A Novel 3D Microstructural Model for Trabecular Bone: I. The Relationship between Fabric and Elasticity

A novel 3D microstructural model is proposed to investigate the relationship between morphology and mechanical properties of trabecular bone. Open and closed cell geometries were selected with varying volume fractions and degrees of anisotropy that simulate the architectures of human cancellous bone over a broad range of anatomical locations. Finite element models of both cells were developed using beams and shells. Volume fraction and mean intercept length were calculated analytically and the effective elastic tensors were computed with linear tissue properties and periodic boundary conditions. Distinct, but strong relationships were obtained between fabric and the elastic tensors for open and closed cell geometries, which bound the experimental results obtained for human bone and support the relevance of the selected model to address trabecular bone fragility.     

A Novel 3D Microstructural Model for Trabecular Bone: I. The Relationship between Fabric and Elasticity

A novel 3D microstructural model is proposed to investigate the relationship between morphology and mechanical properties of trabecular bone. Open and closed cell geometries were selected with varying volume fractions and degrees of anisotropy that simulate the architectures of human cancellous bone over a broad range of anatomical locations. Finite element models of both cells were developed using beams and shells. Volume fraction and mean intercept length were calculated analytically and the effective elastic tensors were computed with linear tissue properties and periodic boundary conditions

Distinct, but strong relationships were obtained between fabric and the elastic tensors for open and closed cell geometries, which bound the experimental results obtained for human bone and support the relevance of the selected model to address trabecular bone fragility.     

Effect of boundary conditions on yield properties of human femoral trabecular bone

Trabecular bone plays an important mechanical role in bone fractures and implant stability. Homogenized nonlinear finite element (FE) analysis of whole bones can deliver improved fracture risk and implant loosening assessment. Such simulations require the knowledge of mechanical properties such as an appropriate yield behavior and criterion for trabecular bone. Identification of a complete yield surface is extremely difficult experimentally but can be achieved in silico by using micro-FE analysis on cubical trabecular volume elements. Nevertheless, the influence of the boundary conditions (BCs), which are applied to such volume elements, on the obtained yield properties remains unknown. Therefore, this study compared homogenized yield properties along 17 load cases of 126 human femoral trabecular cubic specimens computed with classical kinematic uniform BCs (KUBCs) and a new set of mixed uniform BCs, namely periodicity-compatible mixed uniform BCs (PMUBCs). In stress space, PMUBCs lead to 7–72 % lower yield stresses compared to KUBCs. The yield surfaces obtained with both KUBCs and PMUBCs demonstrate a pressure-sensitive ellipsoidal shape. A volume fraction and fabric-based quadric yield function successfully fitted the yield surfaces of both BCs with a correlation coefficient \(R^{2} \ge 0.93\). As expected, yield strains show only a weak dependency on bone volume fraction and fabric. The role of the two BCs in homogenized FE analysis of whole bones will need to be investigated and validated with experimental results at the whole bone level in future studies.     

The role of fabric in the large strain compressive behavior of human trabecular bone

Osteoporosis-related vertebral body fractures involve large compressive strains of trabecular bone. The small strain mechanical properties of the trabecular bone such as the elastic modulus or ultimate strength can be estimated using the volume fraction and a second order fabric tensor, but it remains unclear if similar estimations may be extended to large strain properties. Accordingly, the aim of this work is to identify the role of volume fraction and especially fabric in the large strain compressive behavior of human trabecular bone from various anatomical locations. Trabecular bone biopsies were extracted from human T12 vertebrae (n=31), distal radii (n=43), femoral head (n=44), and calcanei (n=30), scanned using microcomputed tomography to quantify bone volume fraction (BV/TV) and the fabric tensor (M), and tested either in unconfined or confined compression up to very large strains (～70%). The mechanical parameters of the resulting stress-strain curves were analyzed using regression models to examine the respective influence of BV/TV and fabric eigenvalues. The compressive stress-strain curves demonstrated linear elasticity, yielding with hardening up to an ultimate stress, softening toward a minimum stress, and a steady rehardening followed by a rapid densification. For the pooled experiments, the average minimum stress was 1.89 ± 1.77 MPa, while the corresponding mean strain was 7.15 ± 1.84%. The minimum stress showed a weaker dependence with fabric as the elastic modulus or ultimate strength. For the confined experiments, the stress at a logarithmic strain of 1.2 was 8.08 ± 7.91 MPa, and the dissipated energy density was 5.67 ± 4.42 MPa. The latter variable was strongly related to the volume fraction (R(2)=0.83) but the correlation improved only marginally with the inclusion of fabric (R(2)=0.84). The influence of fabric on the mechanical properties of human trabecular bone decreases with increasing strain, while the role of volume fraction remains important. In particular, the ratio of the minimum versus the maximum stress, i.e., the relative amount of softening, decreases strongly with fabric, while the dissipated energy density is dominated by the volume fraction. The collected results will prove to be useful for modeling the softening and densification of the trabecular bone using the finite element method.     

Micromechanical analyses of vertebral trabecular bone based on individual trabeculae segmentation of plates and rods

Trabecular plates play an important role in determining elastic moduli of trabecular bone. However, the relative contribution of trabecular plates and rods to strength behavior is still not clear. In this study, individual trabeculae segmentation (ITS) and nonlinear finite element (FE) analyses were used to evaluate the roles of trabecular types and orientations in the failure initiation and progression in human vertebral trabecular bone. Fifteen human vertebral trabecular bone samples were imaged using micro computed tomography (μCT), and segmented using ITS into individual plates and rods by orientation (longitudinal, oblique, and transverse). Nonlinear FE analysis was conducted to perform a compression simulation for each sample up to 1% apparent strain. The apparent and relative trabecular number and tissue fraction of failed trabecular plates and rods were recorded during loading and data were stratified by trabecular orientation. More trabecular rods (both in number and tissue fraction) failed at the initiation of compression (0.1–0.2% apparent strain) while more plates failed around the apparent yield point (>0.7% apparent strain). A significant correlation between plate bone volume fraction (pBV/TV) and apparent yield strength was found (r²=0.85). From 0.3% to 1% apparent strain, significantly more longitudinal trabecular plate and transverse rod failed than other types of trabeculae. While failure initiates at rods and rods fail disproportionally to their number, plates contribute significantly to the apparent yield strength because of their larger number and tissue volume. The relative failed number and tissue fraction at apparent yield point indicate homogeneous local failure in plates and rods of different orientations.     

Biaxial failure behavior of bovine tibial trabecular bone

Multiaxial failure properties of trabecular bone are important for modeling of whole bone fracture and can provide insight into structure-function relationships. There is currently no consensus on the most appropriate form of multiaxial yield criterion for trabecular bone. Using experimentally validated, high-resolution, non-linear finite element models, biaxial plain strain boundary conditions were applied to seven bovine tibial specimens. The dependence of multiaxial yield properties on volume fraction was investigated to quantify the interspecimen heterogeneity in yield stresses and strains. Two specimens were further analyzed to determine the yield properties for a wide range of biaxial strain loading conditions. The locations and quantities of tissue level yielding were compared for on-axis, transverse, and biaxial apparent level yielding to elucidate the micromechanical failure mechanisms. As reported for uniaxial loading of trabecular bone, the yield strains in multiaxial loading did not depend on volume fraction, whereas the yield stresses did. Micromechanical analysis indicated that the failure mechanisms in the on-axis and transverse loading directions were mostly independent. Consistent with this, the biaxial yield properties were best described by independent curves for on-axis and transverse loading. These findings establish that the multiaxial failure of trabecular bone is predominantly governed by the strain along the loading direction, requiring separate analytical expressions for each orthotropic axis to capture the apparent level yield behavior.     

Multi-axial mechanical properties of human trabecular bone

In the context of osteoporosis, evaluation of bone fracture risk and improved design of epiphyseal bone implants rely on accurate knowledge of the mechanical properties of trabecular bone. A multi-axial loading chamber was designed, built and applied to explore the compressive multi-axial yield and strength properties of human trabecular bone from different anatomical locations. A thorough experimental protocol was elaborated for extraction of cylindrical bone samples, assessment of their morphology by micro-computed tomography and application of different mechanical tests: torsion, uni-axial traction, uni-axial compression and multi-axial compression. A total of 128 bone samples were processed through the protocol and subjected to one of the mechanical tests up to yield and failure. The elastic data were analyzed using a tensorial fabric–elasticity relationship, while the yield and strength data were analyzed with fabric-based, conewise generalized Hill criteria. For each loading mode and more importantly for the combined results, strong relationships were demonstrated between volume fraction, fabric and the elastic, yield and strength properties of human trabecular bone. Despite the reviewed limitations, the obtained results will help improve the simulation of the damage behavior of human bones and bone-implant systems using the finite element method.     

The role of fabric in the quasi-static compressive mechanical properties of human trabecular bone from various anatomical locations

Osteoporosis leads to an increased risk of bone fracture. While bone density and architecture can be assessed in vivo with increasing accuracy using CT and MRI, their relationship with the critical mechanical properties at various anatomical sites remain unclear. The objective of this study was to quantify the quasi-static compressive mechanical properties of human trabecular bone among different skeletal sites and compare their relationships with bone volume fraction and a measure of microstructural anisotropy called fabric. Over 600 trabecular bone samples from six skeletal sites were assessed by and tested in uniaxial compression. Bone volume fraction correlated positively with elastic modulus, yield stress, ultimate stress, and the relationships depended strongly on skeletal site. The account of fabric improved these correlations substantially, especially when the data of all sites were pooled together, but the fabric–mechanical property relationships remained somewhat distinct among the anatomical sites. The study confirms that, beyond volume fraction, fabric plays an important role in determining the mechanical properties of trabecular bone and should be exploited in mechanical analysis of clinically relevant sites of the human skeleton.     

Sensitivity of damage predictions to tissue level yield properties and apparent loading conditions

High-resolution finite element models of trabecular bone failure could be used to augment current techniques for measuring damage in trabecular bone. However, the sensitivity of such models to the assumed tissue yield properties and apparent loading conditions is unknown. The goal of this study was to assess the sensitivity of the amount and mode (tension vs. compression) of tissue level yielding in trabecular bone to these factors. Linear elastic, high-resolution finite element models of nine bovine tibial trabecular bone specimens were used to calculate the fraction of the total tissue volume that exceeded each criterion for apparent level loading to the reported elastic limit in both on-axis and transverse compression and tension, and in shear. Four candidate yield criteria were studied, based on values suggested in the literature. Both the amount and the failure mode of yielded tissue were sensitive to the magnitudes of the tissue yield strains, the degree of tension-compression asymmetry of the yield criterion, and the applied apparent loads. The amount of yielded tissue was most sensitive to the orientation of the applied apparent loading, with the most tissue yielding for loading along the principal trabecular orientation and the least for loading perpendicular to it, regardless of the assumed tissue level yield criterion. Small changes in the magnitudes and the degree of asymmetry of the tissue yield criterion resulted in much larger changes in the amount of yielded tissue in the model. The results indicate that damage predictions based on high-resolution finite element models are highly sensitive to the assumed tissue yield properties. As such, good estimates of these values are needed before high-resolution finite element models can be applied to the study of trabecular bone damage. Regardless of the assumed tissue yield properties, the amount and type of damage that occurs in trabecular bone depends on the relative orientations of the applied apparent loads to the trabecular architecture, and this parameter should be controlled for both experimental and computational damage studies.     

Changes in the Fabric and Compliance Tensors of Cancellous Bone due to Trabecular Surface Remodeling,Predicted by a Digital Image-based Model

Fabric and compliance tensors of a cube of cancellous bone with a complicated three-dimensional trabecular structure were obtained for trabecular surface remodeling by using a digital image-based model combined with a large-scale finite element method. Using mean intercept length and a homogenization method, the fabric and compliance tensors were determined for the trabecular structure obtained in the computer remodeling simulation. The tensorial quantities obtained indicated that anisotropic structural changes occur in cancellous bone adapting to the compressive loading condition. There were good correlations between the fabric tensor, bone volume fraction, and compliance tensor in the remodeling process. The result demonstrates that changes in the structural and mechanical properties of cancellous bone are essentially anisotropic and should be expressed by tensorial quantities.     

Changes in the fabric and compliance tensors of cancellous bone due to trabecular surface remodeling, predicted by a digital image-based model

Fabric and compliance tensors of a cube of cancellous bone with a complicated three-dimensional trabecular structure were obtained for trabecular surface remodeling by using a digital image-based model combined with a large-scale finite element method. Using mean intercept length and a homogenization method, the fabric and compliance tensors were determined for the trabecular structure obtained in the computer remodeling simulation. The tensorial quantities obtained indicated that anisotropic structural changes occur in cancellous bone adapting to the compressive loading condition. There were good correlations between the fabric tensor, bone volume fraction, and compliance tensor in the remodeling process. The result demonstrates that changes in the structural and mechanical properties of cancellous bone are essentially anisotropic and should be expressed by tensorial quantities.     

Mechanisms of uniformity of yield strains for trabecular bone

Variations in yield strains for trabecular bone within a specific anatomic site are only a small fraction of the substantial variations that exist for elastic modulus and strength, and yet the source of this uniformity is not known. Our goal was to investigate the underlying mechanisms by using high-resolution, materially nonlinear finite element models of 12 human femoral neck trabecular bone specimens. The finite element models, used to obtain apparent yield strains in both tension and compression, assumed that the tissue-level yield strains were the same across all specimens. Comparison of the model predictions with the experimental data therefore enabled us to isolate the combined roles of volume fraction and architecture from the role of tissue material properties. Results indicated that, for both tensile and compressive loading, natural variations in volume fraction and architecture produced a negligible coefficient of variation (less than 3%) in apparent yield strains. Analysis of tissue-level strains showed that while bending of individual trabeculae played only a minor role in the apparent elastic behavior, the combined effects of this bending and tissue-level strength asymmetry produced apparent-level failure strains in compression that were 14% lower than those at the tissue level. By contrast, tissue and apparent-level yield strains were equivalent for tensile loading. We conclude that the uniformity of apparent yield strains is primarily the result of the highly oriented architecture that minimizes bending. Most of the variation that does occur is the result of the non-uniformity of the tissue-level yield strains.     

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.     

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.     

Modeling of dynamic fracture and damage in two-dimensional trabecular bone microstructures using the cohesive finite element method

Trabecular bone fracture is closely related to the trabecular architecture, microdamage accumulation, and bone tissue properties. Micro-finite-element models have been used to investigate the elastic and yield properties of trabecular bone but have only seen limited application in modeling the microstructure dependent fracture of trabecular bone. In this research, dynamic fracture in two-dimensional (2D) micrographs of ovine (sheep) trabecular bone is modeled using the cohesive finite element method. For this purpose, the bone tissue is modeled as an orthotropic material with the cohesive parameters calculated from the experimental fracture properties of the human cortical bone. Crack propagation analyses are carried out in two different 2D orthogonal sections cut from a three-dimensional 8 mm diameter cylindrical trabecular bone sample. The two sections differ in microstructural features such as area fraction (ratio of the 2D space occupied by bone tissue to the total 2D space), mean trabecula thickness, and connectivity. Analyses focus on understanding the effect of the rate of loading as well as on how the rate variation interacts with the microstructural features to cause anisotropy in microdamage accumulation and in the fracture resistance. Results are analyzed in terms of the dependence of fracture energy dissipation on the microstructural features as well as in terms of the changes in damage and stresses associated with the bone architecture variation. Besides the obvious dependence of the fracture behavior on the rate of loading, it is found that the microstructure strongly influences the fracture properties. The orthogonal section with lesser area fraction, low connectivity, and higher mean trabecula thickness is more resistant to fracture than the section with high area fraction, high connectivity, and lower mean trabecula thickness. In addition, it is found that the trabecular architecture leads to inhomogeneous distribution of damage, irrespective of the symmetry in the applied loading with the fracture of the entire bone section rapidly progressing to bone fragmentation once the accumulated damage in any trabeculae reaches a critical limit.     

Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state

Two-dimensional simulation of trabecular surface remodeling was conducted for a human proximal femur to investigate the structural change of cancellous bone toward a uniform stress state. Considering that a local mechanical stimulus plays an important role in cellular activities in bone remodeling, local stress nonuniformity was assumed to drive trabecular structural change to seek a uniform stress state. A large-scale pixel-based finite element model was used to simulate structural changes of individual trabeculae over the entire bone. As a result, the initial structure of trabeculae changed from isotropic to anisotropic due to trabecular microstructural changes caused by surface remodeling according to the mechanical environment in the proximal femur. Under a single-loading condition, it was shown that the apparent structural property evaluated by fabric ellipses corresponded to the apparent stress state in cancellous bone. As is observed in the actual bone, a distributed trabecular structure was obtained under a multiple-loading condition. Through these studies, it was concluded that trabecular surface remodeling toward a local uniform stress state at the trabecular level could naturally bring about functional adaptation phenomenon at the apparent tissue level. The proposed simulation model would be capable of providing insight into the hierarchical mechanism of trabecular surface remodeling at the microstructural level up to the apparent tissue level.     

How morphology predicts mechanical properties of trabecular structures depends on intra-specimen trabecular thickness variations

Two observations underlie this work. First, that the architecture of trabecular bone can accurately predict the mechanical stiffness characteristics of bone specimens when considering the combination of volume fraction and fabric, which is a measure of architectural anisotropy. Second, that the same morphological measures could not accurately predict the mechanical properties of porous structures in general. We hypothesize that this discrepancy can be explained by the special nature of trabecular bone as a structure in remodeling equilibrium relative to the external loads. We tested this hypothesis using a generic model of trabecular bone. Five series of 153 different architectures were created with this model. Each architecture was subjected to morphological analysis, and four different fabric measures were calculated to evaluate their effectiveness in characterizing the architecture. Relationships were determined relating morphology to the elastic constants. The quality of these relationships was tested by correlating the predicted elastic constants with those determined from finite element analysis. We found that the four fabric measures used could estimate the mechanical properties almost equally well. So the suggestion that fabric measures based on trabecular bone volume better represent the architecture than mean intercept length could not be affirmed. We conclude that for structures with equally sized elliptical voids the mechanical properties can be predicted well only if trabecular thickness variations within each structure are limited. These structures closely resemble previously developed models of trabecular bone. Furthermore, they are stiff in the principal fabric direction, hence, according to Cowin (J. Biomech. Eng. (108) (1986) 83), they are in remodeling equilibrium. These structures are also stiff over a large range of loading orientations, hence, are relatively insensitive to deviations in direction of loading.     

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.     

Combination of topological parameters and bone volume fraction better predicts the mechanical properties of trabecular bone

Trabecular bone structure may complement bone volume/total volume fraction (BV/TV) in the prediction of the mechanical properties. Nonetheless, the direct in vivo use of information pertaining to trabecular bone structure necessitates some predictive analytical model linking structure measures to mechanical properties. In this context, the purpose of this study was to combine BV/TV and topological parameters so as to better estimate the mechanical properties of trabecular bone. Thirteen trabecular bone mid-sagittal sections were imaged by magnetic resonance (MR) imaging at the resolution of 117 x 117x 300 microm(3). Topological parameters were evaluated in applying the 3D-line skeleton graph analysis (LSGA) technique to the binary MR images. The same images were used to estimate the elastic moduli by finite element analysis (FEA). In addition to the mid-sagittal section, two cylindrical samples were cored from each vertebra along vertical and horizontal directions. Monotonic compression tests were applied to these samples to measure both vertical and horizontal ultimate stresses. BV/TV was found as a strong predictor of the mechanical properties, accounting for 89-94% of the variability of the elastic moduli and for 69-86% of the variability of the ultimate stresses. Topological parameters and BV/TV were combined following two analytical formulations, based on: (1) the normalization of the topological parameters; and on (2) an exponential fit-model. The normalized parameters accounted for 96-98% of the variability of the elastic moduli, and the exponential model accounted for 80-95% of the variability of the ultimate stresses. Such formulations could potentially be used to increase the prediction of the mechanical properties of trabecular bone.     

Compressive fatigue behavior of human vertebral trabecular bone

Damage accumulation under compressive fatigue loading is believed to contribute significantly to non-traumatic, age-related vertebral fractures in the human spine. Only few studies have explored trabecular bone fatigue behavior under compressive loading and none examined the influence of trabecular architecture on fatigue life. In this study, trabecular bone samples of human lumbar and thoracic vertebrae (4 donors from age 29 to 86, n=29) were scanned with a microCT system prior to compressive fatigue testing to determine morphology-mechanical relationships for this relevant loading mode. Inspired from previous fabric-based relationships for elastic properties and quasi-static strength of trabecular bone, a simple power relationship between volume fraction, fabric eigenvalue, applied stress and the number of cycles to failure is proposed. The experimental results demonstrate a high correlation for this relationship (R2=0.95) and detect a significant contribution of the degree of anisotropy towards prediction of fatigue life. Step-wise regression for total and residual strains at failure suggested a weak, but significant correlation with volume fraction. From the obtained results, we conclude that the applied stress normalized by volume fraction and axial fabric eigenvalue can estimate fatigue life of human vertebral trabecular bone in axial compressive loading.