Tony M. Keaveny

Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue.

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 modulus–density relationships depend on anatomic site

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.

A view of the parallel computing landscape

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

Dependence of yield strain of human trabecular bone on anatomic site.

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.

Effects of bone cement volume and distribution on vertebral stiffness after vertebroplasty.

Study Design. The biomechanical behavior of a single lumbar vertebral body after various surgical treatments with acrylic vertebroplasty was parametrically studied using finite-element analysis. Objectives. 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. Summary of Background Data. 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. Methods. 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. Results. 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. Conclusion. Only a small amount of bone cement (∼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.

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone

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.

A 20-year perspective on the mechanical properties of trabecular bone.

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.

Effects of teriparatide and alendronate on vertebral strength as assessed by finite element modeling of QCT scans in women with osteoporosis.

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.

Finite element analysis of the proximal femur and hip fracture risk in older men

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.

Load sharing between the shell and centrum in the lumbar vertebral body.

Study Design A finite element parametric analysis to investigate the relative load carrying roles of the shell and centrum in the lumbar vertebral body. Objective To address the issue of the structural role of the vertebral shell and clarify some of the contradictions raised by previous studies. Summary of Background Data 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. Methods 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 anisotropy, and loading conditions. Results 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. Conclusions 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.