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ABSTRACT: The shear strength of human trabecular bone may influence overall bone strength under fall loading conditions and failure at bone-implant interfaces. Here, we sought to compare shear and compressive yield strengths of human trabecular bone and elucidate the underlying failure mechanisms. We analyzed 54 specimens (5-mm cubes), all aligned with the main trabecular orientation and spanning four anatomic sites, 44 different cadavers, and a wide range of bone volume fraction (0.06-0.38). Micro-CT-based non-linear finite element analysis was used to assess the compressive and shear strengths and the spatial distribution of yielded tissue; the tissue-level constitutive model allowed for kinematic non-linearity and yielding with strength asymmetry. We found that the computed values of both the shear and compressive strengths depended on bone volume fraction via power law relations having an exponent of 1.7 (R(2)=0.95 shear; R(2)=0.97 compression). The ratio of shear to compressive strengths (mean±SD, 0.44±0.16) did not depend on bone volume fraction (p=0.24) but did depend on microarchitecture, most notably the intra-trabecular standard deviation in trabecular spacing (R(2)=0.23, p<0.005). For shear, the main tissue-level failure mode was tensile yield of the obliquely oriented trabeculae. By contrast, for compression, specimens having low bone volume fraction failed primarily by large-deformation-related tensile yield of horizontal trabeculae and those having high bone volume failed primarily by compressive yield of vertical trabeculae. We conclude that human trabecular bone is generally much weaker in shear than compression at the apparent level, reflecting different failure mechanisms at the tissue level.
Journal of biomechanics 08/2012; 45(15):2513-9. · 2.66 Impact Factor
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ABSTRACT: Trabecular bone is a highly porous orthotropic cellular solid material present inside human bones such as the femur (hip bone)
and vertebra (spine). In this study, an infinitesimal plasticity-like model with isotropic/kinematic hardening is developed
to describe yielding of trabecular bone at the continuum level. One of the unique features of this formulation is the development
of the plasticity-like model in strain space for a yield envelope expressed in terms of principal strains having asymmetric
yield behavior. An implicit return-mapping approach is adopted to obtain a symmetric algorithmic tangent modulus and a step-by-step
procedure of algorithmic implementation is derived. To investigate the performance of this approach in a full-scale finite
element simulation, the model is implemented in a non-linear finite element analysis program and several test problems including
the simulation of loading of the human femur structures are analyzed. The results show good agreement with the experimental
data.
Computational Mechanics 04/2012; 40(1):61-72. · 2.07 Impact Factor
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ABSTRACT: To use finite element modeling based on flat-panel volume computed tomography (CT) and bone mineral density (BMD) provided by dual-energy x-ray absorptiometry (DXA) to compare bone failure load, stiffness, and trabecular structure in women with anorexia nervosa (AN) and age-matched normal-weight control subjects.
The study was approved by the institutional review board and complied with HIPAA guidelines. Informed consent was obtained. Fourteen women, eight with AN (mean age, 26.6 years) and six control subjects (mean age, 26.3 years), underwent flat-panel volume CT of the distal radius to determine apparent trabecular bone volume fraction (BV/TV), apparent trabecular number (TbN), apparent trabecular thickness (TbTh), and apparent trabecular separation (TbSp). Bone strength and stiffness were calculated from uniaxial compression tests by using finite element models created from flat-panel volume CT. DXA was used to determine BMD of the radius, lumbar spine, and hip. Means ± standard deviations of all variables were calculated for both groups and compared (Student t test). Univariate regression analysis and stepwise regression modeling were performed.
Patients with AN had lower values for stiffness (284.77 kN/mm ± 76.14 vs 389.97 kN/mm ± 84.90, P = .04), failure load (4.98 kN ± 1.23 vs 7.01 kN ± 1.52, P = .02), BV/TV (0.32% ± 0.09 vs 0.44% ± 0.02, P = .007), and TbN (1.15 mm(-3) ± 0.20 vs 1.43 mm(-3) ± 0.13, P = .008) and higher values for TbSp (0.62 mm ± 0.20 vs 0.40 mm ± 0.04, P = .02) compared with normal-weight control subjects. TbTh was lower in women with AN (P = .1). BMD measurements were significantly lower for the AN group. BMD measurements and trabecular parameters (except TbTh) correlated with stiffness and failure load (r = 0.58 to 0.83).
Failure load and stiffness are abnormal in women with AN compared with those in normal-weight control subjects and correlate with BMD and trabecular parameters.
Radiology 10/2010; 257(1):167-74. · 5.73 Impact Factor
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ABSTRACT: Despite the importance of multiaxial failure of trabecular bone in many biomechanical applications, to date no complete multiaxial failure criterion for human trabecular bone has been developed. By using experimentally validated nonlinear high-resolution, micromechanical finite-element models as a surrogate for multiaxial loading experiments, we determined the three-dimensional normal strain yield surface and all combinations of the two-dimensional normal-shear strain yield envelope. High-resolution finite-element models of three human femoral neck trabecular bone specimens obtained through microcomputed tomography were used. In total, 889 multiaxial-loading cases were analyzed, requiring over 41,000 CPU hours on parallel supercomputers. Our results indicated that the multiaxial yield behavior of trabecular bone in strain space was homogeneous across the specimens and nearly isotropic. Analysis of stress-strain curves along each axis in the 3-D normal strain space indicated uncoupled yield behavior whereas substantial coupling was seen for normal-shear loading. A modified super-ellipsoid surface with only four parameters fit the normal strain yield data very well with an arithmetic error +/-SD less than -0.04 +/- 5.1%. Furthermore, the principal strains associated with normal-shear loading showed excellent agreement with the yield surface obtained for normal strain loading (arithmetic error +/- SD < 2.5 +/- 6.5%). We conclude that the four-parameter "Modified Super-Ellipsoid" yield surface presented here describes the multiaxial failure behavior of human femoral neck trabecular bone very well.
Journal of Biomechanical Engineering 12/2004; 126(6):677-84. · 1.90 Impact Factor
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ABSTRACT: 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.
Journal of Biomechanics 12/2004; 37(11):1671-8. · 2.43 Impact Factor
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ABSTRACT: Apparent yield strains for trabecular bone are uniform within an anatomic site but can vary across site. The overall goal of this study was to characterize the contribution of inter-site differences in trabecular architecture to corresponding variations in apparent yield strains. High-resolution, small deformation finite element analyses were used to compute apparent compressive and tensile yield strains in four sites (n = 7 specimens per site): human proximal tibia, greater trochanter, femoral neck, and bovine proximal tibia. These sites display differences in compressive, but not tensile, apparent yield strains. Inter-site differences in architecture were captured implicitly in the model geometries, and these differences were isolated as the sole source of variability across sites by using identical tissue properties in all models. Thus, the effects inter-site variations in architecture on yield strain could be assessed by comparing computed yield strains across site. No inter-site differences in computed yield strains were found for either loading mode (p > 0.19), indicating that, within the context of small deformations, inter-site variations in architecture do not affect apparent yield strains. However, results of ancillary analyses designed to test the validity of the small deformation assumption strongly suggested that the propensity to undergo large deformations constitutes an important contribution of architecture to inter-site variations in apparent compressive yield strains. Large deformations substantially reduced apparent compressive, but not tensile, yield strains. These findings indicate the importance of incorporating large deformation capabilities in computational analyses of trabecular bone. This may be critical when investigating the biomechanical consequences of trabecular thinning and loss.
Journal of Biomechanics 09/2004; 37(9):1413-20. · 2.43 Impact Factor
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ABSTRACT: The ability to determine trabecular bone tissue elastic and failure properties has biological and clinical importance. To date, trabecular tissue yield strains remain unknown due to experimental difficulties, and elastic moduli studies have reported controversial results. We hypothesized that the elastic and tensile and compressive yield properties of trabecular tissue are similar to those of cortical tissue. Effective tissue modulus and yield strains were calibrated for cadaveric human femoral neck specimens taken from 11 donors, using a combination of apparent-level mechanical testing and specimen-specific, high-resolution, nonlinear finite element modeling. The trabecular tissue properties were then compared to measured elastic modulus and tensile yield strain of human femoral diaphyseal cortical bone specimens obtained from a similar cohort of 34 donors. Cortical tissue properties were obtained by statistically eliminating the effects of vascular porosity. Results indicated that mean elastic modulus was 10% lower (p<0.05) for the trabecular tissue (18.0+/-2.8 GPa) than for the cortical tissue (19.9+/-1.8 GPa), and the 0.2% offset tensile yield strain was 15% lower for the trabecular tissue (0.62+/-0.04% vs. 0.73+/-0.05%, p<0.001). The tensile-compressive yield strength asymmetry for the trabecular tissue, 0.62 on average, was similar to values reported in the literature for cortical bone. We conclude that while the elastic modulus and yield strains for trabecular tissue are just slightly lower than those of cortical tissue, because of the cumulative effect of these differences, tissue strength is about 25% greater for cortical bone.
Journal of Biomechanics 02/2004; 37(1):27-35. · 2.43 Impact Factor
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Proceedings of the ACM/IEEE SC2004 Conference on High Performance Networking and Computing, 6-12 November 2004, Pittsburgh, PA, USA, CD-Rom; 01/2004
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ABSTRACT: One outstanding issue regarding the relationship between elastic modulus and density for trabecular bone is whether the relationship depends on anatomic site. To address this, on-axis elastic moduli and apparent densities were measured for 142 specimens of human trabecular bone from the vertebra (n=61), proximal tibia (n=31), femoral greater trochanter (n=23), and femoral neck (n=27). Specimens were obtained from 61 cadavers (mean+/-SD age=67+/-15 years). Experimental protocols were used that minimized end-artifact errors and controlled for specimen orientation. Tissue moduli were computed for a subset of 18 specimens using high-resolution linear finite element analyses and also using two previously developed theoretical relationships (Bone 25 (1999) 481; J. Elasticity 53 (1999) 125). Resultant power law regressions between modulus and density did depend on anatomic site, as determined via an analysis of covariance. The inter-site differences were among the leading coefficients (p<0.02), but not the exponents (p>0.08), which ranged 1.49-2.18. At a given density, specimens from the tibia had higher moduli than those from the vertebra (p=0.01) and femoral neck (p=0.002); those from the trochanter had higher moduli than the vertebra (p=0.02). These differences could be as large as almost 50%, and errors in predicted values of modulus increased by up to 65% when site-dependence was ignored. These results indicate that there is no universal modulus-density relationship for on-axis loading. Tissue moduli computed using methods that account for inter-site architectural variations did not differ across site (p>0.15), suggesting that the site-specificity in apparent modulus-density relationships may be attributed to differences in architecture.
Journal of Biomechanics 08/2003; 36(7):897-904. · 2.43 Impact Factor
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Proceedings of the ACM/IEEE SC2003 Conference on High Performance Networking and Computing, 15-21 November 2003, Phoenix, AZ, USA, CD-Rom; 01/2003
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ABSTRACT: Although recent nanoindentation studies have revealed the existence of substantial variations in tissue modulus within single specimens of trabecular bone, little is known regarding the biomechanical effects of such intraspecimen variations. In this study, high-resolution finite element modeling was used to investigate these effects. With limited literature information on the spatial distribution of intraspecimen variations in tissue modulus, two plausible spatial distributions were evaluated. In addition, three specimens (human femoral neck, human vertebral body, and bovine proximal tibia) were studied to assess the role of trabecular architecture. Results indicated that for all specimen/distribution combinations, the apparent modulus of the whole specimen decreased nonlinearly with increasing coefficient of variation (COV) of tissue modulus within the specimen. Apparent modulus decreased by <4% when tissue modulus COV was increased from 0% to 20% but decreased by 7-24%, depending on the assumed spatial distribution, for an increase in tissue modulus COV from 20% to 50%. For compressive loading to the elastic limit, increasing tissue modulus COV from 20% to 50% caused up to a 28-fold increase in the amount of failed tissue, depending on assumed spatial distribution and trabecular architecture. We conclude that intraspecimen variations in tissue modulus, if large, may have appreciable effects on trabecular apparent modulus and tissue-level failure. Since the observed effects depended on the assumed spatial distribution of the tissue modulus variations, a description of such distributions, particularly as a function of age, disease, and drug treatment, may provide new insight into trabecular bone structure-function relationships.
Journal of Biomechanics 02/2002; 35(2):237-46. · 2.43 Impact Factor
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ABSTRACT: An improved understanding of the biomechanical role of the vertebral cortical shell with respect to the trabecular bone may improve diagnosis of osteoporosis and provide insight into the effects of disease, aging, and drug treatments. In this study, we present results from finite element simulations of removal of the shell from the vertebral body and the associated mechanical effects in terms of overall change in vertebral structural stiffness and of the tissue-level stresses. Specimen-specific micro-mechanical finite element models of thirteen vertebrae were generated from micro-CT scans with 60-μm voxel size. An algorithm was developed to automatically isolate the thin (and discontinuous) shell and the images were converted into finite element models by mapping each image voxel into a finite element. After removal of the endplates, compressive loading conditions were applied and linear elastic analyses were run for three cases – with and without the shell, and shell-only models. The models contained up to 13.6 million elements and were solved using a maximum of 144 CPUs in parallel, 300 GB memory, and a custom code with a parallel mesh partitioner and algebraic multigrid solver. Results indicated that the shell was on average, 0.38 ± 0.06 mm thick, accounted for 21–39% of the overall bone mass, but accounted for 38–68% of the overall vertebral stiffness. Examination of the tissue-level stresses indicated that this disproportionately large mechanical effect of shell removal was due in part to unloading of the remaining peripheral trabeculae adjacent to the shell. Stress paths were also preferentially within vertically-aligned bone: the cortical shell and vertically-aligned trabeculae. Taken together, these results demonstrate two important roles of the thin vertebral cortical shell: it can carry significant load by virtue of representing a large proportion of the vertically-aligned bone tissue within the vertebra, and, as a shell, it also maximizes the load carrying capacity of the trabecular centrum, particularly around the periphery.
Computer Methods in Applied Mechanics and Engineering.
