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.     

An application of nanoindentation technique to measure bone tissue Lamellae properties

Measuring the microscopic mechanical properties of bone tissue is important in support of understanding the etiology and pathogenesis of many bone diseases. Knowledge about these properties provides a context for estimating the local mechanical environment of bone related cells thait coordinate the adaptation to loads experienced at the whole organ level. The objective of this study was to determine the effects of experimental testing parameters on nanoindentation measures of lamellar-level bone mechanical properties. Specifically, we examined the effect of specimen preparation condition, indentation depth, repetitive loading, time delay, and displacement rate. The nanoindentation experiments produced measures of lamellar elastic moduli for human cortical bone (average value of 17.7 +/- 4.0 GPa for osteons and 19.3 +/- 4.7 GPa for interstitial bone tissue). In addition, the hardness measurements produced results consistent with data in the literature (average 0.52 +/- 0.15 GPa for osteons and 0.59 +/- 0.20 GPa for interstitial bone tissue). Consistent modulus values can be obtained from a 500-nm-deep indent. The results also indicated that the moduli and hardnesses of the dry specimens are significantly greater (22.6% and 56.9%, respectively) than those of the wet and wet and embedded specimens. The latter two groups were not different. The moduli obtained at a 5-nm/s loading rate were significantly lower than the values at the 10- and 20-nm/s loading rates while the 10- and 20-nm/s rates were not significantly different. The hardness measurements showed similar rate-dependent results. The preliminary results indicated that interstitial bone tissue has significantly higher modulus and hardness than osteonal bone tissue. In addition, a significant correlation between hardness and elastic modulus was observed.     

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.     

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.     

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.     

How is the indentation modulus of bone tissue related to its macroscopic elastic response? A validation study

This work consists of the validation of a novel approach to estimate the local anisotropic elastic constants of the bone extracellular matrix using nanoindentation. For this purpose, nanoindentation on two planes of material symmetry were analyzed and the resulting longitudinal elastic moduli compared to the moduli measured with a macroscopic tensile test. A combined lathe and tensile system was designed that allows machining and testing of cylindrical microspecimens of approximately 4mm in length and 300 microm in diameter. Three bovine specimens were tested in tension and their outer geometry and porosity assessed by synchrotron radiation microtomography. Based on the results of the traction test and the precise outer geometry, an apparent longitudinal Young's modulus was calculated. Results between 20.3 and 27.6 GPa were found that match with previously reported values for bovine compact bone. The same specimens were then characterized by nanoindentation on a transverse and longitudinal plane. A longitudinal Young's modulus for the bone matrix was then derived using the numerical scheme proposed by Swadener and Pharr and the fabric-elasticity relationship by Zysset and Curnier. Based on the matrix modulus and a power law effective volume fraction, an apparent longitudinal Young's modulus was predicted for each microspecimen. This alternative approach provided values between 19.9 and 30.0 GPa, demonstrating differences between 2% and 13% to the values provided by the initial tensile test. This study therefore raises confidence in our nanoindentation protocol of the bone extracellular matrix and supports the underlying hypotheses used to extract the anisotropic elastic constants.     

Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response

Anisotropy is one of the most peculiar aspects of cortical bone mechanical behaviour, and the numerical approach can be successfully used to investigate aspects of bone tissue mechanics that analytical methods solve in approximate way or do not cover. In this work, nanoindentation experimental tests and finite element simulations were employed to investigate the elastic-inelastic anisotropic mechanical properties of cortical bone. The model allows for anisotropic elastic and post-yield behaviour of the tissue. A tension-compression mismatch and direction-dependent yield stresses are allowed for. Indentation experiments along the axial and transverse directions were simulated with the purpose to predict the indentation moduli and hardnesses along multiple orientations. Results showed that the experimental transverse-to-axial ratio of indentation moduli, equal to 0.74, is predicted with a ～3% discrepancy regardless the post-yield material behaviour; whereas, the transverse-to-axial hardness ratio, equal to 0.86, can be correctly simulated (discrepancy ～6% w.r.t. the experimental results) only employing an anisotropic post-elastic constitutive model. Further, direct comparison between the experimental and simulated indentation tests evidenced a good agreement in the loading branch of the indentation curves and in the peak loads for a transverse-to-axial yield stress ratio comparable to the experimentally obtained transverse-to-axial hardness ratio. In perspective, the present work results strongly support the coupling between indentation experiments and FEM simulations to get a deeper knowledge of bone tissue mechanical behaviour at the microstructural level. The present model could be used to assess the effect of variations of constitutive parameters due to age, injury, and/or disease on bone mechanical performance in the context of indentation testing.     

Sensitivity of multiple damage parameters to compressive overload in cortical bone

Damage accumulation plays a key role in weakening bones prior to complete fracture and in stimulating bone remodeling. The goal of this study was to characterize the degradation in the mechanical properties of cortical bone following a compressive overload. Longitudinally oriented, low-aspect ratio specimens (n=24) of bovine cortical bone were mechanically tested using an overload-hold-reload protocol. No modulus reductions greater than 5% were observed following overload magnitudes less than 0.73% strain. For each specimen, changes in strength and Poisson's ratio were greater (p=0.02) than that in modulus by 10.8- and 26.6-fold, respectively, indicating that, for the specimen configuration used in this study, longitudinal elastic modulus is one of the least sensitive properties to a compressive overload. Residual strains were also proportionately greater by 6.4-fold (p=0.01) in the transverse than axial direction. These results suggest that efforts to relate microcrack density and morphology to changes in compressive mechanical properties of cortical bone may benefit from considering alternative parameters to modulus reductions.     

Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CT-attenuation

High-resolution architecture-based finite element models are commonly used for characterizing the mechanical behavior of cancellous bone. The vast majority of studies use homogeneous material properties to model trabecular tissue. The objectives of this study were to demonstrate that inhomogeneous finite element models that account for microcomputed tomography-measured tissue modulus variability more accurately predict the apparent stiffness of cancellous bone than homogeneous models, and to examine the sensitivity of an inhomogeneous model to the degree of tissue property variability. We tested five different material cases in finite element models of ten cancellous cubes in simulated uniaxial compression. Three of these cases were inhomogeneous and two were homogeneous. Four of these cases were unique to each specimen, and the remaining case had the same tissue modulus for all specimens. Results from all simulations were compared with measured elastic moduli from previous experiments. Tissue modulus variability for the most accurate of the three inhomogeneous models was then artificially increased to simulate the effects of non-linear CT-attenuation-modulus relationships. Uniqueness of individual models was more critical for model accuracy than level of inhomogeneity. Both homogeneous and inhomogeneous models that were unique to each specimen had at least 8% greater explanatory power for apparent modulus than models that applied the same material properties to all specimens. The explanatory power for apparent modulus of models with a tissue modulus coefficient of variation (COV) range of 21-31% was 13% greater than homogeneous models (COV=0). The results of this study indicate that inhomogenous finite element models that have tissue moduli unique to each specimen more accurately predict the elastic behavior of cancellous cubic specimens than models that have common tissue moduli between all specimens.     

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.     

Bi-directional mechanical properties of the axillary pouch of the glenohumeral capsule: implications for modeling and surgical repair

The objective of this study was to determine the mechanical properties of the axillary pouch of the inferior glenohumeral ligament in the directions perpendicular (transverse) and parallel (longitudinal) to the longitudinal axis of the anterior band of the inferior glenohumeral ligament. A punch was used to excise one transverse and one longitudinal tissue sample from the axillary pouch of each cadaveric shoulder (n = 10). Each tissue sample was preconditioned and then a load-to-failure test was performed. All tissue samples exhibited the typical nonlinear behavior reported for ligaments and tendons. Significant differences (p < 0.05) were detected between the transverse and longitudinal tissue samples for ultimate stress (0.8 +/- 0.4 MPa and 2.0 +/- 1.0 MPa, respectively) and tangent modulus (5.4 +/- 2.9 MPa and 14.8 +/- 13.1 MPa, respectively). No significant differences (p > 0.05) were observed between the ultimate strain (transverse: 23.5 +/- 11.5%, longitudinal: 33.3 +/- 23.6%) and strain energy density (transverse: 10.8 +/- 8.5 MPa, longitudinal: 21.1 +/- 15.4 MPa) of the transverse and longitudinal tissue samples. The ultimate stress determined for the longitudinal axillary pouch tissue samples was comparable to a previous study that reported it to be 5.5 +/- 2.0 MPa. The ratio of the longitudinal to transverse moduli (3.3 +/- 2.8) is considerably less than that of the medial collateral ligament of the knee (30) and interosseous ligament of the forearm (385), suggesting that the axillary pouch functions to stabilize the joint in more than just one direction. Future models of the glenohumeral joint and surgical repair procedures should consider the properties of the axillary pouch in its transverse and longitudinal directions to fully describe the behavior of the inferior glenohumeral ligament.     

Elastic moduli, yield stress, and ultimate stress of cancellous bone in the canine proximal femur

Elastic moduli, yield stress and ultimate compressive stress were determined for cancellous bone from the femoral head and neck regions of the canine femur. Unconfined compression tests were performed on 5 mm cubic samples which were cut from two femurs. Elastic moduli were measured in three orthogonal directions, and the yield stress and ultimate stress were measured along the proximal-distal axis. The results from this investigation support previous assumptions that the mechanical behavior of canine cancellous bone is qualitatively similar to human cancellous bone. The canine cancellous bone was observed to be anisotropic in elastic modulus. For two thirds of the cubic specimens tested, the elastic modulus was largest in the load-bearing, proximal-distal direction. A linear relationship between yield stress and elastic modulus was observed for canine bone, as is typical of human bone. A similar linear relationship between ultimate stress and elastic modulus was observed. Thus, for canine bone as well as for human bone, failure appears to be governed by a strain level which is position independent. The yield strain of 0.0259 and ultimate strain of 0.0288 for canine bone were both less than the yield strain of 0.0395 reported for human bone.     

Tensile properties and fiber alignment of human supraspinatus tendon in the transverse direction demonstrate inhomogeneity,nonlinearity, and regional isotropy

A recent study (Lake et al., 2009); reported the properties of human supraspinatus tendon (SST) tested along the predominant fiber direction. The SST was found to have a relatively disperse distribution of collagen fibers, which may represent an adaptation to multiaxial loads imposed by the complex loading environment of the rotator cuff. However, the multiaxial mechanical properties of human SST remain unknown. The objective of this study, therefore, was to evaluate the mechanical properties, fiber alignment, change in alignment with applied load, and structure–function relationships of SST in transverse testing. Samples from six SST locations were tested in uniaxial tension with samples oriented transverse to the tendon long-axis. Polarized light imaging was used to quantify collagen fiber alignment and change in alignment under applied load. The mechanical properties of samples taken near the tendon–bone insertion were much greater on the bursal surface compared to the joint surface (e.g., bursal moduli 15–30 times greater than joint; p<0.001). In fact, the transverse moduli values of the bursal samples were very similar to values obtained from samples tested along the tendon long-axis (Lake et al., 2009). This key and unexpected finding suggests planar mechanical isotropy for bursal surface samples near the insertion, which may be due to complex in vivo loading. Organizationally, fiber distributions became less aligned along the tendon long-axis in the toe-region of the stress–strain response. Alignment changes occurred to a slightly lesser degree in the linear-region, suggesting that movement of collagen fibers may play a role in mechanical nonlinearity. Transverse mechanical properties were significantly correlated with fiber alignment (e.g., for linear-region modulus r_s=0.74, p<0.0001), demonstrating strong structure–function relationships. These results greatly enhance current understanding of the properties of human SST and provide clinicians and scientists with vital information in attempting to treat or replace this complex tissue.     

Macro-/Micro-Structures of Elytra, Mechanical Properties of the Biomaterial and the Coupling Strength Between Elytra in Beetles

Macro-/Micro-structures and mechanical properties of the elytra of beetles were studied. The Scan Electron Microscope (SEM) and optical microscopy were employed to observe the macro-/micro-structure of the surface texture and cross-section structure of elytra. Nano-indentation was carried out to measure the elastic modulus and the hardness of elytra. Tensile strengths of elytra in lateral and longitudinal directions were measured by a muhifunctional testing machine. The coupling force between elytra was also measured and the clocking mechanism was studied. SEM images show the similar geometric structure in transverse and longitudinal sections and multilayer-dense epicuticle and exocuticle, followed by bridge piers with a helix structured fibers, which connect the exocuticle to the endodermis, and form an ellipse empty to reduce the structure weight. The elastic modulus and the hardness are topologically distributed and the mechanical parameters of fresh elytra are much higher than those of dried elytra. The tensile strength of the fresh biological material is twice that of dried samples, but there is no clear difference between the data in lateral and longitudinal directions. Coupling forces measured are 6.5 to 160 times of beetles' bodyweight, which makes the scutellum very important in controlling the open and close of the elytra. The results provide a biological template to inspire lightweight structure design for aerospace engineering.     

Anisotropy of age-related toughness loss in human cortical bone: a finite element study

A mechanistic understanding of the role of bone quality on fracture processes is essential for determining the underlying causes of age-related changes in the mechanical response of the human bone. In this study, a previously developed cohesive finite element model was used to investigate the effects of age-related changes and the orientation of crack growth on the toughening behavior of human cortical bone. The change in the anisotropy of toughening mechanisms with age was also studied. Finite element method (FEM) simulations showed that the initiation toughness decreased by 3% and 8%/decade for transverse and longitudinal crack growth, respectively. In contrast, fracture resistance curve slope for transverse and longitudinal crack growth decreased by 2% and 3%/decade, respectively. Initiation fracture toughness values were higher for the transverse than for the longitudinal for a given age. On the other hand, propagation fracture toughness values were higher for longitudinal than for transverse crack growth for a given age. With respect to age, the toughness ratio for crack initiation decreased by 6%/decade, but that for propagation showed almost no change (less than 1%). In light of these findings, an analytical model evaluating the crack arresting feature of cement lines, is proposed to explain the factors that determine crack penetration into osteons or its deflection by cement lines.     

Measurement of Elastic Modulus of Collagen Type I Single Fiber

Collagen fibers are the main components of the extra cellular matrix and the primary contributors to the mechanical properties of tissues. Here we report a novel approach to measure the longitudinal component of the elastic moduli of biological fibers under conditions close to those found in vivo and apply it to type I collagen from rat tail tendon. This approach combines optical tweezers, atomic force microscopy, and exploits Euler-Bernoulli elasticity theory for data analysis. This approach also avoids drying for measurements or visualization, since samples are freshly extracted. Importantly, strains are kept below 0.5%, which appear consistent with the linear elastic regime. We find, surprisingly, that the longitudinal elastic modulus of type I collagen cannot be represented by a single quantity but rather is a distribution that is broader than the uncertainty of our experimental technique. The longitudinal component of the single-fiber elastic modulus is between 100 MPa and 360 MPa for samples extracted from different rats and/or different parts of a single tail. Variations are also observed in the fibril-bundle / fibril diameter with an average of 325±40 nm. Since bending forces depend on the diameter to the fourth power, this variation in diameter is important for estimating the range of elastic moduli. The remaining variations in the modulus may be due to differences in composition of the fibril-bundles, or the extent of the proteoglycans constituting fibril-bundles, or that some single fibrils may be of fibril-bundle size.     

An alternative ultrasonic method for measuring the elastic properties of cortical bone

We studied the elastic properties of bone to analyze its mechanical behavior. The basic principles of ultrasonic methods are now well established for varying isotropic media, particularly in the field of biomedical engineering. However, little progress has been made in its application to anisotropic materials. This is largely due to the complex nature of wave propagation in these media. In the present study, the theory of elastic waves is essential because it relates the elastic moduli of a material to the velocity of propagation of these waves along arbitrary directions in a solid. Transducers are generally placed in contact with the samples which are often cubes with parallel faces that are difficult to prepare. The ultrasonic method used here is original, a rough preparation of the bone is sufficient and the sample is rotated. Moreover, to analyze heterogeneity of the structure we measure velocities in different points on the sample. The aim of the present study was to determine in vitro the anisotropic elastic properties of cortical bones. For this purpose, our method allowed measurement of longitudinal and transverse velocities (C(L) and C(T)) in longitudinal (fiber direction) and the radial directions (orthogonal to the fiber direction) of compact bones. Young's modulus E and Poisson's ratio nu, were then deduced from the velocities measured considering the compact bone as transversely isotropic or orthotropic. The results are in line with those of other methods.     

The role of mineral content in determining the micromechanical properties of discrete trabecular bone remodeling packets

In trabecular bone, each remodeling event results in the resorption and/or formation of discrete structural units called ‘packets’. These remodeling packets represent a fundamental level of bone’s structural hierarchy at which to investigate composition and mechanical behaviors. The objective of this study was to apply the complementary techniques of quantitative backscattered electron microscopy (qBSEM) and nanoindentation to investigate inter-relationships between packet mineralization, elastic modulus, contact hardness and plastic deformation resistance. Indentation arrays were performed across nine trabecular spicules from 3 human donors; these spicules were then imaged using qBSEM, and discretized into their composite remodeling packets (127 in total). Packets were classified spatially as peripheral or central, and mean contact hardness, plastic deformation resistance, elastic modulus and calcium content calculated for each. Inter-relationships between measured parameters were analysed using linear regression analyses, and dependence on location assessed using Student’s t-tests. Significant positive correlations were found between all mechanical parameters and calcium content. Elastic modulus and contact hardness were significantly correlated, however elastic modulus and plastic deformation resistance were not. Calcium content, contact hardness and elastic modulus were all significantly higher for central packets than for peripheral, confirming that packet mineral content contributes to micromechanical heterogeneity within individual trabecular spicules. Plastic deformation resistance, however, showed no such regional dependence, indicating that the plastic deformation properties in particular, are determined not only by mineral content, but also by the organic matrix and interactions between these two components.     

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.     

Mechanical properties of metaphyseal bone in the proximal femur

We used a three-point bending test to investigate the structural behavior of 123 rectangular flat plate specimens harvested from the metaphyseal shell of the cervical and intertrochanteric regions of five fresh/frozen human proximal femora. For comparison purposes, 36 specimens of similar geometry were also fabricated from bone of the femoral diaphysis. All specimens were oriented in either the local longitudinal or transverse directions. The mean longitudinal elastic modulus was 9650 +/- 2410 (SD) MPa and demonstrated a 24% decrease from that measured for the diaphysis (12500 +/- 2140 MPa) using the same testing technique. However, the transverse elastic moduli did not differ significantly between the proximal (5470 +/- 1720 MPa) and diaphyseal (5990 +/- 1520 MPa) specimens. The globally averaged values for the ultimate tensile strengths of the metaphyseal shell were 101 +/- 26 MPa in the longitudinal and 50 +/- 12 MPa in the transverse directions. These compared with diaphyseal values of 128 +/- 16 MPa and 47 +/- 12 MPa, respectively. While these differences were largely due to the reduced density of the proximal specimens, a slight decrease in transverse anisotropy for the proximal specimens was also noted by comparing the ratio of longitudinal to transverse moduli (1.76) and tensile strength (2.02) to the diaphyseal values (2.09 and 2.71, respectively). Use of these data should lead to improved performance of analytical models for the proximal femur, and thus help focus increased attention on the structural contribution of trabecular bone to the strength and rigidity of the proximal femur.