Biomechanical structure-function relations for human trabecular bone - comparison of calcaneus, femoral neck, greater trochanter, proximal tibia, and vertebra

MicroCT-based finite element models were used to compute power law relations for uniaxial compressive yield stress versus bone volume fraction for 78 cores of human trabecular bone from five anatomic sites. The leading coefficient of the power law for calcaneus differed from those for most of the other sites (p < 0.05). However, after normalizing by site-specific mean values, neither the leading coefficient (p > 0.5) nor exponent (p > 0.5) differed among sites, suggesting that a given percentage deviation from mean bone volume fraction has the same mechanical consequence for all sites investigated. These findings help explain the success of calcaneal x-ray and ultrasound measurements for predicting hip fracture risk.

Safety analysis of adapted battery-powered ride-on toy car for children with disabilities using a modified test dummy with varying joint stiffness

Adaptive ride-on toy programs have increased in popularity in recent years and provide novel rehabilitation tools as developmental aids for children with disabilities. While the adaptations made to these toys are intended to provide a safer experience for children with disabilities, safety concerns still exist. Within this context, the purpose of this study was to use a model with varying joint stiffness as a first-order approximation of a child with disabilities and to investigate whether modifications to ride-on toys are sufficient to prevent common injuries. Because the population of children with disabilities who are receiving adaptive ride-on toys have a wide range of musculoskeletal disorders, those with both decreased and increased muscle stiffness were considered in this safety study. A 5-point harness reduced movement regardless of change in joint stiffness and therefore, results from this study indicate that the use of these harnesses is effective regardless of joint stiffness. Furthermore, as excursion-related injuries are considered more critical to the user than injuries relating to kinetic variables and no known injury thresholds were exceeded, the addition of a belt is considered a necessary trade-off with little-to-no added risk.

Pediatric safety: review of the susceptibility of children with disabilities to injuries involving movement related events

Background

Toy-related injuries have increased significantly in the past decade, in particular those related to ride-on toys. This increase has been attributed to movement related events such as falls and inertial impacts. Furthermore, children with disabilities have been reported to be at a greater risk of being injured, and are therefore more susceptible to toy-related injuries. Although, efforts are being made to modify ride-on toys as a method for increasing quality of life in children with disabilities, there are very limited pediatric safety studies regarding children with disabilities and modified ride-on toys.

Methods

This manuscript presents a systematic review of literature summarizing the current state of toy-related injuries including children with and without disabilities. Children exposed to inertial impacts in motor vehicle crashes have also been reviewed to present current pediatric safety testing methodologies and injury tolerance thresholds. Out of 2608 articles, 10 studies were included regarding current trends in toy-related injuries and safety testing methodologies.

Conclusions

From this study, a gap in the literature was discovered concerning the susceptibility of children with disabilities to toy-related injuries, specifically in relation to ride-on toys and the repercussion surrounding such injuries. It is theorized that such lack of data is due to the difficulty and costs associated with experimental validation. Hence, it is recommended that computer simulations be used to provide preliminary data analysis.

Heterogeneity of yield strain in low-density versus high-density human trabecular bone

Understanding the off-axis behavior of trabecular yield strains may lend unique insight into the etiology of fractures since yield strains provide measures of failure independent of elastic behavior. We sought to address anisotropy of trabecular yield strains while accounting for variations in both density and anatomic site and to determine the mechanisms governing this behavior. Cylindrical specimens were cored from vertebral bodies (n=22, BV/TV=0.11+/-0.02) and femoral necks (n=28, BV/TV=0.22+/-0.06) with the principal trabecular orientation either aligned along the cylinder axis (on-axis, n=22) or at an oblique angle of 15 degrees or 45 degrees (off-axis, n=28). Each specimen was scanned with micro-CT, mechanically compressed to failure, and analysed with nonlinear micro-CT-based finite element analysis. Yield strains depended on anatomic site (p=0.03, ANOVA), and the effect of off-axis loading was different for the two sites (p=0.04)-yield strains increased for off-axis loading of the vertebral bone (p=0.04), but were isotropic for the femoral bone (p=0.66). With sites pooled together, yield strains were positively correlated with BV/TV for on-axis loading (R(2)=58%, p<0.0001), but no such correlation existed for off-axis loading (p=0.79). Analysis of the modulus-BV/TV and strength-BV/TV relationships indicated that, for the femoral bone, the reduction in strength associated with off-axis loading was greater than that for modulus, while the opposite trend occurred for the vertebral bone. The micro-FE analyses indicated that these trends were due to different failure mechanisms for the two types of bone and the different loading modes. Taken together, these results provide unique insight into the failure behavior of human trabecular bone and highlight the need for a multiaxial failure criterion that accounts for anatomic site and bone volume fraction.

Trabecular bone strength predictions using finite element analysis of micro-scale images at limited spatial resolution

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 influence of boundary conditions and loading mode on high-resolution finite element-computed trabecular tissue properties

A widely used technique for determining the material properties of trabecular tissue is to perform combined experimental and computational testing of trabecular structures in order to calibrate effective tissue properties. To better understand the nature of such properties, we tested n=25 cores of human vertebral trabecular bone under two different boundary conditions (endcap and PMMA embedding) and loading modes (compression and torsion). High-resolution (20 microm) finite element models that explicitly modeled the different experimental conditions were constructed and sensitivity studies were performed to quantify errors arising from uncertainties between model and experiment. Mean (+/-S.D.) effective tissue modulus for the four groups ranged from 9.6+/-1.9 to 11.5+/-3.5 GPa, and the overall mean was 10.3+/-2.4 GPa. For the endcap tests, mean values were the same regardless of loading mode, suggesting that the effective tissue modulus is representative of true material behavior. However, on a specimen-specific basis, the various repeated measures of effective tissue modulus were only moderately correlated with each other (R2=27% to 81%), indicating that the individual measures can be subject to appreciable random errors. The sensitivity studies on the endcap tests indicated that models using lower resolution (40 microm element size) and roller-type platens boundary conditions overestimated effective tissue modulus by 42% on average, although preliminary tests with higher-density femoral neck bone indicated less sensitivity to modeling issues. We conclude that effective tissue properties derived from micro-finite element models do have biomechanical significance if measured correctly, although individual measures of tissue properties may have poor precision.

Effects of suppression of bone turnover on cortical and trabecular load sharing in the canine vertebral body

The relative biomechanical effects of antiresorptive treatment on cortical thickness vs. trabecular bone microarchitecture in the spine are not well understood. To address this, T-10 vertebral bodies were analyzed from skeletally mature female beagle dogs that had been treated with oral saline (n=8 control) or a high dose of oral risedronate (0.5mg/kg/day, n=9 RIS-suppressed) for 1 year. Two linearly elastic finite element models (36-mum voxel size) were generated for each vertebral body-a whole-vertebra model and a trabecular-compartment model-and subjected to uniform compressive loading. Tissue-level material properties were kept constant to isolate the effects of changes in microstructure alone. Suppression of bone turnover resulted in increased stiffness of the whole vertebra (20.9%, p=0.02) and the trabecular compartment (26.0%, p=0.01), while the computed stiffness of the cortical shell (difference between whole-vertebra and trabecular-compartment stiffnesses, 11.7%, p=0.15) was statistically unaltered. Regression analyses indicated subtle but significant changes in the relative structural roles of the cortical shell and the trabecular compartment. Despite higher average cortical shell thickness in RIS-suppressed vertebrae (23.1%, p=0.002), the maximum load taken by the shell for a given value of shell mass fraction was lower (p=0.005) for the RIS-suppressed group. Taken together, our results suggest that-in this canine model-the overall changes in the compressive stiffness of the vertebral body due to suppression of bone turnover were attributable more to the changes in the trabecular compartment than in the cortical shell. Such biomechanical studies provide an unique insight into higher-scale effects such as the biomechanical responses of the whole vertebra.

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

Trabecular plates play an important role in determining elastic moduli of trabecular bone. However, the relative contribution of trabecular plates and rods to strength behavior is still not clear. In this study, individual trabeculae segmentation (ITS) and nonlinear finite element (FE) analyses were used to evaluate the roles of trabecular types and orientations in the failure initiation and progression in human vertebral trabecular bone. Fifteen human vertebral trabecular bone samples were imaged using micro computed tomography (microCT), 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 (r(2)=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.

Complete volumetric decomposition of individual trabecular plates and rods and its morphological correlations with anisotropic elastic moduli in human trabecular bone

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 muCT 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 (r(2) = 0.95 approximately 0.99) compared with BV/TV (r(2) = 0.93 approximately 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 r(2) = 0.95 approximately 0.98) performed equally well as those with standard morphological parameters (adjusted r(2) = 0.94 approximately 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.

Side-artifact errors in yield strength and elastic modulus for human trabecular bone and their dependence on bone volume fraction and anatomic site

In the context of reconciling the mechanical properties of trabecular bone measured from in vitro mechanical testing with the true in situ behavior, recent attention has focused on the "side-artifact" which results from interruption of the trabecular network along the sides of machined specimens. The objective of this study was to compare the magnitude of the side-artifact error for measurements of elastic modulus vs. yield stress and to determine the dependence of these errors on anatomic site and trabecular micro-architecture. Using a series of parametric variations on micro-CT-based finite element models of trabecular bone from the human vertebral body (n=24) and femoral neck (n=10), side-artifact correction factors were quantified as the ratio of the side-artifact-free apparent mechanical property to the corresponding property measured in a typical experiment. The mean (+/-SD) correction factors for yield stress were 1.32+/-0.17 vs. 1.20+/-0.11 for the vertebral body and femoral neck (p<0.05), respectively, and the corresponding factors for modulus were 1.24+/-0.09 vs. 1.10+/-0.04 (p<0.0001). Correction factors were greater for yield stress than modulus (p<0.003), but no anatomic site effect was detected (p>0.29) after accounting for variations in bone volume fraction (BV/TV). Approximately 30-55% of the variation in the correction factors for modulus and yield stress could be accounted for by BV/TV or micro-architecture, representing an appreciable systematic component of the error. Although some scatter in the correction factor-BV/TV relationships may confound accurate correction of modulus and yield stress for individual specimens, side-artifact correction is nonetheless essential for obtaining accurate mean estimates of modulus and yield stress for a cohort of specimens. We conclude that appreciation and correction for the differential effects of the side-artifact in modulus vs. yield stress and their dependence on BV/TV may improve the interpretation of measured elastic and failure properties for trabecular bone.

Influence of bone volume fraction and architecture on computed large-deformation failure mechanisms in human trabecular bone

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.

The effects of side-artifacts on the elastic modulus of trabecular bone

Determining accurate density-mechanical property relationships for trabecular bone is critical for correct characterization of this important structure-function relation. When testing any excised specimen of trabecular bone, an unavoidable experimental artifact originates from the sides of the specimen where peripheral trabeculae lose their vertical load-bearing capacity due to interruption of connectivity, a phenomenon denoted here as the 'side-artifact'. We sought in this study to quantify the magnitude of such side-artifact errors in modulus measurement and to do so as a function of the trabecular architecture and specimen size. Using parametric computational analysis of high-resolution micro-CT-based finite-element models of cores of elderly human vertebral trabecular bone, a specimen-specific correction factor for the side-artifact was quantified as the ratio of the side-artifact-free apparent modulus (Etrue) to the apparent modulus that would be measured in a typical experiment (Emeasured). We found that the width over which the peripheral trabeculae were mostly unloaded was between 0.19 and 0.58 mm. The side-artifact led to an underestimation error in Etrue of over 50% in some specimens, having a mean (+/-SD) of 27+/-11%. There was a trend for the correction factor to linearly increase as volume fraction decreased (p=0.001) and as mean trabecular separation increased (p<0.001). Further analysis indicated that the error increased substantially as specimen size decreased. Two methods used for correcting for the side-artifact were both successful in bringing Emeasured into statistical agreement with Etrue. These findings have important implications for the interpretation of almost all literature data on trabecular bone mechanical properties since they indicate that such properties need to be adjusted to eliminate the substantial effects of side-artifacts in order to provide more accurate estimates of in situ behavior.