Tony M. Keaveny

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.

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.

Trabecular bone is a complex material with substantial heterogeneity. Its elastic and strength properties vary widely across anatomic sites, and with aging and disease. Although these properties depend very much on density, the role of architecture and tissue material properties remain uncertain. It is interesting that the strains at which the bone fails are almost independent of density. Current work addresses the underlying structure-function relations for such behavior, as well as more complex mechanical behavior, such as multiaxial loading, time-dependent failure, and damage accumulation. A unique tool for studying such behavior is the microstructural class of finite element models, particularly the "high-resolution" models. It is expected that with continued progress in this field, substantial insight will be gained into such important problems as osteoporosis, bone fracture, bone remodeling, and design/analysis of bone-implant systems. This article reviews the state of the art in trabecular bone biomechanics, focusing on the mechanical aspects, and attempts to identify important areas of current and future research.

Understanding the dependence of human trabecular bone strength behavior on anatomic site provides insight into structure-function relationships and is essential to the increased success of site-specific finite element models of whole bones. To investigate the hypothesis that the yield strains of human trabecular bone depend on anatomic site, the uniaxial tensile and compressive yield properties were compared for cylindrical specimens from the vertebra (n=61), proximal tibia (n=31), femoral greater trochanter (n=23), and femoral neck (n=27) taken from 61 donors (67+/-15years). Test protocols were used that minimized end artifacts and loaded specimens along the main trabecular orientation. Yield strains by site (mean+/-S.D.) ranged from 0.70+/-0.05% for the trochanter to 0.85+/-0.10% for the femoral neck in compression, from 0.61+/-0.05% for the trochanter to 0.70+/-0.05% for the vertebra in tension, and were always higher in compression than tension (p<0.001). The compressive yield strain was higher for the femoral neck than for all other sites (p<0.001), as was the tensile yield strain for the vertebra (p<0.007). Analysis of covariance, with apparent density as the covariate, indicated that inter-site differences existed in yield stress even after adjusting statistically for density (p<0.035). Coefficients of variation in yield strain within each site ranged from only 5-12%, consistent with the strong linear correlations (r(2)=0.94-0.98) found between yield stress and modulus. These results establish that the yield strains of human trabecular bone can differ across sites, but that yield strain may be considered uniform within a given site despite substantial variation in elastic modulus and yield stress.

If bone adapts to maintain constant strains and if on-axis yield strains in trabecular bone are independent of apparent density, adaptive remodeling in trabecular bone should maintain a constant safety factor (yield strain/functional strain) during habitual loading. To test the hypothesis that yield strains are indeed independent of density, compressive (n = 22) and tensile (n = 22) yield strains were measured without end-artifacts for low density (0.18 +/- 0.04 g cm(-3)) human vertebral trabecular bone specimens. Loads were applied in the superior-inferior direction along the principal trabecular orientation. These 'on-axis' yield strains were compared to those measured previously for high-density (0.51 +/- 0.06 g cm(-3)) bovine tibial trabecular bone (n = 44). Mean (+/- S.D.) yield strains for the human bone were 0.78 +/- 0.04% in tension and 0.84 +/- 0.06% in compression; corresponding values for the bovine bone were 0.78 +/- 0.04 and 1.09 +/- 0.12%, respectively. Tensile yield strains were independent of the apparent density across the entire density range (human p = 0.40, bovine p = 0.64, pooled p = 0.97). By contrast, compressive yield strains were linearly correlated with apparent density for the human bone (p < 0.001) and the pooled data (p < 0.001), and a suggestive trend existed for the bovine data (p = 0.06). These results refute the hypothesis that on-axis yield strains for trabecular bone are independent of density for compressive loading, although values may appear constant over a narrow density range. On-axis tensile yield strains appear to be independent of both apparent density and anatomic site.

Writing programs that scale with increasing numbers of cores should be as easy as writing programs for sequential computers.

The correlation between bone mineral density and vertebral strength is not based on mechanical principles and thus the method cannot reflect the effects of subtle geometric features and densitometric inhomogeneities that may substantially affect vertebral strength. Finite element models derived from quantitative computed tomography (QCT) scans overcome such limitations. The overall goal of this study was to establish that QCT-based "voxel" finite element models are better predictors of vertebral compressive strength than QCT measures of bone mineral density with or without measures of cross-sectional area. QCT scans were taken of 13 vertebral bodies excised from 13 cadavers (L1-L4; age: 37-87 years; M = 6, F = 7) and used to calculate bone mineral density (BMD(QCT)). The QCT voxel data were converted into linearly elastic finite element models of each vertebra, from which measures of vertebral stiffness and strength were computed. The vertebrae were biomechanically tested in compression to measure strength. Vertebral strength was positively correlated with the finite element measures of strength (r(2) = 0.86, P < 0.0001) and stiffness (r(2) = 0.82, P < 0.0001), the product of BMD(QCT) and vertebral minimum cross-sectional area (r(2) = 0.65, P = 0.0008), and BMD(QCT) alone (r(2) = 0.53, P = 0.005). These results demonstrate that highly automated "voxel" finite element models are superior to correlation-based QCT methods in predicting vertebral compressive strength and therefore offer great promise for improvement of clinical fracture risk assessment.

The biomechanical behavior of a single lumbar vertebral body after various surgical treatments with acrylic vertebroplasty was parametrically studied using finite-element analysis.To provide a theoretical framework for understanding and optimizing the biomechanics of vertebroplasty. Specifically, to investigate the effects of volume and distribution of bone cement on stiffness recovery of the vertebral body.Vertebroplasty is a treatment that stabilizes a fractured vertebra by addition of bone cement. However, there is currently no information available on the optimal volume and distribution of the filler material in terms of stiffness recovery of the damaged vertebral body.An experimentally calibrated, anatomically accurate finite-element model of an elderly L1 vertebral body was developed. Damage was simulated in each element based on empirical measurements in response to a uniform compressive load. After virtual vertebroplasty (bone cement filling range of 1-7 cm3) on the damaged model, the resulting compressive stiffness of the vertebral body was computed for various spatial distributions of the filling material and different loading conditions.Vertebral stiffness recovery after vertebroplasty was strongly influenced by the volume fraction of the implanted cement. Only a small amount of bone cement (14% fill or 3.5 cm3) was necessary to restore stiffness of the damaged vertebral body to the predamaged value. Use of a 30% fill increased stiffness by more than 50% compared with the predamaged value. Whereas the unipedicular distributions exhibited a comparative stiffness to the bipedicular or posterolateral cases, it showed a medial-lateral bending motion ("toggle") toward the untreated side when a uniform compressive pressure load was applied.Only a small amount of bone cement ( approximately 15% volume fraction) is needed to restore stiffness to predamage levels, and greater filling can result in substantial increase in stiffness well beyond the intact level. Such overfilling also renders the system more sensitive to the placement of the cement because asymmetric distributions with large fills can promote single-sided load transfer and thus toggle. These results suggest that large fill volumes may not be the most biomechanically optimal configuration, and an improvement might be achieved by use of lower cement volume with symmetric placement.

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure-function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean+/-S.D.) 18.7+/-3.4GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.

Abstract We sought to quantify the systematic and random errors associated with‐artifacts in the platens compression test for trabecular bone. Our hypothesis was that while errors may depend on anatomic site, they do not depend on apparent density and therefore have substantial random components. Trabecular bone specimens were first tested nondestructively using newly developed accurate protocols and then were tested again using the platens compression test. Percentage differences in modulus between the techniques (bovine) proximal tibia [n = 18] and humerus [n = 17] and human lumbar spine, [n = 9] were in the range of 4‐86%. These differences did not depend on anatomic site (p = 0.21) and were only weakly dependent on apparent density and specimen aspect ratio (r 2 &lt; 0.10). The mean percentage difference in modulus was 32.6% representing the systematic component of the end‐artifact error. Neglecting the minor variations explained by density and specimen size (approximately 10%), an upper bound on the random error from end‐artifacts in this experiment was taken as the SD of the modulus difference (±18.2%). Based on a synthesis of data taken from this study and from the literature, we concluded that the systematic underestimation error in the platens compression test can be only approximated and is in the range of 20‐40%; the substantial random error (±12.5%) confounds correction, particularly when the sample size is small. These errors should be considered when interpreting results from the platens test, and more accurate testing techniques should be used when such errors are not acceptable.

Previous bisphosphonate treatment attenuates the bone-forming effect of teriparatide. We compared the effects of 12 months of romosozumab (AMG 785), a sclerostin monoclonal antibody, versus teriparatide on bone mineral density (BMD) in women with postmenopausal osteoporosis transitioning from bisphosphonate therapy.This randomised, phase 3, open-label, active-controlled study was done at 46 sites in North America, Latin America, and Europe. We enrolled women (aged ≥55 to ≤90 years) with postmenopausal osteoporosis who had taken an oral bisphosphonate for at least 3 years before screening and alendronate the year before screening; an areal BMD T score of -2·5 or lower at the total hip, femoral neck, or lumbar spine; and a history of fracture. Patients were randomly assigned (1:1) via an interactive voice response system to receive subcutaneous romosozumab (210 mg once monthly) or subcutaneous teriparatide (20 μg once daily). The primary endpoint was percentage change from baseline in areal BMD by dual-energy x-ray absorptiometry at the total hip through month 12 (mean of months 6 and 12), which used a linear mixed effects model for repeated measures and represented the mean treatment effect at months 6 and 12. All randomised patients with a baseline measurement and at least one post-baseline measurement were included in the efficacy analysis. This trial is registered with ClinicalTrials.gov, number NCT01796301.Between Jan 31, 2013, and April 29, 2014, 436 patients were randomly assigned to romosozumab (n=218) or teriparatide (n=218). 206 patients in the romosozumab group and 209 in the teriparatide group were included in the primary efficacy analysis. Through 12 months, the mean percentage change from baseline in total hip areal BMD was 2·6% (95% CI 2·2 to 3·0) in the romosozumab group and -0·6% (-1·0 to -0·2) in the teriparatide group; difference 3·2% (95% CI 2·7 to 3·8; p<0·0001). The frequency of adverse events was generally balanced between treatment groups. The most frequently reported adverse events were nasopharyngitis (28 [13%] of 218 in the romosozumab group vs 22 [10%] of 214 in the teriparatide group), hypercalcaemia (two [<1%] vs 22 [10%]), and arthralgia (22 [10%] vs 13 [6%]). Serious adverse events were reported in 17 (8%) patients on romosozumab and in 23 (11%) on teriparatide; none were judged treatment related. There were six (3%) patients in the romosozumab group compared with 12 (6%) in the teriparatide group with adverse events leading to investigational product withdrawal.Transition to a bone-forming agent is common practice in patients treated with bisphosphonates, such as those who fracture while on therapy. In such patients, romosozumab led to gains in hip BMD that were not observed with teriparatide. These data could inform clinical decisions for patients at high risk of fracture.Amgen, Astellas, and UCB Pharma.

Observations that dual-energy X-ray absorptiometry (DXA) measures of areal bone mineral density cannot completely explain fracture incidence after anti-resorptive treatment have led to renewed interest in bone quality. Bone quality is a vague term but generally refers to the effects of skeletal factors that contribute to bone strength but are not accounted for by measures of bone mass. Because a clinical fracture is ultimately a mechanical event, it follows then that any clinically relevant modification of bone quality must change bone biomechanical performance relative to bone mass. In this perspective, we discuss a framework for assessing the clinically relevant effects of bone quality based on two general concepts: (1) the biomechanical effects of bone quality can be quantified from analysis of the relationship between bone mechanical performance and bone density; and (2) because of its hierarchical nature, biomechanical testing of bone at different physical scales (<1 mm, 1 mm, 1 cm, etc.) can be used to isolate the scale at which the most clinically relevant changes in bone quality occur. As an example, we review data regarding the relationship between the strength and density in excised specimens of trabecular bone and highlight the fact that it is not yet clear how this relationship changes during aging, osteoporosis development, and anti-resorptive treatment. Further study of new and existing data using this framework should provide insight into the role of bone quality in osteoporotic fracture risk.

Abstract Low areal BMD (aBMD) is associated with increased risk of hip fracture, but many hip fractures occur in persons without low aBMD. Finite element (FE) analysis of QCT scans provides a measure of hip strength. We studied the association of FE measures with risk of hip fracture in older men. A prospective case-cohort study of all first hip fractures (n = 40) and a random sample (n = 210) of nonfracture cases from 3549 community-dwelling men ≥65 yr of age used baseline QCT scans of the hip (mean follow-up, 5.6 yr). Analyses included FE measures of strength and load-to-strength ratio and BMD by DXA. Hazard ratios (HRs) for hip fracture were estimated with proportional hazards regression. Both femoral strength (HR per SD change = 13.1; 95% CI: 3.9–43.5) and the load-to-strength ratio (HR = 4.0; 95% CI: 2.7–6.0) were strongly associated with hip fracture risk, as was aBMD as measured by DXA (HR = 5.1; 95% CI: 2.8–9.2). After adjusting for age, BMI, and study site, the associations remained significant (femoral strength HR = 6.5, 95% CI: 2.3–18.3; load-to-strength ratio HR = 4.3, 95% CI: 2.5–7.4; aBMD HR = 4.4, 95% CI: 2.1–9.1). When adjusted additionally for aBMD, the load-to-strength ratio remained significantly associated with fracture (HR = 3.1, 95% CI: 1.6–6.1). These results provide insight into hip fracture etiology and demonstrate the ability of FE-based biomechanical analysis of QCT scans to prospectively predict hip fractures in men.

<h3>Importance</h3> As men age, they experience decreased serum testosterone concentrations, decreased bone mineral density (BMD), and increased risk of fracture. <h3>Objective</h3> To determine whether testosterone treatment of older men with low testosterone increases volumetric BMD (vBMD) and estimated bone strength. <h3>Design, Setting, and Participants</h3> Placebo-controlled, double-blind trial with treatment allocation by minimization at 9 US academic medical centers of men 65 years or older with 2 testosterone concentrations averaging less than 275 ng/L participating in the Testosterone Trials from December 2011 to June 2014. The analysis was a modified intent-to-treat comparison of treatment groups by multivariable linear regression adjusted for balancing factors as required by minimization. <h3>Interventions</h3> Testosterone gel, adjusted to maintain the testosterone level within the normal range for young men, or placebo gel for 1 year. <h3>Main Outcomes and Measures</h3> Spine and hip vBMD was determined by quantitative computed tomography at baseline and 12 months. Bone strength was estimated by finite element analysis of quantitative computed tomography data. Areal BMD was assessed by dual energy x-ray absorptiometry at baseline and 12 months. <h3>Results</h3> There were 211 participants (mean [SD] age, 72.3 [5.9] years; 86% white; mean [SD] body mass index, 31.2 [3.4]). Testosterone treatment was associated with significantly greater increases than placebo in mean spine trabecular vBMD (7.5%; 95% CI, 4.8% to 10.3% vs 0.8%; 95% CI, −1.9% to 3.4%; treatment effect, 6.8%; 95% CI, 4.8%-8.7%;<i>P</i> &lt; .001), spine peripheral vBMD, hip trabecular and peripheral vBMD, and mean estimated strength of spine trabecular bone (10.8%; 95% CI, 7.4% to 14.3% vs 2.4%; 95% CI, −1.0% to 5.7%; treatment effect, 8.5%; 95% CI, 6.0%-10.9%;<i>P </i>&lt; .001), spine peripheral bone, and hip trabecular and peripheral bone. The estimated strength increases were greater in trabecular than peripheral bone and greater in the spine than hip. Testosterone treatment increased spine areal BMD but less than vBMD. <h3>Conclusions and Relevance</h3> Testosterone treatment for 1 year of older men with low testosterone significantly increased vBMD and estimated bone strength, more in trabecular than peripheral bone and more in the spine than hip. A larger, longer trial could determine whether this treatment also reduces fracture risk. <h3>Trial Registration</h3> clinicaltrials.gov Identifier: NCT00799617

ABSTRACT Finite element analysis of computed tomography (CT) scans provides noninvasive estimates of bone strength at the spine and hip. To further validate such estimates clinically, we performed a 5-year case-control study of 1110 women and men over age 65 years from the AGES-Reykjavik cohort (case = incident spine or hip fracture; control = no incident spine or hip fracture). From the baseline CT scans, we measured femoral and vertebral strength, as well as bone mineral density (BMD) at the hip (areal BMD only) and lumbar spine (trabecular volumetric BMD only). We found that for incident radiographically confirmed spine fractures (n = 167), the age-adjusted odds ratio for vertebral strength was significant for women (2.8, 95% confidence interval [CI] 1.8 to 4.3) and men (2.2, 95% CI 1.5 to 3.2) and for men remained significant (p = 0.01) independent of vertebral trabecular volumetric BMD. For incident hip fractures (n = 171), the age-adjusted odds ratio for femoral strength was significant for women (4.2, 95% CI 2.6 to 6.9) and men (3.5, 95% CI 2.3 to 5.3) and remained significant after adjusting for femoral neck areal BMD in women and for total hip areal BMD in both sexes; fracture classification improved for women by combining femoral strength with femoral neck areal BMD (p = 0.002). For both sexes, the probabilities of spine and hip fractures were similarly high at the BMD-based interventional thresholds for osteoporosis and at corresponding preestablished thresholds for “fragile bone strength” (spine: women ≤ 4500 N, men ≤ 6500 N; hip: women ≤ 3000 N, men ≤ 3500 N). Because it is well established that individuals over age 65 years who have osteoporosis at the hip or spine by BMD criteria should be considered at high risk of fracture, these results indicate that individuals who have fragile bone strength at the hip or spine should also be considered at high risk of fracture. © 2014 American Society for Bone and Mineral Research.

The Testosterone Trials (TTrials) were a coordinated set of seven placebo-controlled, double-blind trials in 788 men with a mean age of 72 years to determine the efficacy of increasing the testosterone levels of older men with low testosterone. Testosterone treatment increased the median testosterone level from unequivocally low at baseline to midnormal for young men after 3 months and maintained that level until month 12. In the Sexual Function Trial, testosterone increased sexual activity, sexual desire, and erectile function. In the Physical Function Trial, testosterone did not increase the distance walked in 6 minutes in men whose walk speed was slow; however, in all TTrial participants, testosterone did increase the distance walked. In the Vitality Trial, testosterone did not increase energy but slightly improved mood and depressive symptoms. In the Cognitive Function Trial, testosterone did not improve cognitive function. In the Anemia Trial, testosterone increased hemoglobin in both men who had anemia of a known cause and in men with unexplained anemia. In the Bone Trial, testosterone increased volumetric bone mineral density and the estimated strength of the spine and hip. In the Cardiovascular Trial, testosterone increased the coronary artery noncalcified plaque volume as assessed using computed tomographic angiography. Although testosterone was not associated with more cardiovascular or prostate adverse events than placebo, a trial of a much larger number of men for a much longer period would be necessary to determine whether testosterone increases cardiovascular or prostate risk.

The conflicting conclusions regarding the relationship between the tensile and compressive strengths of trabecular bone remain unexplained. To help resolve this issue, we compared measurements of the tensile (n = 22) and compressive (n = 22) yield strengths, and yield strains, of trabecular bone specimens taken from 38 bovine proximal tibiae. We also studied how these failure properties depended on modulus and apparent density. To enhance accuracy, trabecular orientation was controlled, and each specimen had a reduced section where strains were measured with a miniature extensometer. We found that the mean yield strength was 30% lower for tensile loading. However, the difference between individual values of the tensile and compressive strengths increased linearly with increasing modulus and density, being negligible for low moduli, but substantial for high moduli. By contrast, both the tensile and compressive yield strains were independent of modulus and density, with the yield strain being 30% lower for tensile loading. Thus, the difference between the tensile and compressive strengths of bovine tibial trabecular bone depends on the modulus, but the difference between yield strains does not. This phenomenon may explain in part that conflicting conclusions reached previously on the tensile and compressive strengths of trabecular bone since the mean modulus has varied among different studies. Realizing that our data pertain only directly to bovine tibial trabecular bone for longitudinal loading, our results nevertheless suggest that failure parameters based on strains may provide more powerful and general comparisons of the failure properties for trabecular bone than measures based on stress.

Using a protocol designed to reduce experimental artifacts associated with the conventional compression test for trabecular bone, we performed in vitro mechanical testing on bovine tibial trabecular bone to obtain accurate descriptions of the elastic and yield behaviors. Reduced-section cylindrical specimens were preconditioned for eight tension-compression (+/- 0.5% strain) cycles and then loaded to failure either in tension (n = 15) or compression (n = 14). We found that the pre-yield behavior for every specimen was fully linear, indicating that the initial nonlinear 'toe' is an experimental artifact. Analysis of variance on the moduli indicated that there was no significant difference between the tensile and compressive moduli before preconditioning. However, preconditioning decreased the tensile and compressive moduli on average by 8.8% (p < 0.01) and 5.3% (p < 0.01), respectively, with the decrease in tensile modulus being larger (p < 0.01). These small but significant decreases in modulus suggest that initial yielding involves microstructural damage (as opposed to plastic slip) of individual trabeculae and also indicate that the tensile and/or the compressive yield strain of (bovine tibial) trabecular bone is less than 0.5%. The mean tensile strength was approximately 70% of the mean compressive strength, although this difference in strengths may have been affected by the preconditioning-induced damage. Taken together, these results suggest that there are more similarities between the elastic and yield behaviors of trabecular and cortical bone than had been assumed previously.

We have reviewed highlights of the research in trabecular bone biomechanics performed over the past 20 years. Results from numerous studies have shown that trabecular bone is an extremely heterogeneous material--modulus can vary 100-fold even within the same metaphysis--with varying degrees of anisotropy. Strictly speaking, descriptions of the mechanical properties of trabecular bone should therefore be accompanied by specification of factors such as anatomic site, loading direction, and age. Research efforts have also been focused on the measurement of mechanical properties for individual trabeculae, improvement of methods for mechanical testing at the continuum level, quantification of the three-dimensional architecture of trabecular bone, and formulation of equations to relate the microstructural and continuum-level mechanical properties. As analysis techniques become more sophisticated, there is now evidence that factors such as anisotropy and heterogeneity of individual trabeculae might also have a significant effect on the continuum-level properties, suggesting new directions for future research. Other areas requiring further research are the time-dependent and multiaxial failure properties at the continuum level, and the stiffness and failure properties at the lamellar level. Continued research in these areas should enhance our understanding of issues such as age-related bone fracture, prosthesis loosening, and bone remodeling.

The biomechanical role of the vertebral cortical shell remains poorly understood. Using high-resolution finite element modeling of a cohort of elderly vertebrae, we found that the biomechanical role of the shell can be substantial and that the load sharing between the cortical and trabecular bone is complex. As a result, a more integrative measure of the trabecular and cortical bone should improve noninvasive assessment of fracture risk and treatments.A fundamental but poorly understood issue in the assessment of both osteoporotic vertebral fracture risk and effects of treatment is the role of the trabecular bone and cortical shell in the load-carrying capacity of the vertebral body.High-resolution microCT-based finite element models were developed for 13 elderly human vertebrae (age range: 54-87 years; 74.6 +/- 9.4 years), and parameter studies-with and without endplates-were performed to determine the role of the shell versus trabecular bone and the effect of model assumptions.Across vertebrae, whereas the average thickness of the cortical shell was only 0.38 +/- 0.06 mm, the shell mass fraction (shell mass/total bone mass)-not including the endplates-ranged from 0.21 to 0.39. The maximum load fraction taken by the shell varied from 0.38 to 0.54 across vertebrae and occurred at the narrowest section. The maximum load fraction taken by the trabecular bone varied from 0.76 to 0.89 across vertebrae and occurred near the endplates. Neither the maximum shell load fraction nor the maximum trabecular load fraction depended on any of the densitometric or morphologic properties of the vertebra, indicating the complex nature of the load sharing mechanism. The variation of the shell load-carrying capacity across vertebrae was significantly altered by the removal of endplates, although these models captured the overall trend within a vertebra.The biomechanical role of the thin cortical shell in the vertebral body can be substantial, being about 45% at the midtransverse section but as low as 15% close to the endplates. As a result of the complexity of load sharing, sampling of only midsection trabecular bone as a strength surrogate misses important biomechanical information. A more integrative approach that combines the structural role of both cortical and trabecular bone should improve noninvasive assessment of vertebral bone strength in vivo.

Abstract The objective of this study was to report our quantitative computed tomography (QCT) density‐mechanical property regressions for trabecular bone for use in biomechanical modelling of the human spine. Cylindrical specimens of human vertebral trabecular bone (from T10 to L4) were cored from 32 cadavers (mean ± SD age = 70.1 ± 16.8; 13 females, 19 males) and scanned using QCT. Mechanical tests were conducted using a protocol that minimized end‐artifacts over the apparent density range tested (0.09–0.38 g/ cm 3 ). To account for the presence of multiple specimens per donor in this data set, donor was treated as a random effect in the regression model. Mean modulus (319 ± 189 MPa) was higher and mean yield strain (0.78 ± 0.06%) was lower than typical values reported previously due to minimization of the end‐artifact errors. QCT density showed a strong positive correlation with modulus ( n = 76) and yield stress ( r 2 = 0.90–0.95, n = 53, p &lt; 0.001). There was a weak positive linear correlation with yield strain ( r 2 = 0.58, n = 53, p = 0.07). Prediction errors, incurred when estimating modulus or strength for specimens from a new donor, were 30–36% of the mean values of these properties. Direct QCT density‐mechanical property regressions gave more precise predictions of mechanical properties than if physically measured wet apparent density was used as an intermediate variable to predict mechanical properties from QCT density. Use of these QCT density‐mechanical property regressions should improve the fidelity of QCT‐based biomechanical models of the human spine for whole bone and bone‐implant analyses. © 2002 Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved.

Abstract FE modeling was used to estimate the biomechanical effects of teriparatide and alendronate on lumbar vertebrae. Both treatments enhanced predicted vertebral strength by increasing average density. This effect was more pronounced for teriparatide, which further increased predicted vertebral strength by altering the distribution of density within the vertebra, preferentially increasing the strength of the trabecular compartment. Introduction : Teriparatide 20 μg/day (TPTD) and alendronate 10 mg/day (ALN) increase areal, measured by DXA, and volumetric, measured by QCT, lumbar spine BMD through opposite effects on bone remodeling. Using finite element (FE) modeling of QCT scans, we sought to compare the vertebral strength characteristics in TPTD‐ and ALN‐treated patients. Materials and Methods : A subset of patients ( N = 28 TPTD; N = 25 ALN) from the Forteo Alendronate Comparator Trial who had QCT scans of the spine at baseline and postbaseline were analyzed. The QCT scans were analyzed for compressive strength of the L 3 vertebra using FE modeling. In addition, using controlled parameter studies of the FE models, the effects of changes in density, density distribution, and geometry on strength were calculated, a strength:density ratio was determined, and a response to bending was also quantified. Results : Both treatments had positive effects on predicted vertebral strength characteristics. At least 75% of the patients in each treatment group had increased strength of the vertebra at 6 months compared with baseline. Patients in both treatment groups had increased average volumetric density and increased strength in the trabecular bone, but the median percentage increases for these parameters were 5‐ to 12‐fold greater for TPTD. Larger increases in the strength:density ratio were also observed for TPTD, and these were primarily attributed to preferential increases in trabecular strength. Conclusions : These results provide new insight into the effects of these treatments on estimated biomechanical properties of the vertebra. Both treatments positively affected predicted vertebral strength through their effects on average BMD, but the magnitudes of the effects were quite different. Teriparatide also affected vertebral strength by altering the distribution of density within the vertebra, so that overall, teriparatide had a 5‐fold greater percentage increase in the strength:density ratio.

The propensity of individual trabeculae to fracture (microfracture) may be important clinically since it could be indicative of bone fragility. Whether or not an overloaded trabecula fractures is determined in part by its structural ductility, a mechanical property that describes how much deformation a trabecula can sustain. The overall goal of this study was to determine the structural ductility of individual trabeculae and the degree to which it is influenced by pyridinium and non-enzymatic collagen cross-links. Vertically oriented rodlike trabeculae were taken from the thoracic vertebral bodies of 32 cadavers (16 male and 16 female, 54 - 94 years of age). A total of 221 trabeculae (4 - 9 per donor) were tested to failure in tension using a micro-tensile loading device. A subset of 76 samples was analyzed to determine the concentration of hydroxylysyl-pyridinoline (HP) and lysyl-pyridinoline (LP) cross-links as well as pentosidine, a marker of non-enzymatic glycation. Structural ductility (defined as the ultimate strain of the whole trabecula) ranged from 1.8% to 20.2% strain (8.8 +/- 3.7%, mean +/- SD) and did not depend on age (P = 0.39), sex (P = 0.57), or thickness of the sample at the point of failure (P = 0.36). Pentosidine was the only marker of collagen cross-linking measured that was found to be correlated with structural ductility (P = 0.01) and explained about 9% of the observed variance. We conclude that the ductility of individual trabeculae varies tremendously, can be substantial, and is weakly influenced by non-enzymatic glycation.

Abstract The “PTH and Alendronate” or “PaTH” study compared the effects of PTH(1-84) and/or alendronate (ALN) in 238 postmenopausal, osteoporotic women. We performed finite element analysis on the QCT scans of 162 of these subjects to provide insight into femoral strength changes associated with these treatments and the relative roles of changes in the cortical and trabecular compartments on such strength changes. Patients were assigned to either PTH, ALN, or their combination (CMB) in year 1 and were switched to either ALN or placebo (PLB) treatment in year 2: PTH-PLB, PTH-ALN, CMB-ALN, and ALN-ALN (year 1-year 2) treatments. Femoral strength was simulated for a sideways fall using nonlinear finite element analysis of the quantitative CT exams. At year 1, the strength change from baseline was statistically significant for PTH (mean, 2.08%) and ALN (3.60%), and at year 2, significant changes were seen for the PTH-ALN (7.74%), CMB-ALN (4.18%), and ALN-ALN (4.83%) treatment groups but not for PTH-PLB (1.17%). Strength increases were primarily caused by changes in the trabecular density regardless of treatment group, but changes in cortical density and mass also played a significant role, the degree of which depended on treatment. For PTH treatment at year 1 and for ALN-ALN treatment at year 2, there were significant negative and positive strength effects, respectively, associated with a change in external bone geometry. Average changes in strength per treatment group were somewhat consistent with average changes in total hip areal BMD as measured by DXA, except for the PTH group at year 1. The relation between change in femoral strength and change in areal BMD was weak (r2 = 0.14, pooled, year 2). We conclude that femoral strength changes with these various treatments were dominated by trabecular changes, and although changes in the cortical bone and overall bone geometry did contribute to femoral strength changes, the extent of these latter effects depended on the type of treatment.

Abstract Trabecular plates and rods are important microarchitectural features in determining mechanical properties of trabecular bone. A complete volumetric decomposition of individual trabecular plates and rods was used to assess the orientation and morphology of 71 human trabecular bone samples. The ITS-based morphological analyses better characterize microarchitecture and help predict anisotropic mechanical properties of trabecular bone. Introduction: Standard morphological analyses of trabecular architecture lack explicit segmentations of individual trabecular plates and rods. In this study, a complete volumetric decomposition technique was developed to segment trabecular bone microstructure into individual plates and rods. Contributions of trabecular type-associated morphological parameters to the anisotropic elastic moduli of trabecular bone were studied. Materials and Methods: Seventy-one human trabecular bone samples from the femoral neck (FN), tibia, and vertebral body (VB) were imaged using μCT or serial milling. Complete volumetric decomposition was applied to segment trabecular bone microstructure into individual plates and rods. The orientation of each individual trabecula was determined, and the axial bone volume fractions (aBV/TV), axially aligned bone volume fraction along each orthotropic axis, were correlated with the elastic moduli. The microstructural type-associated morphological parameters were derived and compared with standard morphological parameters. Their contributions to the anisotropic elastic moduli, calculated by finite element analysis (FEA), were evaluated and compared. Results: The distribution of trabecular orientation suggested that longitudinal plates and transverse rods dominate at all three anatomic sites. aBV/TV along each axis, in general, showed a better correlation with the axial elastic modulus (r2 = 0.95∼0.99) compared with BV/TV (r2 = 0.93∼0.94). The plate-associated morphological parameters generally showed higher correlations with the corresponding standard morphological parameters than the rod-associated parameters. Multiple linear regression models of six elastic moduli with individual trabeculae segmentation (ITS)-based morphological parameters (adjusted r2 = 0.95∼0.98) performed equally well as those with standard morphological parameters (adjusted r2 = 0.94∼0.97) but revealed specific contributions from individual trabecular plates or rods. Conclusions: The ITS-based morphological analyses provide a better characterization of the morphology and trabecular orientation of trabecular bone. The axial loading of trabecular bone is mainly sustained by the axially aligned trabecular bone volume. Results suggest that trabecular plates dominate the overall elastic properties of trabecular bone.

A finite element parametric analysis to investigate the relative load carrying roles of the shell and centrum in the lumbar vertebral body.To address the issue of the structural role of the vertebral shell and clarify some of the contradictions raised by previous studies.A number of experimental and finite element studies have attempted to quantify the relative structural roles of the shell and centrum, but these studies support no consensus on the relative contribution of the shell to vertebral body strength.The authors developed finite element models to predict the fraction of the total compressive force acting on the lumbar vertebral body that is carried by the shell. Parametric variations were investigated to determine how the fraction of shell force was affected by changes in shell thickness, shell and centrum modulus, centrum anistropy, and loading conditions.The fraction of compressive force carried by the shell increased from approximately 0 at the endplate to approximately 0.2 at the mid-transverse plane for a typical case. The shell force was highly sensitive to the degree of anisotropy of the trabecular centrum but was relatively insensitive to changes in shell thickness and the ratio of shell-to-centrum elastic modulus.The conflicting conclusions of previous studies about the structural roles of the vertebral shell and centrum can be explained by differences in their methods. Our findings support the claims that the shell accounts for only approximately 10% of vertebral strength in vivo and that the trabecular centrum is the dominant structural component of the vertebral body.

Although the trabecular bone of the human vertebral body has been well characterized, the thin "cortical" shell and endplate that surround the trabecular centrum have not. In addition, the accuracy of estimating the thickness of the shell and endplate using computed tomography (CT) has not been evaluated directly. To address these issues, we measured the thickness of the vertebral shell and endplate in the mid sagittal plane of 16 human L1 vertebral bodies using direct and CT based methods. Specimens were assigned to four equal sized groups based on age (middle-aged, mean age = 49 years; old, mean age = 84) and gender. We investigated the dependence of the shell and endplate thicknesses on age, gender, and anatomic region. Our findings indicate that the shell and endplate in vertebrae over age 45 are porous and often irregular, with an average thickness of approximately 0.35 mm. However, when measured from CT images, the vertebral shell and endplate appear significantly thicker, indicating that measurements based on clinical CT scans overestimate the thickness by a factor of at least two. In addition, our data indicated that, in the midsagittal plane, the anterior shell is thicker than the posterior shell or either endplate. Although these data indicated that thickness did not depend on age or gender, these particular findings are inconclusive given the small and heterogeneous sample we examined. We conclude that the so-called cortical shell and endplate of the vertebral body are thin (less than one-half of a millimeter) and porous, and perhaps are better thought of as thin membranes of fused trabeculae than as true cortices.

Vertebral fractures are more strongly associated with specific bone density, structure, and strength parameters than with areal BMD, but all of these variables are correlated.It is unclear whether the association of areal BMD (aBMD) with vertebral fracture risk depends on bone density per se, bone macro- or microstructure, overall bone strength, or spine load/bone strength ratios.From an age-stratified sample of Rochester, MN, women, we identified 40 with a clinically diagnosed vertebral fracture (confirmed semiquantitatively) caused by moderate trauma (cases; mean age, 78.6 +/- 9.0 yr) and compared them with 40 controls with no osteoporotic fracture (mean age, 70.9 +/- 6.8 yr). Lumbar spine volumetric BMD (vBMD) and geometry were assessed by central QCT, whereas microstructure was evaluated by high-resolution pQCT at the ultradistal radius. Vertebral failure load ( approximately strength) was estimated from voxel-based finite element models, and the factor-of-risk (phi) was determined as the ratio of applied spine loads to failure load.Spine loading (axial compressive force on L3) was similar in vertebral fracture cases and controls (e.g., for 90 degrees forward flexion, 2639 versus 2706 N; age-adjusted p = 0.173). However, fracture cases had inferior values for most bone density and structure variables. Bone strength measures were also reduced, and the factor-of-risk (phi) was 35-37% greater (worse) among women with a vertebral fracture. By age-adjusted logistic regression, relative risks for the strongest fracture predictor in each of the five main variable categories were bone density (total lumbar spine vBMD: OR per SD change, 2.2; 95% CI, 1.1-4.3), bone geometry (vertebral apparent cortical thickness: OR, 2.1; 95% CI, 1.1-4.1), bone microstructure (none significant); bone strength ("cortical" [outer 2 mm] compressive strength: OR, 2.5; 95% CI, 1.3-4.8), and factor-of-risk (phi for 90 degrees forward flexion/overall vertebral compressive strength: OR, 3.2; 95% CI, 1.4-7.5). These variables were correlated with spine aBMD (partial r, -0.32 to 0.75), but each was a stronger predictor of fracture in the logistic regression analyses.The association of aBMD with vertebral fracture risk is explained by its correlation with more specific bone density, structure, and strength parameters. These may allow deeper insights into fracture pathogenesis.

Abstract Vertebral strength, as estimated by finite element analysis of computed tomography (CT) scans, has not yet been compared against areal bone mineral density (BMD) by dual-energy X-ray absorptiometry (DXA) for prospectively assessing the risk of new clinical vertebral fractures. To do so, we conducted a case-cohort analysis of 306 men aged 65 years and older, which included 63 men who developed new clinically-identified vertebral fractures and 243 men who did not, all observed over an average of 6.5 years. Nonlinear finite element analysis was performed on the baseline CT scans, blinded to fracture status, to estimate L1 vertebral compressive strength and a load-to-strength ratio. Volumetric BMD by quantitative CT and areal BMD by DXA were also evaluated. We found that, for the risk of new clinical vertebral fracture, the age-adjusted hazard ratio per standard deviation change for areal BMD (3.2; 95% confidence interval [CI], 2.0–5.2) was significantly lower (p &amp;lt; 0.005) than for strength (7.2; 95% CI, 3.6–14.1), numerically lower than for volumetric BMD (5.7; 95% CI, 3.1–10.3), and similar for the load-to-strength ratio (3.0; 95% CI, 2.1–4.3). After also adjusting for race, body mass index (BMI), clinical center, and areal BMD, all these hazard ratios remained highly statistically significant, particularly those for strength (8.5; 95% CI, 3.6–20.1) and volumetric BMD (9.4; 95% CI, 4.1–21.6). The area-under-the-curve for areal BMD (AUC = 0.76) was significantly lower than for strength (AUC = 0.83, p = 0.02), volumetric BMD (AUC = 0.82, p = 0.05), and the load-to-strength ratio (AUC = 0.82, p = 0.05). We conclude that, compared to areal BMD by DXA, vertebral compressive strength and volumetric BMD consistently improved vertebral fracture risk assessment in this cohort of elderly men. © 2012 American Society for Bone and Mineral Research.

Background.Adults with osteogenesis imperfecta (OI) have a high risk of fracture.Currently, few treatment options are available, and bone anabolic therapies have not been tested in clinical trials for OI treatment.Methods.79 adults with OI were randomized to receive 20 μg recombinant human parathyroid hormone (teriparatide) or placebo for 18 months in a double-blind, placebo-controlled trial.The primary endpoint was the percent change in areal bone mineral density (aBMD) of the lumbar spine (LS), as determined by dualenergy X-ray absorptiometry.Secondary endpoints included percent change in bone remodeling markers and vertebral volumetric BMD (vBMD) by quantitative computed tomography, estimated vertebral strength by finite element analysis, and self-reported fractures.Results.Compared with the placebo group, the teriparatide group showed increased LS aBMD (6.1% ± 1.0% vs. 2.8% ± 1.0% change from baseline; P < 0.05) and total hip aBMD (2.6% ± 1.0% vs. -2.4% ± 1.0% change; P < 0.001).Vertebral vBMD and strength improved with teriparatide therapy (18% ± 6% and 15% ± 3% change, respectively), but declined with placebo (-5.0%± 6% and -2.0% ± 3% change; P < 0.05 for both comparisons).Serum procollagen type 1 N-terminal propeptide (P1NP) and urine collagen N-telopeptide (NTx) levels increased with teriparatide therapy (135% ± 14% and 64% ± 10% change, respectively).Teriparatide-induced elevation of P1NP levels was less pronounced in severe forms of OI (type III/IV) compared with the milder form (type I).Type I OI patients exhibited robust BMD increases with teriparatide; however, there was no observed benefit for those with type III/IV OI.There was no difference in self-reported fractures between the 2 groups.Conclusions.Adults with OI, particularly those with less severe disease (type I), displayed a teriparatide-induced anabolic response, as well as increased hip and spine aBMD, vertebral vBMD, and estimated vertebral strength.Trial registration.Clinicaltrials.govNCT00131469.

Large-deformation bending and buckling have long been proposed as failure mechanisms by which the strength of trabecular bone can be affected disproportionately to changes in bone density, and thus may represent an important aspect of bone quality. We sought here to quantify the contribution of large-deformation failure mechanisms on strength, to determine the dependence of these effects on bone volume fraction and architecture, and to confirm that the inclusion of large-deformation effects in high-resolution finite element models improves predictions of strength versus experiment. Micro-CT-based finite element models having uniform hard tissue material properties were created from 54 cores of human trabecular bone taken from four anatomic sites (age = 70+/-11; 24 male, 27 female donors), which were subsequently biomechanically tested to failure. Strength predictions were made from the models first including, then excluding, large-deformation failure mechanisms, both for compressive and tensile load cases. As expected, strength predictions versus experimental data for the large-deformation finite element models were significantly improved (p < 0.001) relative to the small deformation models in both tension and compression. Below a volume fraction of about 0.20, large-deformation failure mechanisms decreased trabecular strength from 5-80% for compressive loading, while effects were negligible above this volume fraction. Step-wise nonlinear multiple regression revealed that structure model index (SMI) and volume fraction (BV/TV) were significant predictors of these reductions in strength (R2 = 0.83, p < 0.03). Even so, some low-density specimens having nearly identical volume fraction and SMI exhibited up to fivefold differences in strength reduction. We conclude that within very low-density bone, the potentially important biomechanical effect of large-deformation failure mechanisms on trabecular bone strength is highly heterogeneous and is not well explained by standard architectural metrics.

Odanacatib, a cathepsin K inhibitor, increases spine and hip areal bone mineral density (BMD) in postmenopausal women with low BMD and cortical thickness in ovariectomized monkeys.The objective of the study was to examine the impact of odanacatib on the trabecular and cortical bone compartments and estimated strength at the hip and spine.This was a randomized, double-blind, 2-year trial.The study was conducted at a private or institutional practice.PARTICIPANTS included 214 postmenopausal women with low areal BMD.The intervention included odanacatib 50 mg or placebo weekly.Changes in areal BMD by dual-energy x-ray absorptiometry (primary end point, 1 year areal BMD change at lumbar spine), bone turnover markers, volumetric BMD by quantitative computed tomography (QCT), and bone strength estimated by finite element analysis were measured.Year 1 lumbar spine areal BMD percent change from baseline was 3.5% greater with odanacatib than placebo (P < .001). Bone-resorption marker C-telopeptide of type 1 collagen was significantly lower with odanacatib vs placebo at 6 months and 2 years (P < .001). Bone-formation marker procollagen I N-terminal peptide initially decreased with odanacatib but by 2 years did not differ from placebo. After 6 months, odanacatib-treated women had greater increases in trabecular volumetric BMD and estimated compressive strength at the spine and integral and trabecular volumetric BMD and estimated strength at the hip (P < .001). At the cortical envelope of the femoral neck, bone mineral content, thickness, volume, and cross-sectional area also increased from baseline with odanacatib vs placebo (P < .001 at 24 months). Adverse experiences were similar between groups.Over 2 years, odanacatib decreased bone resorption, maintained bone formation, increased areal and volumetric BMD, and increased estimated bone strength at both the hip and spine.

The combination of finite element modeling, biomechanics, and clinical computed tomography (CT) scanning-biomechanical CT (BCT)-is a powerful research technique for noninvasive assessment of whole-bone strength and is now being used in clinical research studies. Well supported by cadaver studies, the technique is providing substantial new insight into drug treatment effects, can show treatment effects earlier than dual-energy X-ray absorptiometry (DXA), and has shown greater sensitivity than DXA in fracture risk assessment. Because the technique can be used as an ancillary "add-on" analysis to previously acquired CT scans containing either the hip or spine, it should be possible to implement this technology clinically in a highly cost-effective manner. This strategy, if applied to those not previously tested by DXA, has the potential to greatly increase the number of individuals identified as being at high risk for osteoporotic fracture.

The microstructure of trabecular bone is usually perceived as a collection of plate-like and rod-like trabeculae, which can be determined from the emerging high-resolution skeletal imaging modalities such as micro-computed tomography (μCT) or clinical high-resolution peripheral quantitative CT (HR-pQCT) using the individual trabecula segmentation (ITS) technique. It has been shown that the ITS-based plate and rod parameters are highly correlated with elastic modulus and yield strength of human trabecular bone. In the current study, plate-rod (PR) finite element (FE) models were constructed completely based on ITS-identified individual trabecular plates and rods. We hypothesized that PR FE can accurately and efficiently predict elastic modulus and yield strength of human trabecular bone. Human trabecular bone cores from proximal tibia (PT), femoral neck (FN) and greater trochanter (GT) were scanned by μCT. Specimen-specific ITS-based PR FE models were generated for each μCT image and corresponding voxel-based FE models were also generated in comparison. Both types of specimen-specific models were subjected to nonlinear FE analysis to predict the apparent elastic modulus and yield strength using the same trabecular bone tissue properties. Then, mechanical tests were performed to experimentally measure the apparent modulus and yield strength. Strong linear correlations for both elastic modulus (r(2) = 0.97) and yield strength (r(2) = 0.96) were found between the PR FE model predictions and experimental measures, suggesting that trabecular plate and rod morphology adequately captures three-dimensional (3D) microarchitecture of human trabecular bone. In addition, the PR FE model predictions in both elastic modulus and yield strength were highly correlated with the voxel-based FE models (r(2) = 0.99, r(2) = 0.98, respectively), resulted from the original 3D images without the PR segmentation. In conclusion, the ITS-based PR models predicted accurately both elastic modulus and yield strength determined experimentally across three distinct anatomic sites. Trabecular plates and rods accurately determine elastic modulus and yield strength of human trabecular bone.

Background The prevalence of low testosterone levels in men increases with age, as does the prevalence of decreased mobility, sexual function, self-perceived vitality, cognitive abilities, bone mineral density, and glucose tolerance, and of increased anemia and coronary artery disease. Similar changes occur in men who have low serum testosterone concentrations due to known pituitary or testicular disease, and testosterone treatment improves the abnormalities. Prior studies of the effect of testosterone treatment in elderly men, however, have produced equivocal results. Purpose To describe a coordinated set of clinical trials designed to avoid the pitfalls of prior studies and to determine definitively whether testosterone treatment of elderly men with low testosterone is efficacious in improving symptoms and objective measures of age-associated conditions. Methods We present the scientific and clinical rationale for the decisions made in the design of this set of trials. Results We designed The Testosterone Trials as a coordinated set of seven trials to determine if testosterone treatment of elderly men with low serum testosterone concentrations and symptoms and objective evidence of impaired mobility and/or diminished libido and/or reduced vitality would be efficacious in improving mobility (Physical Function Trial), sexual function (Sexual Function Trial), fatigue (Vitality Trial), cognitive function (Cognitive Function Trial), hemoglobin (Anemia Trial), bone density (Bone Trial), and coronary artery plaque volume (Cardiovascular Trial). The scientific advantages of this coordination were common eligibility criteria, common approaches to treatment and monitoring, and the ability to pool safety data. The logistical advantages were a single steering committee, data coordinating center and data and safety monitoring board, the same clinical trial sites, and the possibility of men participating in multiple trials. The major consideration in participant selection was setting the eligibility criterion for serum testosterone low enough to ensure that the men were unequivocally testosterone deficient, but not so low as to preclude sufficient enrollment or eventual generalizability of the results. The major considerations in choosing primary outcomes for each trial were identifying those of the highest clinical importance and identifying the minimum clinically important differences between treatment arms for sample size estimation. Potential limitations Setting the serum testosterone concentration sufficiently low to ensure that most men would be unequivocally testosterone deficient, as well as many other entry criteria, resulted in screening approximately 30 men in person to randomize one participant. Conclusion Designing The Testosterone Trials as a coordinated set of seven trials afforded many important scientific and logistical advantages but required an intensive recruitment and screening effort.

In the randomized, placebo-controlled FREEDOM study of women aged 60 to 90 years with postmenopausal osteoporosis, treatment with denosumab once every 6 months for 36 months significantly reduced hip and new vertebral fracture risk by 40% and 68%, respectively. To gain further insight into this efficacy, we performed a nonlinear finite element analysis (FEA) of hip and spine quantitative computed tomography (QCT) scans to estimate hip and spine strength in a subset of FREEDOM subjects (n = 48 placebo; n = 51 denosumab) at baseline, 12, 24, and 36 months. We found that, compared with baseline, the finite element estimates of hip strength increased from 12 months (5.3%; p < 0.0001) and through 36 months (8.6%; p < 0.0001) in the denosumab group. For the placebo group, hip strength did not change at 12 months and decreased at 36 months (-5.6%; p < 0.0001). Similar changes were observed at the spine: strength increased by 18.2% at 36 months for the denosumab group (p < 0.0001) and decreased by -4.2% for the placebo group (p = 0.002). At 36 months, hip and spine strength increased for the denosumab group compared with the placebo group by 14.3% (p < 0.0001) and 22.4% (p < 0.0001), respectively. Further analysis of the finite element models indicated that strength associated with the trabecular bone was lost at the hip and spine in the placebo group, whereas strength associated with both the trabecular and cortical bone improved in the denosumab group. In conclusion, treatment with denosumab increased hip and spine strength as estimated by FEA of QCT scans compared with both baseline and placebo owing to positive treatment effects in both the trabecular and cortical bone compartments. These findings provide insight into the mechanism by which denosumab reduces fracture risk for postmenopausal women with osteoporosis.

Patient-specific phantomless calibration of computed tomography (CT) scans has the potential to simplify and expand the use of pre-existing clinical CT for quantitative bone densitometry and bone strength analysis for diagnostic and monitoring purposes. In this study, we quantified the inter-operator reanalysis precision errors for a novel implementation of patient-specific phantomless calibration, using air and either aortic blood or hip adipose tissue as internal calibrating reference materials, and sought to confirm the equivalence between phantomless and (traditional) phantom-based measurements. CT scans of the spine and hip for 25 women and 15 men (mean ± SD age of 67 ± 9 years, range 41–86 years), one scan per anatomic site per patient, were analyzed independently by two analysts using the VirtuOst software (O.N. Diagnostics, Berkeley, CA). The scans were acquired at 120 kVp, with a slice thickness/increment of 3 mm or less, on nine different CT scanner models across 24 different scanners. The main parameters assessed were areal bone mineral density (BMD) at the hip (total hip and femoral neck), trabecular volumetric BMD at the spine, and vertebral and femoral strength by finite element analysis; other volumetric BMD measures were also assessed. We found that the reanalysis precision errors for all phantomless measurements were ≤ 0.5%, which was as good as for phantom calibration. Regression analysis indicated equivalence of the phantom- versus phantomless-calibrated measurements (slope not different than unity, R2 ≥ 0.98). Of the main parameters assessed, non-significant paired mean differences (n = 40) between the two measurements ranged from 0.6% for hip areal BMD to 1.1% for mid-vertebral trabecular BMD. These results indicate that phantom-equivalent measurements of both BMD and finite element-derived bone strength can be reliably obtained from CT scans using patient-specific phantomless calibration.

ABSTRACT Methods now exist for analyzing previously taken clinical computed tomography (CT) scans to measure a dual-energy X-ray absorptiometry (DXA)-equivalent bone mineral density (BMD) at the hip and a finite element analysis–derived femoral strength. We assessed the efficacy of this “biomechanical CT” (BCT) approach for identifying patients at high risk of incident hip fracture in a large clinical setting. Using a case-cohort design sampled from 111,694 women and men aged 65 or older who had a prior hip CT scan, a DXA within 3 years of the CT, and no prior hip fracture, we compared those with subsequent hip fracture (n = 1959) with randomly selected sex-stratified controls (n = 1979) and analyzed their CT scans blinded to all other data. We found that the age-, race-, and body mass index (BMI)-adjusted hazard ratio (HR; per standard deviation) for femoral strength was significant before (women: HR = 2.8, 95% confidence interval [CI] 2.2–3.5; men: 2.8, 2.1–3.7) and after adjusting also for the (lowest) hip BMD T-score by BCT (women: 2.1, 1.4–3.2; men: 2.7, 1.6–4.6). The hazard ratio for the hip BMD T-score was similar between BCT and DXA for both sexes (women: 2.1, 1.8–2.5 BCT versus 2.1, 1.7–2.5 DXA; men: 2.8, 2.1–3.8 BCT versus 2.5, 2.0–3.2 DXA) and was higher than for the (lowest) spine/hip BMD T-score by DXA (women: 1.6, 1.4–1.9; men: 2.1, 1.6–2.7). Compared with the latter as a clinical-practice reference and using both femoral strength and the hip BMD T-score from BCT, sensitivity for predicting hip fracture was higher for BCT (women: 0.66 versus 0.59; men: 0.56 versus 0.48), with comparable respective specificity (women: 0.66 versus 0.67; men: 0.76 versus 0.78). We conclude that BCT analysis of previously acquired routine abdominal or pelvic CT scans is at least as effective as DXA testing for identifying patients at high risk of hip fracture. © 2018 American Society for Bone and Mineral Research.

ABSTRACT Romosozumab is a monoclonal antibody that inhibits sclerostin and has been shown to reduce the risk of fractures within 12 months. In a phase II, randomized, placebo-controlled clinical trial of treatment-naïve postmenopausal women with low bone mass, romosozumab increased bone mineral density (BMD) at the hip and spine by the dual effect of increasing bone formation and decreasing bone resorption. In a substudy of that trial, which included placebo and teriparatide arms, here we investigated whether those observed increases in BMD also resulted in improvements in estimated strength, as assessed by finite element analysis. Participants received blinded romosozumab s.c. (210 mg monthly) or placebo, or open-label teriparatide (20 μg daily) for 12 months. CT scans, obtained at the lumbar spine (n = 82) and proximal femur (n = 46) at baseline and month 12, were analyzed with finite element software (VirtuOst, O.N. Diagnostics) to estimate strength for a simulated compression overload for the spine (L1 vertebral body) and a sideways fall for the proximal femur, all blinded to treatment assignment. We found that, at month 12, vertebral strength increased more for romosozumab compared with both teriparatide (27.3% versus 18.5%; p = 0.005) and placebo (27.3% versus –3.9%; p &amp;lt; 0.0001); changes in femoral strength for romosozumab showed similar but smaller changes, increasing more with romosozumab versus teriparatide (3.6% versus –0.7%; p = 0.027), and trending higher versus placebo (3.6% versus −0.1%; p = 0.059). Compartmental analysis revealed that the bone-strengthening effects for romosozumab were associated with positive contributions from both the cortical and trabecular bone compartments at both the lumbar spine and hip. Taken together, these findings suggest that romosozumab may offer patients with osteoporosis a new bone-forming therapeutic option that increases both vertebral and femoral strength within 12 months. © 2017 American Society for Bone and Mineral Research.

It is not clear which non-invasive method is most effective for predicting strength of the proximal femur in those at highest risk of fracture. The primary aim of this study was to compare the abilities of dual energy X-ray absorptiometry (DXA)-derived aBMD, quantitative computed tomography (QCT)-derived density and volume measures, and finite element analysis (FEA)-estimated strength to predict femoral failure load. We also evaluated the contribution of cortical and trabecular bone measurements to proximal femur strength. We obtained 76 human cadaveric proximal femurs (50 women and 26 men; age 74±8.8years), performed imaging with DXA and QCT, and mechanically tested the femurs to failure in a sideways fall configuration at a high loading rate. Linear regression analysis was used to construct the predictive model between imaging outcomes and experimentally-measured femoral strength for each method. To compare the performance of each method we used 3-fold cross validation repeated 10 times. The bone strength estimated by QCT-based FEA predicted femoral failure load (R2adj=0.78, 95%CI 0.76-0.80; RMSE=896N, 95%CI 830-961) significantly better than femoral neck aBMD by DXA (R2adj=0.69, 95%CI 0.66-0.72; RMSE=1011N, 95%CI 952-1069) and the QCT-based model (R2adj=0.73, 95%CI 0.71-0.75; RMSE=932N, 95%CI 879-985). Both cortical and trabecular bone contribute to femoral strength, the contribution of cortical bone being higher in femurs with lower trabecular bone density. These findings have implications for optimizing clinical approaches to assess hip fracture risk. In addition, our findings provide new insights that will assist in interpretation of the effects of osteoporosis treatments that preferentially impact cortical versus trabecular bone.

The surgeon general of the USA defines osteoporosis as "a skeletal disorder characterized by compromised bone strength, predisposing to an increased risk of fracture." Measuring bone strength, Biomechanical Computed Tomography analysis (BCT), namely, finite element analysis of a patient's clinical-resolution computed tomography (CT) scan, is now available in the USA as a Medicare screening benefit for osteoporosis diagnostic testing. Helping to address under-diagnosis of osteoporosis, BCT can be applied "opportunistically" to most existing CT scans that include the spine or hip regions and were previously obtained for an unrelated medical indication. For the BCT test, no modifications are required to standard clinical CT imaging protocols. The analysis provides measurements of bone strength as well as a dual-energy X-ray absorptiometry (DXA)-equivalent bone mineral density (BMD) T-score at the hip and a volumetric BMD of trabecular bone at the spine. Based on both the bone strength and BMD measurements, a physician can identify osteoporosis and assess fracture risk (high, increased, not increased), without needing confirmation by DXA. To help introduce BCT to clinicians and health care professionals, we describe in this review the currently available clinical implementation of the test (VirtuOst), its application for managing patients, and the underlying supporting evidence; we also discuss its main limitations and how its results can be interpreted clinically. Together, this body of evidence supports BCT as an accurate and convenient diagnostic test for osteoporosis in both sexes, particularly when used opportunistically for patients already with CT. Biomechanical Computed Tomography analysis (BCT) uses a patient's CT scan to measure both bone strength and bone mineral density at the hip or spine. Performing at least as well as DXA for both diagnosing osteoporosis and assessing fracture risk, BCT is particularly well-suited to "opportunistic" use for the patient without a recent DXA who is undergoing or has previously undergone CT testing (including hip or spine regions) for an unrelated medical condition.

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 microns and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 microns resolution, the differences in apparent Young's modulus at 40 microns resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 microns resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.

As with any structure, the structural capacity of the proximal femur depends on the applied loads and these can vary as a function of impact direction during a fall. However, despite its potential importance in hip fracture risk assessment, the relative importance of impact direction is unknown. To investigate the role of impact direction in hip fracture, we developed a detailed finite element model of the proximal femur. We analyzed four loading configurations that represent a range of possible falls on the greater trochanter. Our results indicate that a change in the angle between the line of action of the applied force and the axis of the femoral neck from 0 degrees (representing a direct lateral impact) to 45 degrees (representing a posterolateral impact) reduced structural capacity by 26%. This weakening of the femur with changes in impact direction is comparable to the weakening associated with 2-3 decades of age-related bone loss. Our result elucidates the independent contribution of fall mechanics to hip fracture risk by identifying an aspect of the fall (the direction of impact) that is an important determinant of fall severity. The results can also be incorporated into a refined clinical method for assessment of hip fracture risk that accounts for the complex interactions between fall severity and bone fragility.

We performed a series of uniaxial compression tests on wet bovine trabecular bone to compare both modulus and strength when measured using 2:1 aspect ratio (10 mm long, 5 mm diameter) cylinders (n = 30) and 5 mm cubes (n = 29). We also compared the correlation coefficients in the resulting modulus-density and strength-density regressions and the standard errors of the estimate. When comparing the mean values of modulus and strength for each group, the confounding variations in apparent density were accounted for with an analysis of covariance. The Fisher's Z transformation was used to compare the correlation coefficients statistically. Results from the analysis of covariance indicated that the modulus and strength of the cubes were higher by 36% (p < 0.01) and 18% (p < 0.05), respectively, with respect to the 2:1 cylinder values. The correlation coefficients in the modulus-density and strength-density regressions were not sensitive to the regression model (linear versus power law). However, correlation coefficients for both modulus-density and strength-density regressions were higher (p < 0.05) for the 2:1 cylinders (r = 0.90, modulus; r = 0.94, strength) than for the cubes (r = 0.57, modulus; r = 0.82, strength). In addition, the standard errors of the estimate in both modulus and strength were substantially lower for the 2:1 cylinders. These data indicate that both modulus and strength can depend on the specimen geometry when using conventional compression testing techniques. We conclude, therefore, that inter-study comparisons of modulus and strength may be invalid if these confounding effects of different specimen geometries are not addressed. Our data also indicate that density can better explain the observed variance in modulus and strength when 2:1 cylinders are used as opposed to cubes. Using this phenomenon as a rationale for choosing a standard specimen gometry, we recommend that the 2:1 cylinder be used as a standard specimen in studies designed to determine the effects of various treatments on the uniaxial compressive modulus and strength of trabecular bone.

The biomechanical performance of long bones is dictated by four key factors: element size, element shape, loading conditions, and material properties. Our understanding of the latter of these has been mostly limited to eutherian mammals and birds, which show similarity. Whether their possession of comparable material properties reflects common ancestry or independent evolution is uncertain. In the present analysis, we tested the bending strength, modulus, and failure strains of the femur and its pterygiophore homolog in actinpterygian fish. Sixty-nine specimens representing basal character states in seven major vertebrate crown clades were tested. These data were then coupled with avian and mammalian data from the literature and analyzed in an evolutionary context using phylogenetic character analysis. Mean values of 188 MPa for yield strength, 22.4 GPa for Young's modulus, and 8,437 mu epsilon for yield strain were obtained for the long bones. Analysis of variance (ANOVA) revealed comparable values between clades that span a 30,000-fold range of body mass. We conclude that material properties of the first long bones 475 million years ago were conserved throughout evolution. Major locomotory challenges to femora during vertebrate evolution were almost solely accomplished by modifications of element size and shape.

The shear properties of trabecular bone, in particular the shear failure strains, are not well understood despite their potential importance in age-related fractures and prosthesis loosening. We hypothesized that shear failure strains (yield and ultimate) are independent of apparent density and trabecular orientation, i.e. are homogeneous and isotropic. We measured the shear failure properties of bovine tibial trabecular bone, where specimens were loaded to failure in torsion longitudinally (n = 25) or transversely (n = 23) relative to the primary trabecular orientation. We found that although failure stresses depended strongly on apparent density (r2 = 0.61 − 0.80), failure strains were independent of apparent density for both trabecular orientations. Although the mean (± S.D.) yield strain in the longitudinal group (1.46 ± 0.19%) was 10% higher (p = 0.01) than in the transverse group (1.33 ± 0.15%), indicating a slight anisotropy of shear yield strains, the mean ultimate strains did not depend on trabecular orientation (longitudinal group 4.60 ± 0.77% vs transverse group 4.24 ± 1.25%, p = 0.20). These findings indicate that shear failure strains are homogeneous and largely isotropic. By combining our shear data with compressive data from a previous experiment, we also predicted that trabecular bone can fail in shear when subjected to compressive loads that are not aligned with the principal trabecular orientation. If this prediction holds for human bone, shear may be a dominant failure mode during off-axis loading of trabecular bone in vivo, such as during falls on the hip.

Abstract With the etiology of osteoporotic fractures as motivation, the goal of this study was to characterize the mechanical behavior of human trabecular bone after overloading. Specifically, we quantified the reductions in modulus and strength and the development of residual deformations and determined the dependence of these parameters on the applied strain and apparent density. Forty cylindrical specimens of human L1 vertebral trabecular bone were destructively loaded in compression at 0.5% strain per second to strains of up to 3.0% and then immediately unloaded to zero stress and reloaded. (An ancillary experiment on more readily available bovine bone had been performed previously to develop this testing protocol.) In general, the reloading stress‐strain curve had a short initial nonlinear region with a tangent modulus similar to Young's modulus. This was followed by an approximately linear region spanning to 0.7% strain, with a reduced residual modulus. The reloading curve always approached the extrapolated envelope of the original loading curve. Percent modulus reduction (between Young's and residual), a quantitative measure of mechanical damage, ranged from 5.2 to 91.0% across the specimens. It increased with increasing plastic strain (r 2 = 0.97) but was not related to modulus or apparent density. Percent strength reduction, in the range of 3.6–63.8%, increased with increasing plastic strain (r 2 = 0.61) and decreasing apparent density (r 2 = 0.23). The residual strains of up to 1.05% depended strongly on applied strain (r 2 = 0.96). Statistical comparisons with previous data for bovine tibial bone lend substantial generality to these trends and provide an envelope of expected behavior for other sites. In addition to providing a basis for biomechanical analysis of the effects of damage in trabecular bone at the organ level, these findings support the concept that occasional overloads may increase the risk of fracture by substantially degrading the mechanical properties of the underlying trabecular bone.

Although the efficacy of various measures for the assessment of trabecular bone architecture has been widely studied, the impact of spatial resolution on the estimation of these measures has remained relatively unexplored. In this study, ten cubes each of human trabecular bone from the femur and vertebral bodies were obtained from nine cadavers (four males and five females), aged 23–67 years (mean 42.3 years). These specimens were serially milled and imaged at a resolution of 40 μm to produce three-dimensional digitizations from which traditional morphometric and structural anisotropy measures could be computed based on a three-dimensional approach. The cubes were then artificially degraded to an in-plane resolution of 100 μm and an out-of-plane (slice) resolution of 100–1000 μm. These resolutions mimicked in vivo resolutions as seen using magnetic resonance (MR) imaging. All images, original and degraded, were individually segmented using a thresholding algorithm, and both the traditional morphometric and structural anisotropy measures were recomputed. The choice of slice direction was varied along the superior-inferior (axial), anterior-posterior (coronal), and medial-lateral (sagittal) directions to minimize the impact of the lower slice resolution on the architectural measures. It was found that traditional morphometric measures such as trabecular spacing and trabecular number showed weak resolution dependency; measures such as trabecular thickness, however, showed strong resolution dependency and required very high resolutions for precise measurement. In the case of the femur specimens, both structural anisotropy as well as the preferred orientation showed a strong resolution dependency. The resolution dependency of these parameters could be minimized for the femur and the vertebral body specimens if the slice direction was taken along the superior-inferior direction.

Computed tomography-based finite element analysis represents a powerful research tool for investigating the mechanics of skeletal fractures. To provide evidence that this technique can be used to predict failure loads and fracture patterns for bone structures, we compared the observed and predicted failure behaviors of 18 midsagittal sections. 10 mm thick, cut from human vertebral bodies. The specimens were scanned by computed tomography, and finite element models were generated with use of empirically determined density-property relations to assign element-specific material properties. The specimens were loaded to failure in uniaxial compression, and the models were analyzed under matching conditions. The models provided predictions of yield load that were strongly correlated with experimentally measured values (r2 > 0.86) and were typically within 25% of measured values. Predicted stiffness values were moderately correlated with measured values, but large absolute differences existed between them. Comparisons between regions of observed fracture and of high predicted strain indicated that strain was an accurate indicator of the pattern of local fracture in more than two-thirds of the bone specimens. In addition, strain contour plots provided better indicators of local fracture than did stress plots in these heterogeneous bone structures. We conclude that computed tomography-based finite element analysis can be used successfully to predict both global and local failure behavior of simplified skeletal structures.

A theoretical analysis was performed to characterize potential experimental artifacts in conventional compression testing of trabecular bone, where strains are based on the relative displacements of the two loading platens. We assumed that the total experimental artifact for modulus was the sum of a damage and friction artifact and derived equations to describe these artifacts. The two unknown constants in these equations were found using a combination of data derived from linear finite element analyses and in vitro uniaxial compression tests. Subsequent finite element analyses allowed estimation of the artifacts for a wide range of specimens (cube, 1:4-3:1 aspect ratio cylinders). If friction is completely eliminated at the specimen-platen interface, the Young's modulus of a 5 mm sized (1:1 aspect ratio dimension) specimen which has a damage artifact due to machining may be underestimated by at least 45% regardless of specimen geometry; otherwise, the platens modulus may vary from less than 30 to over 175% of the Young's modulus, depending upon the specimen geometry and Poisson's ratio of the bone. Increasing the specimen size reduces the artifact only slightly. Since Poisson's ratio can be large for trabecular bone and is rarely known a priori, the precision of the conventional compression test will, therefore, be poor unless friction is completely eliminated at the specimen-platen interface. However, without friction at the interface, the platens modulus will always underestimate Young's modulus, thereby reducing the accuracy of this test. There was also evidence that the strength may be affected by these artifacts. Taken together, these data suggest that the conventional compression test can be precise but is rarely accurate, and that inter-study comparisons should be made with caution. Use of other methods such as ultrasound or direct attachment of extensometers to material away from the platens may overcome problems with accuracy. Finally, a protocol that eliminates friction and uses a 2:1 aspect ratio specimen may optimize precision.

Repetitive, low-intensity loading from normal daily activities can generate fatigue damage in trabecular bone, a potential cause of spontaneous fractures of the hip and spine. Finite element models of trabecular bone (Guo et al., 1994) suggest that both creep and slow crack growth contribute to fatigue failure. In an effort to characterize these damage mechanisms experimentally, we conducted fatigue and creep tests on 85 waisted specimens of trabecular bone obtained from 76 bovine proximal tibiae. All applied stresses were normalized by the previously measured specimen modulus. Fatigue tests were conducted at room temperature; creep tests were conducted at 4, 15, 25, 37, 45, and 53 degrees C in a custom-designed apparatus. The fatigue behavior was characterized by decreasing modulus and increasing hysteresis prior to failure. The hysteresis loops progressively displaced along the strain axis, indicating that creep was also involved in the fatigue process. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates. Strong and highly significant power-law relationships were found between cycles-to-failure, time-to-failure, steady-state creep rate, and the applied loads. Creep analyses of the fatigue hysteresis loops also generated strong and highly significant power law relationships for time-to-failure and steady-state creep rate. Lastly, the products of creep rate and time-to-failure were constant for both the fatigue and creep tests and were equal to the measured failure strains, suggesting that creep plays a fundamental role in the fatigue behavior of trabecular bone. Additional analysis of the fatigue strain data suggests that creep and slow crack growth are not separate processes that dominate at high and low loads, respectively, but are present throughout all stages of fatigue.

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.

Advances in micro-scanning technology have led to renewed clinical interest in the ability to predict bone strength using finite element (FE) analysis based on images with resolutions in the range of 80 microm. Using such images, we sought to determine whether predictions of yield stress provided by nonlinear FE models could improve correlations with bone strength as compared to the use of predictions of elastic modulus from linear FE models, and if this effect depended on voxel size or bone volume fraction. Linear and nonlinear FE analyses were conducted for 46 trabecular cores from three human anatomic sites using element sizes ranging from 20 to 120 microm to obtain measures of apparent yield stress and elastic modulus, and these measures were correlated against the predicted yield stress from the 20 microm models (assumed to be the gold standard strength for this study). Results indicated that when considering all samples and any resolution, yield stress and elastic modulus were both excellent predictors of strength (R2>0.99). When only low-density samples (BV/TV<0.15) were considered, yield stress was better correlated with 20 microm-strength than was elastic modulus (R2 increased from 0.93 to 0.99 at 40 microm and from 0.90 to 0.95 at 80 microm). However, at a voxel size of 120 microm, the predictive ability of yield stress was slightly less than that of stiffness, likely due to the large convergence-related errors that could develop with larger element sizes. As expected, a limit was observed in the ability of elastic modulus to predict strength--the predictive ability of elastic modulus measured at 20 microm was comparable to that of yield strength at 80 microm. We also found that strength predictions from FE models at clinical-type resolutions had nearly the same power to detect bone quality effects via variations in strength-density relationships as did high-resolution models. We conclude that nonlinear FE models can account for additional variations in strength relative to linear models when using images at resolutions of approximately 80 microm and less, and such models offer a promising method for examining microarchitecture-related bone quality effects associated with aging, disease, and treatment.

The mechanical behavior of damaged trabecular bone may play a role in the etiology of age-related spine fractures since damaged bone exists in and may weaken the elderly vertebral body. To describe some characteristics of damaged trabecular bone, we measured the changes in modulus and strength that occur when bovine trabecular bone is loaded in compression to various strains beyond its elastic range. Twenty-three reduced-section specimens, taken from 17 different bones, were loaded from 0-X-0-9% strain, where X was one of four strains: 1.0% (n = 7), 2.5% (n = 6), 4.0% (n = 5), or 5.5% (n = 5). We found that modulus was reduced for all applied strains, whereas strength was reduced only for strain levels > or = 2.5%; the percentage changes in modulus and strength were independent of Young's modulus but were highly dependent on the magnitude of the applied strains; modulus was always reduced more than strength; and simple statistical models, using knowledge of only the applied strains, predicted well the percentage reductions in modulus (r2 = 0.97) and strength (r2 = 0.74). The modulus reductions reported here are in qualitative agreement with those for cortical bone in tensile loading, supporting the concept that the damage behaviors of cortical and trabecular bone are similar for low strains (< or = 4.0%). In addition, because modulus was always reduced more than strength, damaged trabecular bone may be stress protected in vivo by redistribution of stresses to undamaged bone.

The biomechanical mechanisms underlying sex-specific differences in age-related vertebral fracture rates are ill defined. To gain insight into this issue, we used finite element analysis of clinical computed tomography (CT) scans of the vertebral bodies of L3 and T10 of young and old men and women to assess age- and sex-related differences in the strength of the whole vertebra, the trabecular compartment, and the peripheral compartment (the outer 2 mm of vertebral bone, including the thin cortical shell). We sought to determine whether structural and geometric changes with age differ in men and women, making women more susceptible to vertebral fractures. As expected, we found that vertebral strength decreased with age 2-fold more in women than in men. The strength of the trabecular compartment declined significantly with age for both sexes, whereas the strength of the peripheral compartment decreased with age in women but was largely maintained in men. The proportion of mechanical strength attributable to the peripheral compartment increased with age in both sexes and at both vertebral levels. Taken together, these results indicate that men and women lose vertebral bone differently with age, particularly in the peripheral (cortical) compartment. This differential bone loss explains, in part, a greater decline in bone strength in women and may contribute to the higher incidence of vertebral fractures among women than men.

The role of trabecular microarchitecture in whole-vertebral biomechanical behavior remains unclear, and its influence may be obscured by such factors as overall bone mass, bone geometry, and the presence of the cortical shell. To address this issue, 22 human T(9) vertebral bodies (11 female; 11 male; age range: 53-97 yr, 81.5 +/- 9.6 yr) were scanned with microCT and analyzed for measures of trabecular microarchitecture, BMC, cross-sectional area, and cortical thickness. Sixteen of the vertebrae were biomechanically tested to measure compressive strength. To estimate vertebral compressive stiffness with and without the cortical shell for all 22 vertebrae, two high-resolution finite element models per specimen-one intact model and one with the shell removed-were created from the microCT scans and virtually compressed. Results indicated that BMC and the structural model index (SMI) were the individual parameters most highly associated with strength (R(2) = 0.57 each). Adding microarchitecture variables to BMC in a stepwise multiple regression model improved this association (R(2) = 0.85). However, the microarchitecture variables in that regression model (degree of anisotropy, bone volume fraction) differed from those when BMC was not included in the model (SMI, mean trabecular thickness), and the association was slightly weaker for the latter (R(2) = 0.76). The finite element results indicated that the physical presence of the cortical shell did not alter the relationships between microarchitecture and vertebral stiffness. We conclude that trabecular microarchitecture is associated with whole-vertebral biomechanical behavior and that the role of microarchitecture is mediated by BMC but not by the cortical shell.

We evaluated the effects of resorption cavities on cancellous bone strength using computational methods. Adding cavities to cancellous bone caused reductions in strength and stiffness that were greater than expected from the associated changes in bone volume and more pronounced when cavities were targeted to regions of high tissue strain.The amount of bone turnover in the skeleton has recently been implicated as a factor influencing bone strength. One mechanism proposed to explain this effect is that resorption cavities reduce the effective thickness of trabeculae and modify local stress distributions leading to reduced mechanical performance of the entire structure. In this study, we tested the plausibility of this mechanism.High-resolution finite element models were created from muCT images of 16 vertebral cancellous bone samples, as well as from images of the samples in which cavities had been added digitally-either at regions of high strain (targeted) or placed at random on the bone surface (nontargeted). The effect of resorption cavities on predicted bone strength and stiffness was evaluated by comparing the relationships between mechanical properties and bone volume fraction among the three groups (the original images, those with nontargeted cavities, and those with targeted cavities).Addition of resorption cavities modified the relationship between mechanical properties and bone volume fraction in the finite element models such that, for a given bone volume fraction, stiffness and yield strength were reduced compared with the original images (p < 0.05). The differences in yield strength-volume fraction relationships between the original models and those with targeted cavities were significantly greater than those between the original models and those with nontargeted cavities (p < 0.05). None of the differences in predicted mechanical properties per unit bone volume fraction could be accounted for by 3D measures of microarchitecture.Resorption cavities may influence cancellous bone strength and stiffness independent of their effect on bone volume. The effects of cavities on bone mechanical performance relative to bone volume are greater when cavities are targeted to regions of high strain and cannot be predicted using standard microarchitecture measures.

Finite-element analysis (FEA) of quantitative computed tomography (QCT) scans can estimate site-specific whole-bone strength. However, it is uncertain whether the site-specific detail included in FEA-estimated proximal femur (hip) strength can determine fracture risk at sites with different biomechanical characteristics. To address this question, we used FEA of proximal femur QCT scans to estimate hip strength and load-to-strength ratio during a simulated sideways fall and measured total hip areal and volumetric bone mineral density (aBMD and vBMD) from QCT images in an age-stratified random sample of community-dwelling adults age 35 years or older. Among 314 women (mean age ± SD: 61 ± 15 years; 235 postmenopausal) and 266 men (62 ± 16 years), 139 women and 104 men had any prevalent fracture, whereas 55 Women and 28 men had a prevalent osteoporotic fracture that had occurred at age 35 years or older. Odds ratios by age-adjusted logistic regression analysis for prevalent overall and osteoporotic fractures each were similar for FEA hip strength and load-to-strength ratio, as well as for total hip aBMD and vBMD. C-statistics (estimated areas under ROC curves) also were similar [eg, 0.84 to 0.85 (women) and 0.75 to 0.78 (men) for osteoporotic fractures]. In women and men, the association with prevalent osteoporotic fractures increased below an estimated hip strength of approximately 3000 N. Despite its site-specific nature, FEA-estimated hip strength worked equally well at predicting prevalent overall and osteoporotic fractures. Furthermore, an estimated hip strength below 3000 N may represent a critical level of systemic skeletal fragility in both sexes that warrants further investigation.

Because they are not reliably discriminated by areal bone mineral density (aBMD) measurements, it is unclear whether minimal vertebral deformities represent early osteoporotic fractures. To address this, we compared 90 postmenopausal women with no deformity (controls) with 142 women with one or more semiquantitative grade 1 (mild) deformities and 51 women with any grade 2-3 (moderate/severe) deformities. aBMD was measured by dual-energy X-ray absorptiometry (DXA), lumbar spine volumetric bone mineral density (vBMD) and geometry by quantitative computed tomography (QCT), bone microstructure by high-resolution peripheral QCT at the radius (HRpQCT), and vertebral compressive strength and load-to-strength ratio by finite-element analysis (FEA) of lumbar spine QCT images. Compared with controls, women with grade 1 deformities had significantly worse values for many bone density, structure, and strength parameters, although deficits all were much worse for the women with grade 2-3 deformities. Likewise, these skeletal parameters were more strongly associated with moderate to severe than with mild deformities by age-adjusted logistic regression. Nonetheless, grade 1 vertebral deformities were significantly associated with four of the five main variable categories assessed: bone density (lumbar spine vBMD), bone geometry (vertebral apparent cortical thickness), bone strength (overall vertebral compressive strength by FEA), and load-to-strength ratio (45-degree forward bending ÷ vertebral compressive strength). Thus significantly impaired bone density, structure, and strength compared with controls indicate that many grade 1 deformities do represent early osteoporotic fractures, with corresponding implications for clinical decision making.

To gain insight into the clinical effect of teriparatide and alendronate on the hip, we performed non-linear finite element analysis of quantitative computed tomography (QCT) scans from 48 women who had participated in a randomized, double-blind clinical trial comparing the effects of 18-month treatment of teriparatide 20 μg/d or alendronate 10mg/d. The QCT scans, obtained at baseline, 6, and 18 months, were analyzed for volumetric bone mineral density (BMD) of trabecular bone, the peripheral bone (defined as all the cortical bone plus any endosteal trabecular bone within 3 mm of the periosteal surface), and the integral bone (both trabecular and peripheral), and for overall femoral strength in response to a simulated sideways fall. At 18 months, we found in the women treated with teriparatide that trabecular volumetric BMD increased versus baseline (+4.6%, p<0.001), peripheral volumetric BMD decreased (-1.1%, p<0.05), integral volumetric BMD (+1.0%, p=0.38) and femoral strength (+5.4%, p=0.06) did not change significantly, but the ratio of strength to integral volumetric BMD ratio increased (+4.0%, p=0.04). An increase in the ratio of strength to integral volumetric BMD indicates that overall femoral strength, compared to baseline, increased more than did integral density. For the women treated with alendronate, there were small (<1.0%) but non-significant changes compared to baseline in all these parameters. The only significant between-treatment difference was in the change in trabecular volumetric BMD (p<0.005); related, we also found that, for a given change in peripheral volumetric BMD, femoral strength increased more for teriparatide than for alendronate (p=0.02). We conclude that, despite different compartmental volumetric BMD responses for these two treatments, we could not detect any overall difference in change in femoral strength between the two treatments, although femoral strength increased more than integral volumetric BMD after treatment with teriparatide.

Although age-related variations in areal bone mineral density (aBMD) and the prevalence of osteoporosis have been well characterized, there is a paucity of data on femoral strength in the population. Addressing this issue, we used finite-element analysis of quantitative computed tomographic scans to assess femoral strength in an age-stratified cohort of 362 women and 317 men, aged 21 to 89 years, randomly sampled from the population of Rochester, MN, and compared femoral strength with femoral neck aBMD. Percent reductions over adulthood were much greater for femoral strength (55% in women, 39% in men) than for femoral neck aBMD (26% in women, 21% in men), an effect that was accentuated in women. Notable declines in strength started in the mid-40s for women and one decade later for men. At advanced age, most of the strength deficit for women compared with men was a result of this decade-earlier onset of strength loss for women, this factor being more important than sex-related differences in peak bone strength and annual rates of bone loss. For both sexes, the prevalence of "low femoral strength" (<3000 N) was much higher than the prevalence of osteoporosis (femoral neck aBMD T-score of -2.5 or less). We conclude that age-related declines in femoral strength are much greater than suggested by age-related declines in femoral neck aBMD. Further, far more of the elderly may be at high risk of hip fracture because of low femoral strength than previously assumed based on the traditional classification of osteoporosis.

Endplate failure occurs frequently in osteoporotic vertebral fractures and may be related to the development of high tensile strain. To determine whether the highest tensile strains in the vertebra occur in the endplates, and whether such high tensile strains are associated with the material behavior of the intervertebral disc, we used micro-CT-based finite element analysis to assess tissue-level strains in 22 elderly human vertebrae (81.5 ± 9.6 years) that were compressed through simulated intervertebral discs. In each vertebra, we compared the highest tensile and compressive strains across the different compartments: endplates, cortical shell, and trabecular bone. The influence of Poisson-type expansion of the disc on the results was determined by compressing the vertebrae a second time in which we suppressed the Poisson expansion. We found that the highest tensile strains occurred within the endplates whereas the highest compressive strains occurred within the trabecular bone. The ratio of strain to assumed tissue-level yield strain was the highest for the endplates, indicating that the endplates had the greatest risk of initial failure. Suppressing the Poisson expansion of the disc decreased the amount of highly tensile-strained tissue in the endplates by 79.4 ± 11.3%. These results indicate that the endplates are at the greatest risk of initial failure due to the development of high tensile strains, and that such high tensile strains are associated with the Poisson expansion of the disc. We conclude that initial failure of the vertebra is associated with high tensile strains in the endplates, which in turn are influenced by the material behavior of the disc.

Bone strength and fracture resistance are determined by bone mineral density (BMD) and structural, mechanical, and geometric properties of bone. DESIGN, SETTING, AND OBJECTIVES: This randomized, double-blind, placebo-controlled outpatient study evaluated effects of once-monthly oral ibandronate on hip and lumbar spine BMD and calculated strength using quantitative computed tomography (QCT) with finite element analysis (FEA) and dual-energy x-ray absorptiometry (DXA) with hip structural analysis (HSA).Participants were women aged 55-80 yr with BMD T-scores -2.0 or less to -5.0 or greater (n = 93).Oral ibandronate 150 mg/month (n = 47) or placebo (n = 46) was administered for 12 months.The primary end point was total hip QCT BMD change from baseline; secondary end points included other QCT BMD sites, FEA, DXA, areal BMD, and HSA. All analyses were exploratory, with post hoc P values.Ibandronate increased integral total hip QCT BMD and DXA areal BMD more than placebo at 12 months (treatment differences: 2.2%, P = 0.005; 2.0%, P = 0.003). FEA-derived hip strength to density ratio and femoral, peripheral, and trabecular strength increased with ibandronate vs. placebo (treatment differences: 4.1%, P < 0.001; 5.9%, P < 0.001; 2.5%, P = 0.011; 3.5%, P = 0.003, respectively). Ibandronate improved vertebral, peripheral, and trabecular strength and anteroposterior bending stiffness vs. placebo [7.1% (P < 0.001), 7.8% (P < 0.001), 5.6% (P = 0.023), and 6.3% (P < 0.001), respectively]. HSA-estimated femoral narrow neck cross-sectional area and moment of inertia and outer diameter increased with ibandronate vs. placebo (respectively 3.6%, P = 0.003; 4.0%, P = 0.052; 2.2%, P = 0.049).Once-monthly oral Ibandronate for 12 months improved hip and spine BMD measured by QCT and DXA and strength estimated by FEA of QCT scans.

The etiology of hip fractures remains unclear but might be elucidated by an improved understanding of the microstructural failure mechanisms of the human proximal femur during a sideways fall impact. In this context, we biomechanically tested 12 cadaver proximal femurs (aged 76 ± 10 years; 8 female, 4 male) to directly measure strength for a sideways fall and also performed micro-computed tomography (CT)-based, nonlinear finite element analysis of the same bones (82-micron-sized elements, ∼120 million elements per model) to estimate the amount and location of internal tissue-level failure (by ductile yielding) at initial structural failure of the femur. We found that the correlation between the directly measured yield strength of the femur and the finite element prediction was high (R(2) = 0.94, p < 0.0001), supporting the validity of the finite element simulations of failure. In these simulations, the failure of just a tiny proportion of the bone tissue (1.5% to 6.4% across all bones) led to initial structural failure of the femur. The proportion of failed tissue, estimated by the finite element models, decreased with decreasing measured femoral strength (R(2) = 0.88, p < 0.0001) and was more highly correlated with measured strength than any measure of bone volume, mass, or density. Volume-wise, trabecular failure occurred earlier and was more prominent than cortical failure in all femurs and dominated in the very weakest femurs. Femurs with low measured strength relative to their areal bone mineral density (BMD) (by dual-energy X-ray absorptiometry [DXA]) had a low proportion of trabecular bone compared with cortical bone in the femoral neck (p < 0.001), less failed tissue (p < 0.05), and low structural redundancy (p < 0.005). We conclude that initial failure of the femur during a sideways fall is associated with failure of just a tiny proportion of the bone tissue, failure of the trabecular tissue dominating in the very weakest femurs owing in part to a lack of structural redundancy.

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.

Teriparatide is a skeletal anabolic treatment for patients with osteoporosis at high risk for fracture. Because adequate clinical trials have not yet been conducted to assess the efficacy of teriparatide for reducing the risk of hip fracture, we review here the literature regarding how treatment with teriparatide affects the hip in patients with osteoporosis. Teriparatide increases cancellous bone volume, improves bone architecture, and - uniquely among osteoporosis treatments - increases cortical thickness and cortical porosity. By bone scan and positron emission tomography, teriparatide increases bone formation throughout the skeleton, including the hip. Consistent with these findings, studies using dual-energy X-ray absorptiometry and quantitative computed tomography for longitudinal assessment of changes at the hip have consistently shown increases in areal and volumetric bone mineral density, cortical thickness, and finite element-estimated hip strength in patients treated with teriparatide. Finally, in clinical fracture-outcome trials, treatment with teriparatide has been shown to reduce the risk of nonvertebral fracture, a composite endpoint that includes hip fracture. Taken together, this body of evidence suggests that teriparatide positively affects the hip in patients with osteoporosis.

Many postmenopausal women treated with teriparatide for osteoporosis have previously received antiresorptive therapy. In women treated with alendronate (ALN) or raloxifene (RLX), adding versus switching to teriparatide produced different responses in areal bone mineral density (aBMD) and biochemistry; the effects of these approaches on volumetric BMD (vBMD) and bone strength are unknown. In this study, postmenopausal women with osteoporosis receiving ALN 70 mg/week (n = 91) or RLX 60 mg/day (n = 77) for ≥18 months were randomly assigned to add or switch to teriparatide 20 µg/day. Quantitative computed tomography scans were performed at baseline, 6 months, and 18 months to assess changes in vBMD; strength was estimated by nonlinear finite element analysis. A statistical plan specifying analyses was approved before assessments were completed. At the spine, median vBMD and strength increased from baseline in all groups (13.2% to 17.5%, p < 0.01); there were no significant differences between the Add and Switch groups. In the RLX stratum, hip vBMD and strength increased at 6 and 18 months in the Add group but only at 18 months in the Switch group (Strength, Month 18: 2.7% Add group, p < 0.01 and 3.4% Switch group, p < 0.05). In the ALN stratum, hip vBMD increased in the Add but not in the Switch group (0.9% versus -0.5% at 6 months and 2.2% versus 0.0% at 18 months, both p ≤ 0.004 group difference). At 18 months, hip strength increased in the Add group (2.7%, p < 0.01) but not in the Switch group (0%); however, the difference between groups was not significant (p = 0.076). Adding or switching to teriparatide conferred similar benefits on spine strength in postmenopausal women with osteoporosis pretreated with ALN or RLX. Increases in hip strength were more variable. In RLX-treated women, strength increased more quickly in the Add group; in ALN-treated women, a significant increase in strength compared with baseline was seen only in the Add group.

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.

Prior studies show vertebral strength from computed tomography-based finite element analysis may be associated with vertebral fracture risk. We found vertebral strength had a strong association with new vertebral fractures, suggesting that vertebral strength measures identify those at risk for vertebral fracture and may be a useful clinical tool. We aimed to determine the association between vertebral strength by quantitative computed tomography (CT)-based finite element analysis (FEA) and incident vertebral fracture (VF). In addition, we examined sensitivity and specificity of previously proposed diagnostic thresholds for fragile bone strength and low BMD in predicting VF. In a case-control study, 26 incident VF cases (13 men, 13 women) and 62 age- and sex-matched controls aged 50 to 85 years were selected from the Framingham multi-detector computed tomography cohort. Vertebral compressive strength, integral vBMD, trabecular vBMD, CT-based BMC, and CT-based aBMD were measured from CT scans of the lumbar spine. Lower vertebral strength at baseline was associated with an increased risk of new or worsening VF after adjusting for age, BMI, and prevalent VF status (odds ratio (OR) = 5.2 per 1 SD decrease, 95% CI 1.3–19.8). Area under receiver operating characteristic (ROC) curve comparisons revealed that vertebral strength better predicted incident VF than CT-based aBMD (AUC = 0.804 vs. 0.715, p = 0.05) but was not better than integral vBMD (AUC = 0.815) or CT-based BMC (AUC = 0.794). Additionally, proposed fragile bone strength thresholds trended toward better sensitivity for identifying VF than that of aBMD-classified osteoporosis (0.46 vs. 0.23, p = 0.09). This study shows an association between vertebral strength measures and incident vertebral fracture in men and women. Though limited by a small sample size, our findings also suggest that bone strength estimates by CT-based FEA provide equivalent or better ability to predict incident vertebral fracture compared to CT-based aBMD. Our study confirms that CT-based estimates of vertebral strength from FEA are useful for identifying patients who are at high risk for vertebral fracture.

The relative role of the cortical vs trabecular bone in the load-carrying capacity of the proximal femur—a fundamental issue in both basic-science and clinical biomechanics—remains unclear. To gain insight into this issue, we performed micro-CT-based, linear elastic finite element analysis (61.5-micron-sized elements; ~280 million elements per model) on 18 proximal femurs (5M, 13F, ages 61–93 years) to quantify the fraction of frontal-plane bending moment shared by the cortical vs trabecular bone in the femoral neck, as well as the associated spatial distributions of stress. Analyses were performed separately for a sideways fall and stance loading. For both loading modes and across all 18 bones, we found consistent patterns of load-sharing in the neck: most proximally, the trabecular bone took most of the load; moving distally, the cortical bone took increasingly more of the load; and more distally, there was a region of uniform load-sharing, the cortical bone taking the majority of the load. This distal region of uniform load-sharing extended more for fall than stance loading (77±8% vs 51±6% of the neck length for fall vs. stance; mean±SD) but the fraction of total load taken by the cortical bone in that region was greater for stance loading (88±5% vs. 64±9% for stance vs. fall). Locally, maximum stress levels occurred in the cortical bone distally, but in the trabecular bone proximally. Although the distal cortex showed qualitative stress distributions consistent with the behavior of an Euler-type beam, quantitatively beam theory did not apply. We conclude that consistent and well-delineated regions of uniform load-sharing and load-transfer between the cortical and trabecular bone exist within the femoral neck, the details of which depend on the external loading conditions.

To evaluate the ability of additional analysis of computed tomographic (CT) colonography images to provide a comprehensive osteoporosis assessment.This Health Insurance Portability and Accountability Act-compliant study was approved by our institutional review board with a waiver of informed consent. Diagnosis of osteoporosis and assessment of fracture risk were compared between biomechanical CT analysis and dual-energy x-ray absorptiometry (DXA) in 136 women (age range, 43-92 years), each of whom underwent CT colonography and DXA within a 6-month period (between January 2008 and April 2010). Blinded to the DXA data, biomechanical CT analysis was retrospectively applied to CT images by using phantomless calibration and finite element analysis to measure bone mineral density and bone strength at the hip and spine. Regression, Bland-Altman, and reclassification analyses and paired t tests were used to compare results.For bone mineral density T scores at the femoral neck, biomechanical CT analysis was highly correlated (R(2) = 0.84) with DXA, did not differ from DXA (P = .15, paired t test), and was able to identify osteoporosis (as defined by DXA), with 100% sensitivity in eight of eight patients (95% confidence interval [CI]: 67.6%, 100%) and 98.4% specificity in 126 of 128 patients (95% CI: 94.5%, 99.6%). Considering both the hip and spine, the classification of patients at high risk for fracture by biomechanical CT analysis--those with osteoporosis or "fragile bone strength"--agreed well against classifications for clinical osteoporosis by DXA (T score ≤-2.5 at the hip or spine), with 82.8% sensitivity in 24 of 29 patients (95% CI: 65.4%, 92.4%) and 85.7% specificity in 66 of 77 patients (95% CI: 76.2%, 91.8%).Retrospective biomechanical CT analysis of CT colonography for colorectal cancer screening provides a comprehensive osteoporosis assessment without requiring changes in imaging protocols.

High-resolution peripheral quantitative computed tomography (HR-pQCT) provides in vivo three-dimensional (3D) imaging at the distal radius and tibia and has been increasingly used to characterize cortical and trabecular bone morphology in clinical studies. In this study, we comprehensively examined the accuracy of HR-pQCT and HR-pQCT based micro finite element (μFE) analysis predicted bone elastic stiffness and strength through comparisons with gold-standard micro computed tomography (μCT) based morphological/μFE measures and direct mechanical testing results. Twenty-six sets of human cadaveric distal radius and tibia segments were imaged by HR-pQCT and μCT. Microstructural analyses were performed for the registered HR-pQCT and μCT images. Bone stiffness and yield strength were determined by both HR-pQCT and μCT based linear and nonlinear μFE predictions and mechanical testing. Our results suggested that strong and significant correlations existed between the HR-pQCT standard, model-independent and corresponding μCT measurements. HR-pQCT based nonlinear μFE overestimated stiffness and yield strength while the linear μFE underestimated yield strength, but both were strongly correlated with those predicted by μCT μFE and measured by mechanical testing at both radius and tibia (R(2)>0.9). The microstructural differences between HR-pQCT and μCT were also examined by the Bland-Altman plots. Our results showed HR-pQCT morphological measurements of BV/TV(d), Tb.Th, and Tb.Sp, can be adjusted by correction values to approach true values measured by gold-standard μCT. In addition, we observed moderate correlations of HR-pQCT biomechanical and microstructural parameters between the distal radius and tibia. We concluded that morphological and mechanical properties of human radius and tibia bone can be assessed by HR-pQCT based measures.

ABSTRACT The Active‐Controlled Fracture Study in Postmenopausal Women With Osteoporosis at High Risk (ARCH) trial (NCT01631214; https://clinicaltrials.gov/ct2/show/NCT01631214 ) showed that romosozumab for 1 year followed by alendronate led to larger areal bone mineral density (aBMD) gains and superior fracture risk reduction versus alendronate alone. aBMD correlates with bone strength but does not capture all determinants of bone strength that might be differentially affected by various osteoporosis therapeutic agents. We therefore used quantitative computed tomography (QCT) and finite element analysis (FEA) to assess changes in lumbar spine volumetric bone mineral density (vBMD), bone volume, bone mineral content (BMC), and bone strength with romosozumab versus alendronate in a subset of ARCH patients. In ARCH, 4093 postmenopausal women with severe osteoporosis received monthly romosozumab 210 mg sc or weekly oral alendronate 70 mg for 12 months, followed by open‐label weekly oral alendronate 70 mg for ≥12 months. Of these, 90 (49 romosozumab, 41 alendronate) enrolled in the QCT/FEA imaging substudy. QCT scans at baseline and at months 6, 12, and 24 were assessed to determine changes in integral (total), cortical, and trabecular lumbar spine vBMD and corresponding bone strength by FEA. Additional outcomes assessed include changes in aBMD, bone volume, and BMC. Romosozumab caused greater gains in lumbar spine integral, cortical, and trabecular vBMD and BMC than alendronate at months 6 and 12, with the greater gains maintained upon transition to alendronate through month 24. These improvements were accompanied by significantly greater increases in FEA bone strength ( p &lt; 0.001 at all time points). Most newly formed bone was accrued in the cortical compartment, with romosozumab showing larger absolute BMC gains than alendronate ( p &lt; 0.001 at all time points). In conclusion, romosozumab significantly improved bone mass and bone strength parameters at the lumbar spine compared with alendronate. These results are consistent with greater vertebral fracture risk reduction observed with romosozumab versus alendronate in ARCH and provide insights into structural determinants of this differential treatment effect. © 2021 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

While osteoporosis is a risk factor for adverse outcomes in spinal fusion patients, diagnosing osteoporosis reliably in this population has been challenging due to degenerative changes and spinal deformities. Addressing that challenge, biomechanical computed tomography analysis (BCT) is a CT-based diagnostic test for osteoporosis that measures both bone mineral density and bone strength (using finite element analysis) at the spine; CT scans taken for spinal evaluation or previous care can be repurposed for the analysis.Assess the effectiveness of BCT for preoperatively identifying spinal fusion patients with osteoporosis who are at high risk of reoperation or vertebral fracture.Observational cohort study in a multi-center integrated managed care system using existing data from patient medical records and imaging archives.We studied a randomly sampled subset of all adult patients who had any type of primary thoracic (T4 or below) or lumbar fusion between 2005 and 2018. For inclusion, patients with accessible study data needed a preop CT scan without intravenous contrast that contained images (before any instrumentation) of the upper instrumented vertebral level.Reoperation for any reason (primary outcome) or a newly documented vertebral fracture (secondary outcome) occurring up to 5 years after the primary surgery.All study data were extracted using available coded information and CT scans from the medical records. BCT was performed at a centralized lab blinded to the clinical outcomes; patients could test positive for osteoporosis based on either low values of bone strength (vertebral strength ≤ 4,500 N women or 6,500 N men) and/or bone mineral density (vertebral trabecular bone mineral density ≤ 80 mg/cm3 both sexes). Cox proportional hazard ratios were adjusted by age, presence of obesity, and whether the fusion was long (four or more levels fused) or short (3 or fewer levels fused); Kaplan-Meier survival was compared by the log rank test. This project was funded by NIH (R44AR064613) and all physician co-authors and author 1 received salary support from their respective departments. Author 6 is employed by, and author 1 has equity in and consults for, the company that provides the BCT test; the other authors declare no conflicts of interest.For the 469 patients analyzed (298 women, 171 men), median follow-up time was 44.4 months, 11.1% had a reoperation (median time 14.5 months), and 7.7% had a vertebral fracture (median time 2.0 months). Overall, 25.8% of patients tested positive for osteoporosis and no patients under age 50 tested positive. Compared to patients without osteoporosis, those testing positive were at almost five-fold higher risk for vertebral fracture (adjusted hazard ratio 4.7, 95% confidence interval = 2.2-9.7; p<.0001 Kaplan-Meier survival). Of those positive-testing patients, those who tested positive concurrently for low values of both bone strength and bone mineral density (12.6% of patients overall) were at almost four-fold higher risk for reoperation (3.7, 1.9-7.2; Kaplan-Meier survival p<.0001); the remaining positive-testing patients (those who tested positive for low values of either bone strength or bone mineral density but not both) were not at significantly higher risk for reoperation (1.6, 0.7-3.7) but were for vertebral fracture (4.3, 1.9-10.2). For both clinical outcomes, risk remained high for patients who underwent short or long fusion.In a real-world clinical setting, BCT was effective in identifying primary spinal fusion patients aged 50 or older with osteoporosis who were at elevated risks of reoperation and vertebral fracture.

The biomechanical consequences of an isolated overload to the vertebral body may play a role in the etiology of vertebral fracture. In this context, we quantified residual strains and reductions in stiffness and ultimate load when vertebral bodies were loaded to various levels beyond the elastic regimen and related these properties to the externally applied strain and bone density. Twenty-three vertebral bodies (T11-L4, from 23 cadavers aged 20-90 years) were loaded once in compression to a randomized nominal strain level between 0.37 and 4.5%, unloaded, and then reloaded to 10% strain. Residual strains of up to 1.36% developed on unloading and depended on the applied strain (r2=0.85) but not on density (p = 0.25). Percentage reductions in stiffness and ultimate load of up to 83.7 and 52.5%, respectively, depended on both applied strain (r2 = 0.90 and r2 = 0.32, respectively) and density (r2 = 0.23 and r2 = 0.22, respectively). Development of residual strains is indicative of permanent deformations, whereas percentage reductions in stiffness are direct measures of effective mechanical damage. These results therefore demonstrate that substantial mechanical damage-which is not visible from radiographs-can develop in the vertebral body after isolated overloads, as well as subtle but significant permanent deformations. This behavior is similar to that observed previously for cylindrical cores of trabecular bone. Taken together, these findings indicate that the damage behavior of the lumbar and lower thoracic vertebral body is dominated by the trabecular bone and may be an important factor in the etiology of vertebral fracture.

This study investigated the numerical convergence characteristics of specimen-specific “voxel-based” finite element models of 14 excised human cadaveric lumbar vertebral bodies (age: 37–87; M=6, F=8) that were generated automatically from clinical-type CT scans. With eventual clinical applications in mind, the ability of the model stiffness to predict the experimentally measured compressive fracture strength of the vertebral bodies was also assessed. The stiffness of “low”-resolution models (3×3×3 mm element size) was on average only 4% greater p=0.03 than for “high”-resolution models (1×1×1.5 mm) despite interspecimen variations that varied over four-fold. Damage predictions using low- vs high-resolution models were significantly different p=0.01 at loads corresponding to an overall strain of 0.5%. Both the high r2=0.94 and low r2=0.92 resolution model stiffness values were highly correlated with the experimentally measured ultimate strength values. Because vertebral stiffness variations in the population are much greater than those that arise from differences in voxel size, these results indicate that imaging resolution is not critical in cross-sectional studies of this parameter. However, longitudinal studies that seek to track more subtle changes in stiffness over time should account for the small but highly significant effects of voxel size. These results also demonstrate that an automated voxel-based finite element modeling technique may provide an excellent noninvasive assessment of vertebral strength.

Trabecular architecture is considered important in osteoporosis and has been quantified by a variety of mean parameters characteristic of a whole specimen. Variations within a specimen, however, have been mostly ignored. In this study, the theoretical effects of these intraspecimen variations in architecture on predicted mechanical properties were investigated through a three-dimensional finite element parameter study that simulated variations in trabecular thickness in a controlled manner. An irregularly spaced lattice of different sized rods was used to simulate trabecular bone in three distinct volume fraction ranges, representing young, middle-aged, and elderly vertebral bone. Beta distributions (a type of non-normal distribution) of trabecular thickness with coefficients of variation of either 25%, 40%, or 55% were applied to the rods in each model, and 225 simulations of uniaxial compression tests were performed to obtain modulus values. Percent modulus reductions of 22% and 43% were predicted when the intraspecimen coefficient of variation in trabecular thickness was increased from 25% to 40% and from 25% to 55%, respectively, for models of equal volume fraction. Furthermore, this trend was predicted to be independent of volume fraction. We conclude, therefore, that consideration of the intraspecimen trabecular thickness variation in conjunction with volume fraction may improve the ability to predict trabecular modulus compared with use of volume fraction alone. Further, the model suggests that if age, disease, or drug treatments increase trabecular thickness variation, this may be detrimental to mechanical properties.

Biomechanical properties within cadaveric vertebral bodies were parametrically studied using finite element analysis after calibration to experimental data.To develop and validate three-dimensional finite element models of the human thoracolumbar spine based on quantitative computed tomography scans. Specifically, combine finite element modeling together with biomechanical testing circumventing problems associated with direct measurements of shell properties.Finite element methods can help to understand injury mechanisms and stress distribution patterns within vertebral bodies as an important part in clinical evaluation of spinal injuries. Because of complications in modeling the vertebral shell, it is not clear if quantitative computed tomography-based finite element models of the spine could accurately predict biomechanical properties.We developed a novel finite element modeling technique based on quantitative computed tomography scans of 19 radiographically normal human vertebra bodies and mechanical property data from empirical studies on cylindrical trabecular bone specimens. Structural properties of the vertebral shell were recognized as parametric variables and were calibrated to provide agreement in whole vertebral body stiffness between model and experiment. The mean value of the shell properties thus obtained was used in all models to provide predictions of whole vertebral strength and stiffness.Calibration of n = 19 computer models to experimental stiffness yielded a mean effective modulus of the vertebral shell of 457 +/- 931 MPa ranging from 9 to 3216 MPa. No significant correlation was found between vertebral shell effective modulus and either the experimentally measured stiffness or the average trabecular modulus. Using the effective vertebral shell modulus for all 19 models, the predicted vertebral body stiffness was an excellent predictor of experimental measurements of both stiffness (r2= 0.81) and strength (r2 = 0.79).These findings indicate that modeling of the vertebral shell using a constant thickness of 0.35 mm and an effective modulus of 457 MPa, combined with quantitative computed tomography-based modeling of trabecular properties and vertebral geometry, can accurately predict whole vertebral biomechanical properties. Use of this modeling technique, therefore, should produce substantial insight into vertebral body biomechanical behavior and may ultimately improve clinical indications of fracture risk of this cohort.

Within the context of improving knowledge of the structure-function relations for trabecular bone for cyclic loading, we hypothesized that the S-N curve for cyclic compressive loading of trabecular bone, after accounting for differences in monotonic strength behavior, does not depend on either site or species. Thirty-five cores of fresh-frozen elderly human vertebral trabecular bone, harvested from nine donors (mean+/-S.D., age=74+/-17 years), were biomechanically tested in compression at sigma/E(0) values (ratio of applied stress to pre-fatigue elastic modulus) ranging from 0.0026 to 0.0070, and compared against literature data (J. Biomech. Eng. 120 (1998) 647-654) for young bovine tibial trabecular bone (n=37). As reported for the bovine bone, the number of cycles to failure for the human vertebral bone was related to sigma/E(0) by a power-law relation (r(2)=0.54, n=35). Quantitative comparison of these data against those reported for the bovine bone supported our hypothesis. Namely, when the differences in mean monotonic yield strain between the two types of bone were accounted for, a single S-N curve worked well for the pooled data (r(2)=0.75, n=72). Since elderly human vertebral and young bovine tibial trabecular bone represent two very different types of trabecular bone in terms of volume fraction and architecture, these findings suggest that the dominant failure mechanisms in trabecular bone for cyclic loading occur at the ultrastructural level.

Although there is no consensus as to the precise nature of the mechanostimulatory signals imparted to the bone cells during remodeling, it has been postulated that deformation-induced fluid flow plays a role in the mechanotransduction pathway. In vitro, osteoblasts respond to fluid shear stress with an increase in PGE(2) production; however, the long-term effects of fluid shear stress on cell proliferation and differentiation have not been examined. The goal of this study was to apply continuous pulsatile fluid shear stresses to osteoblasts and determine whether the initial production of PGE(2) is associated with long-term biochemical changes. The acute response of bone cells to a pulsatile fluid shear stress (0.6 +/- 0.5 Pa, 3.0 Hz) was characterized by a transient fourfold increase in PGE(2) production. After 7 days of static culture (0 dyn/cm(2)) or low (0.06 +/- 0.05 Pa, 0.3 Hz) or high (0.6 +/- 0.5 Pa, 3.0 Hz) levels of pulsatile fluid shear stress, the bone cells responded with an 83% average increase in cell number, but no statistical difference (P > 0.53) between the groups was observed. Alkaline phosphatase activity per cell decreased in the static cultures but not in the low- or high-flow groups. Mineralization was also unaffected by the different levels of applied shear stress. Our results indicate that short-term changes in PGE(2) levels caused by pulsatile fluid flow are not associated with long-term changes in proliferation or mineralization of bone cells.

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.

A two-dimensional finite element model of an idealized trabecular bone specimen was developed to study trabecular bone damage accumulation during cyclic compressive loading. The specimen was modeled as a two-dimensional honeycomb-like structure made up of an array of hexagonal cells. Each trabecula was modeled as a linearly elastic beam element with the same material properties as cortical bone. Initial microcracks were assumed to exist within the oblique trabeculae and to grow according to the Paris law. Forces and moments were computed in each trabecula and the microcracks were allowed to propagate until fracture occurred. Between cycles, fractured trabeculae were removed from the finite element mesh, and force and moment distributions were calculated for the next cycle. This iterative process was continued until the simulated trabecular bone specimen showed a 10% reduction in modulus. Creep failure was also studied using a single cell analysis, in which a closed-form solution was obtained after prescribing the creep properties of the trabeculae. The results of the crack propagation analysis showed that fractures of only a small number of individual trabeculae can cause a substantial reduction in the modulus of the trabecular bone specimen model. Statistical tests were performed to compare the slopes and intercepts of the SN curves of our model predictions to those of experimentally derived SN curves for bovine trabecular bone. There was no significant difference (p>0.2 for both slope and intercept) between our model predictions and the experimentally derived SN curves for the low-stress, high-cycle range. For the high-stress, low-cycle range, the crack propagation model overestimated the fatigue life for a given stress level (for slope, p<0.001), while the creep analysis agreed well with the experimental data (for slope, p>0.2). These findings suggest that the primary failure mechanism for low-stress, high-cycle fatigue of trabecular bone is crack growth and propagation, while the primary failure mechanism for high-stress, low-cycle fatigue is creep deformation and fracture. Furthermore, our results suggest that the modulus of trabecular bone at the specimen level may be highly sensitive to fractures of individual trabeculae.

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.

Abstract Trabecular damage may play a role in hip fracture, bone remodeling, and prosthesis loosening. We hypothesized that when trabecular bone is loaded beyond its elastic range, both the type and the amount of damage depend on the applied strains. Thirty specimens of trabecular bone from the bovine tibia underwent compression tests to one of three levels of strain (0.4,1.0, and 2.5%) (n = 10 per group). The 0.4% level was a mechanically nondestructive control group that accounted for any systematic errors. Optical microscopy at magnifications as high as × 200 was then used to quantify the trabecular damage for each group. The amount of damage in the yield group (1.0% strain) did not differ from that in the control group (p = 0.66), whereas damage in the post‐ultimate strain group (2.5% strain) increased more than 3‐fold (p &lt; 0.0008). Four types of damage were observed: transverse cracks, shear bands, parallel cracks, and complete fractures, of which the first two were dominant. These findings therefore indicate that damage occurs within trabeculae at yield. By comparison with our previous work, it can also be concluded that substantial modulus reductions in trabecular bone (as much as 60%) are caused by damage primarily within trabeculae. The ability to detect such damage clinically may improve in vivo estimates of whole‐bone strength by identifying regions of densito metrically normal but mechanically compromised trabecular bone.

A finite-element model of an isolated elderly human L3 vertebral body was developed to study how material properties and loading conditions influence end-plate and cortical-shell displacements and stresses. The model consisted of an idealized geometric representation of an isolated vertebral body, with a 1-mm-thick end plate and cortical shell. For uniform compression, large tensile stresses occurred all around the cortical shell just below the end plate as a result of bending of the cortical shell as it supported the end plate. Large tensile bending stresses also developed in the inferior surface of the end plate. Equal reductions in both trabecular and cortical bone moduli increased displacements but did not affect peak stresses. A 50% reduction in trabecular bone modulus alone increased peak stresses in the end plate by 74%. Elimination of the cortical shell reduced peak stresses in the end plate by approximately 20%. For nonuniform, anteriorly eccentric compression, peak stresses everywhere changed by less than 11% but moved to the anterior aspect. When material properties were adjusted to represent osteoporosis with disproportionate reductions in trabecular (50% decrease) and cortical (25% decrease) bone moduli, anterior compression increased peak stresses by up to 250% compared to uniform compression. If fractures are initiated in regions of large tensile stresses, the results from this relatively simple model may explain how central end-plate and transverse fractures initiate from uniform compression of the end plate. Furthermore, for anterior compression, disproportionate modulus reductions in trabecular and cortical bone may substantially increase end plate and cortical shell stresses, suggesting a cause of age-related spine fractures.

1. The Musculoskeletal System 1.1. Anatomical Overview 1.2. The Functions of the Musculoskeletal System 1.3. Bones 1.4. Joints of the Body 1.5. Soft Tissue Structures 1.6. The Hip, Knee, and Spine 1.7. Damage and Repair 1.8. Summary 1.9. Exercises 2. Loads and Motion in the Musculoskeletal System 2.1. Basic Concepts 2.2. Static Analysis of Skeletal System 2.3. The Musculoskeletal Dynamics Problem 2.4. Joint Stability 2.5. Summary 2.6. Exercises 3. Tissue Mechanics I: Bone 3.1. Introduction 3.2. Composition of Bone 3.3. Bone as a Hierarchical Composite Material 3.4. Elastic Anisotropy 3.5. Material Properties of Cortical Bone 3.6. Material Properties of Trabecular Bone 3.7. Hierarchical Analysis 3.8. Structural Anisotropy 3.9. Biomechanics of Bone Adaptation 3.10. Summary 3.11. Exercises 4. Tissue Mechanics II: Soft Tissue 4.1. Tendon and Ligament 4.2. Articular Cartilage 4.3. Intervertebral Disc 4.4. Muscle 4.5. Viscoelasticity 4.6. Summary 4.7. Exercises 5. Structural Analysis of Musculoskeltal Systems: Beam Theory 5.1. Basic Concepts 5.2. Symmetric Beams 5.3. Unsymmetrical Beams 5.4. Case Studies: Whole Bone Mechanics 5.5. Summary 5.6. Exercises 6. Structural Analysis of Musculoskeltal Systems: Advanced Topics 6.1. Beams on Elastic Foundation 6.2. Torsion of Noncircular Sections 6.3. Contact Stress Analysis 6.4. Summary 6.5. Exercises 7. Bone-Implant Systems 7.1. Implant Materials 7.2. Fracture Fixation Devices 7.3. Joint Replacements 7.4. Design of Bone-Implant Systems 7.5. Summary 7.6. Exercises 8. Fracture Fixation Devices 8.1. Fracture Repair 8.2. Mechanics of Intramedullary Rods 8.3. Combined Behavior of Bone and Rod 8.4. Mechanics of Bone Plates 8.5. Combined Behavior of Bone and Plate 8.6. Plate Fixation: Other Considerations 8.7. Irregular Bone Cross Section with a Plate 8.8. External Fixators 8.9. Controlling Callus Strains 8.10. Bone Screws and Effects of Holes 8.11. Other Issues and Complications 8.12. Summary 8.13. Exercises 9. Total Hip Replacements 9.1. Function: Kinematics and Loads 9.2. Fixation: Femoral Stems 9.3. Stresses in the Central Zone 9.4. BOEF and FEA Models for Bone-Stem Systems 9.5. Summary 9.6. Exercises 10. Total Knee Replacements 10.1. Knee Function 10.2. Knee Structure 10.3. Knee Replacements 10.4. Summary 10.5. Exercises 11. Articulating Surfaces 11.1. Damage Modes 11.2. Design: General Considerations 11.3. Summary 11.4. Exercises Suggestions for Further Reading Index

We thank the Editors for the opportunity to assess Dr. Kaufman's analysis of our data and to further expound on the clinical relevance of our findings. Dr. Kaufman is concerned that our analysis implicitly assumes that “femoral strength as estimated by BCT is a much better quantity to estimate fracture risk than is aBMD.” He also concludes that “the implication that BCT provides superior information on bone strength and fracture risk at the proximal femur to that provided by aBMD is questionable at least based on the data provided in the article by Keaveny and colleagues.” In fact, our analysis does not address assessment of fracture risk, nor does it assume that our BCT-derived estimates of femoral strength are better at fracture risk assessment than aBMD. We were careful in our conclusions not to broach comparatives of fracture risk assessment because we had no fracture outcome data available for this cohort at the time of our analysis. Instead, the focus of this article was on the more general issue of age-related trends for the population, highlighting differences in trends for aBMD and femoral strength, and not addressing superiority of one over the other. As such, Dr. Kaufman mischaracterized our study. In reaching his conclusions, Dr. Kaufman made several unsubstantiated statements. For example, he concluded from analysis of our data that aBMD of the femoral neck is “an excellent proxy for femoral strength.” Dr. Kaufman's argument was based on the relation between age-specific mean values between the two variables. His reported correlation was so high because, after midlife, we found that mean strength and mean aBMD both declined in an approximately linear fashion with age. By Dr. Kaufman's logic, age also would be an excellent proxy for aBMD. However, none of this speaks to the correlation for individuals, which is the relevant issue for fracture risk assessment. In a study of clinically defined postmenopausal osteoporotic women, for example, the correlation between BCT-derived strength and dual-energy X-ray absorptiometry (DXA)–derived aBMD was quite low (R2 ≈ 0.50).1 Dr. Kaufman mischaracterized our second conclusion by extrapolating his paraphrasing to comparisons of fracture risk assessment—but, in fact, we made no conclusions about fracture risk assessment or the superiority of BCT-derived femoral strength over aBMD in this regard. Dr. Kaufman's also dismissed our 3000 N cut point for femoral strength as “largely arbitrary.” Since this empirical cut point was based on prospective, fracture outcome clinical data (albeit for men),2 clearly it was not chosen arbitrarily. Mathematically, of course, one can increase the T-score cut point to match the prevalence for the strength cut point. But this has little relevance in a clinical context because increasing the T-score will compromise specificity, which is not desirable clinically, and changing the World Health Organization aBMD criteria for the definition of osteoporosis is not feasible. Dr. Kaufman also questioned the relevance of our results, stating that our observation of greater changes in strength than aBMD “is of little consequence.” While this viewpoint may be reasonable from a purely mathematical perspective, the clinical implications are more nuanced. aBMD is used widely as an implicit surrogate for bone strength. In this clinical context, our results raise the issue of whether such widespread reliance on aBMD as a surrogate for bone strength may provide a misleading clinical impression that annual percent reductions in femoral strength are on the same order as in aBMD—about 0.5% to 0.7% per year (see Fig. 4 of our paper). Such a rate of loss does not appear too alarming, does not change much with aging, and probably would justify the current approach of waiting until individuals are at very high risk before commencing treatment. However, our results suggest instead that the rate of loss in strength is much greater, particularly in elderly women. This raises the possibility that too few women are being treated and too late. Thus, while our results are indeed consistent with current efforts to improve clinical fracture risk assessment, we believe that they additionally provide unique insight into effects of age on femoral strength and highlight issues central to the debate of how one might improve management of osteoporosis from a public health perspective.

Vertebral strength, a key etiologic factor of osteoporotic fracture, may be affected by the relative amount of vertically oriented trabeculae. To better understand this issue, we performed experimental compression testing, high-resolution micro-computed tomography (µCT), and micro-finite-element analysis on 16 elderly human thoracic ninth (T(9)) whole vertebral bodies (ages 77.5 ± 10.1 years). Individual trabeculae segmentation of the µCT images was used to classify the trabeculae by their orientation. We found that the bone volume fraction (BV/TV) of just the vertical trabeculae accounted for substantially more of the observed variation in measured vertebral strength than did the bone volume fraction of all trabeculae (r(2) = 0.83 versus 0.59, p < .005). The bone volume fraction of the oblique or horizontal trabeculae was not associated with vertebral strength. Finite-element analysis indicated that removal of the cortical shell did not appreciably alter these trends; it also revealed that the major load paths occur through parallel columns of vertically oriented bone. Taken together, these findings suggest that variation in vertebral strength across individuals is due primarily to variations in the bone volume fraction of vertical trabeculae. The vertical tissue fraction, a new bone quality parameter that we introduced to reflect these findings, was both a significant predictor of vertebral strength alone (r(2) = 0.81) and after accounting for variations in total bone volume fraction in multiple regression (total R(2) = 0.93). We conclude that the vertical tissue fraction is a potentially powerful microarchitectural determinant of vertebral strength.

Knowledge of the location of initial regions of failure within the vertebra - cortical shell, cortical endplates vs. trabecular bone, as well as anatomic location--may lead to improved understanding of the mechanisms of aging, disease and treatment. The overall objective of this study was to identify the location of the bone tissue at highest risk of initial failure within the vertebral body when subjected to compressive loading. Toward this end, micro-CT-based 60-micron voxel-sized, linearly elastic, finite element models of a cohort of thirteen elderly (age range: 54-87 years, 75+/-9 years) female whole vertebrae without posterior elements were virtually loaded in compression through a simulated disc. All bone tissues within each vertebra having either the maximum or minimum principal strain beyond its 90th percentile were defined as the tissue at highest risk of initial failure within that particular vertebral body. Our results showed that such high-risk tissue first occurred in the trabecular bone and that the largest proportion of the high-risk tissue also occurred in the trabecular bone. The amount of high-risk tissue was significantly greater in and adjacent to the cortical endplates than in the mid-transverse region. The amount of high-risk tissue in the cortical endplates was comparable to or greater than that in the cortical shell regardless of the assumed Poisson's ratio of the simulated disc. Our results provide new insight into the micromechanics of failure of trabecular and cortical bone within the human vertebra, and taken together, suggest that, during strenuous compressive loading of the vertebra, the tissue near and including the endplates is at the highest risk of initial failure.

Osteoporosis and bone fractures are of particular concern in patients with inflammatory bowel disease (IBD). Biomechanical computed tomography (BCT) is an image-analysis technique that can measure bone strength and dual-energy X-ray absorptiometry (DXA)-equivalent bone mineral density (BMD) from noncontrast CT images. This study seeks to determine whether this advanced technology can be applied to patients with IBD undergoing CT enterography (CTE) with IV contrast.Patients with IBD who underwent a CTE and DXA scan between 2007 and 2011 were retrospectively identified. Femoral neck BMD (g/cm(2)) and T-scores were measured and compared between DXA and BCT analysis of the CTE images. Femoral strength (Newtons) was also determined from BCT analysis.DXA- and CTE-generated BMD T-score values were highly correlated (R(2)=0.84, P<0.0001) in this patient cohort (n=136). CTE identified patients with both osteoporosis (sensitivity, 85.7%; 95% confidence interval (CI), 48.7-97.4 and specificity, 98.5%; 95% CI, 94.5-99.6) and osteopenia (sensitivity, 85.1%; 95% CI, 72.3-92.6 and specificity, 85.4%; 95% CI, 76.6-91.3). Of the 16 patients who had "fragile" bone strength by BCT (placing them at the equivalent high risk of fracture as for osteoporosis), 6 had osteoporosis and 10 had osteopenia by DXA.CTE scans can provide hip BMD, T-scores, and clinical classifications that are comparable to those obtained from DXA; when combined with BCT analysis, CTE can identify a subset of patients with osteopenia who have clinically relevant fragile bone strength. This technique could markedly increase bone health assessments in IBD patients already undergoing CTE to evaluate small bowel disease.

Many natural structures use a foam core and solid outer shell to achieve high strength and stiffness with relatively small amounts of mass. Biological foams, however, must also resist crack growth. The process of crack propagation within the struts of a foam is not well understood and is complicated by the foam microstructure. We demonstrate that in cancellous bone, the foam-like component of whole bones, damage propagation during cyclic loading is dictated not by local tissue stresses but by heterogeneity of material properties associated with increased ductility of strut surfaces. The increase in surface ductility is unexpected because it is the opposite pattern generated by surface treatments to increase fatigue life in man-made materials, which often result in reduced surface ductility. We show that the more ductile surfaces of cancellous bone are a result of reduced accumulation of advanced glycation end products compared with the strut interior. Damage is therefore likely to accumulate in strut centers making cancellous bone more tolerant of stress concentrations at strut surfaces. Hence, the structure is able to recover more deformation after failure and return to a closer approximation of its original shape. Increased recovery of deformation is a passive mechanism seen in biology for setting a broken bone that allows for a better approximation of initial shape during healing processes and is likely the most important mechanical function. Our findings suggest a previously unidentified biomimetic design strategy in which tissue level material heterogeneity in foams can be used to improve deformation recovery after failure.

The mechanism of vertebral wedge fractures remains unclear and may relate to typical variations in the mechanical behavior of the intervertebral disc. To gain insight, we tested 16 individual whole discs (between levels T8 and L5) from nine cadavers (mean±SD: 66±16 years), loaded in compression at different rates (0.05-20.0% strain/s), to measure a homogenized "effective" linear elastic modulus of the entire disc. The measured effective modulus, and average disc height, were then input and varied parametrically in micro-CT-based finite element models (60-μm element size, up to 80 million elements each) of six T9 human vertebrae that were virtually loaded to 3° of moderate forward-flexion via a homogenized disc. Across all specimens and loading rates, the measured effective modulus of the disc ranged from 5.8 to 42.7MPa and was significantly higher for higher rates of loading (p<0.002); average disc height ranged from 2.9 to 9.3mm. The parametric finite element analysis indicated that, as disc modulus increased and disc height decreased across these ranges, the vertebral bone stresses increased but their spatial distribution was largely unchanged: most of the highest stresses occurred in the central trabecular bone and endplates, and not anteriorly. Taken together with the literature, our findings suggest that the effective modulus of the human intervertebral disc should rarely exceed 100MPa and that typical variations in disc effective modulus (and less so, height) minimally influence the spatial distribution but can appreciably influence the magnitude of stress within the vertebral body.

In a population-based study, we found that computed tomography (CT)-based bone density and strength measures from the thoracic spine predicted new vertebral fracture as well as measures from the lumbar spine, suggesting that CT scans at either the thorax or abdominal regions are useful to assess vertebral fracture risk.Prior studies have shown that computed tomography (CT)-based lumbar bone density and strength measurements predict incident vertebral fracture. This study investigated whether CT-based bone density and strength measurements from the thoracic spine predict incident vertebral fracture and compared the performance of thoracic and lumbar bone measurements to predict incident vertebral fracture.This case-control study of community-based men and women (age 74.6 ± 6.6) included 135 cases with incident vertebral fracture at any level and 266 age- and sex-matched controls. We used baseline CT scans to measure integral and trabecular volumetric bone mineral density (vBMD) and vertebral strength (via finite element analysis, FEA) at the T8 and L2 levels. Association between these measurements and vertebral fracture was determined by using conditional logistic regression. Sensitivity and specificity for predicting incident vertebral fracture were determined for lumbar spine and thoracic bone measurements.Bone measurements from T8 and L2 predicted incident vertebral fracture equally well, regardless of fracture location. Specifically, for predicting vertebral fracture at any level, the odds ratio (per 1-SD decrease) for the vBMD and strength measurements at L2 and T8 ranged from 2.0 to 2.7 (p < 0.0001) and 1.8 to 2.8 (p < 0.0001), respectively. Results were similar when predicting fracture only in the thoracic versus the thoracolumbar spine. Lumbar and thoracic spine bone measurements had similar sensitivity and specificity for predicting incident vertebral fracture.These findings indicated that like those from the lumbar spine, CT-based bone density and strength measurements from the thoracic spine may be useful for identifying individuals at high risk for vertebral fracture.

Study of the behavior of trabecular bone at strains below 0.40 percent is of clinical and biomechanical importance. The goal of this work was to characterize, with respect to anatomic site, loading mode, and apparent density, the subtle concave downward stress-strain nonlinearity, that has been observed recently for trabecular bone at these strains. Using protocols designed to minimize end-artifacts, 155 cylindrical cores from human vertebrae, proximal tibiae, proximal femora, and bovine proximal tibiae were mechanically tested to yield at 0.50 percent strain per second in tension or compression. The nonlinearity was quantified by the reduction in tangent modulus at 0.20 percent and 0.40 percent strain as compared to the initial modulus. For the pooled data, the mean +/- SD percentage reduction in tangent modulus at 0.20 percent strain was 9.07+/- 3.24 percent in compression and 13.8 +/- 4.79 percent in tension. At 0.40 percent strain, these values were 23.5 +/- 5.71 and 35.7+/- 7.10 percent, respectively. The magnitude of the nonlineari't depended on both anatomic site (p < 0.001) and loading mode (p < 0.001), and in tension was positively correlated with density. Calculated values of elastic modulus and yield properties depended on the strain range chosen to define modulus via a linear curve fit (p < 0.005). Mean percent differences in 0.20 percent offset yield strains were as large as 10.65 percent for some human sites. These results establish that trabecular bone exhibits nonlinearity at low strains, and that this behavior can confound intersite comparisons of mechanical properties. A nonlinear characterization of the small strain behavior of trabecular bone was introduced to characterize the initial stress-strain behavior more thoroughly.

Compared to trabecular microfracture, the biomechanical consequences of the morphologically more subtle trabecular microdamage are unclear but potentially important because of its higher incidence. A generic three-dimensional finite element model of the trabecular bone microstructure was used to investigate the relative biomechanical roles of these damage categories on reloading elastic modulus after simulated overloads to various strain levels. Microfractures of individual trabeculae were modeled using a maximum fracture strain criterion, for three values of fracture strain (2%, 8%, and 35%). Microdamage within the trabeculae was modeled using a strain-based modulus reduction rule based on cortical bone behavior. When combining the effects of both microdamage and microfracture, the model predicted reductions in apparent modulus upon reloading of over 60% at an applied apparent strain of 2%, in excellent agreement with previously reported experimental data. According to the model, up to 80% of the trabeculae developed microdamage at 2% apparent strain, and between 2% and 10% of the trabeculae were fractured, depending on which fracture strain was assumed. If microdamage could not occur but microfracture could, good agreement with the experimental data only resulted if the trabecular hard tissue had a fracture strain of 2%. However, a high number of fractures (10% of the trabeculae) would need to occur for this case, and this has not been observed in published damage morphology studies. We conclude therefore that if the damage behavior of trabecular hard tissue is similar to that of cortical bone, then extensive microdamage is primarily responsible for the large loss in apparent mechanical properties that can occur with overloading of trabecular bone.

There are almost no published data that describe the creep behavior of trabecular bone (at the specimen level), even though the creep behavior of cortical bone has been well documented. In an effort to characterize the creep behavior of trabecular bone and to compare it with that of cortical bone, we performed uniaxial compressive creep tests on 24 cylindrical specimens of trabecular bone taken from 19 bovine proximal tibiae. Six different load levels were used, with the applied stress normalized by the specimen modulus measured prior to creep loading. We found that trabecular bone exhibits the three creep regimes (primary, secondary, and tertiary) associated with metals, ceramics, and cortical bone. All specimens eventually fractured at strains less than 3.8%. In addition, the general shape of the creep curve was independent of apparent density. Strong and highly significant power law relationships (r2>0.82, p<0.001) were found between the normalized stress σE0 and both time-to-failure tf and steady-state creep rate dεdt: tf=9.66 × 10−33 (σ/E0)−16.18; dεdt=2.21 × 1033 (σ/E0)17.65. These data indicate that the creep behaviors of trabecular and cortical bone are qualitatively similar. In addition, the strength of trabecular bone can be reduced substantially if relatively large stresses (i.e. stresses approximately half the ultimate strength) are applied for 5 h. Such strength reductions may play a role in the etiology of progressive, age-related spine fractures if adaptive bone remodeling does not arrest creep deformations.

In a long-term effort to develop a complete multi-axial failure criterion for human trabecular bone, the overall goal of this study was to compare the ability of a simple cellular solid mechanistic criterion versus the Tsai-Wu, Principal Strain, and von Mises phenomenological criteria--all normalized to minimize effects of interspecimen heterogeneity of strength--to predict the on-axis axial-shear failure properties of bovine trabecular bone. The Cellular Solid criterion that was developed here assumed that vertical trabeculae failed due to a linear superposition of axial compression/tension and bending stresses, induced by the apparent level axial and shear loading, respectively. Twenty-seven bovine tibial trabecular bone specimens were destructively tested on-axis without end artifacts, loaded either in combined tension-torsion (n = 10), compression-torsion (n = 11), or uniaxially (n = 6). For compression-shear, the mean (+/- S.D.) percentage errors between measured values and criterion predictions were 7.7 +/- 12.6 percent, 19.7 +/- 23.2 percent, 22.8 +/- 18.9 percent, and 82.4 +/- 64.5 percent for the Cellular Solid, Tsai-Wu, Principal Strain, and von Mises criteria, respectively; corresponding mean errors for tension-shear were -5.2 +/- 11.8 percent, 14.3 +/- 12.5 percent, 6.9 +/- 7.6 percent, and 57.7 +/- 46.3 percent. Statistical analysis indicated that the Cellular Solid criterion was the best performer for compression-shear, and performed as well as the Principal Strain criterion for tension-shear. These data should substantially improve the ability to predict axial-shear failure of dense trabecular bone. More importantly, the results firmly establish the importance of cellular solid analysis for understanding and predicting the multiaxial failure behavior of trabecular bone.

Although evidence suggests that yield strains for trabecular bone are isotropic, i.e., independent of loading direction, decisive support for this hypothesis has remained elusive. To explicitly test whether yield strains for trabecular bone are isotropic, compressive and tensile yield strains of 51 specimens of bovine tibial trabecular bone (0.41 +/- 0.08 g/cm3 [mean apparent density +/- SD]) were measured without end artifacts in on-axis (along the principal trabecular orientation) and off-axis (30-40 degrees oblique to on-axis) orientations. Yield strains for the on-axis and off-axis orientations were similar in tension (0.80 +/- 0.03% compared with 0.85 +/- 0.04%, p = 0.21) and compression (0.97 +/- 0.05% compared with 0.96 +/- 0.07%, p > 0.99); as expected, modulus and strength depended on loading direction. When considered with an ancillary experiment on bovine tibial trabecular bone that showed yield strains to be similar between on-axis and 90 degrees off-axis bone, these results firmly establish the isotropy of uniaxial yield strains for bovine tibial trabecular bone. This bone is of high density and has a strong, plate-type, anisotropic architecture. Therefore, yield strains for uniaxial loading are expected to be isotropic, or nearly so, for other types of dense trabecular bone, although further work is required to confirm this and to establish this behavior for bone of lower density.

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.