Interrelationship of trabecular mechanical and microstructural properties in sheep trabecular bone

The ability to evaluate fracture risk at an early time point is essential for improved prognostics as well as enhanced treatment in cases of bone loss such as from osteoporosis. Improving the diagnostic ability is inherent upon both high-resolution non-invasive imaging, and a thorough understanding of how the derived indices of structure and density relate to its true mechanical behavior. Using sheep femoral trabecular bone with a range of strength, the interrelationship of mechanical and microstructural parameters was analyzed using multi-directional mechanical testing and micro-computed tomography. Forty-five cubic trabecular bone samples were harvested from 23 adult female sheep, some of whom had received hind-limb vibratory stimuli over the course of 2 years with consequently enhanced mechanical properties. These samples were pooled into a low, medium, or high strength group for further analysis. The findings show that microCT indices that are structural in nature, e.g., structural model index (SMI) (r2=0.85, p<0.0001) is as good as more density oriented indices like bone volume/total volume (BV/TV) (r2=0.81, p<0.0001) in predicting the ultimate strength of a region of trabecular bone. Additionally, those indices more related to global changes in trabecular structure such as connectivity density (ConnD) or degree of anisotropy (DA) are less able to predict the mechanical properties of bone. Interrelationships of trabecular indices such as trabecular number (TbN), thickness (TbTh), and spacing (TbSp) provide clues as to how the trabecular bone will remodel to ultimately achieve differences in the apparent mechanical properties. For instance, the analysis showed that a loss of bone primarily affects the connectedness and overall number of trabeculae, while increased strength results in an increase of the overall thickness of trabeculae while not improving the connectedness. Certainly, the microCT indices studied are able to predict the bulk mechanical properties of a trabecular ROI well, leaving unaccounted only about 15-20% of its inherent variability. Diagnostically, this implies that future work on the early prediction of fracture risk should continue to explore the role of bone quality as the key factors or as an adjuvant to bone quantity (e.g., apparent density).     

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.     

Predicting changes in mechanical properties of trabecular bone by adaptive remodeling

Because changes in the mechanical properties of bone are closely related to trabecular bone remodeling, methods that consider the temporal morphological changes induced by adaptive remodeling of trabecular bone are needed to estimate long-term fracture risk and bone quality in osteoporosis. We simulated bone remodeling using simplified and pig trabecular bone models and estimated the morphology of healthy and osteoporotic cases. We then displayed the fracture risk of the remodeled models based on a cumulative histogram from high stress. The histogram showed more elements had higher stresses in the osteoporosis model, indicating that the osteoporosis model had a greater risk.     

The mechanical properties of trabecular bone: Dependence on anatomic location and function

In 1961, Evans and King documented the mechanical properties of trabecular bone from multiple locations in the proximal human femur. Since this time, many investigators have cataloged the distribution of trabecular bone material properties from multiple locations within the human skeleton to include femur, tibia, humerus, radius, vertebral bodies, and iliac crest. The results of these studies have revealed tremendous variations in material properties and anisotropy. These variations have been attributed to functional remodeling as dictated by Wolff's Law. Both linear and power functions have been found to explain the relationship between trabecular bone density and material properties. Recent studies have re-emphasized the need to accurately quantify trabecular bone architecture proposing several algorithms capable of determining the anisotropy, connectivity and morphology of the bone. These past studies, as well as continuing work, have significantly increased the accuracy of analytical and experimental models investigating bone, and bone/implant interfaces as well as enhanced our perspective towards understanding the factors which may influence bone formation or resorption.     

Combination of topological parameters and bone volume fraction better predicts the mechanical properties of trabecular bone

Trabecular bone structure may complement bone volume/total volume fraction (BV/TV) in the prediction of the mechanical properties. Nonetheless, the direct in vivo use of information pertaining to trabecular bone structure necessitates some predictive analytical model linking structure measures to mechanical properties. In this context, the purpose of this study was to combine BV/TV and topological parameters so as to better estimate the mechanical properties of trabecular bone. Thirteen trabecular bone mid-sagittal sections were imaged by magnetic resonance (MR) imaging at the resolution of 117 x 117x 300 microm(3). Topological parameters were evaluated in applying the 3D-line skeleton graph analysis (LSGA) technique to the binary MR images. The same images were used to estimate the elastic moduli by finite element analysis (FEA). In addition to the mid-sagittal section, two cylindrical samples were cored from each vertebra along vertical and horizontal directions. Monotonic compression tests were applied to these samples to measure both vertical and horizontal ultimate stresses. BV/TV was found as a strong predictor of the mechanical properties, accounting for 89-94% of the variability of the elastic moduli and for 69-86% of the variability of the ultimate stresses. Topological parameters and BV/TV were combined following two analytical formulations, based on: (1) the normalization of the topological parameters; and on (2) an exponential fit-model. The normalized parameters accounted for 96-98% of the variability of the elastic moduli, and the exponential model accounted for 80-95% of the variability of the ultimate stresses. Such formulations could potentially be used to increase the prediction of the mechanical properties of trabecular bone.     

Pullout strength of suture anchors: Effect of mechanical properties of trabecular bone

This study investigated the relationships between trabecular microstructure and elastic modulus, compressive strength, and suture anchor pullout strength. Twelve fresh-frozen humeri underwent mechanical testing followed by micro-computed tomography (μCT). Either compression testing of cylindrical bone samples or pullout testing using an Arthrex 5 mm Corkscrew was performed in synthetic sawbone or at specific locations in the humerus such as the greater tuberosity, lesser tuberosity, and humeral head. Synthetic sawbone underwent identical mechanical testing and μCT analysis. Bone volume fraction (BVF), structural model index (SMI), trabecular thickness (TbTh), trabecular spacing (TbSp), trabecular number (TbN), and connectivity density were compared against modulus, compressive strength, and pullout strength in both materials. In cadaveric bone, modulus showed correlations to all of the microstructural properties, while compressive and pullout strength were only correlated to BVF, SMI, and TbSp. The microstructure of synthetic bone differed from cadaveric bone as SMI and TbTh showed little variation across the densities tested. Therefore, SMI and TbTh were the only microstructural properties that did not show correlations to the mechanical properties tested in synthetic bone. This study helps identify key microstructure–property relationships in cadaveric and synthetic bone as well as illustrate the similarities and differences between cadaveric and synthetic bone as biomechanical test materials.     

High-frequency oscillatory motions enhance the simulated mechanical properties of non-weight bearing trabecular bone

Extremely low-level oscillatory accelerations, applied without constraint, can increase bone formation. Here, we tested the hypothesis that high-frequency oscillations, applied in the absence of functional weight bearing, can be sensed by trabecular bone to produce a structure that is more efficient in sustaining applied loads. The left leg of anesthetized adult female mice (n=18) was subjected to high-frequency oscillations at 45 Hz, 0.6g for 20 min/day, 5 days/week for 3 weeks, while the contralateral leg served as an internal control. To remove the potential interference of the habitual strain environment with the imposed physical signal, the hindlimbs of these mice were chronically unloaded. In vivo microCT scans of the proximal metaphyseal region of the tibia were transformed into finite element meshes to evaluate trabecular and cortical mechanical properties. Simulated longitudinal compression tests showed that the short applications of high-frequency oscillations were sensed primarily by trabecular bone. At the end of the experimental period, apparent trabecular stiffness of the oscillated bones was 38% (p<0.001) greater than that of non-weight bearing controls. Simulated uniaxial loads applied to trabecular bone induced 21%, 52%, and 131% greater (p<0.05) median, peak compressive, and peak tensile longitudinal stresses in control than in stimulated bones. Non-weight bearing control bones were also characterized by greater transverse normal and shear stresses (77% and 54%, respectively, p<0.001) as well as 35% greater (p=0.03) longitudinal shear stresses. Compared to normal age-matched controls (n=18), oscillations were able to attenuate, but not fully prevent, the decline in trabecular mechanical properties associated with the removal of weight bearing. These data indicate not only that bone cells can sense low-level, high-frequency oscillatory accelerations, but also that they can orchestrate a structural response that produces a stiffer trabecular structure that may be less prone to fracture.     

The mechanical properties of human tibial trabecular bone as a function of metaphyseal location

Experimental determination of the elastic modulus and ultimate strength of human tibial trabecular bone as a function of metaphyseal location is presented.

A 1 cm cubic matrix with planes parallel to the subchondral plate was defined on five fresh frozen cadaver tibias. Approximately 400, 7 mm × 10 mm cylindrical bone plugs were cut from the locations defined by the matrix and tested in uniaxial compressive stress at a strain rate of 0.1%s⁻¹. Results of the study indicate that the trabecular bone properties vary as much as two orders of magnitude from one location to another. As might be predicted from Wolff's law, and noted by previous investigators, concentrations of strength arise from the medial and lateral metaphyseal cortices toward the major medial and lateral contact regions.

These results may be valuable for improved analytical modeling and optimal prosthetic design.     

Mechanical properties of trabecular bone. Dependency on strain rate.

The effect of strain rate (epsilon) and apparent density (rho) on stiffness (E), strength (sigma u), and ultimate strain (epsilon u) was studied in 60 human trabecular bone specimens from the proximal tibia. Testing was performed by uniaxial compression to 5% specimen strain. Six different strain rates were used: 0.0001, 0.001, 0.01, 0.1, 1, and 10 s-1. Apparent density ranged between 0.23 and 0.59 g cm-3. Linear and non-linear regression analyses using strength, stiffness and ultimate strain as dependent variables (Y) and strain rate and apparent density as independent variables were performed using the following models: Y = a rho b epsilon c, Y = rho b(a + c epsilon; Y = (a + b rho)epsilon c, Y = a rho 2 epsilon c, E = a rho 3 epsilon c. The variations of strength and stiffness were explained equally well by the linear and the power function relationship to strain rate. The exponent was 0.07 in the power function relationship between strength and strain rate and 0.05 between stiffness and strain rate. The variation of ultimate strain was explained best using a power function relationship to strain rate (exponent = 0.03). The variation of strength and stiffness was explained equally well by the linear, power function and quadratic relationship to apparent density. The cubic relationship between stiffness and apparent density showed a less good fit. Ultimate strain varied independently of apparent density.     

Effects of gamma irradiation on mechanical properties of defatted trabecular bone allografts assessed by speed-of-sound measurement

New sterilization methods for human bone allografts may lead to alterations in bone mechanical properties, which strongly influence short- and medium-term outcomes. In many sterilization procedures, bone allografts are subjected to gamma irradiation, usually with 25 KGy, after treatment and packaging. We used speed-of-sound (SOS) measurements to evaluate the effects of gamma irradiation on bone. All bone specimens were subjected to the same microbial inactivation procedure. They were then separated into three groups, of which one was treated and not irradiated and two were exposed to 10 and 25 KGy of gamma radiation, respectively. SOS was measured using high- and low-frequency ultrasound beams in each orthogonal direction. SOS and Young modulus were altered significantly in the three groups, compared to native untreated bone. Exposure to 10 or 25 KGy had no noticeable effect on the study variables. The impact of irradiation was small compared to the effects of physical or chemical defatting. Reducing the radiation dose used in everyday practice failed to improve graft mechanical properties in this study.     

A global relationship between trabecular bone morphology and homogenized elastic properties.

An alternative concept of the relationship between morphological and elastic properties of trabecular bone is presented and applied to human tissue from several anatomical locations using a digital approach. The three-dimensional morphology of trabecular bone was assessed with a microcomputed tomography system and the method of directed secants as well as the star volume procedure were used to compute mean intercept length (MIL) and average bone length (ABL) of 4 mm cubic specimens. Assuming isotropic elastic properties for the trabecular tissue, the general elastic tensors of the bone specimens were determined using the homogenization method and the closest orthotropic tensors were calculated with an optimization algorithm. The assumption of orthotropy for trabecular bone was found to improve with specimen size and hold within 6.1 percent for a 4 mm cube size. A strong global relationship (r2 = 0.95) was obtained between fabric and the orthotropic elastic tensor with a minimal set of five constants. Mean intercept length and average bone length provided an equivalent power of prediction. These results support the hypothesis that the elastic properties of human trabecular bone from an arbitrary anatomical location can be estimated from an approximation of the anisotropic morphology and a prior knowledge of tissue properties.     

Structural and mechanical adaptations of immature trabecular bone to strenuous exercise

Effects of strenuous exercise on immature bone were examined in two clinically important regions, femoral neck (FN) and lumbar vertebra (L6). Female Sprague-Dawley rats (n = 20, 8 wk of age, 150-170 g) were exercised progressively 5 days/wk for approximately 1 h/day for 10 wk at 75-80% of maximum oxygen capacity on a motor-driven treadmill. Caged age-matched rats served as controls (n = 20). Rat FNs were tested in cantilever bending, and vertebral bodies were compressed to 50% of their initial height at a fast strain rate. In response to the strenuous exercise, the relative area of the FN trabecular core increased significantly at the expense of the cortical shell. With that structural change, the exercised FN had significantly less energy to proportional limit than controls. The FN material properties (normal stresses at proportional limit and maximum) were significantly diminished after 10 wk of strenuous exercise. At the same time, no differences were found in vertebral geometry or structural and material properties. In the immature rate, the differential responses of the FN vs. L6 may relate to load history rather than a general systemic response to the strenuous exercise.     

Evaluation of trabecular mechanical and microstructural properties in human calcaneal bone of advanced age using mechanical testing, microCT, and DXA

Early detection of fracture risk is important for initiating treatment and improving outcomes from both physiologic and pathologic causes of bone loss. While bone mineral density (a quantity measure) has traditionally been used for this purpose, alternative structural imaging parameters (quality measures) are proposed to better predict bone's true mechanical properties. To further elucidate this, trabecular bone from cadaveric human calcanei were used to evaluate the interrelationship of mechanical and structural parameters using mechanical testing, dual energy X-ray absorptiometry (DXA) scanning, and micro computed tomography (microCT) imaging. Directional specific structural properties were assessed in three-dimensional (3-D) and correlated to mechanical testing and DXA. The results demonstrated that microCT-derived indices of bone quality (i.e., volume fraction and structural model index) are better than DXA-derived bone mineral density for the prediction of the mechanical parameters of bone (i.e., elastic modulus, yield stress, and ultimate stress). Diagnostically, this implies that future work on the early prediction of fracture risk should focus as much on bone quality as on quantity. Furthermore, the results of this study show that a loss of bone primarily affects the connectedness and overall number of trabeculae. Ultimate stress, however, is better correlated with trabecular number than thickness. As such, primary prevention of osteoporosis may be more important than later countermeasures for bone loss.     

A structural model for the mechanical behavior of trabecular bone

A quantitative model is developed for trabecular bone by approximating the trabecular geometry with a hypothetical network of compact bone. For the region immediately beneath the articular cartilage in the distal end of the femur, finite element analyses were performed with a high speed computer, assuming a physiological static load. The results indicate that bending and buckling of trabeculae are considerable in any elastic deformation of the bone; that fatigue fracture in some fraction of suitably oriented trabeculae is inevitable in normal ambulation; and that the stiffness varies considerably with lateral position across the subchondral plate. The latter depends totally on trabecular arrangement and may play a role in joint function and degeneration. The adjustments necessary to bring the gross stiffness into agreement with experiment imply that the intertrabecular soft tissues are of no consequence to the mechanical properties and that the compact bone of which trabeculae are made is probably not as stiff as cortical bone.     

Mechanical properties of femoral trabecular bone in dogs

Background  

Studying mechanical properties of canine trabecular bone is important for a better understanding of fracture mechanics or bone disorders and is also needed for numerical simulation of canine femora. No detailed data about elastic moduli and degrees of anisotropy of canine femoral trabecular bone has been published so far, hence the purpose of this study was to measure the elastic modulus of trabecular bone in canine femoral heads by ultrasound testing and to assess whether assuming isotropy of the cancellous bone in femoral heads in dogs is a valid simplification.     

The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens.

The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens was studied by non-destructive uniaxial compression to 0.4% strain using cylindrical specimens with different sizes and length-to-diameter ratios, and by comparing cubic and cylindrical specimens with the same cross-sectional area. Both the length and the cross-sectional area of the specimen had a highly significant influence on the mechanical behaviour (p less than 0.0001). Within the actual range of length (2.75-11.0 mm) the normalized stiffness (Young's modulus) was related nearly linearly to the specimen length. This dependency on specimen length is suggested to be caused mainly by structural disintegrity of the trabecular specimens near the surface. The normalized stiffness (Young's modulus) was also positively correlated to the cross-sectional area. This dependency on cross-sectional area is probably due to friction-induced stress inhomogeneity at the platen-specimen interface. A cube with side length 6.5 mm or a cylindrical specimen with 7.5 mm diameter and 6.5 mm length are suggested as standard specimens for comparative studies on trabecular bone mechanics.     

How morphology predicts mechanical properties of trabecular structures depends on intra-specimen trabecular thickness variations

Two observations underlie this work. First, that the architecture of trabecular bone can accurately predict the mechanical stiffness characteristics of bone specimens when considering the combination of volume fraction and fabric, which is a measure of architectural anisotropy. Second, that the same morphological measures could not accurately predict the mechanical properties of porous structures in general. We hypothesize that this discrepancy can be explained by the special nature of trabecular bone as a structure in remodeling equilibrium relative to the external loads. We tested this hypothesis using a generic model of trabecular bone. Five series of 153 different architectures were created with this model. Each architecture was subjected to morphological analysis, and four different fabric measures were calculated to evaluate their effectiveness in characterizing the architecture. Relationships were determined relating morphology to the elastic constants. The quality of these relationships was tested by correlating the predicted elastic constants with those determined from finite element analysis. We found that the four fabric measures used could estimate the mechanical properties almost equally well. So the suggestion that fabric measures based on trabecular bone volume better represent the architecture than mean intercept length could not be affirmed. We conclude that for structures with equally sized elliptical voids the mechanical properties can be predicted well only if trabecular thickness variations within each structure are limited. These structures closely resemble previously developed models of trabecular bone. Furthermore, they are stiff in the principal fabric direction, hence, according to Cowin (J. Biomech. Eng. (108) (1986) 83), they are in remodeling equilibrium. These structures are also stiff over a large range of loading orientations, hence, are relatively insensitive to deviations in direction of loading.     

An adaptation model for trabecular bone at different mechanical levels

Background  

Bone has the ability to adapt to mechanical usage or other biophysical stimuli in terms of its mass and architecture, indicating that a certain mechanism exists for monitoring mechanical usage and controlling the bone's adaptation behaviors. There are four zones describing different bone adaptation behaviors: the disuse, adaptation, overload, and pathologic overload zones. In different zones, the changes of bone mass, as calculated by the difference between the amount of bone formed and what is resorbed, should be different.     

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.