The prospects of estimating trabecular bone tissue properties from the combination of ultrasound, dual-energy X-ray absorptiometry, microcomputed tomography, and microfinite element analysis.

Osteoporosis commonly is assessed by bone quantity, using bone mineral density (BMD) measurements from dual-energy X-ray absorptiometry (DXA). However, such a measure gives neither information about the integrity of the trabecular architecture nor about the mechanical properties of the constituting trabeculae. We investigated the feasibility of deriving the elastic modulus of the trabeculae (the tissue modulus) from computer simulation of mechanical testing by microfinite element analysis (muFEA) in combination with measurements of ultrasound speed of sound (SOS) and BMD measurements. This approach was tested on 15 postmortem bovine bone cubes. The apparent elastic modulus of the specimens was estimated from SOS measurements in combination with BMD. Then the trabecular morphology was reconstructed using microcomputed tomography (muCT). From the reconstruction a mesh for muFEA was derived, used to simulate mechanical testing. The tissue modulus was found by correlating the apparent moduli of the specimens as assessed by ultrasound with the ones as determined with muFEA. A mean tissue modulus of 4.5 GPa (SD, 0.69) was found. When adjusting the muFEA-determined elastic moduli of the entire specimens with their calculated tissue modulus, an overall correlation of R2 = 96% with ultrasound-predicted values was obtained. We conclude that the apparent elastic stiffness characteristics as determined from ultrasound correlate linearly with those from muFEA. From both methods in combination, the elastic stiffness of the mineralized tissue can be determined as an estimator for mechanical tissue quality. This method can already be used for biopsy specimens, and potentially could be applicable in vivo as well, when clinical CT or magnetic resonance imaging (MRI) tools with adequate resolution reach the market. In this way, mechanical bone quality could be estimated more accurately in clinical practice.     

Quantification of the roles of trabecular microarchitecture and trabecular type in determining the elastic modulus of human trabecular bone.

The roles of microarchitecture and types of trabeculae in determining elastic modulus of trabecular bone have been studied in microCT images of 29 trabecular bone samples by comparing their Young's moduli calculated by finite element analysis (FEA) with different trabecular type-specific reconstructions. The results suggest that trabecular plates play an essential role in determining elastic properties of trabecular bone. INTRODUCTION: Osteoporosis is an age-related disease characterized by low bone mass and architectural deterioration. Other than bone volume fraction (BV/TV), microarchitecture of bone is also believed to be important in governing mechanical properties of trabecular bone. We quantitatively examined the role of microarchitecture and relative contribution of trabecular types of individual trabecula in determining the elastic property of trabecular bone. MATERIALS AND METHODS: Twenty-nine human cadaveric trabecular bone samples were scanned at 21-mum resolution using a microCT system. Digital topological analysis (DTA) consisting of skeletonization and classification was combined with a trabecular type-specific reconstruction technique to extract the skeleton and identify topological type of trabeculae of the original trabecular bone image. Four different microCT-based finite element (FE) models were constructed for each specimen: (1) original full voxel; (2) skeletal voxel; (3) rod-reconstructed, preserving rod volume and plate skeleton; and (4) plate-reconstructed, preserving plate volume and rod skeleton. For each model, the elastic moduli were calculated under compression along each of three image-coordinate axis directions. Plate and rod tissue fractions directly measured from DTA-based topological classification were correlated with the elastic moduli computed from full voxel model. RESULTS: The elastic moduli of skeleton models were significantly correlated with those of full voxel models along all three coordinate axes (r(2) = 0.38 approximately 0.53). The rod-reconstructed model contained 21.3% of original bone mass and restored 1.5% of elastic moduli, whereas the plate-reconstructed model contained 90.3% of bone mass and restored 53.2% of elastic moduli. Plate tissue fraction showed a significantly positive correlation (r(2) = 0.49) with elastic modulus by a power law, whereas rod tissue fraction showed a significantly negative correlation (r(2) = 0.42). CONCLUSIONS: These results quantitatively show that the microarchitecture alone affects elastic moduli of trabecular bone and trabecular plates make a far greater contribution than rods to the bone's elastic behavior.     

Experimental method for the measurement of the elastic modulus of trabecular bone tissue

A procedure has been developed to measure the elastic modulus of small, irregularly shaped specimens without significantly disturbing the specimen's internal or surface structure. This procedure was developed to measure the average elastic modulus of isolated trabeculae from human cancellous bone tissue. The procedure combines direct testing of a cantilever beam-type specimen, along with finite element modeling of the specimen and the testing conditions. Initial estimates for the bone tissue material properties are input into the finite element model; differences between the calculated finite element displacement and the experimentally observed displacement allows the actual material modulus to be determined. Machined aluminum and cortical bone specimens were used to test the accuracy and repeatability of the procedure. Manipulations of the finite element models were performed to examine the effect that mesh construction errors might have on the accuracy of the results. None of the parameters examined resulted in changes in the measured finite element displacements of greater than 8%. In tests on six trabecular bone specimens, an average elastic modulus of 7.8 GPa was calculated. Even taking into account the possible sources of error, this value remains significantly less than the accepted value for cortical bone.     

Three-dimensional microstructural analysis of human trabecular bone in relation to its mechanical properties.

The purpose of this preliminary study is to explore the relationship between elastic modulus, bone mineral density (BMD), and trabecular microstructure in three dimensions. Twenty cubes of trabecular bone were processed from two lumbar vertebrae obtained from one individual. The BMD of each cube was measured by dual-energy X-ray absorptiometry and peripheral quantitative computed tomography. Each cube was serially scanned by microcomputed tomography to produce three-dimensional data sets. By analyzing these data sets, three-dimensional trabecular microstructural indices of connectivity density and fractal dimension were calculated as well as histomorphometric parameters. The cubes were tested mechanically in a nondestructive manner for measurement of their elastic modulus. This preliminary study showed that: (1) bone mass index is correlated with mechanical properties, with coefficients of correlation ranging from 0.552 to 0.601; and (2) when controlling for BMD, no association could be detected between measures of structural complexity (connectivity density and fractal dimension) and elastic modulus in the craniocaudal direction of human vertebral bodies.     

Biomechanical effects of intraspecimen variations in trabecular architecture: a three-dimensional finite element study.

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.     

Three-dimensional morphometry of the L6 vertebra in the ovariectomized rat model of osteoporosis: biomechanical implications.

This article summarizes the results of a three-dimensional study of changes in the morphology of the L6 rat vertebra at 120 days after ovariectomy (OVX), with estrogen replacement therapy used as a positive control. Synchrotron radiation microtomography was used to quantify the structural parameters defining trabecular bone architecture, while finite-element methods were used to explore the relationships between these parameters and the compressive elastic behavior of the vertebrae. There was a 22% decrease in trabecular bone volume (TBV) and a 19% decline in mean trabecular thickness (Tb.Th) with OVX. This was accompanied by a 150% increase in trabecular connectivity, a result of the perforation of trabecular plates. Finite-element analysis of the trabecular bone removed from the cortical shell showed a 37% decline in the Young's modulus in compression after OVX with no appreciable change in the estrogen-treated group. The intact vertebrae (containing its trabecular bone) exhibited a 15% decrease in modulus with OVX, but this decline lacked statistical significance. OVX-induced changes in the trabecular architecture were different from those that have been observed in the proximal tibia. This difference was a consequence of the much more platelike structure of the trabecular bone in the vertebra.     

A decreased subchondral trabecular bone tissue elastic modulus is associated with pre-arthritic cartilage damage.

In osteoarthritis, one postulate is that changes in the mechanical properties of the subchondral bone layer result in cartilage damage. The goal of this study was to examine changes in subchondral trabecular bone properties at the calcified tissue level in the early stages of cartilage damage. Finite element models were constructed from microCT scans of trabectilar bone from the proximal tibia of donors with mild cartilage damage and from normal donors. In the donors with cartilage damage, macroscopic damage was present only in the medial compartment. The effective tissue elastic moduli were determined using a combination of finite element models and mechanical testing. The bone tissue modulus was reduced by 60% in the medial condyle of the cases with cartilage damage compared to the control specimens. Neither the presence of cartilage damage nor the anatomic site (medial vs. lateral) affected the elastic modulus at the apparent level. The volume fraction of trabecular bone was higher in the medial compartment compared to the lateral compartment of tibiae with cartilage damage (but not the controls), suggesting that mechanical properties were preserved in part at the apparent level by an increase in the bone volume fraction. It seems likely that the normal equilibrium between cartilage properties, bone tissue properties and bone volume fraction is disrupted early in the development of osteoarthritis.     

Microstructure Determines Apparent-Level Mechanics Despite Tissue-Level Anisotropy and Heterogeneity of Individual Plates and Rods in Normal Human Trabecular Bone

Trabecular plates and rods determine apparent elastic modulus and yield strength of trabecular bone, serving as important indicators of bone's mechanical integrity in health and disease. Although trabecular bone's apparent-level mechanical properties have been widely reported, tissue mechanical properties of individual trabeculae have not been fully characterized. We systematically measured tissue mineral density (TMD)–dependent elastic modulus of individual trabeculae using microindentation and characterized its anisotropy as a function of trabecular type (plate or rod), trabecular orientation in the global coordinate (longitudinal, oblique, or transverse along the anatomic loading axis), and indentation direction along the local trabecular coordinate (axial or lateral). Human trabecular bone samples were scanned by micro-computed tomography for TMD and microstructural measurements. Individual trabecula segmentation was used to decompose trabecular network into individual trabeculae, where trabecular type and orientation were determined. We performed precise, selective indentation of trabeculae in each category using a custom-built, microscope-coupled microindentation device. Co-localization of TMD at each indentation site was performed to obtain TMD-to-modulus correlations. We found significantly higher TMD and tissue modulus in trabecular plates than rods. Regardless of trabecular type and orientation, axial tissue modulus was consistently higher than lateral tissue modulus, with ratios ranging from 1.13 to 1.41. Correlations between TMD and tissue modulus measured from axial and lateral indentations were strong but distinct: axial correlation predicted higher tissue modulus than lateral correlation at the same TMD level. To assess the contribution of experimentally measured anisotropic tissue properties of individual trabeculae to apparent-level mechanics, we constructed non-linear micro-finite element models using a new set of trabecular bone samples and compared model predictions to mechanical testing measurements. Heterogeneous anisotropic models accurately predicted apparent elastic modulus but were no better than a simple homogeneous isotropic model. Variances in tissue-level properties may therefore contribute nominally to apparent-level mechanics in normal human trabecular bone. © 2021 American Society for Bone and Mineral Research (ASBMR).     

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 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.     

Heterogeneity of bone lamellar-level elastic moduli

Advances in our ability to assess fracture risk, predict implant success, and evaluate new therapies for bone metabolic and remodeling disorders depend on our understanding of anatomically specific measures of local tissue mechanical properties near and surrounding bone cells. Using nanoindentation, we have quantified elastic modulus and hardness of human lamellar bone tissue as a function of tissue microstructures and anatomic location. Cortical and trabecular bone specimens were obtained from the femoral neck and diaphysis, distal radius, and fifth lumbar vertebra of ten male subjects (aged 40–85 years). Tissue was tested under moist conditions at room temperature to a maximum depth of 500 nm with a loading rate of 10 nm/sec. Diaphyseal tissue was found to have greater elastic modulus and hardness than metaphyseal tissues for all microstructures, whereas interstitial elastic modulus and hardness did not differ significantly between metaphyses. Trabecular bone varied across locations, with the femoral neck having greater lamellar-level elastic modulus and hardness than the distal radius, which had greater properties than the fifth lumbar vertebra. Osteonal, interstitial, and primary lamellar tissues of compact bone had greater elastic moduli and hardnesses than trabecular bone when comparing within an anatomic location. Only femoral neck interstitial tissue had a greater elastic modulus than its osteonal counterpart, which suggests that microstructural distinctions can vary with anatomical location and may reflect differences in the average tissue age of cortical bone or mineral and collagen organization.     

Quantitative ultrasound does not reflect mechanically induced damage in human cancellous bone.

This study investigated the ability of quantitative ultrasound (QUS) to detect reductions in the elastic modulus of cancellous bone caused by mechanical damage. Ultrasonic velocity and attenuation were measured using an in-house parametric imaging system in 46 cancellous bone cores from the human calcaneus. Each core was subjected to a mechanical testing regime to (a) determine the predamage elastic modulus, (b) induce damage by applying specified strains in excess of the yield strain, and (c) measure the postdamage elastic modulus. The specimens were divided into four groups: a control group subjected to a nominally nondestructive 0.7% maximum strain (epsilonm) and three damage groups subjected to increasing strain levels (epsilonm = 1.5, 3.0, and 4.5%). QUS measurements before and after the mechanical testing showed no significant differences between the control group and damage groups, despite highly significant (p < 0.001) reductions in the elastic modulus of up to 72%. These results indicate that current QUS techniques do not intrinsically reflect the elastic properties of cancellous bone. This is consistent with ultrasonic properties being determined by other factors (apparent density and/or architecture), which normally are associated strongly with elastic properties, but only when bone is mechanically intact. Clinically, this implies that ultrasound cannot be expected to detect bone fragility in the absence of major changes in bone density and/or trabecular architecture.     

Contributions of trabecular rods of various orientations in determining the elastic properties of human vertebral trabecular bone

Trabecular bone networks consist of two basic microstructural types: plates and rods. Although trabecular rods represent only a small fraction of total bone volume, their existence has important roles in failure initiation and progression. The goal of this study was to quantitatively examine the contributions of trabecular rods in various orientations to the anisotropic elastic moduli of human vertebral trabecular bone. Twenty-one human vertebral trabecular bone specimens were scanned by microcomputed tomography (μCT). A coordinate system of orthotropic axes representing the best elastic orthotropic symmetry was determined for each sample. Individual trabeculae segmentation (ITS), a 3D image analysis technique, was performed to identify each individual trabecular rod and determine its orientation in the orthotropic coordinate system. Next, three rod-removed images were created where longitudinal, oblique, or transverse trabecular rods were removed, respectively, from the original μCT images. The original and three categories of rod-removed images were then converted to finite element (FE) models for evaluation of their elastic moduli and anisotropy. Both the transverse and oblique rod-removal caused significant decreases in all six elastic moduli. However, the removal of longitudinal rods only caused significant changes in E₃₃, G₂₃, and G₃₁ but not in any transverse/in-plane elastic properties (E₁₁, E₂₂, and G₁₂). The analysis of covariance (ANCOVA) with repeated measures was applied to detect the moduli change in the different models caused by the effects beyond just bone volume loss. The results suggested that the loss of transverse rods induced a significant decrease in in-plane mechanical competence, which was greater than what could be explained only by the associated bone volume loss. In contrast, the reduction in the axial Young's modulus caused by the loss of transverse rods was proportional to the bone volume decrease. Furthermore, the loss of longitudinal rods affected the axial Young's modulus through both bone volume loss and architectural change. With aging, the reduction in in-plane mechanical competence would be magnified by the preferential loss of transverse rods. The predictive ability of bone mineral density, a surrogate of BV/TV in clinical measurements, may reduce more quickly for transverse mechanical properties than for the axial mechanical properties.     

In Vivo Assessment of Architecture and Micro-Finite Element Analysis Derived Indices of Mechanical Properties of Trabecular Bone in the Radius

Measurement of microstructural parameters of trabecular bone noninvasively in vivo is possible with high-resolution magnetic resonance (MR) imaging. These measurements may prove useful in the determination of bone strength and fracture risk, but must be related to other measures of bone properties. In this study in vivo MR imaging was used to derive trabecular bone structure measures and combined with micro-finite element analysis (μFE) to determine the effects of trabecular bone microarchitecture on bone mechanical properties in the distal radius. The subjects were studied in two groups: (I) postmenopausal women with normal bone mineral density (BMD) (n= 22, mean age 58 ± 7 years) and (II) postmenopausal women with spine or femur BMD −1 SD to −2.5 SD below young normal (n= 37, mean age 62 ± 11 years). MR images of the distal radius were obtained at 1.5 T, and measures such as apparent trabecular bone volume fraction (App BV/TV), spacing, number and thickness (App TbSp, TbN, TbTh) were derived in regions of interest extending from the joint line to the radial shaft. The high-resolution images were also used in a micro-finite element model to derive the directional Young’s moduli (E1, E2 and E3), shear moduli (G12, G23 and G13) and anisotropy ratios such as E1/E3. BMD at the distal radius, lumbar spine and hip were assessed using dual-energy X-ray absorptiometry (DXA). Bone formation was assessed by serum osteocalcin and bone resorption by serum type I collagen C-terminal telopeptide breakdown products (serum CTX) and urinary CTX biochemical markers. The trabecular architecture displayed considerable anisotropy. Measures of BMD such as the ultradistal radial BMD were lower in the osteopenic group (p<0.01). Biochemical markers between the two groups were comparable in value and showed no significant difference between the two groups. App BV/TV, TbTh and TbN were higher, and App TbSp lower, in the normal group than the osteopenic group. All three directional measures of elastic and shear moduli were lower in the osteopenic group compared with the normal group. Anisotropy of trabecular bone microarchitecture, as measured by the ratios of the mean intercept length (MIL) values (MIL1/MIL3, etc.), and the anisotropy in elastic modulus (E1/E3, etc.), were greater in the osteopenic group compared with the normal group. The correlations between the measures of architecture and moduli are higher than those between elastic moduli and BMD. Stepwise multiple regression analysis showed that while App BV/TV is highly correlated with the mechanical properties, additional structural measures do contribute to the improved prediction of the mechanical measures. This study demonstrates the feasibility and potential of using MR imaging with μFE modeling in vivo in the study of osteoporosis. Received: 13 December 2000 / Accepted: 30 May 2001     

Relative roles of microdamage and microfracture in the mechanical behavior of trabecular bone.

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.     

Properties of growing trabecular ovine bone. Part II: architectural and mechanical properties

We aimed to highlight the relationship between age and the architectural properties of trabecular bone, to outline the patterns in which the variations in these properties take place, and to investigate the influence of the architecture on the mechanical properties of trabecular bone in growing animals. We studied 30 lambs in three age groups and 20 sheep in two age groups. Cubes of subchondral bone were cut from the proximal tibia according to a standardised protocol. They were serially sectioned and their architectural properties were determined. Similar cubes were obtained from the identical anatomical position of the contralateral tibia and their compressive mechanical properties measured. The values obtained from the skeletally immature and mature individuals were compared. Multiple regression analyses were performed between the architectural and the mechanical properties. The bone volume fraction, the mean trabecular volume, the architectural and the mechanical anisotropy, the elastic modulus, the bone strength, the energy absorption to failure, and the elastic energy correlated positively with increasing age whereas the connectivity density, the bone surface density, the ultimate strain, the absorption of viscoelastic energy and the relative loss of energy correlated inversely. The values of all variables were significantly different in the skeletally mature and immature groups. We determined the patterns in which the variations took place. The bone volume fraction of the trabecular bone tissue was found to be the major predictor of its compressive mechanical properties. Together with the mean trabecular volume and the bone surface density, it explained 81% of the variations in the compressive elastic modulus of specimens obtained from the contralateral tibiae.     

Comparison of the trabecular and cortical tissue moduli from human iliac crests

The purpose of this study was to design a method to produce and test mechanically microspecimens of trabecular and cortical tissue from human iliac crests, and compare their measured moduli. Rectangular beam specimens were prepared on a low-speed diamond blade saw and a miniature milling machine. The final specimen dimensions ranged from approximately 50-200 microns for base and height. The modulus of each specimen was measured using three-point bending tests across a span length of 1.04 mm and performed at a constant rate of displacement. A subset of specimens was recovered for a radiographic estimation of degree of mineralization. The results showed the mean trabecular tissue modulus of all iliac crest specimens to be 3.81 GPa, whereas cortical tissue specimens averaged 4.89 GPa. This was a significant difference according to a two-way analysis of variance that controlled for differences between donors. No strong correlations were found between modulus and mineral density. Future investigations that consider other microstructural characteristics and their contributions to modulus, and specimen size effects, are indicated.     

An orientation distribution function for trabecular bone

We describe a new method for quantifying the orientation of trabecular bone from three-dimensional images. Trabecular lattices from five human vertebrae were decomposed into individual trabecular elements, and the orientation, mass, and thickness of each element were recorded. Continuous functions that described the total mass (M(phi,theta)) and mean thickness (tau(phi,theta)) of all trabeculae as a function of orientation were derived. The results were compared with experimental measurements of the elastic modulus in three principal anatomic directions. A power law scaling relationship between the anisotropies in mass and elastic modulus was observed; the scaling exponent was 1.41 (R2=0.88). As expected, the preponderance of trabecular mass was oriented along the cranial-caudal direction; on average, there was 3.4 times more mass oriented vertically than horizontally. Moreover, the vertical trabeculae were 30% thicker, on average, than the horizontal trabeculae. The vertical trabecular thickness was inversely related to connectivity (R2=0.70; P=0.07), suggesting a possible organization into either few, thick trabeculae or many thin trabeculae. The method, which accounts for the mechanical connectedness of the lattice, provides a rapid way to both visualize and quantify the three-dimensional organization of trabecular bone.     

Correlation of mechanical properties of vertebral trabecular bone with equivalent mineral density as measured by computed tomography

We tried to determine whether mineral-equivalent measurements that were obtained using computed tomography could be used to predict the mechanical properties of vertebral trabecular bone. Vertebral bodies that had been obtained during routine autopsy were evaluated by computed tomography. The mechanical properties of the vertebral trabecular bone were determined by subjecting cylindrical specimens to simple compression until failure occurred. The ultimate strength and elastic modulus were determined from load time curves, using constant displacement rate loading. Atomic absorption spectrophotometry was used to determine the weight per cent calcium of each specimen, and quantitative light microscopy was used to determine area fraction bone. Significant positive correlations were found between the observed mechanical properties of the trabecular bone and the equivalent mineral density as measured by computed tomography. Compressive strength (r = 0.720), elastic modulus (r = 0.574), trabecular calcium density (r = 0.780), and area fraction bone (r = 0.579) were all correlated with the equivalent mineral density.     

Trabecular plates and rods determine elastic modulus and yield strength of human trabecular bone

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 (r² = 0.97) and yield strength (r² = 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 (r² = 0.99, r² = 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.