Hierarchies of damage induced loss of mechanical properties in calcified bone after in vivo fatigue loading of rat ulnae

During fatigue loading of whole bone, damage to bone tissue accumulates, coalesces and leads to fractures. Whether damage affects tissue material properties similarly at the nanoscale (less than 1 μm), microscale (less than 1 mm), and whole bone scale has not been fully evaluated. Therefore, in this study, we examine scale-dependent loss of calcified tissue material properties in rat ulnae, after fatigue loading of rat forearms using the forearm compression model. In vivo fatigue loading was conducted on the right forearms until a displacement end-point was reached. The non-fatigued left forearms served as contralateral controls. Subsequently, three-point bending tests to failure on excised ulnae demonstrated a 41% and 49% reduction in the stiffness and ultimate strength as compared to contralateral control ulnae, respectively. Depth-sensing microindentation demonstrated an average decrease in material properties, such as elastic modulus and hardness, of 28% and 29% respectively. Nanoindentation measured elastic modulus and hardness were reduced by 26% and 29% in damaged bone relative to contralateral controls, respectively. The increased loss of whole bone material properties compared to tissue material properties measured using indentation is mainly attributed to the presence of a macrocrack located in the medial compressive region at the site of peak strains. The similar magnitude of changes in material properties by microindentation and nanoindentation is attributed to damage that may originate at an even smaller scale, as inferred from 10% differences in connectivity of osteocyte canaliculi in damaged bone.

Correlation between longitudinal, circumferential, and radial moduli in cortical bone: effect of mineral content

Previous studies indicate that changes in the longitudinal elastic properties of bone due to changes in mineral content are related to the longitudinal strength of bone tissue. Changes in mineral content are expected to affect bone tissue mechanical properties along all directions, albeit to different extents. However, changes in tissue mechanical properties along the different directions are expected to be correlated to one another. In this study, we investigate if radial, circumferential, and longitudinal moduli are related in bone tissue with varying mineral content. Plexiform bovine femoral bone samples were treated in fluoride ion solutions for a period of 3 and 12 days to obtain bones with 20% and 32% lower effective mineral contents. Transmission ultrasound velocities were obtained in the radial, circumferential, and longitudinal axes of bone and combined with measured densities to obtain corresponding tensorial moduli. Results indicate that moduli decreased with fluoride ion treatments and were significantly correlated to one another (r(2) radial vs. longitudinal = 0.80, r(2) circumferential vs. longitudinal = 0.90, r(2) radial vs. circumferential = 0.85). Densities calculated from using ultrasound parameters, acoustic impedance and transmission velocities, were moderately correlated to those measured by the Archimedes principle (r(2)=0.54, p<0.01). These results suggest that radial and circumferential ultrasound measurements could be used to determine the longitudinal properties of bone and that ultrasound may not be able to predict in vitro densities of bones containing unbonded mineral.

A new streaming potential chamber for zeta potential measurements of particulates

A novel streaming potential measurement device has been validated by determining the average electrokinetic (zeta) potential of densely packed particulate such as human erythrocytes and ground bovine cortical bone. The new streaming potential device used in this study is easy to construct in the laboratory, designed to allow dense packing of particles, and determines zeta potentials for a broad range of particle sizes. The streaming potential device consists of four Plexiglas parts: (i) an upper and (ii) a lower chamber, which act as reservoirs for fluid; (iii) a midchamber which connects the upper and lower chambers and holds the sample holder, and (iv) a sample holder. Pressurization of fluid in the top chamber generates a pressure gradient that induces movement of fluid through the stationary sample and into the bottom chamber. Pressure induced flow through the interconnected pores of the densely packed particulate generates a potential difference across the sample that is measured using electrodes housed in the top and bottom chambers. The measured potential difference is then converted to zeta potentials. The advantage of this chamber is its ability to handle densely packed particulates exhibiting a broad distribution of sizes. Dense packing of particulate is achieved by compacting samples at the bottom of the sample holder under centrifugal forces before the device is assembled. This approach allowed us to determine average zeta potentials of densely packed particulate made of soft and hard materials.

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.

Improved mechanical properties of acrylic bone cement with short titanium fiber reinforcement

Acrylic bone cements are widely used in total joint arthroplasties to grout the prosthesis to bone. The changes in the tensile properties and fracture toughness of polymethylmethacrylate (PMMA) bone cements obtained by the addition of control and heat treated short titanium fibers are studied. Heat treatment of titanium fibers is conducted to precipitate titania particles on the fiber surface to improve the biocompatibility of the metal. Control and heat treated short titanium fibers (250 micro long and 20 micro diameter) were used as reinforcements at 3 volume %. X-ray diffraction indicated the presence of a rutile form of titania due to the heat treatments. The tensile and fracture properties were improved by the addition of fibers. Bone cements reinforced with titanium fibers heated at 550 degrees C for 1 h followed by 800 degrees C for 30 minutes show the largest increase in fracture toughness along with the smallest changes in elastic modulus and needs to be further investigated.

Improved mechanical properties of acrylic bone cement with short titanium fiber reinforcement

Acrylic bone cements are widely used in total joint arthroplasties to grout the prosthesis to bone. The changes in the tensile properties and fracture toughness of polymethylmethacrylate (PMMA) bone cements obtained by the addition of control and heat treated short titanium fibers are studied. Heat treatment of titanium fibers is conducted to precipitate titania particles on the fiber surface, which may improve the biocompatibility of the metal. Control (non-heat treated) and heat treated short titanium fibers (250 microm long and 20microm diameter) were used as reinforcements at 3 volume %. X-ray diffraction indicated the presence of a rutile form of titania due to the heat treatments. Results indicate that the tensile and fracture properties of unfilled bone cement were improved by the addition of control and heat-treated fibers. The fracture properties of bone cements reinforced with control titanium fibers were at least 10% higher than those reinforced with heat treated titanium fibers. Therefore, we recommend further studies on the use of non-heat treated titanium fibers to reinforce acrylic bone cement.

Adhesion enhancement of steel fibers to acrylic bone cement through a silane coupling agent

The use of a silane coupling agent (methacryloxypropyl-trichlorosilane) to improve the mechanical properties of steel fiber-reinforced acrylic bone cements was assessed. Changes to the tensile and fracture properties of bone cements reinforced with silane-coated or uncoated 316L stainless steel fibers of different aspect ratios were studied. Contact-angle measurements indicated that the coupling agent coats the metal surface through room temperature treatments in a short time (within 2 h). Push-out tests indicated that the interfacial shear strength of silane-coated 316L stainless steel rods is 141% higher than the uncoated rods. The elastic moduli, ultimate stresses, and fracture toughness of the silane-coated, steel fiber-reinforced bone cements are significantly higher than the bone cements reinforced with uncoated steel fibers. There were no differences in the tensile mechanical properties of the silane-coated or uncoated, steel fiber-reinforced cements after aging in a physiological saline solution, indicating that the bonding effectiveness is decreased by the intrusion of water at the metal-polymer interface. Because of possible biocompatibility issues with leaching of the silane coupling agent and no long-term mechanical benefit in simulated aging experiments, the use of these agents is not recommended for in vivo use.

Experimental and finite element analysis of the rat ulnar loading model-correlations between strain and bone formation following fatigue loading

The rat forelimb compression model has been used widely to study bone response to mechanical loading. We used strain gages to assess load sharing between the ulna and radius in the forelimb of adult Fisher rats. We used histology and peripheral quantitative computed tomography (pQCT) to quantify ulnar bone formation 12 days after in vivo fatigue loading. Lastly, we developed a finite element model of the ulna to predict the pattern of surface strains during compression. Our findings indicate that at the mid-shaft the ulna carries 65% of the applied compressive force on the forelimb. We observed large variations in fatigue-induced bone formation over the circumference and length of the ulna. Bone formation was greatest 1-2 mm distal to the mid-shaft. At the mid-shaft, we observed woven bone formation that was greatest medially. Finite element analysis indicated a strain pattern consistent with a compression-bending loading mode, with the greatest strains occurring in compression on the medial surface and lesser tensile strains occurring laterally. A peak strain of -5190 microepsilon (for 13.3N forelimb compression) occurred 1-2 mm distal to the mid-shaft. The pattern of bone formation in the longitudinal direction was highly correlated to the predicted peak compressive axial strains at seven cross-sections (r2 = 0.89, p = 0.014). The in-plane pattern of bone formation was poorly correlated to the predicted magnitude of axial strain at 51 periosteal locations (r2 = 0.21, p < 0.001), because the least bone formation was observed where tensile strains were highest. These findings indicate that the magnitude of bone formation after fatigue loading is greatest in regions of high compressive strain.

Effect of bone mineral content on the tensile properties of cortical bone: experiments and theory

The effect of mineral volume fraction on the tensile mechanical properties of cortical bone tissue is investigated by theoretical and experimental means. The mineral content of plexiform, bovine bone was lowered by 18% and 29% by immersion in fluoride solutions for 3 days and 12 days, respectively. The elastic modulus, yield strength and ultimate strength of bone tissue decreased, while the ultimate strain increased with a decrease in mineral content. The mechanical behavior of bone tissue was modeled by using a micromechanical shear lag theory consisting of overlapped mineral platelets reinforcing the organic matrix. The decrease in yield stress, by the 0.002 offset method, of the fluoride treated bones were matched in the theoretical curves by lowering the shear yield stress of the organic matrix. The failure criterion used was based on failure stresses determined from a failure envelope (Mohr's circle), which was constructed using experimental data. It was found that the model predictions of elastic modulus got worse with a decrease in mineral content (being 7.9%, 17.2% and 33.0% higher for the control, 3-day and 12-day fluoride-treated bones). As a result, the developed theory could not fully predict the yield strain of bones with lowered mineral content, being 12.9% and 21.7% lower than the experimental values. The predicted ultimate stresses of the bone tissues with lower mineral contents were within +/- 10% of the experimental values while the ultimate strains were 12.7% and 26.3% lower than the experimental values. Although the model developed in this study did not take into account the presence of hierarchical structures, voids, orientation of collagen molecules and micro cracks, it still indicated that the mechanical properties of the organic matrix depend on bone mineral content.

Fracture toughness of steel-fiber-reinforced bone cement

Fractures in the bone-cement mantle (polymethyl methacrylate) have been linked to the failure of cemented total joint prostheses. The heat generated by the curing bone cement has also been implicated in the necrosis of surrounding bone tissue, leading to loosening of the implants. The addition of reinforcements may improve the fracture properties of bone cement and decrease the peak temperatures during curing. This study investigates the changes in the fracture properties and the temperatures generated in the ASTM F451 tests by the addition of 316L stainless steel fibers to bone cement. The influence of filler volume fraction (5-15% by volume) and aspect ratios (19, 46, 57) on the fracture toughness of the acrylic bone cement was assessed. Increasing the volume fraction of the steel fibers resulted in significant increases in the fracture toughness of the steel-fiber-reinforced composite. Fracture-toughness increases of up to 2.63 times the control values were obtained with the use of steel-fiber reinforcements. No clear trend in the fracture toughness was discerned for increasing aspect ratios of the reinforcements. There is a decrease in the peak temperatures reached during the curing of the steel-fiber-reinforced bone cement, though the decrease is too small to be clinically relevant. Large increases in the fatigue life of acrylic bone cement were also obtained by the addition of steel fibers. These results indicate that the use of steel fibers may enhance the durability of cemented joint prostheses.

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.

Increased ash contents and estimation of dissolution from chemical changes due to in-vitro fluoride treatments

The in-vitro fluoride treatment technique has been introduced to investigate the composite behavior of bone tissue. Bone tissue with different mechanical properties can be obtained by varying the concentration, pH and immersion time in fluoride ion solutions. The chemical and physical changes in intact pieces of bone treated in-vitro with different concentrations of fluoride ions are studied. The amount of bone mineral that does not contribute to the mechanical behavior of bone tissue is estimated from the dissolution occurring in the fluoride treated bones. Cortical bones from 18-month-old steers were treated in-vitro with 0.145, 0.5 and 2.0 M sodium fluoride (NaF) solutions for three days. The dissolved bone mineral precipitates as calcium fluoride-like (CaF2/P with some phosphate [P] ions) and fluorapatite(FAp)/fluorhydroxyapatite(FHAp)-like materials within the bone tissue. The dissolution estimated from the presence of the precipitated fluoride phases is 5.6, 11.7, and 13.1% of the initial bone mineral content for the 0.145 M, 0.5 M, and 2.0 M NaF treatments respectively. Estimates of dissolution based on the measurements of phosphate and carbonate ions are lower and higher respectively when compared to the fluoride ion measurements. The wet and dry densities decreased slightly due to dissolution and re-precipitation while the ash content (ratio of the ash weight to dry weight) increased a small amount with increasing concentration of fluoride ion treatments. The increased ash content was due to the excess loss of water in the fluoride treated bones as compare to controls (untreated bone samples) during the drying process. The increased removal of water during the drying process may explain the increased ash contents in some in-vivo treatments.

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.

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.

The effects of interphase and bonding on the elastic modulus of bone: changes with age-related osteoporosis

A simple shear lag model is developed to analyze the physics of the stress transfer between the organic and mineral constituents of bone tissue in the presence of an interphase and changes in bonding. The analytical model is developed assuming interactions between overlapped bone mineral platelets. The platelets are assumed to carry the axial stresses while the organic matrix transfers the stresses from one platelet to another by shear. A decrease in the interphase mechanical properties decreases the elastic modulus due to increased shear between the overlapped platelets. A decrease in bonding decreases the elastic modulus due to an increase in the axial stress transferred from the ends of the platelet. The implications of the changes in parameters on the age-related disorders of bone (osteoporois) are discussed. It is suggested that the aspect ratio and volume fraction of the mineral in the remaining bone tissue would increase due to a reduction in the density of the bone. The mechanical properties of the organic are hypothesized to increase due to a reduction in the density of bone leading to an increased tendency for damage within the organic.

Varying the mechanical properties of bone tissue by changing the amount of its structurally effective bone mineral content

The effect of fluoride ions on the mechanical properties of bone tissue in tension was investigated with an in vitro model. Structurally effective Bone Mineral Content (BMC) of bovine bone tissue was changed by fluoride ion treatment. First, bovine cortical bone specimens were treated with a detergent solution in order to increase the diffusion rates of the treatment ions across the samples. After the initial treatment, different ion solutions were used to treat the tension samples (fluoride, sodium and chloride). Ionic strength and pH were varied. Experimental results showed that the sodium chloride solutions of different ionic strengths, at physiological and high pH, do not affect the mechanical properties of bone tissue in tension. However, uniform fluoride treatment across the samples reduced the mechanical strength of bone tissue by converting small amounts of bone mineral to mostly calcium fluoride. This action reduces the structurally effective BMC and also possibly effects the interface bonding between the bone mineral and the organic matrix of the bone tissue.