Mechanical properties and chemical composition of avian long bones

We have studied the mechanical behaviour of avian long bones as whole structures, by calculating mechanical parameters such as maximum load, stiffness, bending strength and flexural Young's modulus; bones were always tested in three-point bending. Furthermore composition in several chemical elements and amino acids related to collagen content was also analysed. Correlations were established between body mass, mechanical parameters and chemical contents. Both bending strength and Young's modulus were negatively correlated to body mass. Significant correlations were found between nitrogen content and both strength and Young's modulus, with negative slopes in both cases. Magnesium and phosphorus appear to be the most important inorganic elements to the understanding of the mechanical behaviour of avian long bones.     

Avian long bones, flight and bipedalism.

Morphological, geometrical, chemical and mechanical characteristics of avian long bones are reviewed. Important differences exist between long bones of birds and mammals. Differences are also present in appendicular bones of birds, either between wing bones and leg bones or proximal (stylopodial) long bones and distal (zeugopodial) long bones. Special emphasis is put on pneumatization, in terms of both phylogenetic origin and geometrical and mechanical characteristics linked to it. Cortical thickness, bending strength and flexural Young's modulus were significantly lower in pneumatized bones than in marrow-filled bones. Possible adaptive reasons for the differences shown are discussed.     

A comparison of mechanical properties derived from multiple skeletal sites in mice

Laboratory mice provide a versatile experimental model for studies of skeletal biomechanics. In order to determine the strength of the mouse skeleton, mechanical testing has been performed on a variety of bones using several procedures. Because of differences in testing methods, the data from previous studies are not comparable. The purpose of this study was to determine which long bone provides the values closest to the published material properties of bone, while also providing reliable and reproducible results. To do this, the femur, humerus, third metatarsal, radius, and tibia of both the low bone mass C57BL/6H (B6) and high bone mass C3H/HeJ (C3H) mice were mechanically tested under three-point bending. The biomechanical tests showed significant differences between the bones and between mouse strains for the five bones tested (p < 0.05). Computational models of the femur, metatarsal, and radius were developed to visualize the types of measurement error inherent in the three-point bending tests. The models demonstrated that measurement error arose from local deformation at the loading point, shear deformation and ring-type deformation of the cylindrical cross-section. Increasing the aspect ratio (bone length/width) improved the measurement of Young's modulus of the bone for both mouse strains (p < 0.01). Bones with the highest aspect ratio and largest cortical thickness to radius ratio were better for bending tests since less measurement error was observed in the computational models. Of the bones tested, the radius was preferred for mechanical testing because of its high aspect ratio, minimal measurement error, and low variability.     

Nanoindentation and whole-bone bending estimates of material properties in bones from the senescence accelerated mouse SAMP6

The senescence accelerated mouse, strain P6 (SAMP6) has been described as a model of senile osteoporosis. Recent results from whole-bone bending tests indicate that, despite having increased moments of inertia, SAMP6 long bones are weak and brittle compared to SAMR1 controls. In the current study we determined material properties of cortical bone from SAMP6 and SAMR1 femora and tibiae by two methods-nanoindentation and whole-bone bending tests combined with simple beam theory. We hypothesized that: (1) SAMP6 mice have reduced cortical bone material properties compared to SAMR1 controls; and (2) modulus estimated from whole-bone bending tests correlates well with modulus determined by nanoindentation. Results from nanoindentation indicated that modulus and hardness are approximately 10% higher in SAMP6 mice compared to SAMR1 controls (p<0.001), a finding consistent with slightly higher mineralization in SAMP6 bones. Despite their superior elastic and hardness properties, the bending failure properties of SAMP6 bones were markedly inferior--ultimate stress and toughness were reduced by 40% and 60%, respectively (p<0.001). Comparisons between the two testing methods for determining modulus showed poor agreement. Modulus estimated from whole-bone bending tests was not correlated with modulus determined by nanoindentation (p=0.054; r2=0.03) and the absolute values differed by a factor of five between the two methods (bending [wet], 6GPa; nanoindentation [dry], 31GPa). Moreover, relative differences between groups were inconsistent between the two methods. We conclude: (1) cortical bone from the SAMP6 mouse has increased modulus and hardness but poor material strength and toughness, which underscores the relevance of the SAMP6 mouse for studies of skeletal fragility, and (2) values of elastic modulus of bone tissue estimated using simple beam theory and bending tests of mouse femora and tibiae are inaccurate and should be interpreted with caution.     

Spatial orientation in bone samples and Young's modulus

Bone mass is the most important determinant of the mechanical strength of bones, and spatial structure is the second. In general, the spatial structure and mechanical properties of bones such as the breaking strength are direction dependent. The mean intercept length (MIL) and line frequency deviation (LFD) are two methods for quantifying directional aspects of the spatial structure of bone. Young's modulus is commonly used to describe the stiffness of bone, which is also a direction-dependent mechanical property. The aim of this article is to investigate the relation between MIL and LFD on one hand and Young's modulus on the other. From 11 human mandibular condyles, 44 samples were taken and scanned with high-resolution computer tomography equipment (micro-CT). For each sample the MIL and LFD were determined in 72602 directions distributed evenly in 3D space. In the same directions Young's modulus was determined by means of the stiffness tensor that had been determined for each sample by finite element analysis. To investigate the relation between the MIL and LFD on one hand and Young's modulus on the other, multiple regression was used. On average the MIL accounted for 69% of the variance in Young's modulus in the 44 samples and the LFD accounted for 72%. The average percentage of variance accounted for increased to 80% when the MIL was combined with the LFD to predict Young's modulus. Obviously MIL and LFD to some extent are complementary with respect to predicting Young's modulus. It is known that directional plots of the MIL tend to be ellipses or ellipsoids. It is speculated that ellipsoids are not always sufficient to describe Young's modulus of a bone sample and that the LFD partly compensates for this.     

The effect of chemical cleansing procedures combined with peracetic acid-ethanol sterilization on biomechanical properties of cortical bone.

Peracetic acid-ethanol sterilization (PES) with a preceding delipidation step is an effective sterilization method for allograft bone, but its influence on biomechanical properties of bone has not been studied. The aim of this study was to evaluate the effects of different incubation times of water, hydrogen peroxide and alcohol cleansing procedures combined with PES on biomechanical properties of freeze-dried cortical bone. These effects were studied by performing three-point bending tests on cortical samples. The lyophilized cortical samples were rehydrated prior to mechanical testing. The bending strength and the absorbed energy of the processed cortical samples were increased slightly but the Young's modulus was decreased compared to unprocessed samples. However, when the residual moisture content of the processed cortical samples was reduced from <5% to 0% all the biomechanical properties studied were significantly decreased. Hexane elution was used to determine the residual fat content of the processed cortical bone. Reducing the incubation time in cleansing had no effect on the residual fat content of the bone samples. Our in vitro study indicates that the cleansing procedure proposed combined with PES affects the biomechanical properties of cortical bone only on a limited scale.     

The effects of testing methods on the flexural fatigue life of human cortical bone

A flexural model of four-point bending fatigue that has been experimentally validated for human cortical bone under load control was used to determine how load and displacement control testing affects the fatigue behavior of human cortical bone in three-point and symmetric four-point bending. Under load control, it was predicted that three-point bending produced no significant differences in fatigue life when compared to four-point bending. However, three-point bending produced less stiffness loss with increasing cycles than four-point bending. In four-point bending, displacement control was predicted to produce about one and a half orders of magnitude greater fatigue life when compared to load control. This prediction agrees with experimental observations of equine cannon bone tested in load and displacement control (Gibson et al., 1998). Displacement controlled three-point bending was found to produce approximately a 25% greater fatigue life when compared to load control. The prediction of longer fatigue life under displacement control may have clinical relevance for the repair of damaged bone. The model can also be adapted to other geometric configurations, including modeling of whole long bones, and with appropriate fatigue data, other cortical bone types.     

Cortical bone distribution in the femoral neck of strepsirhine primates

The thickness of the inferior and superior cortices of the femoral neck was measured on X-rays of 181 strepsirhine primate femora representing 24 species. Neck length, neck depth and neck-shaft angle were also measured. The strength of the femoral neck in frontal bending was estimated by modeling the neck as a hollow cylinder, with neck depth as the outer diameter and cortical thickness representing the superior and inferior shell dimensions. Results indicate that the inferior cortex is always thicker than the superior cortex. The ratio of superior to inferior cortical thickness is highly variable but distinguishes two of the three locomotor groups in the sample. Vertical clingers and leapers have higher ratios (i.e., a more even distribution of cortical bone) than quadrupeds. The slow climbers tend to have the lowest ratios, although they do not differ significantly from the leapers and quadrupeds. These results do not confirm prior theoretical expectations and reported data for anthropoid primates that link greater asymmetry of the cortical shell to more stereotypical hip excursions. The ratio of superior to inferior cortical thickness is unrelated to body mass, femoral neck length, and neck-shaft angle, calling into question whether the short neck of strepsirhine primates acts as a cantilever beam in bending. On the other hand, the estimated section moduli are highly correlated with body mass and neck length, a correlation that is driven primarily by body mass. In conclusion, we believe that an alternative interpretation to the cantilever beam model is needed to explain the asymmetry in bone distribution in the femoral neck, at least in strepsirhine primates (e.g., a thicker inferior cortex is required to reinforce the strongly curved inferior surface). As in prior studies of cross-sectional geometry of long bones, we found slightly positive allometry of cortical dimensions with body mass.     

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.     

Collagen fiber organization is related to mechanical properties and remodeling in equine bone. A comparsion of two methods

We studied birefringence as an indicator of collagen fiber orientation in the diaphysis of the equine third metacarpal bone. We had previously shown that tissue from the lateral cortex of this bone is stronger monotonically, but less fatigue resistant, than tissue from the medial and dorsal regions. To learn whether collagen fiber orientation might play a role in this regional specialization, we tested three hypotheses using the same specimens: (1) collagen fiber orientation is regionally dependent; (2) remodeling changes collagen fiber orientation; (3) longitudinal collagen fibers correlate positively with modulus and monotonic bending strength and negatively with flexural fatigue life. Beams (N=36) cut parallel to the long axes of six pairs of bones had been tested to determine elastic modulus (N=36), and fatigue life (N=24) or monotonic strength (N=12) in four-point bending. Subsequently, histologic cross-sections were prepared, and porosity, active remodeling and past remodeling were quantified. Birefringence was measured as an indicator of transverse collagen orientation using plane-polarized light (PPL), and again using circularly polarized light (CPL). The CPL measurement was less variable than the PPL measurement. Both birefringence measures indicated that collagen was more longitudinally oriented in the lateral cortex than in the other two cortices. Longitudinally disposed collagen correlated with greater modulus and monotonic strength, but did not correlate with fatigue life. Remodeling was associated with more transverse collagen. Neither measure of birefringence was significantly correlated with porosity. It was concluded that, in the equine cannon bone, longitudinal collagen fiber orientation is regionally variable, contributes to increased modulus and strength but not fatigue life, and is reduced by osteonal remodeling.     

Structural consequences of transcortical holes in long bones loaded in torsion

Finite element models were used to predict the structural consequences of transcortical holes through long bones loaded in torsion. Several parameters were investigated including hole size, anelastic behavior of the bone, cortical wall thickness, cortical wall symmetry, curvature along the bone's long axis and the axial length of the defect. Finite element model predictions of percent intact bone strength were compared to experimental data for sheep femora with transcortical drill holes loaded to failure in torsion. Hole size was expressed as hole diameter divided by the outer bone diameter. Linear finite element model predictions were in conservative agreement with the experimental data for large hole sizes. A transcortical hole with a diameter 50% of the outer bone diameter reduced the torsional strength by 60%. However, the linear models predict a 40% drop in strength for small holes whereas in vitro data suggest that small holes have no significant effect on strength. Models which represent non-linear anelastic behavior in bone over-predicted torsional strengths. Asymmetric cortical wall thickness and long bone bowing have minor effects, while the length of an elongated defect strongly influences the torsional strength. Strength reductions are greatest for bones with thin cortical walls.     

Length-dependence of flexural rigidity as a result of anisotropic elastic properties of microtubules

Unexplained length-dependence of flexural rigidity and Young's modulus of microtubules is studied using an orthotropic elastic shell model. It is showed that vibration frequencies and buckling load predicted by the accurate orthotropic shell model are much lower than that given by the approximate isotropic beam model for shorter microtubules, although the two models give almost identical results for sufficiently long microtubules. It is this inaccuracy of the isotropic beam model used by all previous researchers that leads to reported lower flexural rigidity and Young's modulus for shorter microtubules. In particular, much lower shear modulus and circumferential Young's modulus, which only weaken flexural rigidity of shorter microtubules, are responsible for the observed length-dependence of the flexural rigidity. These results confirm that longitudinal Young's modulus of microtubules is length-independent, and the observed length-dependence of the flexural rigidity and Young's modulus is a result of strongly anisotropic elastic properties of microtubules which have a length-dependent weakening effect on flexural rigidity of shorter microtubules.     

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.     

The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques

Acoustic microscopy (30-60 microm resolution) and nanoindentation (1-5 microm resolution) are techniques that can be used to evaluate the elastic properties of human bone at a microstructural level. The goals of the current study were (1) to measure and compare the Young's moduli of trabecular and cortical bone tissues from a common human donor, and (2) to compare the Young's moduli of bone tissue measured using acoustic microscopy to those measured using nanoindentation. The Young's modulus of cortical bone in the longitudinal direction was about 40% greater than (p<0.01) the Young's modulus in the transverse direction. The Young's modulus of trabecular bone tissue was slightly higher than the transverse Young's modulus of cortical bone, but substantially lower than the longitudinal Young's modulus of cortical bone. These findings were consistent for both measurement methods and suggest that elasticity of trabecular tissue is within the range of that of cortical bone tissue. The calculation of Young's modulus using nanoindentation assumes that the material is elastically isotropic. The current results, i.e., the average anisotropy ratio (E(L)/E(T)) for cortical bone determined by nanoindentation was similar to that determined by the acoustic microscope, suggest that this assumption does not limit nanoindentation as a technique for measurement of Young's modulus in anisotropic bone.     

Body size, body shape, and long bone strength in modern humans

To identify behaviorally significant differences in bone structure it is first necessary to control for the effects of body size and body shape. Here the scaling of cross-sectional geometric properties of long bone diaphyses with different "size" measures (bone length, body mass, and the product of bone length and body mass) are compared in two modern human populations with very different body proportions: Pecos Pueblo Amerindians and East Africans. All five major long bones (excluding the fibula) were examined. Mechanical predictions are that cortical area (axial strength) should scale with body mass, while section modulus (bending/torsional strength) should scale with the product of body mass and moment arm length. These predictions are borne out for section moduli, when moment arm length is taken to be proportional to bone length, except in the proximal femoral diaphysis, where moment arm length is proportional to mediolateral body breadth (as would be expected given the predominance of M-L bending loads in this region). Mechanical scaling of long bone bending/torsional strength is similar in the upper and lower limbs despite the fact that the upper limb is not weight-bearing. Results for cortical area are more variable, possibly due to a less direct dependence on mechanical factors. Use of unadjusted bone length alone as a "size" measure produces misleading results when body shape varies significantly, as is the case between many modern and fossil hominid samples. In such cases a correction factor for body shape should be incorporated into any "size" standardization.     

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.     

Computed-tomography-based finite-element models of long bones can accurately capture strain response to bending and torsion

Finite element (FE) models of long bones constructed from computed-tomography (CT) data are emerging as an invaluable tool in the field of bone biomechanics. However, the performance of such FE models is highly dependent on the accurate capture of geometry and appropriate assignment of material properties. In this study, a combined numerical-experimental study is performed comparing FE-predicted surface strains with strain-gauge measurements. Thirty-six major, cadaveric, long bones (humerus, radius, femur and tibia), which cover a wide range of bone sizes, were tested under three-point bending and torsion. The FE models were constructed from trans-axial volumetric CT scans, and the segmented bone images were corrected for partial-volume effects. The material properties (Young's modulus for cortex, density-modulus relationship for trabecular bone and Poisson's ratio) were calibrated by minimizing the error between experiments and simulations among all bones. The R(2) values of the measured strains versus load under three-point bending and torsion were 0.96-0.99 and 0.61-0.99, respectively, for all bones in our dataset. The errors of the calculated FE strains in comparison to those measured using strain gauges in the mechanical tests ranged from -6% to 7% under bending and from -37% to 19% under torsion. The observation of comparatively low errors and high correlations between the FE-predicted strains and the experimental strains, across the various types of bones and loading conditions (bending and torsion), validates our approach to bone segmentation and our choice of material properties.     

Apparent Young's modulus of human radius using inverse finite-element method

The ability to assess the elastic and failure properties of cortical bone at the radial diaphysis has a clinical importance. A new generation of quantitative ultrasound (QUS) devices and peripheral quantitative computed tomography (p-QCT) has been developed to assess non-invasively bone material and structural properties at the distal radius. This anatomical site is characterized by a thin cortical thickness that complicates traditional mechanical testing methods on specimens. Until now, mechanical properties of cortical bone at distal radius (e.g., elastic modulus, yield stress and strain) remain rarely studied probably due to experimental difficulties. The present study introduces an inverse finite-element method strategy to measure the elastic modulus and yield properties of human cortical specimens of the radial diaphysis. Twenty millimeter-thick portions of diaphysis were cut from 40 human radii (ages 45-90) for biomechanical test. Subsequently the same portion was modeled in order to obtain a specimen-specific three dimensional finite-element model (3D-FEM). Longitudinal elastic constants at the apparent level and stress characterizations were performed by coupling mechanical parameters with isotropic linear-elastic simulations. The results indicated that the mean apparent Young's modulus for radial cortical bone was 16 GPa (SD 1.8) and the yield stress was 153 MPa (SD 33). Breaking load was 12,946 N (SD 3644), cortical thickness 2.9 mm (SD 0.6), structural effective strain at the yield (epsilon(y)=0.0097) and failure (epsilon(u)=0.0154) load were also calculated. The 3D-FEM strategy described here may help to investigate bone mechanical properties when some difficulties arise from machining mechanical sample.     

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 effects of a calcium deficient diet on the mechanical properties and morphology of goose bone

A control group of geese (Anser anser) on a normal calcium diet for egg laying poultry was compared to egg laying geese on a calcium deficient diet. The ultimate compressive strength and modulus of elasticity of femoral cortical bone from each group were determined by compressing right circular cylinders which were 2.4 mm in height and 0.8 mm in diameter. The bending strength and bending modulus of elasticity of tibial cortical bone were determined by three point bend tests on rectangular prisms which were approximately 25 mm by 0.8 mm by 0.8 mm. Bone calcium content and eggshell calcium content were determined by atomic absorption spectrophotometry. Blood samples were analyzed for free calcium ion concentration. Histological observations included studies of cross-sectional microradiographs, examinations of cross sections stained by a modified Masson's technique, and a determination of fractional area of voids by quantitative microscopy. The average compressive modulus for the control birds was 12.0 GPa (S.D.: 6.2 GPa) while the ultimate compressive strength was 165 MPa (S.D.: 27 MPa). Calcium deprived birds showed slight, but not statistically significant, decreases in both the compressive modulus and compressive strength. The tibial three point bending modulus for the control birds was 16.5 GPa (S.D.: 2.6 GPa) while the ultimate bending strength was 256 MPa (S.D.: 58 MPa). Once again, slight though not statistically significant decreases in the bending modulus and strength were seen in the geese on the calcium deficient diet. The average calcium content (wt%) of the femora of the control birds was 20.5% (S.D.: 4.3%) and 20.6% (S.D.: 4.8%) for the tibiae. No significant differences were noted in the calcium deprived birds. The average fractional void area for the control bird femoral bone was 12.0% (S.D.: 2.6%) and 9.8% (S.D.: 1.8%) for the tibial bone. Significantly greater fractional void areas were noted in the calcium deficient birds as were profound changes in the macrocellular structure of these bones.