Spatial distribution of acoustic and elastic properties of human femoral cortical bone

The purpose of this study is to quantify the spatial distribution of acoustic velocities and elastic properties (elastic constants) on Human femoral cortical bone. Four cross sections (average thickness of 2.09+/-0.27 mm) have been cut transversally between 40% and 70% of the total length and between them parallelepiped samples in each quadrant have been cut. Ultrasonic technique in transmission with immersion focused transducers at 5 MHz and contact transducers 2.25 MHz were used on the cross sections and parallelepiped samples, respectively. The first technique allows relative spatial distribution of velocities to be obtained, meanwhile the second technique allows the direct assessment of elastic constants. For both techniques, bulk velocities were found to be lower at the posterior side with an increase along the length (from 40% to 70% total length) (p < 0.05). Densities and elastic constants show equivalent pattern of variation. These variations are mainly due the cortical porosity related to vascularisation environment. The spatial distribution of velocities exhibits significant radial variation from the endosteal to the periosteal region. This is in agreement with variation of the porosity at that location. Same range of velocities was obtained with both techniques. The range of longitudinal velocities values varies from 3548 to 3967 m/s and between 18.5 and 33.1 GPa for the bulk velocities and axial elastic constants, respectively. Our results are within the range with those found in the literature. However, it must be noted that the range of acoustic and elastic properties variation is concerning the same bone. So, our new results show the ability of the technique to quantify accurately local variation of acoustic and elastic properties (within the section and along the length) of human cortical bone. Furthermore, our immersion technique could be used to assess the spatial distribution of the elastic constants with the knowledge of spatial distribution of densities.     

Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue

The ability to determine trabecular bone tissue elastic and failure properties has biological and clinical importance. To date, trabecular tissue yield strains remain unknown due to experimental difficulties, and elastic moduli studies have reported controversial results. We hypothesized that the elastic and tensile and compressive yield properties of trabecular tissue are similar to those of cortical tissue. Effective tissue modulus and yield strains were calibrated for cadaveric human femoral neck specimens taken from 11 donors, using a combination of apparent-level mechanical testing and specimen-specific, high-resolution, nonlinear finite element modeling. The trabecular tissue properties were then compared to measured elastic modulus and tensile yield strain of human femoral diaphyseal cortical bone specimens obtained from a similar cohort of 34 donors. Cortical tissue properties were obtained by statistically eliminating the effects of vascular porosity. Results indicated that mean elastic modulus was 10% lower (p<0.05) for the trabecular tissue (18.0+/-2.8 GPa) than for the cortical tissue (19.9+/-1.8 GPa), and the 0.2% offset tensile yield strain was 15% lower for the trabecular tissue (0.62+/-0.04% vs. 0.73+/-0.05%, p<0.001). The tensile-compressive yield strength asymmetry for the trabecular tissue, 0.62 on average, was similar to values reported in the literature for cortical bone. We conclude that while the elastic modulus and yield strains for trabecular tissue are just slightly lower than those of cortical tissue, because of the cumulative effect of these differences, tissue strength is about 25% greater for cortical bone.     

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.     

Mechanical properties of porcine femoral cortical bone measured by nanoindentation

This study uses a nanoindentation technique to examine variations in the local mechanical properties of porcine femoral cortical bone under hydrated conditions. Bone specimens from three age groups (6, 12 and 42 months), representing developing bone, ranging from young to mature animals, were tested on the longitudinal and transverse cross-sectional surfaces. Elastic modulus and hardness of individual lamellae within bone's microstructure: laminar bone, interstitial bone, and osteons, were measured. Both the elastic modulus and hardness increased with age. However, the magnitudes of these increases were different for each microstructural component. The longitudinal moduli were higher than the transverse moduli. Dehydrated samples were also tested to allow a comparison with hydrated samples and these resulted in higher moduli and hardness than the hydrated samples. Again, the degree of variation was different for each microstructural component. These results indicate that the developmental changes in bone have different rates of mechanical change within each microstructural component.     

Determination of mechanical properties of human femoral cortical bone by the Hopkinson bar stress technique

The Hopkinson bar stress technique and a universal testing machine (Instron 1125) have been used to investigate the dynamic and static mechanical properties of cortical bone taken from a human femur respectively. We found that the average dynamic Young's modulus value (Ed = 19.9 GPa) to be 23% higher than the average static Young's modulus value (Ed = 16.2 GPa). Furthermore, the Poisson's ratio did not exhibit any significant variation for the two different types of loading. No difference was observed between the values of the dynamic Young's modulus in tension and those found in compression. A comparison was made of the results of this study with those found by other researchers using different techniques, such as ultrasonics, and it was found that they agree well with most of the results of previous studies. Finally, the viscosity for cortical bone found in this study correlates with viscosity reported by Tennyson et al. [Expl Mech. 12, 502-507 (1972)] for ten days post mortem age specimens.     

Anatomic variation in the elastic inhomogeneity and anisotropy of human femoral cortical bone tissue is consistent across multiple donors

Numerical models commonly account for elastic inhomogeneity in cortical bone using power-law scaling relationships with various measures of tissue density, but limited experimental data exists for anatomic variation in elastic anisotropy. A recent study revealed anatomic variation in the magnitude and anisotropy of elastic constants along the entire femoral diaphysis of a single human femur (Espinoza Orías et al., 2009). The objective of this study was to confirm these trends across multiple donors while also considering possible confounding effects of the anatomic quadrant, apparent tissue density, donor age, and gender. Cortical bone specimens were sampled from the whole femora of 9 human donors at 20%, 50%, and 80% of the total femur length. Elastic constants from the main diagonal of the reduced fourth-order tensor were measured on hydrated specimens using ultrasonic wave propagation. The tissue exhibited orthotropy overall and at each location along the length of the diaphysis (p < 0.0001). Elastic anisotropy increased from the mid-diaphysis toward the epiphyses (p < 0.05). The increased elastic anisotropy was primarily caused by a decreased radial elastic constant (C(11)) from the mid-diaphysis toward the epiphyses (p < 0.05), since differences in the circumferential (C(22)) and longitudinal (C(33)) elastic constants were not statistically significant (p > 0.29). Anatomic variation in intracortical porosity may account for these trends, but requires further investigation. The apparent tissue density was positively correlated with the magnitude of each elastic constant (p < 0.0001, R(2) > 0.46), as expected, but was only weakly correlated with C(33)/C(11) (p < 0.05, R(2) = 0.04) and not significantly correlated with C(33)/C(22) and C(11)/C(22).     

Multi-scale characterization of swine femoral cortical bone

Multi-scale experimental work was carried out to characterize cortical bone as a heterogeneous material with hierarchical structure, which spans from nanoscale (mineralized collagen fibril), sub-microscale (single lamella), microscale (lamellar structures), to mesoscale (cortical bone) levels. Sections from femoral cortical bone from 6, 12, and 42 months old swine were studied to quantify the age-related changes in bone structure, chemical composition, and mechanical properties. The structural changes with age from sub-microscale to mesoscale levels were investigated with scanning electron microscopy and micro-computed tomography. The chemical compositions at mesoscale were studied by ash content method and dual energy X-ray absorptiometry, and at microscale by Fourier transform infrared microspectroscopy. The mechanical properties at mesoscale were measured by tensile testing, and elastic modulus and hardness at sub-microscale were obtained using nanoindentation. The experimental results showed age-related changes in the structure and chemical composition of cortical bone. Lamellar bone was a prevalent structure in 6 months and 12 months old animals, resorption sites were most pronounced in 6 months old animals, while secondary osteons were the dominant features in 42 months old animals. Mineral content and mineral-to-organic ratio increased with age. The structural and chemical changes with age corresponded to an increase in local elastic modulus, and overall elastic modulus and ultimate tensile strength as bone matured.     

Anisotropic properties of human cortical bone with osteogenesis imperfecta

The heterogeneity of bone shape and size variation is modulated by genetic, mechanical, nutritional, and hormonal patterning throughout its lifetime. Microstructural changes across cross sections are a result of mechanistic optimization that results over the years of evolution while being based on universal, time-invariant ingredients and patterns. Here we report changes across anatomical sections of bone with osteogenesis imperfecta (OI) that undermines the work of evolution through genetic mutation. This work examines the microstructure and molecular composition of different anatomical positions (anterior, medial, posterior, and lateral regions) in the diaphysis of an OI human tibia. The study shows that although there is no significant microstructural difference, molecular changes are observed using FTIR revealing differences in molecular composition of the four anatomical positions. In addition, the nanomechanical properties of anterior section of OI bone seem more heterogeneous. The nanomechanical properties of interstitial lamellae in all these bone samples are consistently greater than those of osteonal lamellae. The nanomechanical properties of bone depend on its anatomical section and on the measurement direction as well. Variations in molecular structure with anatomical positions and also corresponding differences in nanomechanical properties are reported. These are compared to those observed typically in healthy bone illustrating the unique influence of OI on bone multiscale behavior which results from an evolutionary process lasting for many years.     

The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity

The objective of this study was to examine the dependence of the elastic properties of cortical bone as a transversely isotropic material on its porosity. The longitudinal Young's modulus, transverse Young's modulus, longitudinal shear modulus, transverse shear modulus, and longitudinal Poisson's ratio of cortical bone were determined from eighteen groups of longitudinal and transverse specimens using tensile and torsional tests on a servo-hydraulic material testing system. These cylindrical waisted specimens of cortical bone were harvested from the middle diaphysis of three pairs of human femora. The porosity of these specimens was assessed by means of histology. Our study demonstrated that the longitudinal Young's and shear moduli of human femoral cortical bone were significantly (p<0.01) negatively correlated with the porosity of cortical bone. Conversely, the elastic properties in the transverse direction did not have statistically significant correlations with the porosity of cortical bone. As a result, the transverse elastic properties of cortical bone were less sensitive to changes in porosity than those in the longitudinal direction. Additionally, the anisotropic ratios of cortical bone elasticity were found to be significantly (p<0.01) negatively correlated with its porosity, indicating that cortical bone tended to become more isotropic when its porosity increased. These results may help a number of researchers develop more accurate micromechanics models of cortical bone.     

Osteocyte lacunae tissue strain in cortical bone

Current theories suggest that bone modeling and remodeling are controlled at the cellular level through signals mediated by osteocytes. However, the specific signals to which bone cells respond are still unknown. Two primary theories are: (1) osteocytes are stimulated via the mechanical deformation of the perilacunar bone matrix and (2) osteocytes are stimulated via fluid flow generated shear stresses acting on osteocyte cell processes within canaliculi. Recently, much focus has been placed on fluid flow theories since in vitro experiments have shown that bone cells are more responsive to analytically estimated levels of fluid shear stress than to direct mechanical stretching using macroscopic strain levels measured on bone in vivo. However, due to the complex microstructural organization of bone, local perilacunar bone tissue strains potentially acting on osteocytes cannot be reliably estimated from macroscopic bone strain measurements. Thus, the objective of this study was to quantify local perilacunar bone matrix strains due to macroscopically applied bone strains similar in magnitude to those that occur in vivo. Using a digital image correlation strain measurement technique, experimentally measured bone matrix strains around osteocyte lacunae resulting from macroscopic strains of approximately 2000 microstrain are significantly greater than macroscopic strain on average and can reach peak levels of over 30,000 microstrain locally. Average strain concentration factors ranged from 1.1 to 3.8, which is consistent with analytical and numerical estimates. This information should lead to a better understanding of how bone cells are affected by whole bone functional loading.     

Moment coefficients of skewness in the femoral neck cortical bone distribution of BAR 1002’00

The cortical bone distributions in the femoral necks of apes and humans differ as a result of different loading environments caused by the realignment of the hip abductor apparatus. Femoral neck cortical bone in extant humans is very thin superiorly and thicker inferiorly, while the cortical bone in apes tends to be more uniformly thick. The unique internal anatomy of extant humans allows inferences to be made about primary locomotor function from incomplete femora. Here the differences in cortical bone distributions are quantified using moment coefficient of skewness. Skewness coefficients at two locations along the neck of the 6 million years old African femoral specimen BAR 1002’00 were compared to samples of 9 extant adult humans and 10 adult chimpanzees. The skewness coefficients of cortical bone in the femoral neck of BAR 1002’00 are more similar to those of chimpanzees than to humans, although the contrast is less pronounced in the region closer to the neck-shaft junction than more proximally toward the femoral head; this pattern indicates that in at least one respect this specimen attributed to Orrorin tugenensis manifests structural features suggesting influences of a hip abductor apparatus that had not yet evolved to the same extent as in extant humans.     

Constitutive relationship of tissue behavior with damage accumulation of human cortical bone

Microdamage accumulation has been identified as a major conduit for bone tissues to absorb fracture energy. Due to the poor understanding of its underlying mechanism, however, an adequate constitutive relationship between damage accumulation and the mechanical behavior of bone has not yet been established. In this study, the constitutive relationship between the damage accumulation induced by overload and the evolution of mechanical properties of bone with incremental deformation was established based on the experimental results obtained from a novel progressive loading protocol developed in our laboratory. First, a decayed exponential model was proposed to capture the damage accumulation (modulus loss) with increase in applied strain. Next, a power law function was proposed to represent the progression of plastic deformation with damage accumulation. Finally, a linear combination of the Kohlrausch–Williams–Watts (KWW) and the Debye functions was used to depict the viscoelastic behavior of bone associated with damage accumulation. The results of this study may help in developing a constitutive model for predicting the mechanical behavior of cortical bone tissues.     

The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus

The elastic moduli of human subchondral, trabecular, and cortical bone tissue from a proximal tibia were experimentally determined using three-point bending tests on a microstructural level. The mean modulus of subchondral specimens was 1.15 GPa, and those of trabecular and cortical specimens was 4.59 GPa and 5.44 GPa respectively. Significant differences were found in the modulus values between bone tissues, which may have mainly resulted from the differences in the microstructures of each bone tissue rather than in the mineral density. Furthermore, the size-dependency of the modulus was examined using eight different sizes of cortical specimens (heights h = 100-1000 microns). While the modulus values for relatively large specimens (h greater than 500 microns) remained fairly constant (approximately 15 GPa), the values decreased as the specimens became smaller. A significant correlation was found between the modulus and specimen size. The surface area to volume ratio proved to be a key variable to explain the size-dependency.     

Characterization of the mechanical properties of bovine cortical bone treated with a novel tissue sterilization process

Over the past decade chemical processing and engineering of musculoskeletal tissue (tendon and bone) has improved dramatically. The use of bone allograft and xenograft in reconstructive orthopedic and maxillofacial surgeries is increasing, yet severe complications can occur if the material is contaminated in any way. A novel tissue sterilization process, BioCleanse^®, has been developed to clean and sterilize musculoskeletal tissue for implantation. The present study was designed to determine the effect of this novel cleaning process on the biomechanical properties of bovine cortical bone prior to implantation. The mechanical properties of treated bovine bone material were compared to human samples with respect to failure under compression, shear and three-point bending. The data demonstrate that bovine bone treated with the novel sterilization procedure has favorable biomechanical properties compared to that of human bone treated in a similar fashion.     

A comparison of the fatigue behavior of human trabecular and cortical bone tissue

The fatigue properties of trabecular bone tissue (single trabeculae) and similarly sized cortical bone specimens from human tibia were experimentally determined on a microstructural level using four-point bending cyclic tests, and they were compared based on modulus, mineral density, and microstructural characteristics. The results showed that trabecular specimens had significantly lower moduli and lower fatigue strength than cortical specimens, despite their higher mineral density values. Fracture surface and microdamage analyses illustrated different fracture and damage patterns between trabecular and cortical bone tissue, depending upon their microstructural characteristics. Based on the results from mechanical tests and qualitative observations, a possible mechanical role of the cement lines in trabecular tissue microfracture was suggested.     

Anisotropic viscoelastic properties of cortical bone

Relaxation Young's modulus of cortical bone was investigated for two different directions with respect to the longitudinal axis of bone (bone axis, BA): the modulus parallel (P) and normal (N) to the BA. The relaxation modulus was analyzed by fitting to the empirical equation previously proposed for cortical bones, i.e., a linear combination of two Kohlraush-Williams-Watts (KWW) functions (Iyo et al., 2003. Biorheology, submitted): E(t)=E0 (A1 exp[-(t/tau1)beta]+(1-A1) exp[-(t/tau2)gamma]), [0 < A1, beta, gamma < 1], where E0 is the initial modulus value E0. Tau1 and tau2(>tau1) are characteristic times of the relaxation, A1 is the fractional contribution of the fast relaxation (KWW1 process) to the whole relaxation process, and beta and gamma are parameters describing the shape of the relaxation modulus. In both P and N samples, the relaxation modulus was described well by the empirical equation. The KWW1 process of a P sample almost completely coincided with that of an N sample. In the slow process (KWW2 process), there was a difference between the relaxation modulus of a P sample and that of an N sample. The results indicate that the KWW1 process in the empirical equation represents the relaxation in the collagen matrix in bone and that the KWW2 process is related to a higher-order structure of bone that is responsible for the anisotropic mechanical properties of bone.