The mechanical behaviour of cancellous bone

Cancellous bone has a cellular structure: it is made up of a connected network of rods and plates. Because of this, its mechanical behaviour is similar to that of other cellular materials such as polymeric foams. A recent study on the mechanisms of deformation in such materials has led to an understanding of how their mechanical properties depend on their relative density, cell wall properties and cell geometry. In this paper, the results of this previous study are applied to cancellous bone in an attempt to further understand its mechanical behaviour. The results of the analysis agree reasonably well with experimental data available in the literature.     

Analysis of bone tissue mechanical properties

This paper deals with the torsional moment depending on the angle of torsion of the compact bone in laboratory animals and humans. Based on the data from laboratory animals, obtained by measurement, the data on dependence of the torsional moment and the angle of torsion were assumed for humans. Measurements were carried out on four groups of compact bone in laboratory animals. One was the control group, and three other groups were treated by various vitamin D3 metabolites. Equal measurements were performed in only one group of compact bone in humans, due to the impossibility to treat humans with vitamin D3 metabolites. Functional relations between the angle of torsion and the torsional moment for all groups of animal body tissue were determined by measurements, and the results were used to assume the reaction of human compact bone tissue if treated by vitamin D3 metabolites.     

Incompatible mechanical properties in compact bone

The covariation of a number of mechanical of properties, and some physical characteristics, of compact bones from a wide range of bones were examined. Young's modulus was well predicted by a combination of mineral content and porosity. Increasing Young's modulus was associated with: increasing stress at yield, increasing bending strength, and a somewhat higher resilience, tensile strength and fatigue strength. Contrarily, in the post-yield region a higher Young's modulus (and more clearly, a higher mineral content) was associated with: a reduced work to fracture in tension, a reduced impact strength and an increased notch sensitivity in impact. Increasing porosity is associated with deleterious effects in the pre-yield region, but has little effect in the post-yield region. Bone, like many other materials, is unable to have good qualities in both the pre- and post-yield regions. Since an increase in mineral or Young's modulus is more potent, that is deleterious, in the post-yield than it is advantageous in the pre-yield region, it is likely that mineral content will be selected to be slightly lower than would be the case if it were equally potent in both regions. As is usual in biology, different adaptive extremes are incompatible.     

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.     

Heterogeneity of the mechanical properties of demineralized bone

Knowledge of the mechanical properties of the collagenous component of bone is required for composite modeling of bone tissue and for understanding the age- and disease-related reductions in the ductility and strength of bone. The overall goal of this study was to investigate the heterogeneity of the mechanical properties of demineralized bone which remains unexplained and may be due to differences in the collagen structure or organization or in experimental protocols. Uniaxial tension tests were conducted to measure the elastic and failure properties of demineralized human femoral (n = 10) and tibial (n = 13) and bovine humeral (n = 8) and tibial (n = 8) cortical bone. Elastic modulus differed between groups (p = 0.02), varying from 275 +/- 94 MPa (mean +/- SD) to 450 + 50 MPa. Similarly, ultimate stress varied across groups from 15 + 4.2 to 26 + 4.7 MPa (p = 0.03). No significant differences in strain-to-failure were observed between any groups in this study (pooled mean of 8.4 +/- 1.6%; p = 0.42). However, Bowman et al. (1996) reported an average ultimate strain of 12.3 +/- 0.5% for demineralized bovine humeral bone, nearly 40% higher than our value. Taken together, it follows that all the monotonic mechanical properties of demineralized bone can display substantial heterogeneity. Future studies directed at explaining such differences may therefore provide insight into aging and disease of bone tissue.     

Some mechanical properties of goose femoral cortical bone

The ultimate compressive strength and modulus of elasticity of femoral cortical bone from adult geese (Anser anser), were determined by sex and by quadrant by compressing small right circular cylinders which were 2.4 mm in height and 0.8 mm in diameter. The average ultimate compressive strength was 183 +/- 29 MPa. The average modulus of elasticity was 13.2 +/- 3.4 GPa. The bending strength and bending modulus of elasticity were determined by a three point bend test on rectangular prisms which had the approximate dimensions 0.75 mm X 0.75 mm X 25 mm. The average bending strength was 263 +/- 44 MPa while the average bending modulus was 19.6 +/- 3.1 GPa. The calcium content was determined by atomic absorption spectrophotometry and no correlation was found with the mechanical properties. The histology of the cortical bone was examined both quantitatively and qualitatively. A unique type of Haversian bone is described. Goose bone was found to be morphologically similar to adolescent human bone and to have mechanical properties similar to those of adult human bone.     

The evolution of the mechanical properties of amniote bone

162 specimens from 19 species of amniote were tested for various mechanical and physical properties to ascertain whether there were characteristic differences between different groups. All mechanical properties showed very great variation. In general the reptiles were not inferior to the mammals and birds. The histology of living forms was compared to that of fossil forms, to see whether 'weak' histology was more characteristic of primitive amniotes. The earliest reptiles probably had rather complaint bone, but it was probably tough. Modern types of bone appeared over two hundred million years ago. Very specialised bone, like that of the bullae of whales and antlers, may have evolved only in the mammals, but the fossil record is not complete enough to assert this confidently.     

Site specific bone adaptation response to mechanical loading

Over 25 million Americans suffer from osteoporosis. Bone size and strength depends both upon the level of adaptation due to physical activity (applied load), and genetics. We hypothesized that bone adaptation to loads differs among mice breeds and bone sites. Forty-five adult female mice from three inbred strains (C57BL/6 [B6], C3H/HeJ [C3], and DBA/2J [D2]) were loaded at the right tibia and ulna in vivo with non-invasive loading devices. Each loading session consisted of 99 cycles at a force range that induced approximately 2000 microstrain (microepsilon) at the mid-shaft of the tibia (2.5 to 3.5 N force) and ulna (1.5 to 2 N force). The right and left ulnae and tibiae were collected and processed using protocols for histological undecalcified cortical bone slides. Standard histomorphometry techniques were used to quantify new bone formation. The histomorphometric variables include percentage mineralizing surface (%MS), mineral apposition rate (MAR), and bone formation rate (BFR). Net loading response [right-left limb] was compared between different breeds at tibial and ulnar sites using two-way ANOVA with repeated measures (p<0.05). Significant site differences in bone adaptation response were present within each breed (p<0.005). In all the three breeds, the tibiae showed greater percentage MS, MAR and BFR than the ulna at similar in vivo load or mechanical stimulus (strain). These data suggest that the bone formation due to loading is greater in the tibiae than the ulnae. Although, no significant breed-related differences were found in response to loading, the data show greater trends in tibial bone response in B6 mice as compared to D2 and C3 mice. Our data indicate that there are site-specific skeletal differences in bone adaptation response to similar mechanical stimulus.     

Biochemical and mechanical properties of subchondral bone in osteoarthritis

The subchondral bone has long been known to thicken in osteoarthritis. However, recent evidence has demonstrated that the turnover of the bone is increased several fold, and further suggests that the thickening occurs prior to degradation of the articular cartilage, indicating that it plays a role in the pathogenesis of osteoarthritis. The mechanical and biochemical properties of the subchondral bone are therefore of particular interest in any attempt to determine the nature of the factors initiating osteoarthritis. We have shown that the subchondral bone collagen of the femoral head possessed a 20-fold increase in turnover, as assessed by procollagen rate of synthesis and metalloproteinase degradation, and a 25% decrease in mineralisation. This increased metabolism and high lysyl hydroxylation leads to narrower and weaker fibres. Additionally the phenotypic expression of the osteoblasts is modified to produce increasing proportions of type I homotrimer in addition to the normal type I heterotrimer, which further reduces the mechanical strength of the bone. Overall, the narrow immature collagen fibres, the reduction in pyrrole cross-linking, decreased mineralisation, and increased amounts of type I homotrimer, all contribute to a weakening of the mechanical properties of the subchondral bone.     

Effects of tissue preservation on murine bone mechanical properties

Murine bone specimens are used extensively in skeletal research to assess the effects of environmental, physiologic and pathologic factors on their mechanical properties. Given the destructive nature of mechanical testing, it is normally performed as a terminal procedure, where specimens must be preserved without affecting their mechanical properties. To this end, we aimed to study the effects of tissue preservation (freezing and formalin fixation) on the elastic and viscoelastic mechanical properties of murine femur and vertebrae. A total of 120 femurs and 180 vertebral bodies (L3–L5) underwent non-destructive cyclic loading to assess their viscoelastic properties followed by mono-cyclic loading to failure to assess their elastic properties. All specimens underwent re-hydration in 0.9% saline for 30 min prior to mechanical testing. Analysis indicated that stiffness, modulus of elasticity, yield load, yield strength, ultimate load and ultimate strength of frozen and formalin-fixed femurs and vertebrae were not different from fresh specimens. Cyclic loading of both femurs and vertebrae indicated that loss, storage and dynamic moduli were not affected by freezing. However, formalin fixation altered their viscoelastic properties. Our findings suggest that freezing and formalin fixation over a 2-week period do not alter the elastic mechanical properties of murine femurs and vertebrae, provided that specimens are re-hydrated for at least half an hour prior to testing. However, formalin fixation weakened the viscoelastic properties of murine bone by reducing its ability to dissipate viscous energy. Future studies should address the long-term effects of both formalin fixation and freezing on the mechanical properties of murine bone.     

Orientation of mineral in bovine bone and the anisotropic mechanical properties of plexiform bone.

Angular dependent Young's modulus E phi presented by Bonfield and Grynpas [Nature 270, 453-454 (1977)] was simulated by using the distribution function of the orientation of mineral in plexiform bone introduced on the basis of an X-ray pole figure analysis (XPFA) and a small angle X-ray scattering (SAXS) results. Calculations were performed with the aid of a simple model which expresses well the geometrical characteristic of plexiform bone. Estimated angular dependent Young's modulus in terms of the distribution of mineral orientation reproduced the experimental results. The suitable aspect ratio of bone mineral for the reproduction of the empirical data was a reasonable value compared with the morphological study of bone mineral. It is concluded that the angular dependence of mechanical properties of plexiform bone is explained by the distribution of bone mineral orientation and its morphology.