated the material and morphological characteristics of the glenoid by analyzing digitized trabecular bone images obtained from 12 cadaver scapula specimens. Protocol 2 used a finite element analysis (FEA) to compute the principal stress trajectories acting within the glenoid. The principal stresses were derived for five loading conditions, which represent typical functional shoulder activities. The study showed that shoulder activity involved in carrying a light load makes the greatest contribution to the trabecular architecture compared with other shoulder activities considered in this study (p<0.05). With all of the activities considered in this study, the lateral region, particularly in the anterior and posterior portions, showed greater deviation and greater sensitivity to variation under loading conditions than did the other regions (p<0.05). These results suggest that owing to the extra sensitivity of the anterior and posterior parts of the lateral region, these regions may be more informative in the analysis of the trabecular architecture following shoulder musculoskeletal injuries. These results may provide essential design information for shoulder prostheses and contribute to an understanding of morphological changes resulting from injury.     

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.     

Trabecular bone remodeling around smooth and porous implants in an equine patellar model

The objective of this investigation was to examine the stress-morphology relationships for trabecular bone around implants with different surface characteristics. Stainless steel spheres with either a polished surface or a sintered-bead porous coating were implanted unilaterally into equine patellae and maintained for a 6 month period. Stereological methods were used to quantify the trabecular bone morphology and finite element analyses were performed to predict the trabecular bone stresses. In general, the remodeling response around the smooth implants was greater than that around those porous implants that exhibited bone ingrowth. In accordance with these differences, the finite element models predicted greater changes in the stresses adjacent to the smooth implants due to the nonlinear boundary conditions. However, it did not appear that the trajectorial theory, in its simplest form, was applicable to the remodeling induced by the implants. A linear relationship between the change in bone areal density and the change in von Mises effective stress provides support for the hypothesis that the architecture of trabecular bone corresponds to an optimal structure. The results also demonstrated that, under certain circumstances, small changes in the stress state may result in large changes in the principal material orientation.     

Stochastic multi-scale prediction on the apparent elastic moduli of trabecular bone considering uncertainties of biological apatite (BAp) crystallite orientation and image-based modelling

An assessment of the mechanical properties of trabecular bone is important in determining the fracture risk of human bones. Many uncertainty factors contribute to the dispersion of the estimated mechanical properties of trabecular bone. This study was undertaken in order to propose a computational scheme that will be able to predict the effective apparent elastic moduli of trabecular bone considering the uncertainties that are primarily caused by image-based modelling and trabecular stiffness orientation. The effect of image-based modelling which focused on the connectivity was also investigated. A stochastic multi-scale method using a first-order perturbation-based and asymptotic homogenisation theory was applied to formulate the stochastically apparent elastic properties of trabecular bone. The effective apparent elastic modulus was predicted with the introduction of a coefficient factor to represent the variation of bone characteristics due to inter-individual differences. The mean value of the predicted effective apparent Young's modulus in principal axis was found at approximately 460 MPa for respective 15.24% of bone volume fraction, and this is in good agreement with other experimental results. The proposed method may provide a reference for the reliable evaluation of the prediction of the apparent elastic properties of trabecular bone.     

Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue

The ability to determine trabecular bone tissue elastic and failure properties has biological and clinical importance. To date, trabecular tissue yield strains remain unknown due to experimental difficulties, and elastic moduli studies have reported controversial results. We hypothesized that the elastic and tensile and compressive yield properties of trabecular tissue are similar to those of cortical tissue. Effective tissue modulus and yield strains were calibrated for cadaveric human femoral neck specimens taken from 11 donors, using a combination of apparent-level mechanical testing and specimen-specific, high-resolution, nonlinear finite element modeling. The trabecular tissue properties were then compared to measured elastic modulus and tensile yield strain of human femoral diaphyseal cortical bone specimens obtained from a similar cohort of 34 donors. Cortical tissue properties were obtained by statistically eliminating the effects of vascular porosity. Results indicated that mean elastic modulus was 10% lower (p<0.05) for the trabecular tissue (18.0+/-2.8 GPa) than for the cortical tissue (19.9+/-1.8 GPa), and the 0.2% offset tensile yield strain was 15% lower for the trabecular tissue (0.62+/-0.04% vs. 0.73+/-0.05%, p<0.001). The tensile-compressive yield strength asymmetry for the trabecular tissue, 0.62 on average, was similar to values reported in the literature for cortical bone. We conclude that while the elastic modulus and yield strains for trabecular tissue are just slightly lower than those of cortical tissue, because of the cumulative effect of these differences, tissue strength is about 25% greater for cortical bone.