Micro-finite element simulation of trabecular-bone post-yield behaviour – effects of material model,element size and type

Micro-finite element (micro-FE) analysis became a standard tool for the evaluation of trabecular bone mechanical properties. The accuracy of micro-FE models for linear analyses is well established. However, the accuracy of recently developed nonlinear micro-FE models for simulations of trabecular bone failure is not known. In this study, a trabecular bone specimen was compressed beyond the apparent yield point. The experiment was simulated using different micro-FE meshes with different element sizes and types, and material models based on cortical bone. The results from the simulations were compared with experimental results to study the effects of the different element and material models. It was found that a decrease in element size from 80 to 40 μm had little effect on predicted post-yield behaviour. Element type and material model had significant effects. Nevertheless, none of the established material models for cortical bone were able to predict the typical descent in the load-displacement curve seen during compression of trabecular bone.     

Indirect determination of trabecular bone effective tissue failure properties using micro-finite element simulations

Trabecular bone strength is marked not only by the onset of local yielding, but also by post-yield behavior. To study and predict trabecular bone elastic and yield properties, micro-finite element (micro-FE) models were successfully applied. However, trabecular bone strength predictions require micro-FE models incorporating post-yield behavior of trabecular bone tissue. Due to experimental difficulties, such data is currently not available. Here we used micro-FE modeling to determine failure behavior of trabecular bone tissue indirectly, by iteratively fitting FE simulation to experimental results. Failure parameters were fitted to an isotropic plasticity model based on Hill's yield function, using materially and geometrically nonlinear micro-FE models of seven bovine trabecular bone specimens. The predictive value of the averaged effective tissue properties was subsequently tested. The results showed that compression softening had to be included on the tissue level in order to accurately describe the apparent-level behavior of the bone specimens. A sensitivity study revealed that the simulated response was less sensitive to variations in the post-yield properties of the bone tissue than variations in the elastic and yield properties. Due to fitting of the tissue properties, apparent-level behavior could be accurately reproduced for each specimen separately. Predictions based on the averaged and fixed tissue properties were less accurate, due to inter-specimen variations in the tissue properties.     

Simplified boundary conditions alter cortical-trabecular load sharing at the distal radius; A multiscale finite element analysis

High-resolution peripheral quantitative computed tomography (HR-pQCT) derived micro-finite element (FE) modeling is used to evaluate mechanical behavior at the distal radius microstructure. However, these analyses typically simulate non-physiologic simplified platen-compression boundary conditions on a small section of the distal radius. Cortical and trabecular regions contribute uniquely to distal radius mechanical behavior, and various factors affect these regions distinctly. Generalized strength predictions from standardized platen-compression analyses may not adequately capture region specific responses in bone. Our goal was to compare load sharing within the cortical-trabecular compartments between the standardized platen-compression BC simulations, and physiologic BC simulations using a validated multiscale approach. Clinical- and high-resolution images were acquired from nine cadaveric forearm specimens using an HR-pQCT scanner. Multiscale FE models simulating physiologic BCs, and micro-FE only models simulating platen-compression BCs were created for each specimen. Cortical and trabecular loads (N) along the length of the distal radius micro-FE section were compared between BCs using correlations. Principal strain distributions were also compared quantitatively. Cortical and trabecular loads from the platen-compression BC simulations were strongly correlated to the physiologic BC simulations. However, a 30% difference in cortical loads distally, and a 53% difference in trabecular loads proximally was observed under platen BC simulations. Also, distribution of principal strains was clearly different. Our data indicated that platen-compression BC simulations alter cortical-trabecular load sharing. Therefore, results from these analyses should be interpreted in the appropriate mechanical context for clinical evaluations of normal and pathologic mechanical behavior at the distal radius.     

The mechanical behavior of PMMA/bone specimens extracted from augmented vertebrae: a numerical study of interface properties, PMMA shrinkage and trabecular bone damage

Recently published compression tests on PMMA/bone specimens extracted after vertebral bone augmentation indicated that PMMA/bone composites were not reinforced by the trabecular bone at all. In this study, the reasons for this unexpected behavior should be investigated by using non-linear micro-FE models. Six human vertebral bodies were augmented with either standard or low-modulus PMMA cement and scanned with a HR-pQCT system before and after augmentation. Six cylindrical PMMA/bone specimens were extracted from the augmented region, scanned with a micro-CT system and tested in compression. Four different micro-FE models were generated from these images which showed different bone tissue material behavior (with/without damage), interface behavior (perfect bonding, frictionless contact) and PMMA shrinkage due to polymerization. The non-linear stress-strain curves were compared between the different micro-FE models as well as to the compression tests of the PMMA/bone specimens. Micro-FE models with contact between bone and cement were 20% more compliant compared to those with perfect bonding. PMMA shrinkage damaged the trabecular bone already before mechanical loading, which further reduced the initial stiffness by 24%. Progressing bone damage during compression dominated the non-linear part of the stress-strain curves. The micro-FE models including bone damage and PMMA shrinkage were in good agreement with the compression tests. The results were similar with both cements. In conclusion, the PMMA/bone interface properties as well as the initial bone damage due to PMMA polymerization shrinkage clearly affected the stress-strain behavior of the composite and explained why trabecular bone did not contribute to the stiffness and strength of augmented bone.     

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.     

Fracture prediction for the proximal femur using finite element models: Part II--Nonlinear analysis.

In Part I we reported the results of linear finite element models of the proximal femur generated using geometric and constitutive data collected with quantitative computed tomography. These models demonstrated excellent agreement with in vitro studies when used to predict ultimate failure loads. In Part II, we report our extension of those finite element models to include nonlinear behavior of the trabecular and cortical bone. A highly nonlinear material law, originally designed for representing concrete, was used for trabecular bone, while a bilinear material law was used for cortical bone. We found excellent agreement between the model predictions and in vitro fracture data for both the onset of bone yielding and bone fracture. For bone yielding, the model predictions were within 2 percent for a load which simulated one-legged stance and 1 percent for a load which simulated a fall. For bone fracture, the model predictions were within 1 percent and 17 percent, respectively. The models also demonstrated different fracture mechanisms for the two different loading configurations. For one-legged stance, failure within the primary compressive trabeculae at the subcapital region occurred first, leading to load transfer and, ultimately, failure of the surrounding cortical shell. However, for a fall, failure of the cortical and trabecular bone occurred simultaneously within the intertrochanteric region. These results support our previous findings that the strength of the subcapital region is primarily due to trabecular bone whereas the strength of the intertrochanteric region is primarily due to cortical bone.     

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.     

Elastic properties of cancellous bone derived from finite element models of parameterized microstructure cells

Evaluation of constitutive properties of cancellous bone and their relationships to microstructural parameters is a crucial issue in analysis of stresses and strains in bone tissues and simulation of their remodelling. Known limitations of experimental methods as well as of the micro-FE techniques make the analysis and homogenization of 'equivalent' trabecular microstructures an advantageous tool for this task. In this study, parameterized orthotropic constitutive models of cancellous bone are derived from finite element analysis of repeatable microstructure cells. Two cell types are analysed: cube- and prism-based. The models are fully three-dimensional, have realistic curvilinear shapes and are parameterized with three shape parameters. Variation of the parameters allows to imitate most of the typical microstructure patterns observed in real bones, along with variety of intermediate geometries. Finite element models of cells are generated by a special-purpose structured mesh generator for any arbitrary set of shape parameter values. Six static numerical tests are performed for an exhaustive number of parameter value sets (microstructure instances). Multi-point boundary conditions imposed on the models ensure mutual fitting of deformed neighbouring cells. Values of computed stresses allow to determine all coefficients of elastic orthotropic stiffness matrix. Results have a form of tabularized functions of elastic constants versus the shape parameters. Comparison of the results with micro-FE data obtained for a large set of cancellous bone specimens proves a good agreement, though evidently better in the case of the prism-based cell model.     

Subject-specific finite element model of the pelvis: development, validation and sensitivity studies

A better understanding of the three-dimensional mechanics of the pelvis, at the patient-specific level, may lead to improved treatment modalities. Although finite element (FE) models of the pelvis have been developed, validation by direct comparison with subject-specific strains has not been performed, and previous models used simplifying assumptions regarding geometry and material properties. The objectives of this study were to develop and validate a realistic FE model of the pelvis using subject-specific estimates of bone geometry, location-dependent cortical thickness and trabecular bone elastic modulus, and to assess the sensitivity of FE strain predictions to assumptions regarding cortical bone thickness as well as bone and cartilage material properties. A FE model of a cadaveric pelvis was created using subject-specific computed tomography image data. Acetabular loading was applied to the same pelvis using a prosthetic femoral stem in a fashion that could be easily duplicated in the computational model. Cortical bone strains were monitored with rosette strain gauges in ten locations on the left hemipelvis. FE strain predictions were compared directly with experimental results for validation. Overall, baseline FE predictions were strongly correlated with experimental results (r2=0.824), with a best-fit line that was not statistically different than the line y=x (experimental strains = FE predicted strains). Changes to cortical bone thickness and elastic modulus had the largest effect on cortical bone strains. The FE model was less sensitive to changes in all other parameters. The methods developed and validated in this study will be useful for creating and analyzing patient-specific FE models to better understand the biomechanics of the pelvis.     

Finite element analysis of ramming in Ovis canadensis

The energy produced during the ramming of bighorn sheep (Ovis canadensis) would be expected to result in undesirable stresses in their frontal skull, which in turn would cause brain injury; yet, this animal seems to suffer no ill effects. In general, horn is made of an α-keratin sheath covering a bone. Despite volumes of data on the ramming behavior of Ovis canadensis, the extent to which structural components of horn and horn-associated structure or tissue absorb the impact energy generated by the ramming event is still unknown. This study investigates the hypothesis that there is a mechanical relationship present among the ramming event, the structural constituents of the horn, and the horn-associated structure. The three-dimensional complex structure of the bighorn sheep horn was successfully constructed and modeled using a computed tomography (CT) scan and finite element (FE) method, respectively. Three different three-dimensional quasi-static models, including a horn model with trabecular bone, a horn model with compact bone that instead of trabecular bone, and a horn model with trabecular bone as well as frontal sinuses, were studied. FE simulations were used to compare distributions of principal stress in the horn and the frontal sinuses and the strain energy under quasi-static loading conditions. It was noticed that strain energy due to elastic deformation of the complex structure of horn modeled with trabecular bone and with trabecular bone and frontal sinus was different. In addition, trabecular bone in the horn distributes the stresses over a larger volume, suggesting a mechanical link between the structural constituents and the ramming event. This phenomenon was elucidated through the principal stress distribution in the structure. This study will help designers in choosing appropriate material combinations for the successful design of protective structures against a similar impact.     

An accurate estimation of bone density improves the accuracy of subject-specific finite element models

An experimental-numerical study was performed to investigate the relationships between computed tomography (CT)-density and ash density, and between ash density and apparent density for bone tissue, to evaluate their influence on the accuracy of subject-specific FE models of human bones. Sixty cylindrical bone specimens were examined. CT-densities were computed from CT images while apparent and ash densities were measured experimentally. The CT/ash-density and ash/apparent-density relationships were calculated. Finite element models of eight human femurs were generated considering these relationships to assess their effect on strain prediction accuracy. CT and ash density were linearly correlated (R(2)=0.997) over the whole density range but not equivalent (intercep t <0, slope >1). A constant ash/apparent-density ratio (0.598+/-0.004) was found for cortical bone. A lower ratio, with a larger dispersion, was found for trabecular bone (0.459+/-0.100), but it became less dispersed, and equal to that of cortical tissue, when testing smaller trabecular specimens (0.598+/-0.036). This suggests that an experimental error occurred in apparent-density measurements for large trabecular specimens and a constant ratio can be assumed valid for the whole density range. Introducing the obtained relationships in the FE modelling procedure improved strain prediction accuracy (R(2)=0.95, RMSE=7%). The results suggest that: (i) a correction of the densitometric calibration should be used when evaluating bone ash-density from clinical CT scans, to avoid ash-density underestimation and overestimation for low- and high-density bone tissue, respectively; (ii) the ash/apparent-density ratio can be assumed constant in human femurs and (iii) the correction improves significantly the model accuracy and should be considered in subject-specific bone modelling.     

Micro-mechanical properties of different sites on woodpecker’s skull

The uneven distributed microstructure featured with plate-like spongy bone in woodpecker’s skull has been found to further help reduce the impact during woodpecker’s pecking behavior. Therefore, this work was to investigate the micro-mechanical properties and composition on different sites of Great Spotted woodpecker’s (GSW) skull. Different sites were selected on forehead, tempus and occiput, which were also compared with those of Eurasian Hoopoe (EH) and Lark birds (LB). Micro structural parameters assessed from micro computed tomography (μCT) occurred significantly difference between GSW, EH and LB. The micro finite element (micro-FE) models were developed and the simulation was performed as a compression process. The maximal stresses of GSW’s micro-FE models were all lower than those of EH and LB respectively and few concentrated stresses were noticed on GSW’s trabecular bone. Fourier transform infrared mapping suggesting a greater organic content in the occiput of GSW’s cranial bone compared with others. The nano-hardness of the GSW’s occiput was decreasing from forehead to occiput. The mechanical properties, site-dependent hardness distribution and special material composition of GSW’s skull bone are newly found in this study. These factors may lead to a new design of bulk material mimicking these characteristics.     

Effects of thresholding techniques on microCT-based finite element models of trabecular bone

Microimaging based finite element analysis is widely used to predict the mechanical properties of trabecular bone. The choice of thresholding technique, a necessary step in converting grayscale images to finite element models, can significantly influence the predicted bone volume fraction and mechanical properties. Therefore, we investigated the effects of thresholding techniques on microcomputed tomography (micro-CT) based finite element models of trabecular bone. Three types of thresholding techniques were applied to 16-bit micro-CT images of trabecular bone to create three different models per specimen. Bone volume fractions and apparent moduli were predicted and compared to experimental results. In addition, trabecular tissue mechanical parameters and morphological parameters were compared among different models. Our findings suggest that predictions of apparent mechanical properties and structural properties agree well with experimental measurements regardless of the choice of thresholding methods or the format of micro-CT images.     

About the inevitable compromise between spatial resolution and accuracy of strain measurement for bone tissue: A 3D zero-strain study

The accurate measurement of local strain is necessary to study bone mechanics and to validate micro computed tomography (µCT) based finite element (FE) models at the tissue scale. Digital volume correlation (DVC) has been used to provide a volumetric estimation of local strain in trabecular bone sample with a reasonable accuracy. However, nothing has been reported so far for µCT based analysis of cortical bone. The goal of this study was to evaluate accuracy and precision of a deformable registration method for prediction of local zero-strains in bovine cortical and trabecular bone samples. The accuracy and precision were analyzed by comparing scans virtually displaced, repeated scans without any repositioning of the sample in the scanner and repeated scans with repositioning of the samples.     

A Femur-Implant Model for the Prediction of Bone Remodeling Behavior Induced by Cementless Stem

Bone remodeling simulation is an effective tool for the prediction of long-term effect of implant on the bone tissue, as well as the selection of an appropriate implant in terms of architecture and material. In this paper, a finite element model of proximal femur was developed to simulate the structures of internal trabecular and cortical bones by incorporating quantitative bone functional adaptation theory with finite element analysis. Cementless stems made of titanium, two types of Functionally Graded Material (FGM) and flexible ‘iso-elastic’ material as comparison were implanted in the structure of proximal femur respectively to simulate the bone remodeling behaviors of host bone. The distributions of bone density, von Mises stress, and interface shear stress were obtained. All the prosthetic stems had effects on the bone remodeling behaviors of proximal femur, but the degrees of stress shielding were different. The amount of bone loss caused by titanium implant was in agreement with the clinical observation. The FGM stems caused less bone loss than that of the titanium stem, in which FGM I stem (titanium richer at the top to more HAP/Col towards the bottom) could relieve stress shielding effectively, and the interface shear stresses were more evenly distributed in the model with FGM I stem in comparison with those in the models with FGM II (titanium and bioglass) and titanium stems. The numerical simulations in the present study provided theoretical basis for FGM as an appropriate material of femoral implant from a biomechanical point of view. The next steps are to fabricate FGM stem and to conduct animal experiments to investigate the effects of FGM stem on the remodeling behaviors using animal model.     

Intravoxel bone micromechanics for microCT-based finite element simulations

While micro-FE simulations have become a standard tool in computational biomechanics, the choice of appropriate material properties is still a relevant topic, typically involving empirical grey value-to-elastic modulus relations. We here derive the voxel-specific volume fractions of mineral, collagen, and water, from tissue-independent bilinear relations between mineral and collagen content in extracellular bone tissue (J. Theor. Biol. 287: 115, 2011), and from the measured X-ray attenuation information quantified in terms of grey values. The aforementioned volume fractions enter a micromechanics representation of bone tissue, as to deliver voxel-specific stiffness tensors. In order to check the relevance of this strategy, we convert a micro Computer Tomograph of a mouse femur into a regular Finite Element mesh, apply forces related to the dead load of a standing mouse, and then compare simulation results based on voxel-specific heterogeneous elastic properties to results based on homogeneous elastic properties related to the spatial average over the solid bone matrix compartment, of the X-ray attenuation coefficients. The element-specific strain energy density illustrates that use of homogeneous elastic properties implies overestimation of the organ stiffness. Moreover, the simulation reveals large tensile normal stresses throughout the femur neck, which may explain the mouse femur neck's trabecular morphology being quite different from the human case, where the femur neck bears compressive forces and bending moments.     

Comparison of HR-pQCT- and microCT-based finite element models for the estimation of the mechanical properties of the calcaneus trabecular bone

The calcaneus bone is formed of extensive trabecular bone and is therefore well suited to be used as an example of loaded bone to establish the ability of combining microfinite element (microFE) technique with high-resolution peripheral quantitative computed tomography (HR-pQCT) in determining its mechanical properties. HR-pQCT is increasingly used as a tool for in vivo bone clinical research, but its use has been limited to the distal radius and tibia. The goal of this study was to determine the applicability of HR-pQCT-derived microFE models of the calcaneus trabecular bone with 82 μm voxel size with reference to higher-resolution microCT-based models taken as gold standard. By comparing the outputs of microFE models generated from both HR-pQCT and microCT images of the trabecular bone of five calcaneus cadaveric specimens, it was found that the HR-pQCT-based models predicted mechanical properties for fracture load, total reaction force and von Mises stress are considerably different from microCT-based counterparts by 33, 64 and 70%, respectively. Also, the morphological analysis showed a comprehensive geometrical difference between HR-pQCT-based microFE models and their microCT-based equivalents. The results of the HR-pQCT-based models were found to have strong dependency on the threshold value chosen to binarise the images prior to finite element modelling. In addition, it was found that the voxel size has a strong impact on accuracy of imaged-based microFE models compared to other factors such as the presence of soft tissue and image scanning integration time. Therefore, although HR-pQCT has shown to be useful to predict overall structural and biomechanical changes, it is limited in providing local accurate biomechanical properties of trabecular bone and therefore should be used with caution when assessing bone remodelling through local changes of trabecular bone apposition and resorption in disease treatment monitoring.     

Finite element modeling of trabecular bone damage

This paper presents a finite element-based, computational model for analysis of structural damage to trabecular bone tissues. A modulus reduction method was formulated from elasto-plasticity theory, and was used to account for site-specific trabecular bone tissue damage. Trabecular bone tissue damage is illustrated using a large-scale, anatomically accurate, two-dimensional, microstructural finite element model of a human thoracic vertebral body. Four models with varying specifications for damage accumulation were subjected to compressive loading and unloading cycles. The numerical results and experimental validation demonstrated that the modulus reduction method reproduced the non-linear mechanical behaviour of vertebal trabecular bone. The iterative computational approach presented provides a methodology to study trabecular bone damage, and should provide researchers with a computational approach to study bone fracture and repair and to predict vertebral fragility.     

Mapping anisotropy of the proximal femur for enhanced image based finite element analysis

Finite element (FE) models of bone derived from quantitative computed tomography (QCT) rely on realistic material properties to accurately predict bone strength. QCT cannot resolve bone microarchitecture, therefore QCT-based FE models lack the anisotropy apparent within the underlying bone tissue. This study proposes a method for mapping femoral anisotropy using high-resolution peripheral quantitative computed tomography (HR-pQCT) scans of human cadaver specimens. Femur HR-pQCT images were sub-divided into numerous overlapping cubic sub-volumes and the local anisotropy was quantified using a ‘direct-mechanics’ method. The resulting directionality reflected all the major stress lines visible within the trabecular lattice, and provided a realistic estimate of the alignment of Harvesian systems within the cortical compartment. QCT-based FE models of the proximal femur were constructed with isotropic and anisotropic material properties, with directionality interpolated from the map of anisotropy. Models were loaded in a sideways fall configuration and the resulting whole bone stiffness was compared to experimental stiffness and ultimate strength. Anisotropic models were consistently less stiff, but no statistically significant differences in correlation were observed between material models against experimental data. The mean difference in whole bone stiffness between model types was approximately 26%, suggesting that anisotropy can still effect considerable change in the mechanics of proximal femur models. The under prediction of whole bone stiffness in anisotropic models suggests that the orthotropic elastic constants require further investigation. The ability to map mechanical anisotropy from high-resolution images and interpolate information into clinical-resolution models will allow testing of new anisotropic material mapping strategies.     

Incorporating tissue anisotropy and heterogeneity in finite element models of trabecular bone altered predicted local stress distributions

Trabecular bone is composed of organized mineralized collagen fibrils, which results in heterogeneous and anisotropic mechanical properties at the tissue level. Recently, biomechanical models computing stresses and strains in trabecular bone have indicated a significant effect of tissue heterogeneity on predicted stresses and strains. However, the effect of the tissue-level mechanical anisotropy on the trabecular bone biomechanical response is unknown. Here, a computational method was established to automatically impose physiologically relevant orientation inherent in trabecular bone tissue on a trabecular bone microscale finite element model. Spatially varying tissue-level anisotropic elastic properties were then applied according to the bone mineral density and the local tissue orientation. The model was used to test the hypothesis that anisotropy in both homogeneous and heterogeneous models alters the predicted distribution of stress invariants. Linear elastic finite element computations were performed on a 3 mm cube model isolated from a microcomputed tomography scan of human trabecular bone from the distal femur. Hydrostatic stress and von Mises equivalent stress were recorded at every element, and the distributions of these values were analyzed. Anisotropy reduced the range of hydrostatic stress in both tension and compression more strongly than the associated increase in von Mises equivalent stress. The effect of anisotropy was independent of the spatial redistribution high compressive stresses due to tissue elastic heterogeneity. Tissue anisotropy and heterogeneity are likely important mechanisms to protect bone from failure and should be included for stress analyses in trabecular bone.