Tensile behavior of cortical bone: dependence of organic matrix material properties on bone mineral content

A porous composite model is developed to analyze the tensile mechanical properties of cortical bone. The effects of microporosity (volksman's canals, osteocyte lacunae) on the mechanical properties of bone tissue are taken into account. A simple shear lag theory, wherein tensile loads are transferred between overlapped mineral platelets by shearing of the organic matrix, is used to model the reinforcement provided by mineral platelets. It is assumed that the organic matrix is elastic in tension and elastic-perfectly plastic in shear until it fails. When organic matrix shear stresses at the ends of mineral platelets reach their yield values, the stress-strain curve of bone tissue starts to deviate from linear behavior. This is referred as the microscopic yield point. At the point where the stress-strain behavior of bone shows a sharp curvature, the organic phase reaches its shear yield stress value over the entire platelet. This is referred as the macroscopic yield point. It is assumed that after macroscopic yield, mineral platelets cannot contribute to the load bearing capacity of bone and that the mechanical behavior of cortical bone tissue is determined by the organic phase only. Bone fails when the principal stress of the organic matrix is reached. By assuming that mechanical properties of the organic matrix are dependent on bone mineral content below the macroscopic yield point, the model is used to predict the entire tensile mechanical behavior of cortical bone for different mineral contents. It is found that decreased shear yield stresses and organic matrix elastic moduli are required to explain the mechanical behavior of bones with lowered mineral contents. Under these conditions, the predicted values (elastic modulus, 0.002 yield stress and strain, and ultimate stress and strain) are within 15% of experimental data.     

In vitro sodium fluoride exposure decreases torsional and bending strength and increases ductility of mouse femora

Fluoride exposure in vivo can reduce the material strength of bone, an effect that has been attributed to a change in mineral structure. An in vitro model of fluoride exposure offers the potential to study directly the effects of fluoride on bone mineral. Previous investigators have reported that soaking bones in sodium fluoride in vitro reduces bone strength. However, long soaking times and the absence of physiological buffering ions from their treatment solutions may have caused mineral dissolution that contributed to the decrease in bone strength. Our objectives were to further characterize the effects of in vitro fluoride exposure on bone mechanical properties and to determine if the changes reported in previous studies of bovine cortical bone would be observed for whole rodent bones. We soaked 60 mouse femora in sodium fluoride solutions, with and without physiological buffering ions, and evaluated their torsional and bending properties. Fluoride soaked bones had a 30-fold increase in fluoride content and a 23% increase in water content compared to controls. These changes were associated with average reductions in ultimate load of 45%, reductions in rigidity of 70%, and increases in deformation to failure of 80%. The effect of fluoride was similar for bones treated in buffered and non-buffered solutions, and was observed in both torsion and bending. Our findings confirm those of previous studies and highlight the strong effect that in vitro fluoride exposure has on bone mechanical properties. The in vitro model of fluoride exposure offers a tool to further study the effects of ion substitution in bone.     

Tensile damage and its effects on cortical bone

Plexiform bovine bone samples are repeatedly loaded in tension along their longitudinal axis. In order to induce damage in the bone tissue, bone samples are loaded past their yield point. Half of the bone samples from the damaged group were stored in saline to allow for viscoelastic recovery while the others were decalcified. Tensile tests were conducted on these samples to characterize the effects of damage on the mechanical behavior of the organic matrix (decalcified samples) as well as on bone tissue (stored in saline). The ultimate strain of the damaged decalcified bone is 29% higher compared to that of non-damaged decalcified (control) bone. The ultimate stresses as well as the elastic moduli are similar in both decalcified groups. This phenomenon is also observed in other collagenous tissue (tendon and ligament). This may suggest that damage in bone is caused by shear failure of the organic matrix; transverse separation of the collagen molecules or microfibrils from each other. In contrast, there is a trend towards lowered ultimate strains in damaged bone, which is soaked in saline, with respect to control bone samples (not damaged). The damaged bone tissue exhibits a bi-linear behavior in contrast to the mechanical behavior of non-damaged bone. The initial elastic modulus (below 55 MPa) and ultimate strength of damaged bone are similar to that in non-damaged bone.     

Changing the structurally effective mineral content of bone with in vitro fluoride treatment

Bovine femur cortical bone specimens were tested in tension after being treated in vitro for 3 days with sodium fluoride solutions of different molarity (0.145, 0.5, and 2.0M). The treatments alter the mechanical properties of the bone samples with different degrees as compared to control samples (untreated). The mechanical properties of the treated samples have lower elastic modulus, yield and ultimate stress, acoustic impedance and hardness, and higher ultimate strain and toughness as compared to control samples. The observed effects were intensified with the increasing molarity of the treatment solutions. This study shows that the fluoride treatment can be used to investigate the composite behavior of bone tissue by altering the structurally important bone mineral content in a controlled manner.     

Modeling the tensile mechanical behavior of bone along the longitudinal direction

The tensile stress-strain behavior of bone along its longitudinal axis is modeled by using a simple shear-lag theory, wherein, stresses and strains in a unit cell consisting of an organic matrix reinforced by overlapped mineral platelets are computed. It is assumed that loads are transferred between overlapped mineral-platelets by shear in the organic matrix. The mechanical behavior of bone in which the matrix partially or completely debonds from the sides of the overlapped mineral platelets (after an ultimate interfacial shear stress value is exceeded) is modeled. It is shown that the tensile mechanical behavior of bone can be modeled only by assuming little or no debonding of the organic from the mineral. A physical phenomenon that explains the tensile behavior of bone is, after the interfacial shear stress has reached a constant value over the length of the mineral platelets, the collagen molecules/microfibrils (with the associated mineral platelets) move relative to one another. The tensile stress-strain curve of bovine bone is modeled using this model. The theory predicts the mechanical behavior of the tissue in the elastic, yield and post-yield region. The ultimate strain and strengths are not predicted in the present model.     

Infrared spectroscopic assessment of the inflammation-mediated osteoporosis (IMO) model applied to rabbit bone

A model of osteoporosis based on induced inflammation (IMO) was applied on rabbit bones. The structural heterogeneity and molecular complexity of bone significantly affect bone mechanical properties. A tool like Fourier transform infrared spectroscopy, able to analyze both the inorganic and organic phase simultaneously, could provide compositional information regarding cortical and trabecular sections under normal and osteoporotic conditions. In this study, we assessed the mineral/matrix ratio, carbonate and phosphate content and labile (i.e., non-apatitic) species contribution to bone mineral and collagen cross-linking patterns. Clear differences were observed between cortical and trabecular bone regarding mineral and carbonate content. Induced inflammation lowers the mineral/matrix ratio and increases the overall carbonate accumulation. Elevated concentrations of labile species were detected in osteoporotic samples, especially in the trabecular sections. Collagen cross-linking patterns were indirectly observed through the 1660/1690 cm^− 1 ratio in the amide I band and a positive correlation was found with the mineralization index. Principal component analysis (PCA) applied to female samples successfully clustered trabecular and osteoporotic cases. The important role played by the phosphate ions was confirmed by corresponding loadings plots. The results suggest that the application of the IMO model to rabbit bones effectively alters bone remodeling and forms an osteoporotic bone matrix with a dissimilar composition compared to the normal one.     

Effects of pregnancy on bone matrix proteins in Wistar rats

Using an EDTA extraction procedure, bones from pregnant Wistar rats were analyzed for their content of collagen and non-collagenous components (sialoprotein, proteoglycan and carbohydrate). The bone matrix size was found to be smaller in pregnant rats than in normal rats (19.5% vs 17.5% of the dry weight bone). The EDTA extractability of the bone protein from pregnant rats was higher than that from controls (2.6% vs 1.9% dry weight bone). EDTA extracts from pregnant rats contained higher amounts of soluble collagen (1.6% vs 0.5% of dry weight tissue) and lower amounts of non-collagenous components (1.65% vs 2.23% for hexoses, 2.38% vs 3.95% for sialic acid and 1.24% vs 1.73% for uronic acid). In bone matrix, collagen content was lower in the pregnant rats (9.45% vs 10.6%). Similarly, the amounts of non-collagenous components were slightly decreased in the bone matrix from the pregnant rats. The respective values were: 0.91% vs 0.93% for hexoses, 0.45% vs 0.52% for sialic acid and 0.39% vs 0.50% for uronic acid. These results suggest that in pregnancy collagen and non-collagenous protein content in bone is decreased while the total mineral content is increased.     

Bone demineralization mechanisms at level of free radicals and nanoscale subsystems of bone tissue

Influence of simulated microgravity on characteristics of rat bones was investigated by electron paramagnetic resonance (EPR). For simulation of microgravity condition the hanging of animal by tail was used. The main measurements were performed for diaphysis of femoral bones. The quantity of native radicals Rn, localized in an organic matrix, and carbonate radicals CO2-, localized on a surface of bioapatite nanocrystals, were determined. The decrease of CO2- radical quantity in bones of experimental animals have shown, that due to simulation of microgravity the decrease of "collagen-nanocrystals" interaction takes place. It is shown that the EPR method open possibilities to receive the unique information about bone demineralization processes at level of free radicals and nanoscale subsystems of bone tissue.     

Shear strength and toughness of trabecular bone are more sensitive to density than damage

Microdamage occurs in trabecular bone under normal loading, which impairs the mechanical properties. Architectural degradation associated with osteoporosis increases damage susceptibility, resulting in a cumulative negative effect on the mechanical properties. Treatments for osteoporosis could be targeted toward increased bone mineral density, improved architecture, or repair and prevention of microdamage. Delineating the relative roles of damage and architectural degradation on trabecular bone strength will provide insight into the most beneficial targets. In this study, damage was induced in bovine trabecular bone samples by axial compression, and the effects on the mechanical properties in shear were assessed. The damaged shear modulus, shear yield stress, ultimate shear stress, and energy to failure all depended on induced damage and decreased as the architecture became more rod-like. The changes in ultimate shear strength and toughness were proportional to the decrease in shear modulus, consistent with an effective decrease in the cross-section of trabeculae based on cellular solid analysis. For typical ranges of bone volume fraction in human bone, the strength and toughness were much more sensitive to decreased volume fraction than to induced mechanical damage. While ultimately repairing or avoiding damage to the bone structure and increasing bone density both improve mechanical properties, increasing bone density is the more important contributor to bone strength.     

Bone mineral density and microarchitecture in participants of a 105-day experiment in isolated environment

A study on the bone system state in healthy volunteers has been performed before and after 105-day experiment in hermetically isolated environment (the Mars-105 experiment) using dual energy X-ray absorptiometry (DXA) and peripheral quantitative computed tomography (pQCT). The values of bone mineral density (BMD), volumetric bone mineral density (VBMD), and bone structural characteristics of distal segments in radius and tibia have been evaluated. No significant DXA changes have been revealed in segments of skeleton critically important in terms of biomechanics. Microarchitectural deterioration (a decrease in the trabecula number and increase in the bone tissue heterogeneity) has been found using the pQCT technique in the radius of the majority of subjects. A VBMD decrease has been revealed for both cortical and trabecular bones in tibia, along with an unexpected trabecular bone improvement in the form of an increase in the trabecula quantity and decrease in bone tissue heterogeneity. Comprehensive studies, including estimation of projective and volumetric bone mineral densities (the bone mineral content) and bone structural characteristics (bone quality) are required to have a clear view on the changes in the bone system under the conditions of a simulation experiment.     

Quality assessment for processed and sterilized bone using Raman spectroscopy

To eliminate the potential for infection, many tissue banks routinely process and terminally sterilize allografts prior to transplantation. A number of techniques, including the use of scanning electron microscopy, bone graft models, and mechanical property tests, are used to evaluate the properties of allograft bone. However, as these methods are time consuming and often destroy the bone sample, the quality assessment of allograft bones are not routinely performed after processing and sterilization procedures. Raman spectroscopy is a non-destructive, rapid analysis technique that requires only small sample volumes and has recently been used to evaluate the mineral content, mineral crystallinity, acid phosphate and carbonate contents, and collagen maturity in human and animal bones. Here, to establish a quality assessment method of allograft bones using Raman spectroscopy, the effect of several common sterilization and preservation procedures on rat femoral bones were investigated. We found that freeze-thawing had no detectable effects on the composition of bone minerals or matrix, although heat treatment and gamma irradiation resulted in altered Raman spectra. Our findings suggest Raman spectroscopy may facilitate the quality control of allograft bone after processing and sterilization procedures.     

On the role of bone damage in calcium homeostasis

Bone serves as the reservoir of some minerals including calcium. If calcium is needed anywhere in the body, it can be removed from the bone matrix by resorption and put back into the blood flow. During bone remodelling the resorbed tissue is replaced by osteoid which gets mineralized very slowly. Then, calcium homeostasis is controlled by bone remodelling, among other processes: the more intense is the remodelling activity, the lower is the mineral content of bone matrix. Bone remodelling is initiated by the presence of microstructural damage. Some experimental evidences show that the fatigue properties of bone are degraded and more microdamage is accumulated due to the external load as the mineral content increases. That damage initiates bone remodelling and the mineral content is so reduced. Therefore, this process prevents the mineral content of bone matrix to reach very high (non-physiological) values. A bone remodelling model has been used to simulate this regulatory process. In this model, damage is an initiation factor for bone remodelling and is estimated through a fatigue algorithm, depending on the macroscopic strain level. Mineral content depends on bone remodelling and mineralization rate. Finally, the bone fatigue properties are defined as dependent on the mineral content, closing the interconnection between damage and mineral content. The remodelling model was applied to a simplified example consisting of a bar under tension with an initially heterogeneous mineral distribution. Considering the fatigue properties as dependent on the mineral content, the mineral distribution tends to be homogeneous with an ash fraction within the physiological range. If such dependance is not considered and fatigue properties are assumed constant, the homogenization is not always achieved and the mineral content may rise up to high non-physiological values. Thus, the interconnection between mineral content and fatigue properties is essential for the maintenance of bone's structural integrity as well as for the calcium homeostasis.     

Compressive axial mechanical properties of rat bone as functions of bone volume fraction,apparent density and micro-ct based mineral density

Mechanical testing has been regarded as the gold standard to investigate the effects of pathologies on the structure–function properties of the skeleton. With recent advances in computing power of personal computers, virtual alternatives to mechanical testing are gaining acceptance and use. We have previously introduced such a technique called structural rigidity analysis to assess mechanical strength of skeletal tissue with defects. The application of this technique is predicated upon the use of relationships defining the strength of bone as a function of its density for a given loading mode. We are to apply this technique in rat models to assess their compressive skeletal response subjected to a host of biological and pharmaceutical stimulations. Therefore, the aim of this study is to derive a relationship expressing axial compressive mechanical properties of rat cortical and cancellous bone as a function of equivalent bone mineral density, bone volume fraction or apparent density over a range of normal and pathologic bones.We used bones from normal, ovariectomized and partially nephrectomized animals. All specimens underwent micro-computed tomographic imaging to assess bone morphometric and densitometric indices and uniaxial compression to failure.We obtained univariate relationships describing 71–78% of the mechanical properties of rat cortical and cancellous bone based on equivalent mineral density, bone volume fraction or apparent density over a wide range of density and common skeletal pathologies. The relationships reported in this study can be used in the structural rigidity analysis introduced by the authors to provide a non-invasive method to assess the compressive strength of bones affected by pathology and/or treatment options.     

Effects of boron and calcium supplementation on mechanical properties of bone in rats

OBJECTIVE: The objective of this study was to consider the effects of boron (B) and calcium (Ca) supplementation on mechanical properties of bone tissues and mineral content of the selected bones in rats. METHODS: Adult male Sprague Dawley rats underwent three different treatments with boron and calcium in their drinking water, while taking diet ad libitum for 4 weeks. Rats in the three treatment groups received 2 mg B/d, 300 mg Ca/d, and a combination of 2 mg B+ 300 mg Ca/d, respectively. After the experimental period body weights were recorded and bone mechanical properties were determined on the tibiae, femurs, and fifth lumbar vertebral bones and the mineral contents of these bones was calculated as the ash percentage. RESULTS: Better measurement of bone mechanical properties were observed for boron supplementation. The stiffness of the lumbar vertebral bones tended to increase in all groups and was significant for Ca supplementation. The significant maximal load obtained for boron in all bones indicates higher strength and less strength for apparently a high level of calcium, while this negative defect in the case of lumbar vertebral bones was corrected in the presence of boron. Highest mean energy to maximal load was shown with boron supplementation, demonstrating significant values with Ca group, and lower energy for the lumbar vertebral bones in Ca group in comparison with the controls. Less deformation at the yield points was shown in Ca group. There were no significant differences in ash weights among the four groups. CONCLUSIONS: Additional and longer studies are warranted to further determine the effects of supplemental boron with different calcium levels and possibly other minerals involved in bone mechanical properties in rats.     

Natural distribution of uranium in skeletal bones and bone tissue fractions

It was shown that uranium is deposited in the mineral and the organic matrix of bones, and approximately 50% of uranium is bound with the latter. In the bone mineral, uranium is deposited not on the surface of hydroxyl apatite crystals but distributed uniformly within them.     

A two-parameter model of the effective elastic tensor for cortical bone

Multiscale models of cortical bone elasticity require a large number of parameters to describe the organization and composition of the tissue. We hypothesize that the macro-scale anisotropic elastic properties of different bones can be modeled retaining only two variable parameters, and setting the others to universal values identical for all bones. Cortical bone is regarded as a two-phase composite material: a dense mineralized matrix (ultrastructure) and a soft phase (pores). The ultrastructure is assumed to be a homogeneous and transversely isotropic tissue whose elastic properties in different directions are mutually dependent and can be scaled with a single parameter driving the overall rigidity. This parameter is taken to be the volume fraction of mineral f(ha). The pore network is modeled as an ensemble of water-filled cylinders and described only by the porosity p. The effective macroscopic elasticity tensor C(ij)(f(ha),p) is calculated with a multiscale micromechanics approach starting from existing models. The modeled stiffness coefficients compare favorably to four literature datasets which were chosen because they provide the full stiffness tensors of groups of human samples. Since the physical counterparts of f(ha) and p were unknown for the datasets, their values which allow the best fit of experimental tensors by the modeled ones were determined by optimization. Optimum values of f(ha) and p are found to be unique and realistic. These results suggest that a two-parameter model may be sufficient to model the elasticity of different samples of human femora and tibiae. Such a model would in particular be useful in large-scale parametric studies of bone mechanical response.     

Modern analysis of bone loss mechanisms in microgravity

A summary of results of investigations by the author and a brief review of some literature data on human bone tissue deprived of mechanical loading (spaceflight, hypokinesia) is given. The direction and markedness of changes in bone mass--the bone mineral density and the bone mineral content--in different skeletal segments depend on their position relative to the gravity vector. A theoretically expected bone mass reduction was revealed in the trabecular structures of the bones of the lower part of the skeleton (local osteopenia). In the upper part of the skeleton, an increase in the bone mineral content is observed, which is considered as a secondary response and is due to redistribution of body fluids cephalad. The main cause of osteopenia is mechanical unloading. Arguments are presented that osteocyte osteolysis, delayed osteoblast histogenesis, and osteoclast resorption provoked by rearrangement in the hierarchy of the systems of fluid volume and ion regulation, and the endocrine control of calcium homeostasis are the main mechanisms of osteopenia.     

Effects of differences in mineralization on the mechanical properties of bone

There is a considerable variation in the mineralization of bone; normal, non-pathological compact bone has ash masses ranging from 45 to 85% by mass. This range of mineralization results in an even greater range of mechanical properties. The Young modulus of elasticity can range from 4 to 32 GPa, bending strength from 50 to 300 MPa, and the work of fracture from 200 to 7000 Jm-2. It is not possible for any one type of bone to have high values for all three properties. Very high values of mineralization produce high values of Young modulus but low values of work of fracture (which is a measure of fracture toughness). Rather low values of mineralization are associated with high values of work of fracture but low values of Young modulus and intermediate values of bending strength. The reason for the high value for the Young modulus associated with high mineralization is intuitively obvious, but has not yet been rigorously modelled. The low fracture toughness associated with high mineralization may be caused by the failure of various crack-stopping mechanisms that can act when the mineral crystals in bone have not coalesced, but which become ineffective when the volume fraction of mineral becomes too high. The adoption of different degrees of mineralization by different bones, leading to different sets of mechanical properties, is shown to be adaptive in most cases studied, but some puzzles still remain.     

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure–function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean±S.D.) 18.7±3.4 GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.