Tensile properties of rat femoral bone as functions of bone volume fraction, apparent density and volumetric bone mineral density

Mechanical testing has been regarded as the gold standard to investigate the effects of pathologies on the structure-function properties of the skeleton. Tensile properties of cancellous and cortical bone have been reported previously; however, no relationships describing these properties for rat bone as a function of volumetric bone mineral density (ρ(MIN)), apparent density or bone volume fraction (BV/TV) have been reported in the literature. We have shown that at macro level, compression and torsion properties of rat cortical and cancellous bone can be well described as a function of BV/TV, apparent density or ρ(MIN) using non-destructive micro-computed tomographic imaging and mechanical testing to failure. Therefore, the aim of this study is to derive a relationship expressing the tensile properties of rat cortical bone as a function of BV/TV, apparent density or ρ(MIN) over a range of normal and pathologic bones. We used bones from normal, ovariectomized and osteomalacic animals. All specimens underwent micro-computed tomographic imaging to assess bone morphometric and densitometric indices and uniaxial tension to failure. We obtained univariate relationships describing 74-77% of the tensile properties of rat cortical bone as a function of BV/TV, apparent density or ρ(MIN) over a range of density and common skeletal pathologies. The relationships reported in this study can be used in the structural rigidity to provide a non-invasive method to assess the tensile behavior of bones affected by pathology and/or treatment options.     

Ash content modulation of torsionally derived effective material properties in cortical mouse bone

The purpose of this study was to evaluate the effects of isolated alterations in mineral content on mouse bone torsional properties. The femora and tibiae from 25 eight-week-old male A/J strain mice were divided into five groups and selectively decalcified from 5% to 20%. The right femora were then tested to failure in torsion while the tibiae were ashed to determine final mineral content of the decalcified bones. Contralateral femora were serially cross-sectioned to determine geometric properties, and effective material properties were then calculated from the geometric and structural properties of each femoral pair. We found that the relationship between ash content and effective shear modulus or maximum effective shear stress could best be characterized through a power law, with an exponential factor of 6.79 (R2 = 0.85) and 4.04 (R2 = 0.67), respectively. This indicates that in a murine model, as with other species, small changes in ash content significantly influence effective material properties. Furthermore, it appears that (in adolescent A/J strain mice) effective shear modulus is more heavily affected by changes in mineralization than is maximum effective shear stress when these properties are derived from whole bone torsional tests to failure.     

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

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

Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur

PURPOSE: In a meta-analysis of the literature we evaluated the present knowledge of the material properties of cortical and cancellous bone to answer the question whether the available data are sufficient to realize anisotropic finite element (FE)-models of the proximal femur. MATERIAL AND METHOD: All studies that met the following criteria were analyzed: Young's modulus, tensile, compressive and torsional strengths, Poisson's ratio, the shear modulus and the viscoelastic properties had to be determined experimentally. The experiments had to be carried out in a moist environment and at room temperature with freshly removed and untreated human cadaverous femurs. All material properties had to be determined in defined load directions (axial, transverse) and should have been correlated to apparent density (g/cm(3)), reflecting the individually variable and age-dependent changes of bone material properties. RESULTS: Differences in Young's modulus of cortical [cancellous] bone at a rate of between 33% (58%) (at low apparent density) and 62% (80%) (at high apparent density), are higher in the axial than in the transverse load direction. Similar results have been seen for the compressive strength of femoral bone. For the tensile and torsional strengths, Poisson's ratio and the shear modulus, only ultimate values have been found without a correlation to apparent density. For the viscoelastic behaviour of bone only data of cortical bone and in axial load direction have been described up to now. CONCLUSIONS: Anisotropic FE-models of the femur could be realized for most part with the summarized material properties of bone if characterized by apparent density and load directions. Because several mechanical properties have not been correlated to these main criteria, further experimental investigations will be necessary in future.     

Long bone torsion: II. A combined experimental and computational method for determining an effective shear modulus

A technique is established which allows an effective torsional shear modulus to be determined for long bones, while remaining nondestructive to whole bone specimens. Strain gages are bonded to the diaphysis of the bone. Strains are then recorded under pure torsional loads. Theoretical stress predictions are combined with experimental strain recordings to arrive at a modulus value. Shear modulus calculations for four canine radii are reported using theoretical stress predictions from circular, elliptical and finite element models of the transverse bone geometry. The effective shear modulus, obtained from an average of the shear moduli determined at strain gage locations, serves to average the heterogeneous shear modulus distribution over the cross section. The shear modulus obtained is that associated with the "circumferential" direction in transverse planes.     

On shear properties of trabecular bone under torsional loading: effects of bone marrow and strain rate

To further improve our understanding of trabecular bone mechanical behavior in torsion, our objective was to determine the effects of strain rate, apparent density, and presence of bone marrow on trabecular bone shear material properties. Torsion tests of cylindrical trabecular bone specimens from sheep lumbar vertebrae with and without bone marrow were conducted. The bones with marrow were divided into two groups and tested at shear strain rates of 0.002 and 0.05s(-1) measured at the specimen perimeter. The bones without marrow were divided into three groups and tested at shear strain rates of 0.002, 0.015, and 0.05s(-1). Comparing the results of bones with and without marrow tested at low (0.002s(-1)) and high (0.05s(-1)) strain rates, presence of bone marrow did not have any significant effect on trabecular bone shear modulus and strength. In specimens without marrow, power relationships were used to define shear strength and modulus as dependent variables in terms of strain rate and apparent density as independent variables. The shear strength was proportional to the apparent density raised to the 1.02 power and to the strain rate raised to the 0.13 power. The shear modulus was proportional to the apparent density raised to the 1.08 power and to the strain rate raised to the 0.07 power. This study provides further insight into the mechanism of bone failure in trauma as well as failure at the interface between bone and implants as it relates to prediction of trabecular bone shear properties.     

Structural properties of a new design of composite replicate femurs and tibias

The purpose of this study was to compare the structural properties of a new vs. established design of composite replicate femurs and tibias. The new design has a cortical bone analog consisting of short-glass-fiber-reinforced (SGFR) epoxy, rather than the fiberglass-fabric-reinforced (FFR) epoxy in the currently available design. The hypothesis was that this new cortical bone analog would improve the uniformity of structural properties between specimens, while having mean stiffness values in the range of natural human bones. The composite replicate bones were tested under bending, axial, and torsional loads. In general, the new SGFR bones were significantly less stiff than the FFR bones, although both bone designs reasonably approximated the structural stiffnesses of natural human bones. With the exceptions of the FFR bone axial tests, the highest variability between specimens was 6.1%. The new SGFR bones had similar variability in structural properties when compared to the FFR bones under bending and torsional loading, but had significantly less variability under axial loading. Differences in epiphyseal geometry between the FFR and SGFR bones, and subsequent seating in the testing fixtures, may account for some of the differences in structural properties; axial stiffness was especially dependent on bone alignment. Stiffness variabilities for the composite replicate bones were much smaller than those seen with natural human bones. Axial strain distribution along the proximal-medial SGFR femur had a similar shape to what was observed on natural human femurs by other investigators, but was considerably less stiff in the more proximal locations.     

The dynamic shear modulus of bone in dependence on the form.

Torsional testing of fresh cortical bovine bone showed highly divergent shear moduli at various sites in the middle part of the diaphysis of the right metacarpus. Two hundred samples taken from twenty-five bones were investigated with a free oscillating torsional pendulum to determine the dynamic shear modulus. The results clearly demonstrate the mutual dependence between the shape of the metacarpus and the modulus of the material. On the basis of the analysis of forty-eight samples, a positive correlation was found between the amount of Ca2+ and PO4(3)-ions in the bone and the shear modulus. The hypothesis is put forward that in bone, normal adaptation to increasing stress is obtained by a change in the modulus values, Wolff's law only being operative for extreme cases.     

Stochastic multi-scale prediction on the apparent elastic moduli of trabecular bone considering uncertainties of biological apatite (BAp) crystallite orientation and image-based modelling

An assessment of the mechanical properties of trabecular bone is important in determining the fracture risk of human bones. Many uncertainty factors contribute to the dispersion of the estimated mechanical properties of trabecular bone. This study was undertaken in order to propose a computational scheme that will be able to predict the effective apparent elastic moduli of trabecular bone considering the uncertainties that are primarily caused by image-based modelling and trabecular stiffness orientation. The effect of image-based modelling which focused on the connectivity was also investigated. A stochastic multi-scale method using a first-order perturbation-based and asymptotic homogenisation theory was applied to formulate the stochastically apparent elastic properties of trabecular bone. The effective apparent elastic modulus was predicted with the introduction of a coefficient factor to represent the variation of bone characteristics due to inter-individual differences. The mean value of the predicted effective apparent Young's modulus in principal axis was found at approximately 460 MPa for respective 15.24% of bone volume fraction, and this is in good agreement with other experimental results. The proposed method may provide a reference for the reliable evaluation of the prediction of the apparent elastic properties of trabecular bone.     

The biomechanics of human femurs in axial and torsional loading: comparison of finite element analysis, human cadaveric femurs, and synthetic femurs

To assess the performance of femoral orthopedic implants, they are often attached to cadaveric femurs, and biomechanical testing is performed. To identify areas of high stress, stress shielding, and to facilitate implant redesign, these tests are often accompanied by finite element (FE) models of the bone/implant system. However, cadaveric bone suffers from wide specimen to specimen variability both in terms of bone geometry and mechanical properties, making it virtually impossible for experimental results to be reproduced. An alternative approach is to utilize synthetic femurs of standardized geometry, having material behavior approximating that of human bone, but with very small specimen to specimen variability. This approach allows for repeatable experimental results and a standard geometry for use in accompanying FE models. While the synthetic bones appear to be of appropriate geometry to simulate bone mechanical behavior, it has not, however, been established what bone quality they most resemble, i.e., osteoporotic or osteopenic versus healthy bone. Furthermore, it is also of interest to determine whether FE models of synthetic bones, with appropriate adjustments in input material properties or geometric size, could be used to simulate the mechanical behavior of a wider range of bone quality and size. To shed light on these questions, the axial and torsional stiffness of cadaveric femurs were compared to those measured on synthetic femurs. A FE model, previously validated by the authors to represent the geometry of a synthetic femur, was then used with a range of input material properties and change in geometric size, to establish whether cadaveric results could be simulated. Axial and torsional stiffnesses and rigidities were measured for 25 human cadaveric femurs (simulating poor bone stock) and three synthetic "third generation composite" femurs (3GCF) (simulating normal healthy bone stock) in the midstance orientation. The measured results were compared, under identical loading conditions, to those predicted by a previously validated three-dimensional finite element model of the 3GCF at a variety of Young's modulus values. A smaller FE model of the 3GCF was also created to examine the effects of a simple change in bone size. The 3GCF was found to be significantly stiffer (2.3 times in torsional loading, 1.7 times in axial loading) than the presently utilized cadaveric samples. Nevertheless, the FE model was able to successfully simulate both the behavior of the 3GCF, and a wide range of cadaveric bone data scatter by an appropriate adjustment of Young's modulus or geometric size. The synthetic femur had a significantly higher stiffness than the cadaveric bone samples. The finite element model provided a good estimate of upper and lower bounds for the axial and torsional stiffness of human femurs because it was effective at reproducing the geometric properties of a femur. Cadaveric bone experiments can be used to calibrate FE models' input material properties so that bones of varying quality can be simulated.     

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.     

Is callus calcium content an indicator of the mechanical strength of healing fractures? An experimental study in rat metatarsals

Changes in the mechanical properties and the calcium content of healing fracture callus were followed, using rat metatarsals. By 24 weeks post-fracture the mean ultimate tensile stress and elastic modulus were still less than half that of the contralateral unfractured bone, whereas the mean torsional modulus had almost reached that of the unfractured bone. The calcium content of the callus formed immediately between the fractured ends of the bone showed changes which coincided with the increases in mechanical strength and the moduli, thus measurement of callus calcium content would enable the prediction of the strength of a healing fracture.     

The mechanical heterogeneity of the hard callus influences local tissue strains during bone healing: a finite element study based on sheep experiments

During secondary fracture healing, various tissue types including new bone are formed. The local mechanical strains play an important role in tissue proliferation and differentiation. To further our mechanobiological understanding of fracture healing, a precise assessment of local strains is mandatory. Until now, static analyses using Finite Elements (FE) have assumed homogenous material properties. With the recent quantification of both the spatial tissue patterns (Vetter et al., 2010) and the development of elastic modulus of newly formed bone during healing (Manjubala et al., 2009), it is now possible to incorporate this heterogeneity. Therefore, the aim of this study is to investigate the effect of this heterogeneity on the strain patterns at six successive healing stages. The input data of the present work stemmed from a comprehensive cross-sectional study of sheep with a tibial osteotomy (Epari et al., 2006). In our FE model, each element containing bone was described by a bulk elastic modulus, which depended on both the local area fraction and the local elastic modulus of the bone material. The obtained strains were compared with the results of hypothetical FE models assuming homogeneous material properties. The differences in the spatial distributions of the strains between the heterogeneous and homogeneous FE models were interpreted using a current mechanobiological theory (Isakson et al., 2006). This interpretation showed that considering the heterogeneity of the hard callus is most important at the intermediate stages of healing, when cartilage transforms to bone via endochondral ossification.     

Validation of a voxel-based FE method for prediction of the uniaxial apparent modulus of human trabecular bone using macroscopic mechanical tests and nanoindentation

Assessment of the mechanical properties of trabecular bone is of major biological and clinical importance for the investigation of bone diseases, fractures and their treatments. Finite element (FE) methods are getting increasingly popular for quantifying the elastic and failure properties of trabecular bone. In particular, voxel-based FE methods have been previously used to calculate the effective elastic properties of trabecular microstructures. However, in most studies, bone tissue moduli were assumed or back-calculated to match the apparent elastic moduli from experiments, which often lead to surprisingly low values when compared to nanoindentation results. In this study, voxel-based FE analysis of trabecular bone is combined with physical measures of volume fraction, micro-CT (microCT) reconstructions, uniaxial mechanical tests and specimen-specific nanoindentation tests for proper validation of the method. Cylindrical specimens of cancellous bone were extracted from human femurs and their volume fraction determined with Archimede's method. Uniaxial apparent modulus of the specimens was measured with an improved tension-compression testing protocol that minimizes boundary artefacts. Their microCT reconstructions were segmented to match the measured bone volume fraction and used to create full-size voxel models with 30-45 microm element size. For each specimen, linear isotropic elastic material properties were defined based on specific nanoindentation measurements of its embedded bone tissue. Linear FE analyses were finally performed to simulate the uniaxial mechanical tests. Additional parametric analyses were performed to evaluate the potential errors on the predicted apparent modulus arising from variations in segmentation threshold, tissue modulus, and the use of 125-mm(3) cubic sub-regions. The results demonstrate an excellent correspondence between experimental measures and FE predictions of uniaxial apparent modulus. In conclusion, the adopted voxel-based FE approach is found to be a robust method to predict the linear elastic properties of human cancellous bone, provided segmentation of the microCT reconstructions is carefully calibrated, tissue modulus is known a priori and the entire region of interest is included in the analysis.     

Analysis of avian bone response to mechanical loading—Part One: Distribution of bone fluid shear stress induced by bending and axial loading

Mechanical loading-induced signals are hypothesized to be transmitted and integrated by a bone-connected cellular network (CCN) before reaching the bone surfaces where adaptation occurs. Our objective is to establish a computational model to explore how bone cells transmit the signals through intercellular communication. In this first part of the study the bone fluid shear stress acting on every bone cell in a CCN is acquired as the excitation signal for the computational model. Bending and axial loading-induced fluid shear stress is computed in transverse sections of avian long bones for two adaptation experiments (Gross et al. in J Bone Miner Res 12:982-988, 1997 and Judex et al. in J Bone Miner Res 12:1737-1745, 1997). The computed fluid shear stress is found to be correlated with the radial strain gradient but not with bone formation. These results suggest that the radial strain gradient is the driving force for bone fluid flow in the radially distributed lacunar-canalicular system and that bone formation is not linearly related to the loading-induced local stimulus.     

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.     

Axial-shear interaction effects on microdamage in bovine tibial trabecular bone

Because many osteoporotic fractures occur during a fall, understanding the effect of off-axis loads on initiation and propagation of microdamage in trabecular bone should provide further insight into the biomechanics of age-related fractures. Fourteen on-axis cylindrical specimens were prepared from 12 bovine tibiae. Fluorescent stains were used to label the microdamage due to a sequence of compressive and torsional damaging loads. The mean decrease in Young's modulus was over four times greater than that in the shear modulus after the compressive overload, while there was no difference between the decrease in the axial and torsional stiffnesses after the torsional overload. The total microcrack density due to compression was uniform across the radius of the cylindrical specimens, while the mean density of microcracks due to torsional overloading increased from the axis of the cylindrical specimen to the circumference. The high density of microcracks near the axis of the specimen following torsional overloading was unexpected because of the low strains. Nearly 40% of the microcracks due to torsion propagated from pre-existing microcracks caused by axial compression, indicating that existing microcracks may extend at relatively low strain if the loading mode changes. The propagating microcracks were, on average, longer than the initiating microcracks due to either compressive or torsional loading. Damage due to axial compression appears to increase the susceptibility of trabecular bone to damage propagation during subsequent torsional loads, but it has little effect on the elastic properties in shear.     

Non-invasive assessment of failure torque in rat bones with simulated lytic lesions using computed tomography based structural rigidity analysis

This study applies CT-based structural rigidity analysis (CTRA) to assess failure torque of rat femurs with simulated lytic defects at different locations (proximal and distal femur) and diameters (25% and 50% of the cross-section at the site), and compared the results to those obtained from mechanical testing. Moreover, it aims to compare the correlation coefficients between CTRA-based failure torque and DXA-based aBMD versus actual failure torque. Twenty rats were randomly assigned to four equal groups of different simulated lesions based on size and location. Femurs from each animal underwent micro-computed tomography to assess three-dimensional micro-structural data, torsional rigidity using structural rigidity analysis and dual energy X-ray absorptiometry to assess bone mineral density. Following imaging, all specimens were subjected to torsion. Failure torque predicted from CT-derived structural rigidity measurements was better correlated with mechanically derived failure torque [R(2)=0.85] than was aBMD from DXA [R(2)=0.32]. In summary, the results of this study suggest that computed tomography based structural rigidity analysis can be used to accurately and quantitatively measure the mechanical failure torque of bones with osteolytic lesions in an experimental rat model. Structural rigidity analysis can provide more accurate predictions on maximal torque to mechanical failure than dual energy X-ray absorptiometry based on bone mineral density.     

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.     

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

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