The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques

Acoustic microscopy (30-60 microm resolution) and nanoindentation (1-5 microm resolution) are techniques that can be used to evaluate the elastic properties of human bone at a microstructural level. The goals of the current study were (1) to measure and compare the Young's moduli of trabecular and cortical bone tissues from a common human donor, and (2) to compare the Young's moduli of bone tissue measured using acoustic microscopy to those measured using nanoindentation. The Young's modulus of cortical bone in the longitudinal direction was about 40% greater than (p<0.01) the Young's modulus in the transverse direction. The Young's modulus of trabecular bone tissue was slightly higher than the transverse Young's modulus of cortical bone, but substantially lower than the longitudinal Young's modulus of cortical bone. These findings were consistent for both measurement methods and suggest that elasticity of trabecular tissue is within the range of that of cortical bone tissue. The calculation of Young's modulus using nanoindentation assumes that the material is elastically isotropic. The current results, i.e., the average anisotropy ratio (E(L)/E(T)) for cortical bone determined by nanoindentation was similar to that determined by the acoustic microscope, suggest that this assumption does not limit nanoindentation as a technique for measurement of Young's modulus in anisotropic bone.     

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

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

Effect of microcomputed tomography voxel size on the finite element model accuracy for human cancellous bone

The level of structural detail that can be acquired and incorporated in a finite element (FE) analysis might greatly influence the results of microcomputed tomography (microCT)-based FE simulations, especially when relatively large bones, such as whole vertebrae, are of concern. We evaluated the effect of scanning and reconstruction voxel size on the microCT-based FE analyses of human cancellous tissue samples for fixed- and free-end boundary conditions using different combinations of scan/reconstruction voxel size. We found that the bone volume fraction (BV/TV) did not differ considerably between images scanned at 21 and 50 microm and reconstructed at 21, 50, or 110 microm (-0.5% to 7.8% change from the 21/21 microm case). For the images scanned and reconstructed at 110 microm, however, there was a large increase in BV/TV compared to the 21/21 microm case (58.7%). Fixed-end boundary conditions resulted in 1.8% [coefficient of variation (COV)] to 14.6% (E) difference from the free-end case. Dependence of model output parameters on scanning and reconstruction voxel size was similar between free- and fixed-end simulations. Up to 26%, 30%, 17.8%, and 32.3% difference in modulus (E), and average (VMExp), standard deviation (VMSD) and coefficient of variation (COV) of von Mises stresses, respectively, was observed between the 21/21 microm case and other scan/reconstruction combinations within the same (free or fixed) simulation group. Observed differences were largely attributable to scanning resolution, although reconstruction resolution also contributed significantly at the largest voxel sizes. All 21/21 microm results (taken as the gold standard) could be predicted from the 21/50 (r2adj= 0.91-0.99;p<0.001), 21/110 (r2adj =0.58-0.99;p<0.02) and 50/50 results (r2adj=0.61-0.97;p<0.02). While BV/TV, VMSD, and VMExp/sigma(z) from the 21/21 could be predicted by those from the 50/110 (r2adj =0.63-0.93;p<0.02) and 110/110 (r2adj =0.41-0.77;p<0.05) simulations as well, prediction of E, VMExp, and COV became marginally significant (0.04相似文献   

Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression

Articular cartilage exhibits complex mechanical properties such as anisotropy, inhomogeneity and tension-compression nonlinearity. This study proposes and demonstrates that the application of compressive loading in the presence of osmotic swelling can be used to acquire a spectrum of incremental cartilage moduli (EYi) and Poisson's ratios (upsilon ij) from tension to compression. Furthermore, the anisotropy of the tissue can be characterized in both tension and compression by conducting these experiments along three mutually perpendicular loading directions: parallel to split-line (1-direction), perpendicular to split-line (2-direction) and along the depth direction (3-direction, perpendicular to articular surface), accounting for tissue inhomogeneity between the surface and deep layers in the latter direction. Tensile moduli were found to be strain-dependent while compressive moduli were nearly constant. The peak tensile (+) Young's moduli in 0.15M NaCl were E+Y1=3.1+/-2.3, E+Y2=1.3+/-0.3, E+Y3(Surface)=0.65+/-0.29 and E+Y3(Deep)=2.1+/-1.2 MPa. The corresponding compressive (-) Young's moduli were E-Y1=0.23+/-0.07, E-Y2=0.22+/-0.07, E-Y3(Surface)=0.18+/-0.07 and E-Y3(Deep)=0.35+/-0.11 MPa. Peak tensile Poisson's ratios were upsilon+12=0.22+/-0.06, upsilon+21=0.13+/-0.07, upsilon+31(Surface)=0.10+/-0.03 and upsilon+31(Deep)=0.20+/-0.05 while compressive Poisson's ratios were upsilon-12=0.027+/-0.012, upsilon-21=0.017+/-0.07, upsilon-31(Surface)=0.034+/-0.009 and upsilon-31(Deep)=0.065+/-0.024. Similar measurements were also performed at 0.015 M and 2 M NaCl, showing strong variations with ionic strength. Results indicate that (a) a smooth transition occurs in the stress-strain and modulus-strain responses between the tensile and compressive regimes, and (b) cartilage exhibits orthotropic symmetry within the framework of tension-compression nonlinearity. The strain-softening behavior of cartilage (the initial decrease in EYi with increasing compressive strain) can be interpreted in the context of osmotic swelling and tension-compression nonlinearity.     

Physical and mechanical properties of calf lumbosacral trabecular bone.

The physical and mechanical properties of calf lumbar and sacral trabecular bone were determined and compared with those of human trabecular bone. The mean tissue density (1.66 +/- 0.12 g cm-3), equivalent mineral density (169 +/- 36 mg cm-3), apparent density (453 +/- 89 mg cm-3), ash density (194 +/- 59 mg cm-3), ash content (0.6 +/- 0.05%), compressive strength (7.1 +/- 3.0 MPa) and compressive modulus (173 +/- 97 MPa) of calf trabecular bone are similar to those of young human. There were moderate, positive linear correlations between apparent density and equivalent mineral density, ash density, and compressive strength; and between compressive strength and equivalent mineral density (R2 ranging from 0.35 to 0.48, p less than 0.001). Apparent density, ash density, and equivalent mineral density did not differ significantly in different regions. In contrast to humans, the compressive strength increased from posterior, near the facet, to the anterior vertebral body. These comparisons of physical and mechanical properties, as well as anatomical comparisons by others, indicate that the calf spine is a good model of the young non-osteoporotic human spine and thus useful for the testing of spinal instrumentation.     

Similarity in the fatigue behavior of trabecular bone across site and species

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.     

In vivo micro-CT scanning of a rabbit distal femur: repeatability and reproducibility

Before in vivo micro-CT scanning can be used to investigate femoral trabecular microarchitecture over time in rabbits, its repeatability and reproducibility must be demonstrated. To accomplish this, both distal femurs of two 6-month-old New Zealand white rabbits were scanned five times each in 1 day under different conditions (repeatability). Scanning was done at 28 microm isotropic voxel size to produce five image stacks of each femur. Three operators then followed a standard image processing protocol (reproducibility) to isolate two separate cubes from each anterior femoral condyle [total n = (8 cube sites)(5 scans)(3 operators) = 120]. Bone volume fraction (BV/TV) of the eight different cube sites (sample) ranged from 0.408 to 0.501 (mean: 0.453); trabecular thickness (Tb.Th) ranged from 158.1 to 185.5 microm (mean: 168.6 microm); and trabecular separation (Tb.Sp) ranged from 179.4 to 233.1 microm (mean: 204.7 microm). Using ANOVA and the variance component method, the total process variation was +/- 14.1% of the mean BV/TV of 0.453. The sample variation was +/- 13.9% (p < 0.001), the repeatability was +/- 2.1% (p < 0.001), and the reproducibility was +/- 0.1% (p > 0.05). Results were similar for Tb.Th and Tb.Sp. Though the contribution due to repeatability was statistically significant for each of the three indices, the natural sample differences were far greater than differences caused by repeated scanning under different conditions or by different operators processing the images. These findings suggest that in vivo micro-CT scanning of rabbit distal femurs was repeatable and reproducible and can be used with confidence to measure differences in trabecular bone microarchitecture at a single location in a longitudinal study design.     

Linear viscoelasticity - bone volume fraction relationships of bovine trabecular bone

Trabecular bone has been previously recognized as time-dependent (viscoelastic) material, but the relationships of its viscoelastic behaviour with bone volume fraction (BV/TV) have not been investigated so far. Therefore, the aim of the present study was to quantify the time-dependent viscoelastic behaviour of trabecular bone and relate it to BV/TV. Uniaxial compressive creep experiments were performed on cylindrical bovine trabecular bone samples (\(\textit{n}\,{=}\,13\)) at loads corresponding to physiological strain level of 2000 \({\upmu }{\upvarepsilon }\). We assumed that the bone behaves in a linear viscoelastic manner at this low strain level and the corresponding linear viscoelastic parameters were estimated by fitting a generalized Kelvin–Voigt rheological model to the experimental creep strain response. Strong and significant power law relationships (\(r^2\,{=}\,0.73,\ p\,{<}\,0.001\)) were found between time-dependent creep compliance function and BV/TV of the bone. These BV/TV-based material properties can be used in finite element models involving trabecular bone to predict time-dependent response. For users’ convenience, the creep compliance functions were also converted to relaxation functions by using numerical interconversion methods and similar power law relationships were reported between time-dependent relaxation modulus function and BV/TV.     

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.     

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.     

Anisotropic viscoelastic properties of cortical bone

Relaxation Young's modulus of cortical bone was investigated for two different directions with respect to the longitudinal axis of bone (bone axis, BA): the modulus parallel (P) and normal (N) to the BA. The relaxation modulus was analyzed by fitting to the empirical equation previously proposed for cortical bones, i.e., a linear combination of two Kohlraush-Williams-Watts (KWW) functions (Iyo et al., 2003. Biorheology, submitted): E(t)=E0 (A1 exp[-(t/tau1)beta]+(1-A1) exp[-(t/tau2)gamma]), [0 < A1, beta, gamma < 1], where E0 is the initial modulus value E0. Tau1 and tau2(>tau1) are characteristic times of the relaxation, A1 is the fractional contribution of the fast relaxation (KWW1 process) to the whole relaxation process, and beta and gamma are parameters describing the shape of the relaxation modulus. In both P and N samples, the relaxation modulus was described well by the empirical equation. The KWW1 process of a P sample almost completely coincided with that of an N sample. In the slow process (KWW2 process), there was a difference between the relaxation modulus of a P sample and that of an N sample. The results indicate that the KWW1 process in the empirical equation represents the relaxation in the collagen matrix in bone and that the KWW2 process is related to a higher-order structure of bone that is responsible for the anisotropic mechanical properties of bone.     

Finite Element Analysis of Foot and Ankle Impact Injury: Risk Evaluation of Calcaneus and Talus Fracture

IntroductionFoot and ankle impact injury is common in geriatric trauma and often leads to fracture of rearfoot, including calcaneus and talus. The objective of this study was to assess the influence of foot impact on the risk of calcaneus and talus fracture via finite element analysis.MethodsA three-dimensional finite element model of foot and ankle was constructed based on magnetic resonance images of a female aged 28. The foot sustained a 7-kg passive impact through a foot plate. The simulated impact velocities were from 2.0 to 7.0 m/s with 1.0 m/s interval.ResultsAt 5.0 m/s impact velocity, the maximum von Mises stress of the trabecular calcaneus and talus were 3.21MPa and 2.41MPa respectively, while that of the Tresca stress were 3.46MPa and 2.55MPa. About 94% and 84% of the trabecular calcaneus and talus exceeded the shear yielding stress, while 21.7% and 18.3% yielded the compressive stress. The peak stresses were distributed around the talocalcaneal articulation and the calcaneal tuberosity inferiorly, which corresponded to the common fracture sites.ConclusionsThe prediction in this study showed that axial compressive impact at 5.0 m/s could produce considerable yielding of trabecular bone in both calcaneus and talus, dominantly by shear and compounded with compression that predispose the rearfoot in the risk of fracture. This study suggested the injury pattern and fracture mode of high energy trauma that provides insights in injury prevention and fracture management.     

Modeling the onset and propagation of trabecular bone microdamage during low-cycle fatigue

Relatively small amounts of microdamage have been suggested to have a major effect on the mechanical properties of bone. A significant reduction in mechanical properties (e.g. modulus) can occur even before the appearance of microcracks. This study uses a novel non-linear microdamaging finite-element (FE) algorithm to simulate the low-cycle fatigue behavior of high-density trabecular bone. We aimed to investigate if diffuse microdamage accumulation and concomitant modulus reduction, without the need for complete trabecular strut fracture, may be an underlining mechanism for low-cycle fatigue failure (defined as a 30% reduction in apparent modulus). A microCT constructed FE model was subjected to a single cycle monotonic compression test, and constant and variable amplitude loading scenarios to study the initiation and accumulation of low-cycle fatigue microdamage. Microcrack initiation was simulated using four damage criteria: 30%, 40%, 50% and 60% reduction in bone element modulus (el-MR). Evaluation of structural (apparent) damage using the four different tissue level damage criteria resulted in specimen fatigue failure at 72, 316, 969 and 1518 cycles for the 30%, 40%, 50% and 60% el-MR models, respectively. Simulations based on the 50% el-MR model were consistent with previously published experimental findings. A strong, significant non-linear, power law relationship was found between cycles to failure (N) and effective strain (Deltasigma/E(0)): N=1.394x10(-25)(Deltasigma/E(0))(-12.17), r(2)=0.97, p<0.0001. The results suggest that microdamage and microcrack propagation, without the need for complete trabecular strut fracture, are mechanisms for high-density trabecular bone failure. Furthermore, the model is consistent with previous numerical fatigue simulations indicating that microdamage to a small number of trabeculae results in relatively large specimen modulus reductions and rapid failure.     

Tensile experiments and SEM fractography on bovine subchondral bone

Subchondral bone undecalcified samples, extracted from bovine femoral heads, are subjected to a direct tensile load. The Young's modulus of each sample is determined from repeated tests within the elastic limit. In a last test, the tensile load is increased up to the specimen failure, determining the ultimate tensile strength. The investigation is performed on both dry and wet specimens. The measured Young's modulus for dry samples is 10.3+/-2.5GPa, while that of wet samples is 3.5+/-1.2GPa. The ultimate tensile strengths are 36+/-10 and 30+/-7.5MPa for dry and wet specimens, respectively. SEM micrographs of failure surfaces show characteristic lamellar bone structures, with lamellae composed of calcified collagen fibers. Rudimentary osteon-like structures are also observed. Failure surfaces of wet samples show a marked fiber pull-out, while delamination predominates in dry samples. The obtained results are interpreted on the basis of the deformation mechanisms typical of fiber-reinforced laminated composite materials.     

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.     

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

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

European Society of Biomechanics S.M. Perren Award 2008: using temporal trends of 3D bone micro-architecture to predict bone quality

In longitudinal studies, three-dimensional (3D) bone images are acquired at sequential time points essentially resulting in four-dimensional (4D) data for an individual. Based on the 4D data, we propose to calculate temporal trends and project these trends to estimate future bone architecture. Multiple consecutive deformation fields, calculated with Demons deformable image registration algorithm, were extrapolated on a voxel-by-voxel basis. Test data were from in vivo micro-computed tomography (microCT) scans of the proximal tibia of Wistar rats that were either ovariectomized (OVX; N=5) or sham operated (SHAM; N=6). Measurements performed at baseline, 4 and 8 weeks were the basis to predict the 12 week data. Predicted and actual 12 week data were compared using qualitative (3D rendering) and quantitative (geometry, morphology and micro-finite element, microFE) methods. The results indicated a voxel-based linear extrapolation scheme yielded mean geometric errors that were smaller than the voxel size of 15 microm. Key morphological parameters that were estimated included bone volume ratio (BV/TV; mean error 0.4%, maximum error 9%), trabecular thickness (Tb.Th; -1.1%, 11%), connectivity density (Conn.D; 9.0%, 18.5%) and the apparent Young's modulus (E(1); 6.0%, 32%). These data demonstrated a promising and novel approach for quantitatively capturing in vivo bone dynamics at the local trabecular level. The method does not require an a priori understanding of the diseases state, and can provide information about the trends of the bone remodeling process that may be used for better monitoring and treatment of diseases such as osteoporosis.     

Finite element modeling of trabecular bone damage

This paper presents a finite element-based, computational model for analysis of structural damage to trabecular bone tissues. A modulus reduction method was formulated from elasto-plasticity theory, and was used to account for site-specific trabecular bone tissue damage. Trabecular bone tissue damage is illustrated using a large-scale, anatomically accurate, two-dimensional, microstructural finite element model of a human thoracic vertebral body. Four models with varying specifications for damage accumulation were subjected to compressive loading and unloading cycles. The numerical results and experimental validation demonstrated that the modulus reduction method reproduced the non-linear mechanical behaviour of vertebal trabecular bone. The iterative computational approach presented provides a methodology to study trabecular bone damage, and should provide researchers with a computational approach to study bone fracture and repair and to predict vertebral fragility.     

Tensile strength of bovine trabecular bone

Data on the tensile and compressive properties of trabecular bone are needed to define input parameters and failure criteria for modeling total joint replacements. To help resolve differences in reports comparing tensile and compressive properties of trabecular bone, we have developed new methods, based on porous foam technology, for tensile testing of fresh/frozen trabecular bone specimens. Using bovine trabecular bone from an isotropic region from the proximal humerus as a model material, we measured ultimate strengths in tension and compression for two groups of 24 specimens each. The average ultimate strength in tension was 7.6 +/- 2.2 (95% C.I.) MPa and in compression was 12.4 +/- 3.2 MPa. This difference was statistically significant (p = 0.013) and was not related to density differences between the test groups (p = 0.28). Strength was related by a power-law function of the local apparent density, but, even accounting for density influences, isotropic bovine trabecular bone exhibits significantly lower strengths in tension than in compression.     

Micro-mechanical sensing platform for the characterization of the elastic properties of the ovum via uniaxial measurement

Stiffness is an important parameter in determining the physical properties of living tissue. Recently, considerable biomedical attention has centered on the mechanical properties of living tissues at the single cell level. In the present paper, the Young's modulus of zona pellucida of bovine ovum was calculated using Micro Tactile Sensor (MTS) fabricated using piezoelectric (PZT) material. The sensor consists of a needle-shaped 20-microm transduction point made using a micro-electrode puller and mounted on a micro-manipulator platform. Measurements were made under microscopic control, using a suction pipette to support the ovum in the same horizontal axis as the MTS. Young's modulus of ovum was found to be 25.3+/-7.94 kPa (n=28). This value was indirectly determined based on calibration curves relating change in resonance frequency (Deltaf(0)) of the sensor with tip displacement for gelatin at concentrations of 4%, 6%, and 8%. The regression equation between the rate of change in resonance frequency (versus sensor tip displacement), Deltaf(0)/x and Young's modulus is Deltaf(0)/x (Hz/microm)=0.2992 x Young's modulus (kPa)-1.0363. It is concluded that a reason that the stiffness of ovum measured in the present study is approximately six times larger than previously reported, may be due to the absence of large deformation present in of existing methodologies.