Assessment of Mechanobiological Models for the Numerical Simulation of Tissue Differentiation around Immediately Loaded Implants

Nowadays, there is a growing consensus on the impact of mechanical loading on bone biology. A bone chamber provides a mechanically isolated in vivo environment in which the influence of different parameters on the tissue response around loaded implants can be investigated. This also provides data to assess the feasibility of different mechanobiological models that mathematically describe the mechanoregulation of tissue differentiation. Before comparing numerical results to animal experimental results, it is necessary to investigate the influence of the different model parameters on the outcome of the simulations. A 2D finite element model of the tissue inside the bone chamber was created. The differentiation models developed by Prendergast, et al. [“Biophysical stimuli on cells during tissue differentiation at implant interfaces”, Journal of Biomechanics, 30(6), (1997), 539–548], Huiskes et al. [“A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation”, Journal of Material Science: Materials in Medicine, 8 (1997) 785–788] and by Claes and Heigele [“Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing”, Journal of Biomechanics, 32(3), (1999) 255–266] were implemented and integrated in the finite element code. The fluid component in the first model has an important effect on the predicted differentiation patterns. It has a direct effect on the predicted degree of maturation of bone and a substantial indirect effect on the simulated deformations and hence the predicted phenotypes of the tissue in the chamber. Finally, the presence of fluid also causes time-dependent behavior.

Both models lead to qualitative and quantitative differences in predicted differentiation patterns. Because of the different nature of the tissue phenotypes used to describe the differentiation processes, it is however hard to compare both models in terms of their validity.     

NACOB presentation to ASB Young Scientist Award: Postdoctoral. The impact of boundary conditions and mesh size on the accuracy of cancellous bone tissue modulus determination using large-scale finite-element modeling. North American Congress on Biomechanics.

The apparent properties of cancellous bone are determined by a combination of both hard tissue properties and microstructural organization. A method is desired to extract the underlying hard tissue properties from simple mechanical tests, free from the complications of microstructure. It has been suggested that microCT voxel-based large-scale finite element models could be employed to accomplish this goal (van Rietbergen et al., 1995, Journal of Biomechanics, 28, 69-81). This approach has recently been implemented and it is becoming increasingly popular as finite element models increase in size and sophistication (Fyhrie et al., 1997, Proceedings of the 43rd Annual Meeting of the Orthopaedic Research Society, San Francisco, CA, p. 815; van Rietbergen et al., 1997, Proceedings of the 43rd Annual Meeting of the Orthopaedic Research Society, San Francisco, CA, p. 62). However, no direct quantitative measurements of the accuracy of this method applied to porous structures such as cancellous bone have been made. This project demonstrates the feasibility of this approach by quantifying its best-case accuracy in determining the trabecular hard tissue modulus of analogues fabricated of a material with known material properties determined independently by direct testing. In addition we were able to assess the impact of mesh size and boundary conditions on accuracy. We found that the assumption of a frictionless boundary condition in the parallel plate compression loading configuration was a significant source of error that could be overcome with the use of rigid end-caps similar to those used by Keaveny et al. (1997 Journal of Orthopaedic Research, 15(1), 101-110). In conclusion, we found that this approach is an effective method for determining the average trabecular hard tissue properties of human cancellous bone with an expected practical accuracy level better than 5%.     

Numerical simulation of tissue differentiation around loaded titanium implants in a bone chamber

The application of a bone chamber provides a controlled environment for the study of tissue differentiation and bone adaptation. The influence of different mechanical and biological factors on the processes can be measured experimentally. The goal of the present work is to numerically model the process of peri-implant tissue differentiation inside a bone chamber, placed in a rabbit tibia. 2D and 3D models were created of the tissue inside the chamber. A number of loading conditions, corresponding to those applied in the rabbit experiments, were simulated. Fluid velocity and maximal distortional strain were considered as the stimuli that guide the differentiation process of mesenchymal cells into fibroblasts, chondrocytes and osteoblasts. Mesenchymal cells migrate through the chamber from the perforations in the chamber wall. This process is modelled by the diffusion equation. The predicted tissue phenotypes as well as the process of tissue ingrowth into the chamber show a qualitative agreement with the results of the rabbit experiments. Due to the limited number of animal experiments (four) and the observed inter-animal differences, no quantitative comparison could be made. These results however are a strong indication of the feasibility of the implemented theory to predict the mechano-regulation of the differentiation process inside the bone chamber.     

Application of mechanoregulatory models to simulate peri-implant tissue formation in an in vivo bone chamber

Several mechanoregulatory tissue differentiation models have been proposed over the last decade. Corroboration of these models by comparison with experimental data is necessary to determine their predictive power. So far, models have been applied with various success rates to different experimental set-ups investigating mainly secondary fracture healing. In this study, the mechanoregulatory models are applied to simulate the implant osseointegration process in a repeated sampling in vivo bone chamber, placed in a rabbit tibia. This bone chamber provides a mechanically isolated environment to study tissue differentiation around titanium implants loaded in a controlled manner. For the purpose of this study, bone formation around loaded cylindrical and screw-shaped implants was investigated. Histologically, no differences were found between the two implant geometries for the global amount of bone formation in the entire chamber. However, a significantly larger amount of bone-to-implant contact was observed for the screw-shaped implant compared to the cylindrical implant. In the simulations, a larger amount of bone was also predicted to be in contact with the screw-shaped implant. However, other experimental observations could not be predicted. The simulation results showed a distribution of cartilage, fibrous tissue and (im)mature bone, depending on the mechanoregulatory model that was applied. In reality, no cartilage was observed. Adaptations to the differentiation models did not lead to a better correlation between experimentally observed and numerically predicted tissue distribution patterns. The hypothesis that the existing mechanoregulatory models were able to predict the patterns of tissue formation in the in vivo bone chamber could not be fully sustained.     

Characterization of the mechanical properties of skin by inverse analysis combined with the indentation test

This study proposes a new method to determine the mechanical properties of human skin by the use of the indentation test [Pailler-Mattei, 2004. Caractérisation mécanique et tribologique de la peau humaine in vivo, Ph.D. Thesis, ECL-no. 2004-31; Pailler-Mattei, Zahouani, 2004. Journal of Adhesion Science and Technology 18, 1739-1758]. The principle of the measurements consists in applying an in vivo compressive stress [Zhang et al., 1994. Proceedings of the Institution of Mechanical Engineers 208, 217-222; Bosboom et al., 2001. Journal of Biomechanics 34, 1365-1368; Oomens et al., 1984. Selected Proceedings of Meetings of European Society of Biomechanics, pp. 227-232; Oomens et al., 1987. Journal of Biomechanics 20(9), 877-885] on the skin tissue of an individual's forearm. These measurements show an increase in the normal contact force as a function of the indentation depth. The interpretation of such results usually requires a long and tedious phenomenological study. We propose a new method to determine the mechanical parameters which control the response of skin tissue. This method is threefold: experimental, numerical, and comparative. It consists combining experimental results with a numerical finite elements model in order to find out the required parameters. This process uses a scheme of extended Kalman filters (EKF) [Gu et al., 2003. Materials Science and Engineering A345, 223-233; Nakamura et al., 2000. Acta Mater 48, 4293-4306; Leustean and Rosu, 2003. Certifying Kalman filters. RIACS Technical Report 03.02, 27pp. http://gureni.cs.uiuc.edu/~grosu/download/luta + leo.pdf; Welch and Bishop, An introduction to Kalman filter, University of North Carolina at Chapel Hill, 16p. http://www.cs.unc.edu/~welch/kalman/]. The first results presented in this study correspond to a simplified numerical modeling of the global system. The skin is assumed to be a semi-infinite layer with an isotropic linear elastic mechanical behavior [Zhang et al., 1994. Proceedings of the Institution of Mechanical Engineers 208, 217-222] This analysis will be extended to more realistic models in further works.     

Bone ingrowth into a porous coated implant predicted by a mechano-regulatory tissue differentiation algorithm

Bone ingrowth into a porous surface is one of the primary methods for fixation of orthopaedic implants. Improved understanding of bone formation and fixation of these devices should improve their performance and longevity. In this study predictions of bone ingrowth into an implant porous coating were investigated using mechano-reculatory models. The mechano-regulatory tissue differentiation algorithm proposed by Lacroix et al., and a modified version that enforces a tissue differentiation pathway by transitioning from differentiation to bone adaptation were investigated. The modified algorithm resulted in nearly the same behavior as the original algorithm when applied to a fracture-healing model. The algorithms were further compared using micromechanical finite element model of a beaded porous scaffold. Predictions of bone and fibrous tissue formation were compared between the two algorithms and to clinically observed phenomena. Under loading conditions corresponding to a press-fit hip stem, the modified algorithm predicted bone ingrowth into approximately 25% of the pore space, which is similar to that reported in experimental studies, while the original algorithm was unstable. When micromotion at the bone-implant interface was simulated, 20 mum of transverse displacement resulted in soft tissue formation at the bone-implant interface and minimal bone ingrowth. In contrast, 10 and 5 mum of micromotion resulted in bone filling 40% of the pore space and a stable interface, again consistent with clinical and experimental observations.     

Compression testing of very soft biological tissues using semi-confined configuration--a word of caution

We analyse semi-confined (i.e. using no-slip boundary conditions) compression experiment of very soft tissue sample using finite element method. We show that the assumption that the planes perpendicular to the direction of the applied force remain plane during the experiments is not satisfied for compression levels lower than previously stated in Miller [2005. Method for testing very soft biological tissues in compression. Journal of Biomechanics 38, 153-158]. Therefore, we recommend that the parameters for constitutive models of very soft tissues be determined by fitting a solution of the finite element models of the experimental set-up to the measurements obtained using semi-confined compression experiments.     

Bone ingrowth around porous-coated acetabular implant: a three-dimensional finite element study using mechanoregulatory algorithm

Fixation of uncemented implant is influenced by peri-prosthetic bone ingrowth, which is dependent on the mechanical environment of the implant–bone structure. The objective of the study is to gain an insight into the tissue differentiation around an acetabular component. A mapping framework has been developed to simulate appropriate mechanical environment in the three-dimensional microscale model, implement the mechanoregulatory tissue differentiation algorithm and subsequently assess spatial distribution of bone ingrowth around an acetabular component, quantitatively. The FE model of implanted pelvis subjected to eight static load cases during a normal walking cycle was first solved. Thereafter, a mapping algorithm has been employed to include the variations in implant–bone relative displacement and host bone material properties from the macroscale FE model of implanted pelvis to the microscale FE model of the beaded implant–bone interface. The evolutionary tissue differentiation was observed in each of the 13 microscale models corresponding to 13 acetabular regions. The total implant–bone relative displacements, averaged over each region of the acetabulum, were found to vary between 10 and 60 \(\upmu \hbox {m}\). Both the linear elastic and biphasic poroelastic models predicted similar mechanoregulatory peri-prosthetic tissue differentiation. Considerable variations in bone ingrowth (13–88 %), interdigitation depth (0.2–0.82 mm) and average tissue Young’s modulus (970–3430 MPa) were predicted around the acetabular cup. A progressive increase in the average Young’s modulus, interdigitation depth and decrease in average radial strains of newly formed tissue layer were also observed. This scheme can be extended to investigate tissue differentiation for different surface texture designs on the implants.     

A nonlinear biphasic viscohyperelastic model for articular cartilage

Experiments on articular cartilage have shown nonlinear stress-strain curves under finite deformations as well as intrinsic viscous effects of the solid phase. The aim of this study was to propose a nonlinear biphasic viscohyperelastic model that combines the intrinsic viscous effects of the proteoglycan matrix with a nonlinear hyperelastic constitutive equation. The proposed equation satisfies objectivity and reduces for uniaxial loading to a solid type viscous model in which the actions of the springs are represented by the hyperelastic function proposed by Holmes and Mow [1990. J. Biomechanics 23, 1145-1156.]. Results of the model, that were efficiently implemented in an updated Lagrangian algorithm, were compared with experimental infinitesimal data reported by DiSilverstro and Suh [2001. J. Biomechanics 34, 519-525.] and showed acceptable fitting for the axial force (R(2)=0.991) and lateral displacement (R(2)=0.914) curves in unconfined compression as well as a good fitting of the axial indentation force curve (R(2)=0.982). In addition, the model showed an excellent fitting of finite-deformation confined compression stress relaxation data reported by Ateshian et al. [1997. J. Biomechanics 30, 1157-1164.] and Huang et al. [2005. J. Biomechanics 38, 799-809.] (R(2)=0.993 and R(2)=0.995, respectively). The constitutive equation may be used to represent the mechanical behavior of the proteoglycan matrix in a fiber reinforced model of articular cartilage.     

Material model of pelvic bone based on modal analysis: a study on the composite bone

Biomechanics and Modeling in Mechanobiology - Digital models based on finite element (FE) analysis are widely used in orthopaedics to predict the stress or strain in the bone due to...     

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.     

An open source lower limb model: Hip joint validation

Musculoskeletal lower limb models have been shown to be able to predict hip contact forces (HCFs) that are comparable to in vivo measurements obtained from instrumented prostheses. However, the muscle recruitment predicted by these models does not necessarily compare well to measured electromyographic (EMG) signals. In order to verify if it is possible to accurately estimate HCFs from muscle force patterns consistent with EMG measurements, a lower limb model based on a published anatomical dataset (Klein Horsman et al., 2007. Clinical Biomechanics. 22, 239-247) has been implemented in the open source software OpenSim. A cycle-to-cycle hip joint validation was conducted against HCFs recorded during gait and stair climbing trials of four arthroplasty patients (Bergmann et al., 2001. Journal of Biomechanics. 34, 859-871). Hip joint muscle tensions were estimated by minimizing a polynomial function of the muscle forces. The resulting muscle activation patterns obtained by assessing multiple powers of the objective function were compared against EMG profiles from the literature. Calculated HCFs denoted a tendency to monotonically increase their magnitude when raising the power of the objective function; the best estimation obtained from muscle forces consistent with experimental EMG profiles was found when a quadratic objective function was minimized (average overestimation at experimental peak frame: 10.1% for walking, 7.8% for stair climbing). The lower limb model can produce appropriate balanced sets of muscle forces and joint contact forces that can be used in a range of applications requiring accurate quantification of both. The developed model is available at the website https://simtk.org/home/low_limb_london.     

Buckling of adaptive elastic bone-plate: theoretical and numerical investigation

During day-to-day activities, many bones in the axial and appendicular skeleton are subjected to repetitive, cyclic loading that often results directly in an increased risk of bone fracture. In clinical orthopedics, trabecular fatigue fractures are observed as compressive stress fractures in the proximal femur, vertebrae, calcaneus and tibia, that are often preceded by buckling and bending of microstructural elements (Müller et al. in J Biomechanics 31:150 1998; Gibson in J Biomechanics 18:317-328 1985; Gibson and Ashby in Cellular solids 1997; Lotz et al. in Osteoporos Int 5:252-261 1995; Carter and Hayes in Science 194:1174-1176 1976). However, the relative importance of bone density and architecture in the etiology of these fractures are poorly understood and consequently not investigated from a biomechanical point of view. In the present contribution, an attempt is made to formulate a bone-plate buckling theory using Cowin's concepts of adaptive elasticity (Cowin and Hegedus in J Elast 6:313-325 1976; Hegedus and Cowin J Elast 6:337-352 1976). In particular, the buckling problem of a Kirchhoff-Love bone plate is investigated numerically by using the finite difference method and an iterative solving approach (Chen in Comput Methods Appl Mech Eng 167:91-99 1998; Hildebland in Introduction to numerical analysis 1974; Richtmyer and Morton in Difference methods for initial-value problems 1967).     

The effects of misalignment during in vivo loading of bone: Techniques to detect the proximity of objects in three-dimensional models

Theories of mechanical adaptation of bone suggest that mechanical loading causes bone formation at discrete locations within bone microstructure experiencing the greatest mechanical stress/strain. Experimental testing of such theories requires in vivo loading experiments and high-resolution finite element models to determine the distribution of mechanical stresses. Finite element models of in vivo loading experiments typically assume idealized boundary conditions with applied load perfectly oriented on the bone, however small misalignments in load orientation during an in vivo experiment are unavoidable, and potentially confound the ability of finite element models to predict locations of bone formation at the scale of micrometers. Here we demonstrate two different three-dimensional spatial correlation methods to determine the effects of misalignment in load orientation on the locations of high mechanical stress/strain in the rodent tail loading model. We find that, in cancellous bone, the locations of tissue with high stress are maintained under reasonable misalignments in load orientation (p<0.01). In cortical bone, however, angular misalignments in the dorsal direction can alter the locations of high mechanical stress, but the locations of tissue with high stress are maintained under other misalignments (p<0.01). We conclude that, when using finite element models of the rodent tail loading model, small misalignments in loading orientation do not affect the predicted locations of high mechanical stress within cancellous bone.     

Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation

Computational models have shown that biophysical stimuli can be correlated with observed patterns of tissue differentiation, and simulations have been performed that predict the time course of tissue differentiation in, for example, long bone fracture healing. Some simulations have used a diffusion model to simulate the migration and proliferation of cells with the differentiating tissue. However, despite the convenience of the diffusion model, diffusion is not the mechanism of cell dispersal: cells disperse by crawling or proliferation, or are transported in a moving fluid. In this paper, a random-walk model (i.e., a stochastic model), with and without a preferred direction, is studied as an approach to simulate cell proliferation/migration in differentiating tissues and it is compared with the diffusion model. A simulation of tissue differentiation of gap tissue in a two-dimensional model of a bone/implant interface was performed to demonstrate the differences between diffusion vs. random walk with a preferred direction. Results of diffusion and random-walk models are similar with respect to the change in the stiffness of the gap tissue but rather different results are obtained regarding tissue patterning in the differentiating tissues; the diffusion approach predicted continuous patterns of tissue differentiation whereas the random-walk model showed a more discontinuous pattern-histological results are not available that can unequivocally establish which is most similar to experimental observation. Comparing isotropic to anisotropic random walk (preferred direction of proliferation and cell migration), a more rapid reduction of the relative displacement between implant and bone is predicted. In conclusion, we have shown how random-walk models of cell dispersal and proliferation can be implemented, and shown where differences between them exist. Further study of the random-walk model is warranted, given the importance of cell seeding and cell dispersal/proliferation in many mechanobiological problems.     

A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading

Bone has a capability to repair itself when it is fractured. Repair involves the generation of intermediate tissues, such as fibrous connective tissue, cartilage and woven bone, before final bone healing can occur. The intermediate tissues serve to stabilise the mechanical environment and provide a scaffold for differentiation of new tissues. The repair process is fundamentally affected by mechanical loading and by the geometric configuration of the fracture fragments. Biomechanical analyses of fracture healing have previously computed the stress distribution within the callus and identified the components of the stress tensor favouring or inhibiting differentiation of particular tissue phenotypes. In this paper, a biphasic poroelastic finite element model of a fracture callus is used to simulate the time-course of tissue differentiation during fracture healing. The simulation begins with granulation tissue (post-inflammation phase) and finishes with bone resorption. The biomechanical regulatory model assumes that tissue differentiation is controlled by a combination of shear strain and fluid flow acting within the tissue. High shear strain and fluid flows are assumed to deform the precursor cells stimulating formation of fibrous connective tissue, lower levels stimulate formation of cartilage, and lower again allows ossification. This mechano-regulatory scheme was tested by simulating healing in fractures with different gap sizes and loading magnitudes. The appearance and disappearance of the various tissues found in a callus was similar to histological observation. The effect of gap size and loading magnitude on the rate of reduction of the interfragmentary strain was sufficiently close to confirm the hypothesis that tissue differentiation phenomena could be governed by the proposed mechano-regulation model.     

Congruency effects on load bearing in diarthrodial joints

Modelling load bearing in diarthrodial joints is challenging, due to the complexity of the materials, the boundary and interface conditions and the geometry. The articulating surfaces are covered with cartilage layers that are filled with a fluid that plays a major role in load bearing [Mow, V.C., Holmes, M.H., Lai, W.M. (1984) "Survey article: fluid transport and mechanical properties of articular cartilage: a review", Journal of Biomechanics 17(5), 377-394]. Researchers have tended to approximate joint geometry using axisymmetry [Donzelli, P.S., Spilker, R.L., Ateshian, G.A., Mow, V.C. (1999) "Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure", Journal of Biomechanics 32, 1037-1047], often with a rounded upper articulating surface, creating a form of Hertz problem [Donzelli, P.S., Spilker, R.L., Ateshian, G.A., Mow, V.C. (1999) "Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure", Journal of Biomechanics 32, 1037-1047]. However, diarthrodial joints (shoulder, hip and knee) are equipped with peripheral structures (glenoid labrum, acetabular labrum and meniscus, respectively) that tend to deepen the joint contact and thus cause initial contact to be established at the periphery of the joint rather than "centrally". The surface geometries are purposefully incongruent, and the incongruency has a significant effect on the stresses, pressures and pressure gradients inside the tissue. The models show the importance of the peripheral structures and the incongruency from a load-bearing perspective. Joint shapes must provide a compromise between demands for load-bearing, lubrication and the supply of nutrients to the chondrocytes of the cartilage and cells of the peripheral structures. Retention and repair of the functionality of these peripheral structures should be a prime consideration in any surgical treatment of an injured joint.     

Validation of subject-specific automated p-FE analysis of the proximal femur

Background: The use of subject-specific finite element (FE) models in clinical practice requires a high level of automation and validation. In Yosibash et al. [2007a. Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations. J. Biomechanics 40, 3688–3699] a novel method for generating high-order finite element (p-FE) models from CT scans was presented and validated by experimental observations on two fresh frozen femurs (harvested from a 30 year old male and 21 year old female). Herein, we substantiate the validation process by enlarging the experimental database (54 year old female femur), improving the method and examine its robustness under different CT scan conditions.Approach: A fresh frozen femur of a 54 year old female was scanned under two different environments: in air and immersed in water (dry and wet CT). Thereafter, the proximal femur was quasi-statically loaded in vitro by a 1000 N load. The two QCT scans were manipulated to generate p-FE models that mimic the experimental conditions. We compared p-FE displacements and strains of the wet CT model to the dry CT model and to the experimental results. In addition, the material assignment strategy was reinvestigated. The inhomogeneous Young's modulus was represented in the FE model using two different methods, directly extracted from the CT data and using continuous spatial functions as in Yosibash et al. [2007a. Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations. J. Biomechanics 40, 3688–3699].Results: Excellent agreement between dry and wet FE models was found for both displacements and strains, i.e. the method is insensitive to CT conditions and may be used in vivo. Good agreement was also found between FE results and experimental observations. The spatial functions representing Young's modulus are local and do not influence strains and displacements prediction. Finally, the p-FE results of all three fresh frozen human femurs compare very well to experimental observations exemplifying that the presented method may be in a mature stage to be used in clinical computer-aided decision making.     

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.