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.     

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).     

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.     

The effect of constraint on the mechanical behaviour of trabecular bone specimens

The effect of the boundary conditions between trabecular bone specimens and the test columns of the testing machine was studied together with the effect of side-constraint on the mechanical behaviour of trabecular bone during axial compression. Cylindrical specimens taken from the upper tibial epiphysis of autopsy knees were tested non-destructively by cyclic compression to 0.8% strain under different conditions. Fixation of the specimens to the test columns by a thin layer of bone cement increased the stiffness by 40% and reduced the energy dissipation to 67% of those measured under unconstrained conditions (p less than 0.001). The thin cement layer alone increased the stiffness 19% and reduced energy dissipation to 86% (n.s.). When the machine was equipped with polished steel columns coated by a film of low-viscous oil, both the stiffness and the energy dissipation were reduced to 93% of those measured under standard conditions (p less than 0.005). Trabecular bone specimens tested side-constrained by the surrounding trabecular bone (in situ) showed a 19% larger stiffness than that measured during later testing of the corresponding machined specimens (p less than 0.005) whereas the energy dissipation was not altered significantly. The same specimens showed a 22% increase of stiffness and a 68% increase of energy dissipation when they were side-constrained by a closely fitting steel cylinder (p less than 0.005).     

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.     

The role of fabric in the quasi-static compressive mechanical properties of human trabecular bone from various anatomical locations

Osteoporosis leads to an increased risk of bone fracture. While bone density and architecture can be assessed in vivo with increasing accuracy using CT and MRI, their relationship with the critical mechanical properties at various anatomical sites remain unclear. The objective of this study was to quantify the quasi-static compressive mechanical properties of human trabecular bone among different skeletal sites and compare their relationships with bone volume fraction and a measure of microstructural anisotropy called fabric. Over 600 trabecular bone samples from six skeletal sites were assessed by and tested in uniaxial compression. Bone volume fraction correlated positively with elastic modulus, yield stress, ultimate stress, and the relationships depended strongly on skeletal site. The account of fabric improved these correlations substantially, especially when the data of all sites were pooled together, but the fabric–mechanical property relationships remained somewhat distinct among the anatomical sites. The study confirms that, beyond volume fraction, fabric plays an important role in determining the mechanical properties of trabecular bone and should be exploited in mechanical analysis of clinically relevant sites of the human skeleton.     

The influence of mechanical stimulation on osteoclast localization in the mouse maxilla: bone histomorphometry and finite element analysis

The mechanism of traumatic bone resorption in the denture-bearing bone has not yet been established with regard to the osteoclastic activity in relation to the mechanical stimulus. The purpose of this study was to clarify whether osteoclast appearance in maxilla depends on the strain intensity, using the murine loading model. The maxillary palate of thirteen-week-old male C57BL/6 mice was subjected to continuous pressure of 2 kPa (low stimulation, n = 4) or 7 kPa (high stimulation, n = 4) for 30 min/day for 7 consecutive days, and the mice were sacrificed after the last loading. The control group underwent the same protocol without load (n = 4). An animal-specific finite element model was constructed based on morphology and characteristics obtained from the micro-CT data and used to calculate the strain intensity of the bone. The bone histomorphometric technique revealed significant reduction of cortical bone volume and significant increase of bone resorption parameters such as osteoclast number in the bone tissue under the loading contact in comparison to the control (p < 0.05). The osteoclasts were observed in the subsurface region adjacent to the loading contact and the peripheral region of the marrow space in the intracortical region of the cortical bone in the mouse maxilla in both stimulation groups. An average of more than 90 % of the osteoclasts was observed in the areas with strain intensity higher than 85.0μ strain for the high stimulation group. The result suggests that the osteoclastic resorption is location-dependent and is also sensitive to the local strain intensity.     

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.     

Physical and mechanical properties of calf lumbosacral trabecular bone.

The physical and mechanical properties of calf lumbar and sacral trabecular bone were determined and compared with those of human trabecular bone. The mean tissue density (1.66 +/- 0.12 g cm-3), equivalent mineral density (169 +/- 36 mg cm-3), apparent density (453 +/- 89 mg cm-3), ash density (194 +/- 59 mg cm-3), ash content (0.6 +/- 0.05%), compressive strength (7.1 +/- 3.0 MPa) and compressive modulus (173 +/- 97 MPa) of calf trabecular bone are similar to those of young human. There were moderate, positive linear correlations between apparent density and equivalent mineral density, ash density, and compressive strength; and between compressive strength and equivalent mineral density (R2 ranging from 0.35 to 0.48, p less than 0.001). Apparent density, ash density, and equivalent mineral density did not differ significantly in different regions. In contrast to humans, the compressive strength increased from posterior, near the facet, to the anterior vertebral body. These comparisons of physical and mechanical properties, as well as anatomical comparisons by others, indicate that the calf spine is a good model of the young non-osteoporotic human spine and thus useful for the testing of spinal instrumentation.     

The modified super-ellipsoid yield criterion for human trabecular bone

Despite the importance of multiaxial failure of trabecular bone in many biomechanical applications, to date no complete multiaxial failure criterion for human trabecular bone has been developed. By using experimentally validated nonlinear high-resolution, micromechanical finite-element models as a surrogate for multiaxial loading experiments, we determined the three-dimensional normal strain yield surface and all combinations of the two-dimensional normal-shear strain yield envelope. High-resolution finite-element models of three human femoral neck trabecular bone specimens obtained through microcomputed tomography were used. In total, 889 multiaxial-loading cases were analyzed, requiring over 41,000 CPU hours on parallel supercomputers. Our results indicated that the multiaxial yield behavior of trabecular bone in strain space was homogeneous across the specimens and nearly isotropic. Analysis of stress-strain curves along each axis in the 3-D normal strain space indicated uncoupled yield behavior whereas substantial coupling was seen for normal-shear loading. A modified super-ellipsoid surface with only four parameters fit the normal strain yield data very well with an arithmetic error +/-SD less than -0.04 +/- 5.1%. Furthermore, the principal strains associated with normal-shear loading showed excellent agreement with the yield surface obtained for normal strain loading (arithmetic error +/- SD < 2.5 +/- 6.5%). We conclude that the four-parameter "Modified Super-Ellipsoid" yield surface presented here describes the multiaxial failure behavior of human femoral neck trabecular bone very well.     

The response of bone to mechanical loading and disuse: fundamental principles and influences on osteoblast/osteocyte homeostasis

Bone’s response to increased or reduced loading/disuse is a feature of many clinical circumstances, and our daily life, as habitual activities change. However, there are several misconceptions regarding what constitutes loading or disuse and why the skeleton gains or loses bone. The main purpose of this article is to discuss the fundamentals of the need for bone to experience the effects of loading and disuse, why bone loss due to disuse occurs, and how it is the target of skeletal physiology which drives pathological bone loss in conditions that may not be seen as being primarily due to disuse. Fundamentally, if we accept that hypertrophy of bone in response to increased loading is a desirable occurrence, then disuse is not a pathological process, but simply the corollary of adaptation to increased loads. If adaptive processes occur to increase bone mass in response to increased load, then the loss of bone in disuse is the only way that adaptation can fully tune the skeleton to prevailing functional demands when loading is reduced. The mechanisms by which loading and disuse cause bone formation or resorption are the same, although the direction of any changes is different. The osteocyte and osteoblast are the key cells involved in sensing and communicating the need for changes in mass or architecture as a result of changes in experienced loading. However, as those cells are affected by numerous other influences, the responses of bone to loading or disuse are not simple, and alter under different circumstances. Understanding the principles of disuse and loading and the mechanisms underlying them therefore represents an important feature of bone physiology and the search for targets for anabolic therapies for skeletal pathology.     

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.     

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.     

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.     

Effects of mechanical stimulation on the proliferation of bone marrow-derived human mesenchymal stem cells

To support and enhance thein vitro growth and activity of mesenchymal stem cells (MSCs), the cell culture medium may be supplemented with various proteins and factors to mimic the physiological environment in which the cells optimally proliferate and differentiate. In this study, the effects of mechanical factors on cellular metabolic responses were investigated experimentally using a bioreactor. The effects of various chemical factors, such as growth factors, cytokines, and hormones, were also investigated. Based on previous reports demonstrating the important roles of mechanical factors in the growth and activity of MSCs, we sought to evaluate the effects of mechanical stimuli on the proliferation of bone marrow-derived MSCs using a cell training bioreactor that imposed cyclic mechanical stretch, with parameters of 240 min/day, 0.03 Hz, and 5–15% strain. The application of cyclic stretch (5–15% strain) to the MSCs enhanced their proliferation during the early stage (3 days), but not the late stage (14 days), of batch culture. Mechanical stretch did not increase the release of lactate dehydrogenase (LDH) from the MSCs during culture. Appropriate levels of mechanical stretch (5–10% strain) increased collagen synthesis, but did not alter MSC surface antigen expression. It is thought that the appropriate level of mechanical stretch was able to serve as a potent positive modulator of MSC proliferation during the initial stages of culture.